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Anglemetry of neural axis cell differentiation genes by structural pressurotopy of DNA loop strand segment tropy in reference to tissue macro-compliance

  • Hemant SarinEmail author
Open Access
Research
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Abstract

Background

Even as the eukaryotic stranded DNA is known to heterochromatinize at the nuclear envelope in response to mechanical strain, the precise mechanistic basis for alterations in chromatin gene transcription in differentiating cell lineages has been difficult to determine due to limited spatial resolution for detection of shifts in reference to a specific gene in vitro. In this study, heterochromatin shift during euchromatin gene transcription has been studied by parallel determinations of DNA strand loop segmentation tropy nano-compliance (esebssiwaagoTQ units, linear nl), gene positioning angulation in linear normal two-dimensional (2-D) z, y-vertical plane (anglemetry, 0), horizontal alignment to the z, x-plane (vectormetry; mA, mM, a.u.), and by pressuromodulation mapping of differentiated neuron cell sub-class operating range for neuroaxis gene expression in reference to tissue macro-compliance (Peff).

Methods

The esebssiwaagoTQ effective pressure unit (Peff) maxima and minima for horizontal gene intergene base segment tropy loop alignment were determined (n = 224); the Peff esebssiwaagoTQ quotient were determined (n = 28) for analysis of gene intergene base loop segment tropy structure nano-compliance (n = 28; n = 188); and gene positioning anglemetry and vectormetry was performed (n = 42). The sebs intercept-to-sebssiwa intercept quotient for linear normalization was determined (bsebs/bsebssiwa) by exponential plotting of sub-episode block sum (sebs) (x1, y1; x2, y2) and sub-episode block sum split integrated weighted average (sebssiwa) functions was performed, and the sebs – sebssiwa function residuals were determined. The effective cell pressure (Peff)-to-angle conversion factor was determined, ϴA = (1E + 02) {0.90 – [(0.000 + a ≥ x < 0.245) (1.208)] form was applied for anisotropic gene anglemetry, and the ϴM = (1E + 02) {0.90 – [1.208 (0.245 ≥ x ≤ m)] form was applied for mesotropic gene anglemetry. Two-step Tukey range t-test was performed for inter-group comparisons of bsebs/bsebssiwa quotients and sebs – sebssiwa normalized residuals between tier 1 (Peff ≤ 0.200; n = 11) and tier 2 (Peff > 0.200 ≤ 0.300; n = 6), between tier 1 and tier 3 (Peff > 0.300; n = 8), and between tier 3 and tier 2 (α = 0.05).

Results

Based on the results of this study, I) heterochromatin strand DNA loop micro-segmentation structural nano-compliance is either amorphousity, anisotropy or mesotropy loop segment forms perceiving various grades of the asymmetric tropy viscosity effect, where between 3-to-5 and 8-to-11 genes are arranged as one or two in-tandem alternating anisotropic and mesotropic gene(s), or as in-tandem anisotropic or mesotropic genes in juxtaposition separated by intergene tropy base distance; for example, the anisotropy loop segment form between positions − 12 to + 15 in reference LMNA (Peff, 0.184; θA = 68.40) on human 1q22 (+) is: 5′-0.234-(a− 12)-0.272 (m− 11)-0.229 (a− 10)-0.211 (a− 9)-0.269 (m− 8)-0.144 (a− 7)-0.314 (m− 6)-0.268 (m− 5)-0.176 (a− 4)-0.260 (m− 3)-0.259 (m− 2)-0.270 (m− 1)-0.184 (a0)-0.135 (m+ 1)-0.395 (m+ 2)-0.146 (a+ 3)-0.212 (a+ 4)-0.336 (m+ 5)-0.287 (m+ 6)-0.153 (a+ 7)-0.283 (m+ 8)-0.193 (a+ 9)-0.269 (m+ 10)-0.199 (a+ 11)-0.146 (a+ 12)-0.190 (a+ 13)-0.188 (a+ 14)-0.243 (a+ 15)-3′, which begins at the 5′ end with DAP3 (Peff 0.234); II) mesotropy loop form genes are positioned between 11.7 and 60.40 (CD34) in the z, y-vertical plane, whereas anisotropy loop form genes positioned between 60.5 and 82.30 (MIR4537) in the z, y-vertical plane; III) the relationship between effective pressure and momentum is inverse proportionality, Peff (0.064 ≥ x < 0.245) · mA = Peff (0.245 ≥ x ≤ 0.648) · mM; IV) the interval for peripheral lower motor neuron (lmn) gene expression is definable as being between a Peff of 0.434 and 0.311 (> 0.305), between a Peff of 0.305 and 0.213 for cerebrocortical upper motor neurons, between a Peff of 0.318 and 0.203 for hippocampocortical neurons, and between a Peff of 0.298 and 0.217 for basal ganglia spiny neurons; therefore, there exists an inverse relationship between effective range of whole cell compliance and tissue macro-compliance (Reffective whole cell compliance ˑ Tmacro-compliance = k), in which case the range for mesenchymal cell (MSC) gene expression is delineable as being between a Peff of 0.648 and <= 0.118 esebssiwaagoTQ units; and V) RGS18 (Peff 0.205; θM = 65.20), RGS16 (Peff 0.251; θM = 59.70; human paralog of murine RGS4), lnc-RXFP4–5 (Peff, 0.314; θM = 52.10; pituit), RGS13 (Peff; 0.360, θM = 46.50), CEACAM1 (Peff, 0.384; θM = 43.60), SLC25A44 (Peff, 0.395; θM = 42.30) and RGS21 (Peff, 0.413; θM = 40.10) are expressed within the lower motor neuron (lmn)-upper motor neuron (umn) neural cell axis; and TSACC (Peff, 0.336; θM = 49.40) and JUND (Peff, 0.344; θM = 48.40) are non-cell specific developmental biomarkers.

Conclusions

Based on the findings of this study considered together, the precise mechanistic basis for alterations in chromatin gene transcription eukaryotic stranded heterochromatin arranged by structural pressurotopy nano-compliance in DNA stand loop segments is effective cell pressure (Peff) regulated shifting of transcriptionally active DNA in-between the inner nuclear envelope margin and the peripheral nucleoplasm edge and the z, x-plane horizontal alignment of a gene by gene specific Peff within the cell specific effective range of whole cell compliance in reference to tissue macro-compliance. The findings of this study are therefore applicable to the further study of changes in gene transcription in response to applied mechanical strain-mediated alterations in nuclear envelope deformability in silico.

Keywords

Membrane proteins Lamins Nuclear pore Mechanical loading Substrate stiffness Viscosity Growth factor Small molecule Stem cell Cell differentiation 

Abbreviations

ACM

Anisotropy converted to mesotropy

bsebs/bsebssiwa

Intercept sebs/intercept sebssiwa linearization quotient

d, dM , dA

Distance of gene intergene base tropy

dppasebs

Downstream part anisotropic sub-episode block sum

dppasebs

Downstream part anisotropic sub-episode block sum

dppasebssiwa

Downstream part anisotropic sub-episode block sum split integrated weighted average

dppasebssiwa

Downstream part anisotropic sub-episode block sum split integrated weighted average

NCA

Non-contributory anisotropy

Peff

Effective intracellular pressure, esebssiwaagoTQ

prpTQ

Paired point tropy quotient

SEB

Sub-episode block

stIAfM, stIMfA or stIMfM

0.5-factor adjusted stabilizing isotropy for anisotropy or mesotropy

uppasebs

Upstream part anisotropic sub-episode block sum

uppasebssiwa

Upstream part anisotropic sub-episode block sum split integrated weighted average

uppmsebs

Upstream part mesotropic sub-episode block sum

uppmsebssiwa

Upstream part mesotropic sub-episode block sum split integrated weighted average

Θ,ΘM, ΘA, ΘH

Gene angle

meff,mA (mch tropy), mM (mch tropy + mch nmn tropy)

Effective momentum

Introduction

Non-constitutively less active heterochromatin and constitutively more active heterochromatin commonly known as euchromatin are the two forms of eukaryotic euchromatic chromatins [1, 2, 3, 4, 5]. Adenine and thymine nucleobase-rich G-banded DNA of heterochromatin binds to less hydrophilic staining dyes such as 4′,6-diamidino-2-phenylindole (DAPI; -4.37 nm-1) with cationicity sufficiently separated in space (1+ SS 1+), whereas guanine and cytosine nucleobase-rich R-banded DNA of constitutive heterochromatin (euchromatin) binds to more hydrophilic dyes such as Oligomycin (-6.75 nm-1) with polyhydroxylated hydrophilicity sufficiently separated in space (OH SS OH), which is more transcriptionally-active due to protein affinity interactions of the same [5, 6], both of which are loosely wound around the nucleosome core histone proteins in the pressurized state of a cell. Adenine and T-rich G-banded non-constitutive heterochromatin resides in affinity with non-histone polypeptides lamin A/C or B1/B2 [7, 8, 9, 10, 11, 12, 13], from which genes are episodically-transcribed in fully-differentiated cells [1, 2, 3, 4, 5], in contrast to G and C-rich R-banded constitutive heterochromatin resides in affinity with nuclear pore complex subunits rather than in affinity with the lamins and lamin-associated proteins, from which regulatory housekeeping genes are transcribed [1, 2, 3, 4, 5, 11]. During the Go resting transcriptionally active cell stage, both of the chromatins are located in one of two locations in the nucleus, either at the inner nuclear membrane-bound to lamins A/C or B1/B2 via lamin-associated polypeptides (LAP) polypeptides (LAP) 1 and 2 isoforms and emerin (EMD), or closer to the center at peripheral edge central nucleoplasm interface during the non-transcription of lamin/lamin-associated polypeptides [14, 15, 16, 17, 18], during which there is differential gene transcription [15] in comparison to that at the inner nuclear membrane in apposition to nuclear pore complex subunits [16].

During the DNA synthesis stage [1, 2, 3], both forward and reverse strands of early and late-replicating chromatins become DNA polymerase substrates when replication forks form at defined intervals resembling radial loops at the inner nuclear membrane [19, 20, 21, 22], a process that continues at the nuclear envelope to the point of MKI67 protein expression [23], which is a 359 kDa G2 interphase enzyme involved in translocation of tetraploid chromatin from the inner nuclear membrane to the nuclear center by mass effect, as the nuclear envelope dissolutes and chromatids align at the metaphase plate. A mass effect mechanism has been suggested for horizontal alignment of DNA during the S phase is the 900 kDa molecular weight of multi-subunit DNA polymerase during which multiple assembled DNA polymerases simultaneously walk forward (+) or reverse (-) strand intergene segments at replication forks based on recent determinations that during the process of gene transcription the DNA synthesis (S1) phase begins when effective cell pressure (Peff) increases into the 0.261 to 0.283 (PCNA) pressure units range [24, 25, 26, 27, 28].

Nuclear envelope elastance (E) responses to pressure application and alterations in initial envelope elastance to tonicity or dynamic strain over time have been studied by micropipette aspiration techniques in LMNA (-/-) or emerin (EMD, -/y) gene-deficient cells (J, creep compliance; kpa-1·sec-1; α power) [29, 30, 31, 32, 33, 34, 35]; cell morphology alterations in response to grades of substrate stiffness have been studied by spectrophotometry of gel viscoelasticity (G’; Pa) and cell tissue tensional homeostasis by traction force microscopy [36, 37]; and cell mechanosensitivity changes and nuclear deformability alterations in response to mechanical loading during pharmacological application in vitro studied by the chromatin condensation parameter (CCP, %) and the nucleus deformability index (NDI, %; NAR, a.u.) [38, 39, 40, 41], in addition to differential gene transcription in mesenchymal stem and transformed cells studied in situ by qRT-PCR mRNA expression, based on the findings of which mechanoforce transduction can be defined as downstream molecular signaling events that result in alterations in chromatin gene transcription [28].

It has been recently hypothesized that alterations in cell membrane compliance in relation to mitochondrial membrane compliance results in increases or decreases in effective cell pressure secondary to that alterations in cell membrane compliance by membrane domain-binding of growth factors and small molecule ligand binding to cell surface receptors [24, 25, 26, 27]. The modes of cellular pressurization in the biological system in vivo is have been further defined as the combination of (a) synergistic positive macro-pressuromodulation due to the presence of a rigidified extracellular matrix or cortical bone, which increases effective cell pressure, or non-synergistic negative macro-pressuromodulation due to the presence of surrounding cells, which decreases effective cell pressure; and (b) positve or negative micro-pressuromodulation at cell membrane domains by way of endocrine, paracrine and autocrine small molecule hormones, growth factors and cytokines, which either increases or decreases effective cell pressure. Therefore, the effective cell pressure for horizontal alignment of gene tropy and maximal gene transcription is related to cell compliance by Compliancecell membrane micro-pressuromulation + Elastancecell membrane integrin-to-collagen or sub-cortical bone macro-pressuromodulation ˑ Pressureeffective intracellular = k during synergistic macro-pressuromodulation, and by Compliancecell membrane micro-pressuromulation - Elastancecell junction-to-cell junction macro-pressuromodulation Pressureeffective intracellular = k during non-synergistic macro-pressuromodulation, where Peffective intracellular (Peff) = Peffective intranuclear.

A fractional measure has been recently developed to quantify the effective intracellular pressure required to horizontally align a gene for its maximal transcription, as there are non-specific avidity associations of nuclear protoplasm proteins and non-coding RNAs in a tropic manner with the intergene segment bases of genes located upstream and downstream with respect to a gene; and represents the 5’ → 3’ reading direction intergene distance tropy that needs to be overcome for a gene to horizontally align for transcription and has a specificity and sensitivity of 100% as validated [25]. This measure, the episodic sub-episode block sums split-integrated weighted average-averaged gene overexpression tropy quotient (esebssiwaagoTQ). The esebssiwaagoTQ, a physical property of a gene, is less than 0.245 units for infra-pressuromodulated anisotropic genes, and in between 0.245 and 0.745 units for supra-pressuromodulated mesotropic genes.

Even as the eukaryotic stranded chromatin has shown to be heterochromatinized to various degrees at the nuclear envelope in response to application of mechanical strain in vitro, the precise mechanistic basis for alterations in chromatin gene transcription in differentiating cell lineages has been difficult to determine due to limited spatial resolution for detection of shifts in reference to specific genes in vitro. Therefore, in this study heterochromatin DNA strand loop structure gene positioning angulation in the z, y-vertical plane is studied by segmentation of DNA strand loops in terms of mesotropy and anisotropy utilizing the sebs intercept-to-sebssiwa intercept linearization quotient, bsebs/bsebssiwa, for validation of linear normalization and the effective cell pressure unit (Peff) -to-gene angulation conversion factor for gene anglemetry and momentum vectormetry analysis in linear nl two-dimensional (2-D) protoplasmic cell space; henceforth, these normalized heterochromatin gene angulation parameters are applied for determination of the esebssiwaagoTQ-based pressuromodulation map for gene expression of the subtypes of neuronal cells that constitute the peripheral to central nervous system neuroaxis in correlation with changes in tissue macro-compliance.

Methods

Selection of genes for study

Human chromatin forward and reverse strand genes were sampled from 17 of 24 chromosome loci for determination of minima and maxima effective intracellular pressure unit (Peff) for the episodic sub-episode block sums split-integrated weighted average-averaged gene overexpression tropy quotient (esebssiwaagoTQ), n = 224 [25, 26, 27]; the sampled representative genes include ch 14 (n = 188, heavy chain immunoglobin locus, native and recombined) [26, 27], ch 1 (PDPN, S100A2, S100A14, CDH11, SELE, CD34, PTPRC and CR2; n = 8), ch 2 (TGFA), ch 3 (ACPP), ch 4 (CD38), ch 6 (PRR3, PRDM1, ENPP1), ch 7 (ABCB1, FOXP2), ch 10 (MRC1, MKI67), ch 11 (SORL1, MS4A1, RAG1, RAG2), ch 12 (BTG1, CD27, AICDA, ESPL1), ch 14 (IFI27), ch 16 (CDH11, CD19), ch 17 (CD79B), ch 16 (PHLPP, ZCCHC2), ch 19 (CD79A), ch 20 (CD20, PCNA), ch 22 (APOBEC3A, APOBEC3, APOBEC3H) and ch 23-X (DMD) [25, 26, 27]. Three different sets of additional genes were selected for study: 1) twenty-eight sequentially located protein coding and non-coding RNA genes in native positions on the Ch 1 q arm forward (+) strand in reference to LMNA for the Peff esebssiwaagoTQ-based sub-analysis study of native intergene base loop segment tropy structure nano-compliance (n = 28); 2) protein coding genes located on various chromosomes and overexpressed during cell differentiation were selected for Peff esebssiwaagoTQ-based sub-analysis study of gene angulation positioning in the linear normalized z, y-vertical plane and momentum vectormetry to the z, x-horizontal plane (n = 28), and include genes involved in cell membrane adhesion (CD34, CEACAM1), cell membrane ligand binding (INSL3, ENPP1), extracellular matrix formation (COL1A1, COL2A1, COL6A1, CCN2), cell cycle regulation (RGS13, RGS4, RGS1), inner nuclear envelope matrix stabilization (LMNA, LMNB1, LMNB2, EMD, NUMA1), transcriptional regulation (MYC, JUND, SOX18, PRKCH, EGR1, ESRRB, GABPA, NFE2L2), NFκB survival pathway (IER3), oxygen sensing (CYGB), and in B-cell function (PRDM1, MIR4537); and 3) protein coding genes located on various chromosomes and overexpressed during central-to-peripheral neural cell differentiation were selected for predictive sub-analysis study of neural axis gene overexpression in reference to tissue macro-compliance by esebssiwaagoTQ-based effective intracellular pressure units (n = 14), and include genes involved in neurotransmitter ligand binding (DRD1, DRD2, DRD3, GRIN1), synaptic cleft stabilization (UNC13A, SHANK2), cell cycle regulation (RGS21, RGS2, RGS16, RGS18), nuclear RNA splicing (RBFOX3), transcriptional regulation (SOX1, SOX14), and in oxygen sensing (NGB).

Gene locus coordinates were mined as per the GRch38/hg38 gene location classification system at Gene Cards (https://www.genecards.org) and LNCipedia (https://lncipedia.org). Genes were stratified by gene locus episode and initial sub-episode block structure (SEB) as either Episode 2 (> 11,864 ≤ 265,005 bases; 5 SEB), Episode 3 (≤ 11,864; 7 SEB) and for Episode 4 (>265,005 <607,463; 9 SEB), Episode 5 (≥ 607,463 < 2,242,933; 11 SEB) or Episode 6 (≥ 2,242,933; 13 SEB) to determine the initial sub-episode block structure count for determination of the episodic sub-episode block sums split-integrated weighted average-averaged gene overexpression tropy quotient were determined [25, 26, 27].

Determination of native gene location intergene base segment loop tropy and strand loop structure in reference to LMNA

The sequentially located gene locus gene loop segment tropies in reference to LMNA on ch 1q22 (+) for sub-group structural analysis included DAP3, MSTO2P, PIR32612, LOC100132108, SYT11, GC01P155896, lnc-RXFP4-5, RXFP4, lnc-RXFP4-2, ENSG00000224276 / LOC105371729, GC01P156042 (LAMTOR2), RAB25, LMNA, SEMA4A, SLC25A44, PMF1-BGLAP, TMEM79, TSACC, RHBG, ENSG00000237390, lnc-TTC24-5, lnc-TTC24-4, ENSG00000260460, lnc-TTC24-1, GC01P156524, TTC24, NAXE, HALPN2 and BCAN from 5’ to 3’ end (n = 28).

The esebssiwaagoTQ-based Σ intergene base segment tropy was determined as the integrated upstream part anisotropic sub-episode block sum (uppasebs), downstream part anisotropic sub-episode block sum (dppasebs), the upstream part mesotropic sub-episode block sum (uppmsebs) and the downstream part anisotropic sub-episode block sum (dppasebs) by the final sequentially integrated (ʃ) paired point tropy quotient (prpTQ) point of final sub-episode block structure based on which the gene intergene base segment loop structure was determined in terms of segmental anisotropy, segmental mesotropy or segmental amorphousosity for the respective genes in native configuration in reference to the LMNA gene locus.

Determination of the linearization quotient for z, y-plane gene anglemetry by exponential function plotting of sebs and sebssiwa

Genes selected for sub-group analysis anglemetry include episode 2 (n = 14), episode 3 (n = 11), episode 4 (n = 2) and episode 6 (n = 1), n = 28. Episode 2 genes selected for sub-group study include (ch, strand) LMNA (1q22, +), RGS13 (1q31.2, +), CD34 (1q32.2, -), LMNB1 (5q23.2, +), PRDM1 (6q21, +), ENPP1 (6q23.2, +), NUMA1 (11q13.3-q13.4, -), COL2A1 (12q13.11, -), ESRRB (14q24.3, +), COL1A1 (17q21.33, -), CYGB (17q25.1, -), CEACAM1 (19q13.2, -), GABPA (21q21.3, +) and COL6A1 (21q22.3, +); episode 3 genes selected for sub-group study include RGS4 (1q23.3, +), RGS1 (1q31.2, +), EGR1 (5q31.2, +), IER3 (6q21.33, -), CCN2 (6q23.2, -), MYC (8q24.21, +), MIR4537 (14q32.3, -), INSL3 (19q13.11, -), JUND (19q13.11, -), SOX18 (20q13.33, -) and EMD (Xq28, +); the episode 4 genes selected for sub-group study include LMNB2 (19q13.3, -) and PRKCH (14q32.2, +); and the episode 6 gene(s) selected for sub-group study include NFE2L2 (2q31.2, -).

The esebssiwaagoTQ-based uppasebs, dppasebs, uppmsebs, and dppasebs and the correlate upstream part anisotropic sub-episode block sum split integrated weighted average (uppasebssiwa), downstream part anisotropic sub-episode block sum split integrated weighted average (dppasebssiwa), the upstream part mesotropic sub-episode block sum split integrated weighted average (uppmsebssiwa), and the downstream part anisotropic sub-episode block sum split integrated weighted average (dppasebssiwa) were determined. The y-intercept exponential function for each sub-group analysis gene locus sub-episode block sum (sebs; upstream part, upp; downstream part, dpp) and sub-episode block sum split integrated weighted average (sebssiwa; upstream, downstream) was plotted (x1, y1; x2, y2) for determination of the normalized uppasebs, uppmsebs::uppasebssiwa, uppmsebssiwa effect; the x-intercept plot was utilized for determination of the normalized dppasebs, dppmsebs::dppasebssiwa, dppmsebssiwa effect when the uppasebs and uppmsebs sums part-effect was equivalent; and a hybrid intercept plot was utilized in case of equivalent magnitude ratio uppasebs : dppasebs and uppmsebs : dppmsebs sums part-effects. Each function is represented in form, b·em·x, where b represents the downstream anisotropic effect. The y- or x-sebs intercept to sebssiwa intercept quotient for linearization was determined in form, bsebs/bsebssiwa. The sub-episode block sum (sebs) - sub-episode block sum split integrated weighted average (sebssiwa) was determined as the normalized subtractive residual for each function, adjusted residual.

3-tier pairwise statistical comparison of b sebs/b sebssiwa linearization quotients and sebs - sebssiwa residuals by esebssiwaagoT Q stratum

Sub-group analysis genes were stratified by Peff interval in ≤ 0.200, > 0.200 ≤ 0.300 and > 0.300 tiers for pairwise comparisons of the bsebs/bsebssiwa intercept linearization quotient and subtractive residual determinations of uppasebs, dppasebs, uppmsebs, dppmsebs and correlate uppasebssiwa, dppasebssiwa, uppmsebssiwa, dppmsebssiwaa as independent sums and averages for genes with non-nil residual normalizing adjustments. Two-step Tukey range t-test was performed for inter-group comparisons of bsebs/bsebssiwa quotients and sebs – sebssiwa normalized residuals between tier 1 (Peff ≤ 0.200; n = 11) and tier 2 (Peff > 0.200 ≤ 0.300; n = 6), between tier 1 and tier 3 (Peff > 0.300; n = 8), and between tier 3 and tier 2 (α = 0.05); likewise comparisons were performed for determination of differences in Σ intergene tropy between the tiers (α = 0.05).

Determination of the effective pressure unit quotient to angle conversion factor gene anglemetry from the z, y-vertical to z, x-horizontal plane

The pressure unit to angle conversion factor was determined in reference to the z, x-axis horizontal plane and two-dimensional gene anglemetry analysis was performed for the sub-group analysis genes (n = 28; n = 14). The ϴA = (1E + 02) {0.90 – [(0.000 + ax < 0.245) (1.208)] form was applied for anisotropic gene anglemetry, where a is the minimum pressure for anisotropic gene expression, and the ϴM = (1E + 02) {0.90 – [1.208 (0.245 ≥ xm)] form was applied for mesotropic gene anglemetry, where m is the maximum pressure for mesotropic gene expression (n = 224), based on linear regression of the esebssiwaagoTQs of the gene set of the study (R2 = 1). Gene position arc distance in the z, y-vertical plane in reference to the z, x-horizontal plane was defined for anisotropic and mesotropic genes based on gene anglemetry thetas, ϴA and ϴM. The hypotenusal intergene tropy base distance for anisotropic genes was then defined as dA for anisotropic genes, and as dM for mesotropic genes, in which case d is the final sub-episode block sum of intergene tropy base distance for anisotropic genes (ASEB) or for mesotropic genes (MESEB). The Σ intergene base tropy distance is defined in reference to the horizontal line of unity (H0) as either dA·sin ΘA for anisotropic genes and as dM·sin ΘM for mesotropic genes, wherein the arc gene tropy intergene base distance is definable as dM·sin ΘM in reference to the line of unity; and wherein the Σ hypotenusal gene intergene tropy distance dA (or dM) is defined as a non-component scalar at H0 = 00 in which case dA (or M)·cos Θ A (or M) + x A (or M).

Vectormetry for z, x-plane horizontal alignment of anisotropic and mesotropic genes

Vectormetry for horizontal alignment of anisotropic and mesotropic genes was performed empirically for anisotropic and mesotropic genes based on the z, y-vertical plane position angle, ϴA for anisotropic genes and ϴM for mesotropic genes, and effective cell pressure (Peff) for horizontal alignment, Peff (0.000 + ax < 0.245) for anisotropic and Peff (0.245 ≥ x ≤ 0.745 – m) for mesotropic. Defined knowns were applied for vectormetry, where momental vector, m, is a product of the mass of DNA-associated nuclear proteins (m) and the velocity of gene tropy to horizontal (v). The origination momentum vector for chromatin-associated protein viscosity at intergene segment effect was then defined as mch tropy; the initial origination momentum vector for nuclear membrane nucleoplasm chromatin-associated protein viscosity at intergene segment effect was then defined as mch nmn tropy; and the origination gravitational momentum vector was then defined as mpro-grav ch tropy. The effective momentum, meff, for z, x-horizontal plane alignment of anisotropic gene tropy was then defined, mA (mch tropy - mpro-grav ch tropy); and the effective momentum for z, x-horizontal plane alignment of mesotropic gene tropy was then defined, mM [m ch tropy + mch nmn tropy (- mpro-grav ch tropy)]. The relationship between effective pressure (Peff) and momentum (meff) was definable for anisotropic gene horizontal alignment (mA) and mesotropic gene horizontal alignment (mM).

Determination of the heterochromatinization parameters for neural axis cell differentiation genes

Genes selected for sub-group analysis include episode 2 (n = 5), episode 3 (n = 5) and episode 4, 5 or 6 (n = 4), n = 14. Episode 2 genes selected for sub-group study include (ch, strand) UNC13A (19p13.11, -), RGS21 (1q31.2, +), SOX1 (13q34, +), DRD2 (11q23.2, -), GRIN1 (9q34.3, +); episode 3 genes selected for sub-group study include NGB (14q24.3, -), RGS2 (1q31.2, +), RGS16 (1q23.3, -), SOX14 (3q22.3, +), DRD1 (5q35.2, +) and EGR1 (5q31.2, +); the Episode 4 genes selected for sub-group study include RGS18 (1q31.2, +) and DRD3 (3q13.31, -); and the Episode 5 to 6 genes selected for sub-group study include RBFOX3 (17q25.3, -) and SHANK2 (11q13.3-q13.4, -).

The uppasebs, dppasebs, uppmsebs, dppasebs, uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa were determined as per the esebssiwaagoTQ method and its adjusted residual (x1, y1; x2, y2). The exponential function pair was y-intercept or reverse x-intercept plotted for determination of the sebs-to-sebssiwa intercept linearization quotient (bsebs/bsebssiwa). The uppesebssiwaa/dppesebssiwaa quotient effective intracellular pressure (Peff) was then determined for classifying of predicted gene overexpression of the genes selected for neural axis cell differentiation. Two-dimensional gene anglemetry analysis was performed for the mesotropic and anisotropic gene set by effective pressure for gene expression for determination of gene position in the z, y-vertical plane position angle (ϴA, ϴM). The tropy of the intergene base segments and interposed gene segment bases was determined as the hypotenusal Σ gene intergene base segment tropy for z, y-plane to z, x-horizontal plane alignment.

Results

Sequentially located forward strand native genes in 5′ → 3′ chronology on ch 1q22 in reference to LMNA by P eff esebssiwaagoT Q units

DAP3 is a 2 A 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 3.09108E + 05 bases at position -12. Sequential integration (∫) to the final esebssiwaagoTQ for DAP3 is 0.093, 0.157, 0.210, 0.247. The final uppesebssiwaa and dppesebssiwaa for DAP3 are 1.1196E + 04 and 4.7835E + 04 intergene bases. The Peff for gene locus DAP3 is 0.234 esebssiwaagoTQ units.

MSTO2P is a 3 M 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 5.94486E + 05 bases at position -11. Sequential integration (∫) to the final esebssiwaagoTQ for MSTO2P is 0.680, 0.417, 0.358, 0.340, 0.309, 0.269 (DfC). The final uppesebssiwaa and dppesebssiwaa for MSTO2P are 1.8354E + 04 and 6.7448E + 04 intergene bases. The Peff for gene locus MSTO2P is 0.272 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).
Table 1

Sequentially located forward strand native genes of human chromosome 1 q arm locus 22 in reference to LMNA within intergene loop tropy segments with nano-compliance of the same with respect to the gene

 

Germline gene locusa

Episode category

(sub-episode block structure)b, c

Gene locus start and end base location

(no of locus bases;

Σ intergene base segment tropy)

Sequential integration (∫) to final esebssiwaagoTQ (fract)d

Final uppesebssiwaa, dppesebssiwaa

Peff esebssiwaagoTQ (fract)e

-12

DAP3, death associated protein 3

2 A 5

5′-155,687,960 – 155,739,010

(51,051; 3.09108E + 05)

0.093, 0.157, 0.210, 0.247

1.1196E + 04,

4.7835E + 04

0.234

-11

MSTO2P, misato family member, pseudogene

3 M 7

155,745,768 – 155,750,688

(4,921; 5.94486E + 05)

0.680, 0.417, 0.358, 0.340, 0.309, 0.269

1.8354E + 04,

6.7448E + 04

0.272

-10

PIR32612

3 A 7

155,750,710 – 155,750,759

(30;

5.26775E + 05)

0.0002, 0.242, 0.282, 0.218, 0.232, 0.224

1.3367E + 04,

5.8380E + 04

0.229

-9

LOC100132108

3 A 7

155,845,340 – 155,847,270

(1,931; 5.82948E + 05)

0.262, 0.357, 0.258, 0.198, 0.225, 0.205

1.4504E + 04,

6.8778E + 04

0.211

-8

SYT11, synaptotagmin 11

2 A 5

155,859,469 –

155,885,199

(25,731; 4.15371E + 05)

0.166, 0.401, 0.333, 0.266

1.8089E + 04,

6.7250E + 04

0.269

iiii-7

GC01P155896

3 A 7 (+ 1)

ACM

155,894,280 – 155,894,386

(107; 1.201927E+ 06)

0.188, 0.330, 0.205, 0.198, 0.144, 0.138, 0.131

1.8900E + 04,

1.31341E + 05

0.144

-6

lnc-RXFP4–5

3 M 7 (− 2)

NCA

155,934,457 – 155,936,536

(2,080; 5.72477E + 05)

0.335, 0.274, 0.292, 0.233, 0.314, 0.272, 0.250

2.6779E + 04,

8.5304E + 04

0.314

-5

RXFP4, relaxin family peptide//INSL5 receptor 4

3 A 7

155,941,689 – 155,942,949

(1,261; 4.25027E + 05)

0.144, 0.453, 0.451, 0.376, 0.299, 0.260

1.2920E + 04,

4.8207E + 04

0.268

-4

lnc-RXFP4–2

(ENSG00000273002)

3 M 7

155,978,659 – 155,983,018

(4,380; 1.210734E+ 06)

0.551, 0.184, 0.225, 0.208, 0.199, 0.162

2.7911E + 04,

1.58180E + 05

0.176

-3

ENSG00000224276/

LOC105371729

2 M 5

155,991,390 – 156,033,225

(41,836; 3.67426E + 05)

0.527, 0.209, 0.211, 0.236, 0.260, 0.247

1.4498E + 04,

5.5694E + 04

0.260

-2

GC01P156042 (LAMTOR2, late endosomal/lysosomal adaptor, MAPK and MTOR activator 2)

2 M 5 (−2)

NCA

156,042,571 – 156,060,811

(18,241; 2.91985E + 05)

0.358, 0.278, 0.259, 0.273

1.3666E + 04,

5.2795E + 04

0.259

-1

RAB25, member RAS oncogene family

3 A 7 (−2)

ACM

156,061,160 – 156,070,514

(9,355; 6.29741E + 05)

0.030, 0.356, 0.297, 0.434, 0.270, 0.242, 0.233

2.6153E + 04,

9.7028E + 04

0.270

 

LMNA, prelamin-A/C

2 A 5

156,082,156 – 156,140,089

(57,934; 9.51609E + 05)

0.156, 0.206, 0.162, 0.240

2.8948E + 04,

1.57549E + 04

0.184

1

SEMA4A, semaphorin 4A

2 M 5

156,147,359 – 156,177,752

(30,394; 2.95365E + 05)

0.449, 0.170, 0.173, 0.136

7.891E + 03,

5.8332E + 04

0.135

2

SLC25A44, solute carrier family 25 member 44

2 A 5

156,193,932 – 156,212,796

(18,865; 3.62292E + 05)

0.184, 0.226, 0.268, 0.399, 0.395, 0.378, 0.270

2.1658E + 04,

5.4827E + 04

0.395

3

PMF1-BGLAP, PMF1 (polyamine modulated factor 1)-BGLAP (bone gamma-carboxyglutamate protein) readthrough

2 A 5

156,212,982 – 156,243,332

(27,090; 3.92203E + 05)

0.005, 0.230, 0.161, 0.133

9.594E + 03,

6.5791E + 04

0.146

4

TMEM79, transmembrane Protein 79

3 A 7 (+1) ACM

156,282,913 – 156,293,185

(10,273; 1.848556E + 06)

0.335, 0167, 0.208, 0.194, 0.247, 0.245, 0.228

4.0434E + 04,

1.90636E + 05

0.212

5

TSACC, TSSK6 activating cochaperone

3 A 7

156,337,314 –

156, 346,395

(9,682; 7.43872E + 05)

0.028, 0.250, 0.327, 0.340, 0.364, 0.318

2.7118E + 04,

8.0818E + 04

0.336

6

RHBG, Rh family B glycoprotein

2 M 5

156,366,043 – 156,385,234

(19,192; 6.05950E + 05)

0.419, 0.280, 0.315, 0.302

2.6125E + 04,

9.1097E + 04

0.287

7

ENSG00000237390

3 A 7

156,388,226 – 156,395,609

(7,384; 9.58633E + 05)

0.020, 0.110, 0.164, 0.154, 0.137, 0.144

1.7374E + 04,

1.13726E + 05

0.153

8

lnc-TTC24–5

3 M 7

156,500,997 –

156,502,475

(1,479; 9.02656E + 05)

0.369, 0.321, 0.355, 0.242, 0.267, 0.290

4.1211E + 04,

9.6908E + 04

0.283

9

lnc-TTC24–4

3 A 7 (+2)

ACM

156,503,086 – 156,503,834

(749;

1.138955E + 05)

0.055, 0.276, 0.152, 0.193, 0.223, 0.235, 0.194

2.3007E + 04,

1.19362E + 05

0.193

10

lnc-TTC24–1

3 M 7

156,509,584 –

156,513,960

(4,377; 4.86984E + 05)

0.544, 0.097, 0.267, 0.342, 0.312, 0.264

1.4861E + 04,

5.5298E + 04

0.269

11

GC01P156524

3 A 7 (+ 2) ACM

156,524,535 – 156,525,810

(476;

1.492171E + 06)

0.141, 0.225, 0.162, 0.212, 0.223, 0.217, 0.232, 0.217, 0.199, 0.196, 0.205

2.6686E + 04,

1.34141E + 053 A 7

0.199

12

TTC24, tetratricopeptide repeat domain 24

3 M 7

156,579,727 – 156,587,797

(8,071; 8.54954E + 05)

0.406, 0.197, 0.184, 0.116, 0.145, 0.159

1.6633E + 04, 1.14108E + 05

0.146

13

NAXE, NAD(P) HX epimerase

3 A 7

156,591,762 – 156,594,299

(2,538; 1.422774E + 06)

0.125, 0.218, 0.153, 0.144, 0.159, 0.187

2.7892E + 04, 1.61601E + 05

0.190

14

HAPLN2, hyaluronan and proteoglycan link protein 2

3 M 7

156,618, 801–3 M 7 156,625,725

(6,925; 7.92243E + 05)

0.636 0.505, 0.456, 0.243, 0.209, 0.211, 0.188, 0.209, 0.194

1.8695E + 04,

9.9190E + 04

0.188

15

BCAN, brevican

2 M 5

156,641,390 – 156,659,532–3′

(18,143; 7.28923E + 05)

0.389, 0.212, 0.235, 0.262

2.7104E + 04,

1.11335E + 05

0.243

a) RNA genes included are protein encoding genes, non-coding GC_, PIR_, ENSG_ and long non-coding lnc- naming convention mRNA genes including functional pseudogenes; b) Gene loci episodic structure sub-episode block categories include Episode 2 (> 11,864 ≤ 265,005 bases; 5 SEB), Episode 3 (≤ 11,864; 7 SEB), Episode 4 (>265,005 < 607,463; 9 SEB), Episode 5 (≥ 607,463 < 2,242,933; 11 SEB) or Episode 6 (≥ 2,242,933; 13 SEB); c) Gene loci sub-episode block structure variations include non-contributory anisotropy (NCA), anisotropy converted to mesotropy (ACM), and/or 0.5-factor adjusted stabilizing mesotropy or anisotropy converted to stabilizing isotropy for anisotropy or mesotropy (stIAfM, stIMfA or stIMfM) that result in initial to final SEB conversion; d) Integration is in underlined italics where the sequential sub-episode block structure is deviation from constancy (DfC) [25], as in the cases of gene locuses MSTO2P (pos − 11), lnc-RXFP4–5 (pos −6), ENSG00000224276 / LOC105371729 (pos −3), GC01P156042 (pos − 2), RAB25 (pos − 1), SLC25A44 (pos + 2), GC01P156524 (pos + 11) and HALPN2 (pos + 14); and e) Peff esebssiwaagoTQ is in italics where three (3) or more anisotropic or mesotropic genes are situated in tandem within the intergene tropy of the same in reference to LMNA located in native configuration

Fig. 1

Angulation of intergene base arc distance tropy in reference to the z, x-axis horizontal plane for amorphous heterochromatin loop segment genes. Amorphous heterochromatin strand loop micro-structural segmentation is a series of intergene base distance-separated alternating anisotropic (a) and mesotropic genes (m) in the form of one or two in-tandem anisotropic or mesotropic genes of the same at angulation (ΘA, ΘM) in the z, y-vertical axis plane. The prelamin-A/C gene (Peff, 0.184)-containing amorphous form heterochromatin strand loop segment for example is arranged as LMNA (ΘA = 67.80)-SEMA4A (ΘA = 73.70)-SLC25A44 (ΘM = 42.30)-PMF1-BGLAP (ΘA = 72.40)-TMEM79 (ΘA = 64.40)-TSACC (ΘM = 49.40)-RHBG (ΘM = 55.30) in series from 5’ to 3’ on human ch 1q22 at positions +1 through +6 in reference to LMNA. As shown is an anisotropic gene within its hypotenusal gene intergene base distance tropy positioned at angulation, ΘA ≤ 82.30 in the z, y-vertical plane with Σ gene + intergene base distance, dA· sin ΘA, juxtaposed to a mesotropic gene within its hypotenusal gene intergene base distance tropy positioned at angulation, ΘM ≥ 11.70, from the horizontal line of unity in a heterochromatin strand amorphous form loop segment. A transcribable gene can be either an anisotropic segment loop gene (ΘA) or a mesotropic gene segment loop gene (ΘM) in an amorphous segment loop of alternating in-tandem genes. Legend. dA, hypotenusal distance of anisotropic gene intergene tropy bases; dM, hypotenusal distance of mesotropic gene intergene tropy bases. Note: 3’, downstream

Fig. 2

Angulation of intergene base arc distance tropy in reference to the z, x-axis horizontal plane for anisotropic heterochromatin loop segment genes. Anisotropic heterochromatin strand loop micro-structural arrangement is a series of ≥ 3 intergene base distance-separated genes perceiving the asymmetric tropy viscosity effect with nano-compliance of the same, ΘA, lncRNA class gene GC01P156524 (Peff, 0.199)-containing anisotropic form heterochromatin strand loop segment for example is arranged as GC01P156524 (ΘA = 660)-TTC24 (ΘA = 72.40)-NAXE (ΘA = 67.00)-HALPN2 (ΘA = 67.30)-BCAN (ΘA = 60.60) in series from 5’ to 3’ on human ch 1q22 at positions +11 through +15 in reference to LMNA. As shown is a gene of an anisotropic heterochromatin segment loop positioned at ΘA = 60.490 (Peff, 0.2445) in the z, y-axis plane is transcriptionally active at ΘA = ΘH, and ch 14q32.3 reverse strand (-) IGH_ immunoglobin heavy chain locus gene, MIR4537, positioned at the upper limit of angulation ΘA = 82.30, aligns for z, x-horizontal plane transcription at a Peff = 0.064 esebssiwaagoTQ units. Legend. ΘH, zero degree horizontal axis line of unity; dA, hypotenusal distance of anisotropic gene intergene tropy bases; dA sin ΘA, distance to horizontal for anisotropic gene intergene tropy distance; dA at H0 = 00, dA·cos ΘA + xA; Peffective intracellular pressure (Peff) = Peffective intranuclear pressure

Fig. 3

Angulation of intergene base arc distance tropy in reference to the z, x-axis horizontal plane mesotropic heterochromatin loop segment genes. Mesotropic heterochromatin strand loop micro-structural arrangement is a series of ≥ 3 intergene base distance-separated genes perceiving the lesser grade asymmetric tropy viscosity effect with nano-compliance of the same, ΘM. RNA/ncRNA class gene locus ENSG00000224276 / LOC105371729 (Peff, 0.260)-containing mesotropic form heterochromatin strand loop segment consisting of three genes in-series is arranged as ENSG00000224276 / LOC105371729 (ΘM = 58.60)-GC01P156042 (LAMTOR2) (ΘM = 58.70)-RAB25 (ΘM = 57.40) from 5’ to 3’ on the forward (+) strand of human ch 1q22 at positions -3 through -1 in reference to LMNA; and the heavy chain immunoglobin gene locus (IGH_) containing mesotropic form heterochromatin strand loop segment consisting of 8 diversity genes in-series is arranged as IGHD1-20 (nf) (ΘM = 410)-IGHD6-19 (ΘM = 52.70)-IGHD5-18 (ΘM = 59.30)-IGHD4-17 (ΘM = 52.50)-IGHD3-16 (ΘM = 52.80)-IGHD2-15 (ΘM = 54.50)-IGHD1-14 (ΘM = 54.70)-IGHD6-13 (ΘM = 55.40) from 3’ to 5’ on the reverse (-) strand of human ch 14q32.3 in native configuration. As shown is a gene of a mesotropic heterochromatin segment loop positioned at the lower limit of angulation ΘM = 11.70 in the z, y-vertical plane that horizontally aligns for transcription in z, x-axis at a Peff of 0.648 esebssiwaagoTQ units. Legend. ΘH, zero degree horizontal; dM, hypotenusal distance of anisotropic gene intergene tropy bases; dM sin ΘM, distance to horizontal for anisotropic gene intergene tropy distance; dM at H0 = 00, dM·cos ΘM + xM; Peffective intracellular pressure (Peff) = Peffective intranuclear pressure

PIR32612 is a 3 A 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 5.26775E + 05 intergene bases at position -10. Sequential integration (∫) to the final esebssiwaagoTQ for PIR32612 is 0.0002, 0.242, 0.261, 0.247, 0.279, 0.248. The final uppesebssiwaa and dppesebssiwaa for PIR32612 are 1.3367E + 04 and 5.8380E + 04 intergene bases. The Peff for gene locus PIR32612 is 0.229 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

LOC100132108 is a 3 A 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 5.82948E + 05 intergene bases at position -9. Sequential integration (∫) to the final esebssiwaagoTQ for LOC100132108 is 0.262, 0.357, 0.258, 0.198, 0.225, 0.205. The final uppesebssiwaa and dppesebssiwaa for LOC100132108 are 1.4504E + 04 and 6.8778E + 04 intergene bases. The Peff for gene locus LOC100132108 is 0.211 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

SYT11 is a 2 A 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 4.15371E + 05 intergene bases at position -8. Sequential integration (∫) to the final esebssiwaagoTQ for SYT11 is 0.166, 0.401, 0.333, 0.266. The final uppesebssiwaa and dppesebssiwaa for SYT11 are 1.8089E + 04 and 6.7250E + 04 intergene bases. The Peff for gene locus SYT11 is 0.269 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

GC01P155896 is a 3 A 7 (+1) ACM final SEB gene locus with a Σ intergene base segment tropy of 1.201927E + 06 intergene bases at position -7. Sequential integration (∫) to the final esebssiwaagoTQ for GC01P155896 is 0.188, 0.330, 0.205, 0.198, 0.144, 0.138, 0.131. The final uppesebssiwaa and dppesebssiwaa for GC01P155896 are 1.8900E + 04 and 1.31341E + 05 intergene bases. The Peff for gene locus GC01P155896 is 0.144 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

lnc-RXFP4-5 is a 3 M 7 (-2) NCA final SEB gene locus with a Σ intergene base segment tropy of 5.72477E + 05 intergene bases at position -6. Sequential integration (∫) to the final esebssiwaagoTQ for lnc-RXFP4-5 is 0.335, 0.274, 0.292, 0.233, 0.314 (DfC), 0.272, 0.250. The final uppesebssiwaa and dppesebssiwaa for lnc-RXFP4-5 are 2.6779E + 04 and 8.5304E + 04 intergene bases. The Peff for gene locus lnc-RXFP4-5 is 0.314 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

RXFP4 is a 3 A 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 4.25027E + 05 intergene bases at position -5. Sequential integration (∫) to the final esebssiwaagoTQ for RXFP4 is 0.144, 0.453, 0.451, 0.376, 0.299, 0.260. The final uppesebssiwaa and dppesebssiwaa for RXFP4 are 1.2920E + 04 and 4.8207E + 04 intergene bases. The Peff for gene locus RXFP4 is 0.268 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

lnc-RXFP4-2 is a 3 M 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 1.210734E + 06 intergene bases at position -4. Sequential integration (∫) to the final esebssiwaagoTQ for lnc-RXFP4-2 is 0.551, 0.184, 0.225, 0.208, 0.199, 0.162. The final uppesebssiwaa and dppesebssiwaa for lnc-RXFP4-2 are 2.7911E + 04 and 1.58180E + 05 intergene bases. The Peff for gene locus lnc-RXFP4 is 0.176 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

ENSG00000224276 / LOC105371729 is a 2 M 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 3.67426E + 05 intergene bases at position -3. Sequential integration (∫) to the final esebssiwaagoTQ for ENSG00000224276 / LOC105371729 is 0.527, 0.209, 0.211, 0.236, 0.260 (DfC), 0.247. The final uppesebssiwaa and dppesebssiwaa for ENSG00000224276 / LOC105371729 are 1.4498E + 04 and 5.5694E + 04 intergene bases. The Peff for gene locus ENSG00000224276/LOC105371729 is 0.260 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

GC01P156042 (LAMTOR2) is a 2 M 5 (-2) ACM final SEB gene locus with a Σ intergene base segment tropy of 2.91985E + 05 intergene bases at position -2. Sequential integration (∫) to the final esebssiwaagoTQ for GC01P156042 (LAMTOR2) is 0.358, 0.278, 0.259 (DfC), 0.273. The final uppesebssiwaa and dppesebssiwaa for GC01P156042 (LAMTOR2) are 1.3666E + 04 and 5.2795E + 04 intergene bases. The Peff for gene locus GC01P156042 (LAMTOR2) is 0.259 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

RAB25 is a 3 A 7 (-2) ACM final SEB gene locus with a Σ intergene base segment tropy of 6.29741E + 05 intergene bases at position -1. Sequential integration (∫) to the final esebssiwaagoTQ for RAB25 is 0.030, 0.356, 0.297, 0.434, 0.270 (DfC), 0.242, 0.233. The final uppesebssiwaa and dppesebssiwaa for RAB25 are 2.6153E + 04 and 9.7028E + 04 intergene bases. The Peff for gene locus RAB25 is 0.270 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

LMNA is a 2 A 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 9.51609E + 05 intergene bases at position 0. Sequential integration (∫) to the final esebssiwaagoTQ for LMNA is 0.156, 0.206, 0.162, 0.240. The final uppesebssiwaa and dppesebssiwaa for LMNA are 2.8948E + 04 and 1.57549E + 04 intergene bases. The Peff for gene locus LMNA is 0.184 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

SEMA4A is a 2 M 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 2.95365E + 05 intergene bases at position +1. Sequential integration (∫) to the final esebssiwaagoTQ for SEMA4A is 0.449, 0.170, 0.173. The final uppesebssiwaa and dppesebssiwaa for SEMA4A are 7.891E + 03 and 5.8332E + 04 intergene bases. The Peff for gene locus for SEMA4A is 0.135 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

SLC25A44 is a 2 A 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 3.62292E + 05 intergene bases at position +2. Sequential integration (∫) to the final esebssiwaagoTQ for SLC25A44 is 0.184, 0.226, 0.268, 0.399, 0.395 (DfC), 0.378, 0.270. The final uppesebssiwaa and dppesebssiwaa for SLC25A44 are 2.1658E + 04 and 5.4827E + 04 intergene bases. The Peff for gene locus for SLC25A44 is 0.395 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

PMF1-BGLAP is a 2 A 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 3.92203E + 05 intergene bases at position +3. Sequential integration (∫) to the final esebssiwaagoTQ for PMF1-BGLAP is 0.005, 0.230, 0.161, 0.133. The final uppesebssiwaa and dppesebssiwaa for PMF1-BGLAP are 9.594E + 03 and 6.5791E + 04 intergene bases. The Peff for gene locus for PMF1-BGLAP is 0.146 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

TMEM79 is a 3 A 7 (+1) ACM final SEB gene locus with a Σ intergene base segment tropy of 1.848556E + 06 intergene bases at position +4. Sequential integration (∫) to the final esebssiwaagoTQ for TMEM79 is 0.335, 0167, 0.208, 0.194, 0.247, 0.245, 0.228. The final uppesebssiwaa and dppesebssiwaa for TMEM79 are 4.0434E + 04 and 1.90636E + 05 intergene bases. The Peff for gene locus for TMEM79 is 0.212 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

TSACC is a 3 A 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 7.43872E + 05 intergene bases at position +5. Sequential integration (∫) to the final esebssiwaagoTQ for TSACC is 0.028, 0.250, 0.327, 0.340, 0.364, 0.318. The final uppesebssiwaa and dppesebssiwaa for TSACC are 2.7118E + 04 and 8.0818E + 04 intergene bases. The Peff for gene locus for TSACC is 0.336 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

RHBG is a 2 M 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 6.05950E + 05 intergene bases at position +6. Sequential integration (∫) to the final esebssiwaagoTQ for RHBG is 0.419, 0.280, 0.315, 0.302. The final uppesebssiwaa and dppesebssiwaa for RHBG are 2.6125E + 04 and 9.1097E + 04 intergene bases. The Peff for gene locus for RHBG is 0.287 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

ENSG00000237390 is a 3 A 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 9.58633E + 05 intergene bases at position +7. Sequential integration (∫) to the final esebssiwaagoTQ for ENSG00000237390 is 0.020, 0.110, 0.164, 0.154, 0.137, 0.144. The final uppesebssiwaa and dppesebssiwaa for ENSG00000237390 are 1.7374E + 04 and 1.13726E + 05 intergene bases. The Peff for gene locus for ENSG00000237390 is 0153 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

lnc-TTC24-5 is a 3 M 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 9.02656E + 05 intergene bases at position +8. Sequential integration (∫) to the final esebssiwaagoTQ for lnc-TTC24-5 is 0.369, 0.321, 0.355, 0.242, 0.267, 0.290. The final uppesebssiwaa and dppesebssiwaa for lnc-TTC24-5 are 4.1211E + 04 and 9.6908E + 04 intergene bases. The Peff for gene locus for lnc-TTC24-5 is 0.283 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

lnc-TTC24-4 is a 3 A 7 (+1) ACM final SEB gene locus with a Σ intergene base segment tropy of 1.138955E + 05 intergene bases at position +9. Sequential integration (∫) to the final esebssiwaagoTQ for lnc-TTC24-4 is 0.055, 0.276, 0.152, 0.193, 0.223, 0.235, 0.194. The final uppesebssiwaa and dppesebssiwaa for lnc-TTC24-4 are 2.3007E + 04 and 1.19362E + 05 intergene bases. The Peff for gene locus for lnc-TTC24-4 is 0.193 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

lnc-TTC24-1 is a 3 M 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 4.86984E + 05 intergene bases at position +10. Sequential integration (∫) to the final esebssiwaagoTQ for lnc-TTC24-1 is 0.544, 0.097, 0.267, 0.342, 0.312, 0.264. The final uppesebssiwaa and dppesebssiwaa for lnc-TTC24-1 are 1.4861E + 04 and 5.5298E + 04 intergene bases. The Peff for gene locus for lnc-TTC24-1 is 0.269 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

GC01P156524 is a 3 A 7 (+2) ACM final SEB gene locus with a Σ intergene base segment tropy of 1.492171E + 06 intergene bases at position +11. Sequential integration (∫) to the final esebssiwaagoTQ for GC01P156524 is 0.141, 0.225, 0.162, 0.212, 0.223, 0.217, 0.232, 0.217, 0.199 (DfC), 0.196, 0.205. The final uppesebssiwaa and dppesebssiwaa for GC01P156524 are 2.6686E + 04 and 1.34141E + 05 intergene bases. The Peff for gene locus for GC01P156524 is 0.199 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

TTC24 is a 3 M 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 8.54954E + 05 intergene bases at position +12. Sequential integration (∫) to the final esebssiwaagoTQ for TTC24 is 0.406, 0.197, 0.184, 0.116, 0.145, 0.159. The final uppesebssiwaa and dppesebssiwaa for TTC24 are 1.6633E + 04 and 1.14108E + 05 intergene bases. The Peff for gene locus for TTC24 is 0.146 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

NAXE is a 3 M 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 1.422774E + 06 intergene bases at position +13. Sequential integration (∫) to the final esebssiwaagoTQ for NAXE is 0.125, 0.218, 0.153, 0.144, 0.159, 0.187. The final uppesebssiwaa and dppesebssiwaa for NAXE are 2.7892E + 04 and 1.61601E + 05 intergene bases. The Peff for gene locus for NAXE is 0.190 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

HAPLN2 is a 3 M 7 initial and final SEB gene locus with a Σ intergene base segment tropy of 7.92243E + 05 intergene bases at position +14. Sequential integration (∫) to the final esebssiwaagoTQ for HAPLN2 is 0.636, 0.505, 0.456, 0.243, 0.209, 0.211, 0.188 (DfC), 0.209, 0.194. The final uppesebssiwaa and dppesebssiwaa for HAPLN2 are 1.8695E + 04 and 9.9190E + 04 intergene bases. The Peff for gene locus for HAPLN2 is 0.188 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

BCAN is a 2 M 5 initial and final SEB gene locus with a Σ intergene base segment tropy of 7.28923E + 05 intergene bases at position +15. Sequential integration (∫) to the final esebssiwaagoTQ for BCAN is 0.389, 0.212, 0.235, 0.262. The final uppesebssiwaa and dppesebssiwaa for BCAN are 2.7104E + 04 and 1.11335E + 05 intergene bases. The Peff for gene locus for BCAN is 0.243 esebssiwaagoTQ units (Table 1; Figs. 1, 2 and 3).

Anisotropic gene intergene tropy sub-episode block sum for linear two-dimensional z, y-plane anglemetry

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus MIR4537 are 7.232E + 03, 1.72400E + 05, 5.896E + 03 and 1.1694E + 04. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus MIR4537 are 2.411E + 03, 5.7467E + 04, 1.474E + 03 and 2.934E + 03. The sebs and sebssiwa exponential function pair for anisotropic gene locus MIR4537 is 5.799E+03 e8E-03x and 1.424E+03 e1.72E+02x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus MIR4537 is 4.07. The sebs - sebssiwa residual for anisotropic gene locus MIR4537 is 4,821, 114,933, 4,422 and 8,770. The uppesebssiwaa and dppesebssiwaa for anisotropic gene MIR4537 are 1.942E + 03 and 3.0195E + 04. The esebssiwaagoTQ for anisotropic gene locus MIR4537 is 0.064. Anisotropic gene locus MIR4537 is positioned at angle ϴA = 82.20 in the z, y-axis vertical plane.

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus COL2A1 are 9.2758E + 04, 1.390995E + 06, 6.4607E + 04 and 1.46229E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus COL2A1 are 3.0919E + 04, 4.63665E + 05, 3.2304E + 04 and 7.3115E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus COL2A1 is 6.1920E + 04 e3E-07x and 2.8989E+04 e2E-06x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus COL2A1 is 2.14. The sebs - sebssiwa residual for anisotropic gene locus COL2A1 is 61,839, 927,330, 32,304 and 73,115. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus COL2A1 are 3.1611E + 04 and 2.68390E + 05. The esebssiwaagoTQ for anisotropic gene locus COL2A1 is 0.118. Anisotropic gene locus COL2A1 is positioned at angle ϴA = 75.80 in the z, y-axis vertical plane (Table 2).
Table 2

Angulation of anisotropic genes in reference to the horizontal for the linear normal esebssiwaagoTQ effective intracellular pressure unit

Gene (no. of locus bases; no. of gene bases or n/a)

Gene locus (strand)

Episode category (final SEB structure)

sebs f(x)a

sebssiwa f(x)a

bsebs/bsebssiwab

sebs – sebssiwa (x1, y1; x2, y2), residual

uppesebssiwaa, dppesebssiwaa (Peff esebssiwaagoTQ)

Angulation (0)

MIR4537, microRNA 4537

(70; n/a)

14q32.3 (−)

3 A 7

5.799E+ 03

e 8E-03x

1.424E+ 03

e 1.72E+02x

4.07

4,821, 114,933;

4,422, 8,770

1,942, 30,195

(0.064c)

82.3

COL2A1, collagen type VI alpha 1 chain

(23,314; n/a)

12q13.11 (−)

2 A 5

6.1920E+ 04 e3E-07x

3.2569E+ 04 e1E-07x

1.90

61,839, 927,330; 32,304, 73,115

31,611, 268,390

(0.118)

75.8

RGS4, regulator of g protein signaling 4

(8,197; n/a)

1q23.3 (+)

3 M 7

7.8415E+ 04

e -2E-07x

2.5014E+ 04

e2E-07x

3.14

54,373, 797,384; 75,774, 139,206

26,223, 222,547

(0.118)

75.8

MYC, MYC proto-oncogene

(6,001; n/a)

8q24.21 (+)

3 A 5

8.8964E+ 04 e3E-08x

2.4479E+ 04 e2E-06x

3.63

58,846, 695,321; 42,913, 113,936

36,168, 230,798

(0.157)

71

CCN2, cellular communication network factor 2

(3,203; n/a)

6q23.2 (−)

3 A 8

1.21063E+05

e 3E-09x

3.0266E+04

e 1E-08x

4.00

91,067, 837,824;

90,880, 256,983

30,325, 182,468

(0.166)

70

LMNB2, lamin B2

(288,491; 29,359)

19q13.3 (−)

4 A 7

3.0747E+04

e 7E-07x

1.1944E+04

e 9E-06x

2.57

18,824, 220,250;

19,549,

45,732

8,024, 48,141

(0.167)

69.8

ESRRB, Estrogen Related Receptor Beta

(196,759; 191,128)

14q24.3 (+)

2 A 5

1.05918E+04

e 1E-06x

3.4501E+04

e 2E-06x

3.07

64,086, 539,533; 22,161, 45,003

27,102, 157,268

(0.172)

69.2

LMNA, lamin A/C

(57,934; 57,544)

1q22 (+)

2 A 5

6.65237E+05

e 2E-05x

1.92333E+05 e6E-06x

3.46

28,935, 382,265;

43,439,

123,966

28,945, 157,549 (0.184)

67.8

LMNB1, lamin B1

(60,398; n/a)

5q23.2 (+)

2 A 5

1.0E+05

e 5E-07x

2.96910E+05 e1E-05x

3.37

32,013, 478,625; 58,014, 135,885

37,010, 187,599

(0.197)

66.2

EGR1, early growth response 1

(3,826; n/a)

5q31.2 (+)

3 M 7

7.93682E+05

e 5E-06x

4.04638E+05

e 4E-05x

1.96

18,244, 199,860; 39,226 88,802

28,735, 144,331

(0.199)

66.0

PRKCH, protein kinase C eta type

(471,621; 363,422)

14q32.2 (+)

4 A 5

2.0E+06

e 1E-05x

3.86798E+05

e 1E-05x

5.17

35,062, 628,017; 76,455, 155,817

46,994, 234,912

(0.200)

65.8

IER3, immediate early response 3

(1,356; n/a)

6q21.33 (−)

3 M 5

6.75603E+05

e 2E-05x

3.08411E+05

e 9E-06x

2.78

11,982, 102,979; 35,375, 84,093

14,835, 72,513

(0.205)

65.3

EMD,

emerin

(2,327; n/a)

Xq28 (+)

3 A 5

2.70939E+05

e 4E-06x

8.5425E+04

e 3E-06x

3.17

7,078, 172,964; 39,612, 98,034

21,576,92,258 (0.234)

61.7

COL6A1, collagen type VI alpha 1 chain

(23,314; n/a)

21q22.3 (+)

2 A 4 q term

7.1790E+04 e1E-05x

3.5895E+04 e3E-05x

2.00

807, 36,660; 23,271, 65,941

12,039, 51,301

(0.235)

61.6

COL1A1, collagen type I alpha 1 chain

(18,360; n/a)

17q21.33 (−)

2 A 5

3.1489E+04

e 9E-07x

1.5175E+04

e 6E-06x

2.08

20,066, 140,511; 13,062, 25,468

11,547,47,862 (0.241)

60.9

af(x) = b·em·x, where b is the downstream anisotropic effect (intercept and slope are absolute values); bbsebs/bsebssiwa is the linearization quotient; and cpreviously reported episode and sub-episode block structure and esebssiwaagoTQ value as per references, MIR4537 [26, 27]. Note: 1) Gene loci sub-episode block structure (SEB) variations include non-contributory anisotropy (NCA), anisotropy converted to mesotropy (ACM), and/or 0.5-factor adjusted stabilizing mesotropy or anisotropy converted to stabilizing isotropy for anisotropy or mesotropy (stIAfM, stIMfA or stIMfM) that result in an initial to final SEB conversion; 2) Sub-episode block structures for initial to final SEB converted genes are MYC, 3 A 7 (−2); CCN2, 3 A 7 (+1) stIAfA; LMNB2, 4 A 9 (−2) NCA; PRKCH, 4 A 9 (−2) (−2) NCA ACM; COL6A1, 2 A 5 (−1) q terminal end; IER3, 3 M 7 (− 2) ACM; and EMD, 3 A 7 (− 2) stIAfA; and 3) bsebs/bsebssiwa for MIR4357, COL2A1, RGS4, MYC, CCN2, LMNB2, ESRRB and COL1A1 is by reverse x-intercept plotting of the uppasebs, uppamsebs, dppasebs and dppmsebs and the corelate uppasebssiwa, uppamsebssiwa, dppasebssiwa and dppmsebssiwa; and the same for LMNA and PRKCH is by x-, y- function bsebs and bsebssiwa intercept hybridization

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus RGS4 are 8.1560E + 04, 1.196076E + 06, 1.01032E + 05 and 1.85608E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus RGS4 are 2.7187E + 04, 3.98692E + 05, 2.5258E + 04 and 4.6402E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus RGS4 is 7.8415E+04 e2E-07x and 2.5014E+04 e2E-07x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus RGS4 is 3.14. The sebs - sebssiwa residual for anisotropic gene locus RGS4 is 54,373, 797,384, 75,774 and 139,206. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus RGS4 are 2.6223E + 04 and 2.22547E + 05. The esebssiwaagoTQ for anisotropic gene locus RGS4 is 0.118. Anisotropic gene locus RGS4 is positioned at angle ϴA = 75.80 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus MYC are 8.8269E + 04, 1.042981E + 06, 8.5825E + 04 and 2.27872E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus MYC are 2.9423E + 04, 3.47660E + 05, 4.2913E + 04 and 1.13936E + 05. The sebs and sebssiwa exponential function pair for anisotropic gene locus MYC is 8.8964E+04 e3E-08x and 2.4479E+04 e2E-06x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus MYC is 3.63. The sebs - sebssiwa residual for anisotropic gene locus MYC is 58,846, 695,321, 42,913 and 113,936. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus MYC are 3.6168E + 04 and 2.30798E + 05. The esebssiwaagoTQ for anisotropic gene locus MYC is 0.157. Anisotropic gene locus MYC is positioned at angle ϴA = 71.00 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus LMNA are 4.3403E + 04, 5.73397E + 05, 8.6878E + 04 and 2.47931E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus LMNA are 1.4468E + 04, 1.91132E + 05, 4.3439E + 04 and 1.23966E + 05. The sebs and sebssiwa exponential function pair for anisotropic gene locus LMNA is 6.65237E+05 e2E-05x and 1.92333E+05 e6E-06x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus LMNA is 3.46. The sebs - sebssiwa residual for anisotropic gene locus LMNA is 28,935, 382,265, 43,439 and 123,966. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus LMNA are 2.8995E + 04 and 1.57549E + 05. The esebssiwaagoTQ for anisotropic gene locus LMNA is 0.184. Anisotropic gene locus LMNA is positioned at angle ϴA = 67.80 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus CCN2 are 1.21423E + 05, 1.117098E + 06, 1.21173E + 05 and 3.42644E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus CCN2 are 3.0356E + 04, 2.79275E + 05, 3.0293E + 04 and 8.5661E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus CCN2 is 1.21063E+05 e3E-09x and 3.0266E+04 e1E-08x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus CCN2 is 4.00. The sebs - sebssiwa residual for anisotropic gene locus CCN2 is 91,067, 837,824, 90,880 and 256,983. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus CCN2 are 3.0325E + 04 and 1.82468E + 05. The esebssiwaagoTQ for anisotropic gene locus CCN2 is 0.166. Anisotropic gene locus CNN2 is positioned at angle ϴA = 70.00 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus ESRRB are 9.6129E + 04, 8.08599E + 05, 4.4321E + 04 and 9.0006E + 04. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus ESRRB are 3.2043E + 04, 2.69533E + 05, 2.2161E + 04 and 4.5003E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus ESRRB is 1.05918E+04 e1E-06x and 3.4501E+04 e2E-06x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus ESRRB is 3.07. The sebs - sebssiwa residual for anisotropic gene locus ESRRB is 64,086, 539,533, 22,161 and 45,003. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus ESRRB are 2.7102E + 04 and 1.57268E + 05. The esebssiwaagoTQ for anisotropic gene locus ESRRB is 0.172. Anisotropic gene locus ESRRB is positioned at angle ϴA = 69.20 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus LMNB1 are 4.8020E + 04, 7.17938E + 05, 1.16027E + 05 and 2.71770E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus LMNB1 are 1.6007E + 04, 2.39313E + 05, 5.8014E + 04 and 1.35885E + 05. The sebs and sebssiwa exponential function pair for anisotropic gene locus LMNB1 is 1.0E+05 e5E-07x and 2.96910E+05 e1E-05x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus LMNB1 is 3.37. The sebs - sebssiwa residual for anisotropic gene locus LMNB1 is 32,013, 478,625, 58,014 and 135,885. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus LMNB1 are 3.7010E + 04 and 1.87599E + 05. The esebssiwaagoTQ for anisotropic gene locus LMNB1 is 0.197. Anisotropic gene locus LMNB1 is positioned at angle ϴA = 66.20 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus EGR1 are 5.4733E + 04, 5.99581E + 05, 1.56904E + 05 and 3.55209E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus EGR1 are 1.8244E + 04, 1.99860E + 05, 3.9226E + 04 and 8.8802E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus EGR1 is 7.93682E+05 e5E-06x and 4.04638E+05 e4E-05x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus EGR1 is 1.96. The sebs - sebssiwa residual for anisotropic gene locus EGR1 is 36,489, 399,721, 117,678 and 266,407. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus EGR1 are 2.8735E + 04 and 1.44331E + 05. The esebssiwaagoTQ for anisotropic gene locus EGR1 is 0.199. Anisotropic gene locus EGR1 is positioned at angle ϴA = 66.00 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus PRKCH are 5.2593E + 04, 9.42026E + 05, 1.52911E + 05 and 3.11633E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus PRKCH are 1.7531E + 04, 3.14009E + 05, 7.6456E + 04 and 1.55816E + 05. The sebs and sebssiwa exponential function pair for anisotropic gene locus PRKCH is 1.129582E+06

e6E-06x and 3.56470E+05 e1E-05x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus PRKCH is 3.17. The sebs - sebssiwa residual for anisotropic gene locus PRKCH is 35,062, 628,017, 79,455 and 155,817. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus PRKCH are 4.6994E + 04 and 2.34912E + 05. The esebssiwaagoTQ for anisotropic gene locus PRKCH is 0.200. Anisotropic gene locus PRKCH is positioned at angle ϴA = 65.80 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus LMNB2 are 2.0538E + 04, 2.16613E + 05, 3.4762E + 04 and 8.6623E + 04. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus LMNB2 are 5.135E + 03, 5.4153E + 04, 1.1587E + 04 and 2.8874E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus LMNB2 is 4.9363E+04 e4E-06x and 2.9359E+04 e3E-06x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus LMNB2 is 1.68. The sebs - sebssiwa residual for anisotropic gene locus LMNB2 is 15,404, 162,460, 23,175 and 57,749. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus LMNB2 are 8.361E + 03 and 4.1514E + 04. The esebssiwaagoTQ for anisotropic gene locus LMNB2 is 0.201. Anisotropic gene locus LMNB2 is positioned at angle ϴA = 65.70 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus IER3 are 2.3964E + 04, 2.05958E + 05, 5.3063E + 04 and 1.26140E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus IER3 are 1.1982E + 04, 1.02979E + 05, 1.7688E + 04 and 4.2047E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus IER3 is 6.75603E+05 e2E-05x and 3.08411E+05 e9E-06x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus IER3 is 2.78. The sebs - sebssiwa residual for anisotropic gene locus IER3 is 11,982, 102,979, 35,375 and 84,093. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus IER3 are 1.4835E + 04 and 7.2513E + 04. The esebssiwaagoTQ for anisotropic gene locus IER3 is 0.205. Anisotropic gene locus IER3 is positioned at angle ϴA = 65.30 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus EMD are 1.0617E + 04, 2.59446E + 05, 7.9224E + 04 and 1.96068E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus EMD are 3.539E + 03, 8.6482E + 04, 3.9612E + 04 and 9.8034E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus EMD is 2.70939E+05 e4E-06x and 8.5425E+04 e3E-06x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus EMD is 3.17. The sebs - sebssiwa residual for anisotropic gene locus EMD is 7,078, 172,964, 39,612 and 98,034. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus EMD are 2.1576E + 04 and 9.2258E + 04. The esebssiwaagoTQ for anisotropic gene locus EMD is 0.234. Anisotropic gene locus EMD is positioned at angle ϴA = 61.70 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus COL6A1 are 1.614E + 03, 7.3320E + 04, 4.6541E + 04 and 1.31882E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus COL6A1 are 8.07E + 02, 3.6660E + 04, 2.3271E + 04 and 6.5941E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus COL6A1 is 7.1790E+04 e1E-05x and 3.5895E+04 e3E-05x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus COL6A1 is 2.00. The sebs - sebssiwa residual for anisotropic gene locus COL6A1 is 807, 36,660, 23,271 and 65,941. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus COL6A1 are 1.2039E + 04 and 5.1301E + 04. The esebssiwaagoTQ for anisotropic gene locus COL6A1 is 0.235. Anisotropic gene locus COL6A1 is positioned at angle ϴA = 61.60 in the z, y-axis vertical plane (Table 2).

The uppasebs, dppasebs, uppmsebs and dppasebs for anisotropic gene locus COL1A1 are 3.0099E + 04, 2.10767E + 05, 2.6123E + 04 and 5.0936E + 04. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for anisotropic gene locus COL1A1 are 1.0033E + 04, 7.0256E + 04, 1.3062E + 04 and 2.5468E + 04. The sebs and sebssiwa exponential function pair for anisotropic gene locus COL1A1 is 4.4873E+04 e1E-06x and 4.8093E+04 e2E-05x. The bsebs/bsebssiwa linearization quotient for anisotropic gene locus COL1A1 is 2.08. The sebs - sebssiwa residual for anisotropic gene locus COL1A1 is 20,066, 140,511, 13,062 and 25,468. The uppesebssiwaa and dppesebssiwaa for anisotropic gene locus COL1A1 are 1.1547E + 04 and 4.7862E + 04. The esebssiwaagoTQ for anisotropic gene locus COL1A1 is 0.241. Anisotropic gene locus COL1A1 is positioned at angle ϴA = 69.20 in the z, y-axis vertical plane (Table 2).

Mesotropic gene intergene tropy sub-episode block sum exponential functions for linear two-dimensional z, y-plane anglemetry

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus CYGB are 3.5180E + 04, 2.22499E + 05, 4.6604E + 04 and 1.07321E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus CYGB are 1.7590E + 04, 1.11250E + 05, 2.3302E + 04 and 5.3661E + 04. The sebs and sebssiwa exponential function pair for mesotropic gene locus CYGB is 6.0565E+04 e2E-06x and 3.0282E+04 e5E-06x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus CYGB is 2.00. The sebs - sebssiwa residual for mesotropic gene locus CYGB is 17,590, 111,250, 23,302 and 53,661. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus CYGB are 2.0446E + 04 and 8.2455E + 04. The esebssiwaagoTQ for mesotropic gene locus CYGB is 0.248. Mesotropic gene locus CYGB is positioned at angle ϴM = 60.00 in the z, y-axis vertical plane.

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus RGS1 are 1.79174E + 05, 1.237585E + 06, 3.68331E + 05 and 6.86424E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus RGS1 are 8.9587E + 04, 6.18793E + 05, 1.84166E + 05 and 3.43212E + 05. The sebs and sebssiwa exponential function pair for mesotropic gene locus RGS1 is 9.03665E+05 e1E-06x and 4.51832E+05 e3E-06x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus RGS1 is 2.00. The sebs - sebssiwa residual for mesotropic gene locus RGS1 is 89,587, 616,793, 184,166 and 343,212. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus RGS1 are 1.36876E + 05 and 4.81002E + 05. The esebssiwaagoTQ for mesotropic gene locus RGS1 is 0.285. Mesotropic gene locus RGS1 is positioned at angle ϴM = 55.60 in the z, y-axis vertical plane (Table 3).
Table 3

Angulation of mesotropic genes in reference to the horizontal for the linear normal esebssiwaagoTQ effective intracellular pressure unit

Gene (no. of locus bases; no. of gene bases or n/a)

Gene locus (ch, strand)

Episode category (final SEB structure)

sebs f(x) a

sebssiwa f(x) a

bsebs/bsebssiwab

sebs – sebssiwa (x1, y1; x2, y2), residual

uppesebssiwaa, dppesebssiwaa

(Peff esebssiwaagoTQ)

Angulation (0)

CYGB, cytoglobin

(30,336; 30,250)

17q25.1

(−)

2 A 4

6.0565E+ 04 e2E-06x

3.0282E+ 04 e5E-06x

2.00

17,590, 111,250; 23,302, 53,661

20,446, 82,455

(0.248)

60

RGS1, regulator of g protein signaling 1 (4,305; n/a)

1q31.2

(+)

3 M 4

9.03665E+ 05 e1E-06x

4.51832E+ 05

e 3E-06x

2.00

89,587, 616,793; 184,166, 343,212

136,876, 481,002

(0.285)

55.6

ENPP1, ectonucleotide pyrophosphatase phosphodiesterase 1

(87,140; n/a)

6q23.2 (+)

2 A 5

1.94930E+05 e5E-06x

5.1723E+04

e 1E-05x

3.77

18,018, 114,138; 30,875, 72,458

19,942,64,814

(0.308c)

52.8

SOX18,

SRY-Box 18

(2,060; n/a)

20q13.33

(−)

3 M 3 q term

̶

̶

n/a

nil, nil;

30,318, 61,868

21,741, 70,370

(0.309)

52.7

NUMA1, nuclear mitotic apparatus protein 1

(5,063; n/a)

11q13.3-q13.4

(−)

2 A 5

3.67204E+05 e1E-05x

9.0203E + 04

e 4E-06x

4.07

21,080, 172,300; 39,809, 75,825

25,175, 80,987

(0.311)

52.4

INSL3, insulin like 3

(5,063; n/a)

19p13.11

(−)

3 A 7

4.59932E+05 e7E-06x

9.0816E+04

e 8E-06x

5.06

32,763, 248,680; 74,198, 133,207

74,198, 133,207

(0.321)

51.2

NFE2L2, Nuclear Factor Erythroid 2-Related Factor 2

(880,745; n/a)

2q31.2

(−)

6 A 11

5.23516E+05 e2E-06x

8.7324E+04

e 1E-05x

5.995

49,163, 482,332;

448,729, 1,087,741

61,007, 184,201

(0.331)

50.2

JUND, JunD proto-oncogene, AP-1 transcription factor subunit

(1,963; n/a)

19p13.11

(−)

3 M 7

1.18726E+05 e7E-06x

3.9484E+04 e2E-05x

3.01

14,691, 92,423; 126,964, 294,152

24,833, 72,144

(0.344)

48.4

PRDM1, PR/SET domain 1

(23,620; n/a)

6q21

(+)

2 A 5

1.55684E+05 e2E-06x

4.5086E+04 e2E-05x

3.45

22,702, 109,291; 39,270, 87,689

25,311,71,167 (0.356c)

47

RGS13, regulator of g protein signaling 1

(24,174; n/a)

1q31.2

(+)

2 M 5

2.77812E+05 e3E-06x

1.39157E+05 e5E-06x

1.996

9,939, 146,229; 294,492, 580,065

78,592 218,130 (0.360)

46.5

CEACAM1, carcinoembryonic antigen-related cell adhesion molecule 1

(54,447; 53,931)

19q13.2 (−)

2 M 5

1.13842E+05 e7E-06x

5.6780E+04

e 1E-05x

2.005

13,221, 67,686; 126,663, 263,463

38,276, 99,708

(0.384)

43.6

GABPA, GA binding protein transcription factor subunit alpha

(37,891; n/a)

21q21.3

(+)

2 M 3

̶

̶

n/a

nil, nil;

231,930,

438,396

120,417, 243,978

(0.494)

30.3

CD34, CD34 molecule

(34,319; 30,431)

1q32.2

(−)

2 M 3

̶

̶

n/a

nil, nil;

97,262, 145,422

48,882, 75,493

(0.648c)

11.7

af(x) = b·em·x, where b is the downstream anisotropic effect (intercept and slope are absolute values); bbsebs/bsebssiwa is the linearization quotient; and cpreviously reported episode and sub-episode block structure and esebssiwaagoTQ value as per references, ENPP1, PRDM1 and CD34 [26, 27]. Note: 1) Gene loci sub-episode block structure (SEB) variations include non-contributory anisotropy (NCA), anisotropy converted to mesotropy (ACM), and/or 0.5-factor adjusted stabilizing mesotropy or anisotropy converted to stabilizing isotropy for anisotropy or mesotropy (stIAfM, stIMfA or stIMfM) that result in an initial to final SEB conversion; 2) previously reported episode and sub-episode block structure is applied in all cases as per reference [25], in which gene/gene loci at cusps of the delineated base intervals, in which case NFE2L2 (880.745) classifies into the adjacent interval; 3) Sub-episode block structures for initial to final SEB converted genes are CYGB, 2 A 5 (−1) ACM; RGS1, 3 M 7 (−3) stIMfA stIMfA; SOX18, 3 M 7 (−4) q terminal end; NFE2L2, 6 A 13 (−2) ACM; GABPA, 2 M 5 (− 2) ACM; and CD34, 2 M 5(− 2) NCA; and 3) the bsebs/bsebssiwa for CYGB and RGS1 is by reverse x-intercept plotting of the uppasebs, uppamsebs, dppasebs and dppmsebs and the corelate uppasebssiwa, uppamsebssiwa, dppasebssiwa and dppmsebssiwa

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus ENPP1 are 2.7027E + 04, 1.71207E + 05, 6.1750E + 04 and 1.44916E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus ENPP1 are 9.009E + 03, 5.7169E + 04, 3.0875E + 04 and 7.2458E + 04. The sebs and sebssiwa exponential function pair for mesotropic gene locus ENPP1 is 1.94930E+05 e5E-06x and 5.1723E+04 e1E-05x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus ENPP1 is 3.77. The sebs - sebssiwa residual for mesotropic gene locus ENPP1 is 18,018, 114,138, 30,875 and 72,458. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus ENPP1 are 1.9942E + 04 and 6.4814E + 04. The esebssiwaagoTQ for mesotropic gene locus ENPP1 is 0.308. Mesotropic gene locus ENPP1 is positioned at angle ϴM = 52.80 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus SOX18 are 1.3165E + 04, 7.8872E + 04, 6.0635E + 04 and 1.23734E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus SOX18 are 1.3165E + 04, 7.8872E + 04, 3.0318E + 04 and 6.1867E + 04. The bsebs/bsebssiwa linearization quotient for SOX18 is not applicable. The sebs - sebssiwa residual for mesotropic gene locus SOX18 is nil, nil, 30,318 and 61,868. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus SOX18 are 2.1741E + 04 and 7.0370E + 04. The esebssiwaagoTQ for mesotropic gene locus SOX18 is 0.309. Mesotropic gene locus SOX18 is positioned at angle ϴM = 52.70 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus NUMA1 are 3.1620E + 04, 2.58450E + 05, 7.9618E + 04 and 1.51649E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus NUMA1 are 1.0540E + 04, 8.6150E + 04, 3.9809E + 04 and 7.5825E + 04. The sebs and sebssiwa exponential function pair for mesotropic gene locus NUMA1 is 3.67204E+05 e1E-05x and 9.0203E+04 e4E-06x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus NUMA1 is 4.07. The sebs - sebssiwa residual for mesotropic gene locus NUMA1 is 21,080, 172,300, 39,809 and 75,825. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus NUMA1 are 2.5175E + 04 and 8.0987E + 04. The esebssiwaagoTQ for mesotropic gene locus NUMA1 is 0.311. Mesotropic gene locus NUMA1 is positioned at angle ϴM = 52.40 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus INSL3 are 4.3684E + 04, 3.31573E + 05, 1.11297E + 05 and 1.99810E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus INSL3 are 1.0921E + 04, 8.2893E + 04, 3.7099E + 04 and 6.6603E + 04. The sebs and sebssiwa exponential function pair for mesotropic gene locus INSL3 is 4.59932E+05 e7E-06x and 9.0816E+04 e8E-06x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus INSL3 is 5.06. The sebs - sebssiwa residual for mesotropic gene locus INSL3 is 32,763, 248,680; 74,198 and 133,207. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus INSL3 are 7.4198E + 04 and 1.33207E + 05. The esebssiwaagoTQ for mesotropic gene locus INSL3 is 0.321. Mesotropic gene locus INSL3 is positioned at angle ϴM = 51.20 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus NFE2L2 are 5.8996E + 04, 5.78798E + 05, 5.60911E + 05 and 1.359677E + 06. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus NFE2L2 are 9.833E + 03, 9.6466E + 04, 1.12182E + 05 and 2.71935E + 05. The sebs and sebssiwa exponential function pair for mesotropic gene locus NFE2L2 is 5.23516E+05 e2E-06x and 8.7324E+04 e1E-05x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus NFE2L2 is 5.995. The sebs - sebssiwa residual for mesotropic gene locus NFE2L2 is 49,163, 482,332, 448,729 and 1,087,741. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus NFE2L2 are 6.1007E + 04 and 1.84201E + 05. The esebssiwaagoTQ for mesotropic gene locus NFE2L2 is 0.331. Mesotropic gene locus NFE2L2 is positioned at angle ϴM = 50.20 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus JUND are, 2.2037E + 04, 1.38709E + 05, 1.69285E + 05 and 3.92203E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus JUND are 7.346E + 03, 4.6236E + 04, 4.2321E + 04 and 9.8051E + 04. The sebs and sebssiwa exponential function pair for mesotropic gene locus JUND is 1.18726E+05 e7E-06x and 3.9484E+04 e2E-05x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus JUND is 3.01. The sebs - sebssiwa residual for mesotropic gene locus JUND is 14,691, 92,423, 126,964, and 294,152. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus JUND are 2.4833E + 04 and 7.2144E + 04. The esebssiwaagoTQ for mesotropic gene locus JUND is 0.344. Mesotropic gene locus JUND is positioned at angle ϴM = 48.40 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus PRDM1 are 3.4053E + 04, 1.63936E + 05, 7.8539E + 04 and 1.75378E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus PRDM1 are 1.1351E + 04, 5.4645E + 04, 3.9270E + 04 and 8.7689E + 04. The sebs and sebssiwa exponential function pair for mesotropic gene locus PRDM1 is 1.55684E+05 e2E-06x and 4.5086E+04 e2E-05x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus PRDM1 is 3.45. The sebs - sebssiwa residual for mesotropic gene locus PRDM1 is 2.2702E + 04, 1.09291E + 05, 3.9270E + 04 and 8.7689E + 04. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus PRDM1 are 2.5311E + 04 and 7.1167E + 04. The esebssiwaagoTQ for mesotropic gene locus PRDM1 is 0.356. Mesotropic gene locus PRDM1 is positioned at angle ϴM = 47.00 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus RGS13 are 1.9877E + 04, 2.92457E + 05, 4.41738E + 05 and 8.70097E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus RGS13 are 9.939E + 03, 1.46229E + 05, 1.47246E + 05 and 2.90032E + 05. The sebs and sebssiwa exponential function pair for mesotropic gene locus RGS13 is 2.77812E+05 e3E-06x and 1.39157E+05 e5E-06x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus RGS13 is 1.996. The sebs - sebssiwa residual for mesotropic gene locus RGS13 is 9,939, 146,229, 294,492 and 580,065. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus RGS13 are 7.8592E + 04 and 2.18130E + 05. The esebssiwaagoTQ for mesotropic gene locus RGS13 is 0.360. Mesotropic gene locus RGS13 is positioned at angle ϴM = 46.50 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus CEACAM1 are 2.6442E + 04, 1.35371E + 05, 1.89995E + 05 and 3.95194E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus CEACAM1 are 13,221, 67,686, 63,332 and 131,731. The sebs and sebssiwa exponential function pair for mesotropic gene locus CEACAM1 is 1.13842E+05 e2E-06x and 5.6780E+04 e1E-05x. The bsebs/bsebssiwa linearization quotient for mesotropic gene locus CEACAM1 is 2.005. The sebs - sebssiwa residual for mesotropic gene locus CEACAM1 is 13,221, 67,686, 126,663 and 263,463. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus CEACAM1 are 3.8276E + 04 and 9.9708E + 04. The esebssiwaagoTQ for mesotropic gene locus CEACAM1 is 0.384. Mesotropic gene locus CEACAM1 is positioned at angle ϴM = 43.60 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus GABPA are 8.904E + 03, 4.9560E + 04, 4.63859E + 05 and 8.76791E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus GABPA are 8.904E + 03, 4.9560E + 04, 2.31930E + 05 and 4.38396E + 05. The bsebs/bsebssiwa linearization quotient for GABPA is not applicable. The sebs - sebssiwa residual for mesotropic gene locus GABPA is nil, nil, 231,930 and 438,396. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus GABPA are 1.20417E + 05 and 2.43978E + 05. The esebssiwaagoTQ for mesotropic gene locus GABPA is 0.494. Mesotropic gene locus GABPA is positioned at angle ϴM = 30.30 in the z, y-axis vertical plane (Table 3).

The uppasebs, dppasebs, uppmsebs and dppasebs for mesotropic gene locus CD34 are 5.03E + 02, 5.565E + 03, 1.94524E + 05 and 2.90844E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for mesotropic gene locus CD34 are 5.03E + 02, 5.565E + 03, 9.7262E + 04 and 1.45422E + 05. The bsebs/bsebssiwa linearization quotient for CD34 is not applicable. The sebs - sebssiwa residual for mesotropic gene locus CD34 is nil, nil, 97,262 and 145,422. The uppesebssiwaa and dppesebssiwaa for mesotropic gene locus CD34 are 4.8882E + 04 and 7.5493E + 04. The esebssiwaagoTQ for mesotropic gene locus CD34 is 0.648. Mesotropic gene locus CD34 is positioned at angle ϴM = 11.70 in the z, y-axis vertical plane (Table 3).

b sebs/b sebssiwa linearization quotient and sebs - sebssiwa residual statistical significance by effective intracellular pressure gene esebssiwaagoT Q stratum

The bsebs/bsebssiwa linearization quotient is 3.143 ± 0.688 for tier 1 (Peff ≤ 0.200, n = 11). The Σ intergene tropy for tier 1 is 1.162733E+06 ± 497,383 intergene bases. The bsebs/bsebssiwa linearization quotient is 2.240 ± 0.463 for tier 2 (Peff > 0.200 ≤ 0.300, n = 6; p = 0.006 vs tier 1). The Σ intergene tropy for tier 2 is 7.34813E+05 ± 856,523 intergene bases (p = 0.103 vs tier 1). The bsebs/bsebssiwa linearization quotient is 3.670 ± 1.393 for tier 3 (Peff > 0.300, n = 8, non-nil; p = 0.145 vs tier 1; p = 0.017 vs tier 2). The Σ intergene tropy is 9.64537E+05 ± 749,407 intergene bases for tier 3 (p = 0.248 vs tier 1; p = 0.301 vs tier 2).

The uppasebs, uppasebssiwa residual is 4.4214E+04 ± 24,373 for tier 1 (Peff ≤ 0.200, n = 11). The dppasebs, dppasebssiwa residual is 5.47340E+05 ± 258,360 for tier 1 (n = 11). The uppmsebs, uppmsebssiwa residual is 5.3053E+04 ± 34,298 for tier 1 (n = 11). The dppmsebs, dppmsebssiwa residual is 1.24074E+05 ± 82,270 for tier 1 (n = 11).

The uppasebs, uppasebssiwa residual is 2.5470E+04 ± 32,476 for tier 2 (Peff > 0.200 ≤ 0.300, n = 6; p = 0.098 vs tier 1). The dppasebs, dppasebssiwa residual is 1.87595E+05 ± 217,367 for tier 2 (n = 6; p = 0.006 vs tier 1). The uppmsebs, uppmsebssiwa residual is 5.2179E+04 ± 65,457 for tier 2 (n = 6; p = 0.486 vs tier 1). The dppmsebs, dppmsebssiwa residual is 1.21333E+05 ± 112,712 for tier 2 (n = 6; p = 0.477 vs tier 1).

The uppasebs, uppasebssiwa residual is 3.6877E+04 ± 38,272 for tier 3 (Peff > 0.300, n = 8, non-nil; p = 0.308 vs tier 1; p = 0.284 vs tier 2). The dppasebs, dppasebssiwa residual is 2.03613E+05 ± 129,187 for tier 3 (n = 8, non-nil; p = 0.002 vs tier 1; p = 0.433 vs tier 2). The uppmsebs, uppmsebssiwa residual is 1.33445E+05 ± 156,526 for tier 3 (n = 8; p = 0.057 vs tier 1; p = 0.129 vs tier 2). The dppmsebs, dppmsebssiwa residual is 2.99853E+05 ± 364,084 for tier 3 (n = 8, non-nil; p = 0.068 vs tier 1; p = 0.136 vs tier 2).

Heterochromatinization parameters for differentiated neural axis gene angulation positioning in linear 2-dimensional z, y-vertical plane

The uppasebs, dppasebs, uppmsebs and dppasebs for UNC13A are 5.888E + 03, 2.8975E + 04, 1.65112E + 05, 3.50047E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for UNC13A are 5.888E + 03, 2.8975E + 04, 8.2556E + 04 and 1.75024E + 05. The bsebs/bsebssiwa linearization quotient for UNC13A is not applicable. The sebs - sebssiwa residual for UNC13A is nil, nil, 82,556 and 175,024. The uppesebssiwaa and dppesebssiwaa for UNC13A are 4.4222E + 04 and 1.01999E + 05. The esebssiwaagoTQ for UNC13A is 0.434. UNC13A is positioned at angle ϴM = 37.60 in the z, y-axis vertical plane.

The uppasebs, dppasebs, uppmsebs and dppasebs for RGS21 are 1.3087E + 04, 2.29159E + 05, 3.56158E + 05 and 5.66939E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for RGS21 are 6.544E + 03, 1.14580E + 05, 1.18719E + 05 and 1.88980E + 05. The sebs and sebssiwa exponential function pair for RGS21 is 1.11284E+05 e4E-06x and 2.2137E+04 e3E-06x. The bsebs/bsebssiwa linearization quotient for RGS21 is 5.03. The sebs - sebssiwa residual for RGS21 is 6,544, 114,580, 237,439 and 377,959. The uppesebssiwaa and dppesebssiwaa for RGS21 are 6.2631E + 04 and 1.51780E + 05. The esebssiwaagoTQ for RGS21 is 0.413. RGS21 is positioned at angle ϴM = 40.10 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).
Table 4

Heterochromatinization parameters for z, y-plane gene angulation positioning and pressuromodulation mapping of effective cell pressures for neuroaxis gene expression of differentiated neuron cell sub-types in reference to tissue macro-compliance

Gene (no. of locus bases; no. of gene bases or n/a)

Gene locus (strand)

Episode category (final SEB structure)

uppesebssiwaa, dppesebssiwaa (Peff esebssiwaagoTQ)

f(x) sebs

bsebs/bsebssiwab

Angulation (0)

Neural axis overexpression (predicted range)a

f(x) sebssiwa c

UNC13A, unc-13 homolog A

(87,038; n/a)

19p13.11 (−)

2 M 3

44,222, 101,999

(0.434)

n/a

37.6

lmn (a)

RGS21, regulator of G protein signaling 21 (50,294; n/a)

1q31.2

(+)

2 M 5

62,631, 151,780

(0.413)

1.11284E+05

e 4E-06x

5.03

40.1

̶

2.2137E+04

e 3E-06x

SOX1, SRY-Box 1 (160,765; 4,108)

13q34 (+)

2 M 7 q term end

24,498, 77,119

(0.318)

1.20477E+05

e 7E-06x

3.01

51.6

pituit, capc, bell (pj)

3.9963E+04

e 2E-05x

NGB, neuroglobin (5,830; n/a)

14q24.3

(−)

3 A 5

14,618, 48,000

(0.305)

2.50250E+05

e 2E-05x

3.78

53.2

thal, bral, umn (arc)

6.6186E+04

e 2E-05x

SHANK2, SH3 And Multiple Ankyrin Repeat Domains 2 (784,883; n/a)

11q13.3-q13.4

(−)

6 A 13

27,834, 92,467

(0.301)

6.12243E+05

e 1E-07x

7.42

53.6

umn (asc, dsc)

8.2498E+04

e 4E-06x

RGS2, regulator of G protein signaling 2 (3,245; n/a)

1q31.2 (+)

3 M 7

95,617, 321,146

(0.298)

6.84931E+05

e 1E-06x

2.95

54

bgnc

2.31902E+05

e 3E-06x

RGS16, regulator of G protein signaling 16 (5,791, n/a)

1q23.3

(−)

3 M 5

32,709, 130,446

(0.251)

2.45881E+05

e 3E-06x

1.57

59.7

̶

1.56958E+05

e 6E-06x

DRD1, Dopamine Receptor D1

(4,170; n/a)

5q35.2

(+)

3 M 8

50,934, 204,294

(0.249)

6.93874E+05

e 2E-06x

4.00

59.9

̶

1.73469E+05

e 6E-06x

SOX14, SRY-Box 14 (2,055; n/a)

3q22.3

(+)

3 A 7

43,588, 198,734

(0.219)

1.209365E+06

e 4.5E-06x

3.62

63.5

̶

3.34544E+05

e 1E-05x

DRD2, Dopamine Receptor D2

(66,097; n/a)

11q23.2

(−)

2 A 5

38,628, 178,043

(0.217)

1.10192E+05

e 4E-07x

1.51

63.8

bgnc

7.2871E+04

e 4E-06x

RBFOX3, RNA Binding Fox-1 Homolog 3 (521,757, n/a)

17q25.3 (−)

5 M 13

21,887, 102,648

(0.213)

1.0E+06

e 3E-06x

4.29

64.3

bell (gr); bral, umn (arc)

2.08197E+05

e 3E-05x

RGS18, regulator of G protein signaling 18 (378,397;

28,716)

1q31.2

(+)

4 M 11

46,829, 227,894

(0.205)

2.0E+06

e 2E-06x

4.19

65.2

̶

4.77757E+05

e 2E-05x

GRIN1, Glutamate Ionotropic Receptor NMDA Type Subunit 1 (30,373; n/a)

9q34.3 (+)

2 M 5

14,630, 72,035

(0.203)

1.86172E+05

e 2E-06x

1.46

65.5

̶

1.27295E+05

e 4E-05x

DRD3, Dopamine Receptor D3

(347,501; 71,611)

3q13.31

(−)

4 A 9

16,088, 79,289

(0.203)

6.3965E+04

e 3E-07x

3.81

65.5

capc

1.6772E+04

e 5E-07x

aNeuroanatomic location cell-specific ranges of effective cell pressure for gene overexpression: lmn (a), lower motor neuron (afferent), Peff 0.434 ≥ 0.301; umn (asc, dsc, arc), upper motor neuron (ascending, descending, arcuate association), Peff ≤ 0.301; pituit, hypothalamic posterior pituitary axis neurons, upper limit Peff 0.331 ≥ 0.311; thal, peri-ventricular thalamic deep nuclei neurons, upper limit Peff 0.311 ≥ 0.305; capc, cornu ammonis/Papez circuit (pyramidal neuron, 3-layer cortex), Peff 0.318–0.203; bell, cerebellar cortex neurons [bell (pj), purkinje cell layer, Peff 0.301; bell (gr), granule cell layer, Peff 0.213]; bral, cerebral cortex (pyramidal neuron, 6-layer), Peff < 0.318 ≥ 0.305–0.213; and bgnc, basal ganglia nuclei substantia nigra circuit (spiny neuron, dopaminergic), Peff 0.298 - < 0.217 > 0.213. cf(x) = b·em·x, where b is the downstream anisotropic effect (intercept and slope are absolute values). bbsebs/bsebssiwa is the linearization quotient. Note: 1) gene loci sub-episode block structure (SEB) variations include non-contributory anisotropy (NCA), anisotropy converted to mesotropy (ACM), and/or 0.5-factor adjusted stabilizing mesotropy or anisotropy converted to stabilizing isotropy for anisotropy or mesotropy (stIAfM, stIMfA or stIMfM) that result in an initial to final SEB conversion; 2) previously reported episode and sub-episode block structure is applied in all cases as per reference [25], in which gene/gene loci at cusps of the delineated base intervals, SHANK2 (784,883), RBFOX3 (521,757) classify into the adjacent interval; 3) Sub-episode block structures for initial to final SEB converted genes are as follows: NGB, 3 A 7 (−2) stIMfA NCA; SOX1, 2 M 5 (+2) ACM q terminal end; RGS18, 4 M 9 (+2) ACM; RBFOX3, 5 M 11 (+2) ACM; RGS16, 3 M 7 (−2) NCA; DRD1, 3 A 7 (+1) ACM; and UNC13A, 2 M 5 (−2) ACM; and 4) bsebs/bsebssiwa quotients for DRD1, DRD2 and DRD3 are by reverse x-intercept plotting the uppasebs, uppamsebs, dppasebs and dppmsebs and the corelate uppasebssiwa, uppamsebssiwa, dppasebssiwa and dppmsebssiwa

The uppasebs, dppasebs, uppmsebs and dppasebs for SOX1 are 1.6642E + 04, 1.36246E + 05, 1.73795E and 4.35291E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for SOX1 are 5.547E + 03, 4.5415E + 04, 4.3449E + 04 and 1.08823E + 05. The sebs and sebssiwa exponential function pair for SOX1 is 1.20477E+05e7E-06x and 3.9963E+04 e2E-05x. The bsebs/bsebssiwa linearization quotient for SOX1 is 3.01. The sebs - sebssiwa residual for SOX1 is 11,095, 90,830, 130,346 and 326,468. The uppesebssiwaa and dppesebssiwaa for SOX1 are 2.4498E + 04 and 7.7119E + 04. The esebssiwaagoTQ for SOX1 is 0.318. SOX1 is positioned at angle ϴM = 51.60 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for NGB are 1.6465E + 04, 1.68356E + 05, 4.7494E + 04 and 7.9764E + 04. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for NGB are 5.488E + 03, 5.6119E + 04, 2.3747E + 04 and 3.9882E + 04. The sebs and sebssiwa exponential function pair for NGB is 2.50250E+05 e2E-05x and 6.6186E+04 e2E-05x. The bsebs/bsebssiwa linearization quotient for NGB is 3.78. The sebs - sebssiwa residual for NGB is 10,977, 112,238, 23,747 and 39,882. The uppesebssiwaa and dppesebssiwaa for NGB are 1.4618E + 04 and 4.8000E + 04. The esebssiwaagoTQ for NGB is 0.305. NGB is positioned at angle ϴM = 53.20 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for SHANK1 are 7.9764E + 04, 8.2330E + 04, 6.05471E + 05, 2.63439E + 05 and 5.90625E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for SHANK1 are 1.1761E + 04, 8.6496E + 04, 4.3907E + 04 and 9.8438E + 04. The sebs and sebssiwa exponential function pair for SHANK1 is 6.12243E+05 e1E-07x and 8.2498E+04 e4E-06x. The bsebs/bsebssiwa linearization quotient for SHANK1 is 7.42. The sebs - sebssiwa residual for SHANK1 is 70,569, 518,975, 219,533 and 492,188. The uppesebssiwaa and dppesebssiwaa for SHANK1 are 2.7834E + 04 and 9.2467E + 04. The esebssiwaagoTQ for SHANK1 is 0.301. SHANK1 is positioned at angle ϴM = 53.60 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for RGS2 are 7.9267E + 04, 7.56237E + 05, 6.59244E + 05 and 1.560848E + 06. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for RGS2 are 2.6422E + 04, 2.52079E + 05, 1.64811E + 05 and 3.90212E + 05. The sebs and sebssiwa exponential function pair for RGS2 is 6.84931E+05 e1E-06x and 2.31902E+05 e3E-06x. The bsebs/bsebssiwa linearization quotient for RGS2 is 2.95. The sebs - sebssiwa residual for RGS2 is 52,845, 504,158, 494,433 and 1,170,636. The uppesebssiwaa and dppesebssiwaa for RGS2 are 9.5617E + 04 and 3.21146E + 05. The esebssiwaagoTQ for RGS2 is 0.298. RGS2 is positioned at angle ϴM = 540 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for RGS16 are 4.1927E + 04, 2.78410E + 05, 1.33362E + 05 and 6.5059E + 04. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for RGS16 are 2.0964E + 04, 1.39205E + 05, 4.4454E + 04 and 1.21686E + 05. The sebs and sebssiwa exponential function pair for RGS16 is 2.45881E+05 e3E-06x and 1.56958E+05 e6E-06x. The bsebs/bsebssiwa linearization quotient for RGS16 is 1.57. The sebs - sebssiwa residual for RGS16 is 20,964, 139,205, 88,908 and 243,373. The uppesebssiwaa and dppesebssiwaa for RGS16 are 3.2709E + 04 and 1.30446E + 05. The esebssiwaagoTQ for RGS16 is 0.251. RGS16 is positioned at angle ϴM = 59.70 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for DRD1 are 1.27930E + 05, 1.062852E + 06, 2.79538E + 05 and 5.71499E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for DRD1 are 3.1983E + 04, 2.65713E + 05, 6.9885E + 04 and 1.42875E + 05. The sebs and sebssiwa exponential function pair for DRD1 is 6.93874E+05 e2E-06x and 1.73469E+05 e6E-06x. The bsebs/bsebssiwa linearization quotient for DRD1 is 4.00. The sebs - sebssiwa residual for DRD1 is 95,948, 797,139, 209,654 and 428,624. The uppesebssiwaa and dppesebssiwaa for DRD1 are 5.0934E + 04 and 2.04294E + 05. The esebssiwaagoTQ for DRD1 is 0.249. DRD1 is positioned at angle ϴM = 59.90 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for SOX14 are 7.6621E + 04, 1.016347E + 06, 2.04065E + 05 and 4.30144E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for SOX14 are 1.9155E + 04, 2.54087E + 05, 6.8022E + 04 and 1.43381E + 05. The sebs and sebssiwa exponential function pair for SOX14 is 1.209365E+06 e4.5E-06x and 3.34544E+05 e1E-05x. The bsebs/bsebssiwa linearization quotient for SOX14 is 3.62. The sebs - sebssiwa residual for SOX14 is 57,466, 762,260, 136,043 and 286,763. The uppesebssiwaa and dppesebssiwaa for SOX14 are 4.3588E + 04 and 1.98734E + 05. The esebssiwaagoTQ for SOX14 is 0.219. SOX14 is positioned at angle ϴA = 63.50 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for DRD2 are 7.8907E + 04, 7.90658E + 05, 1.01906E + 05 and 1.85067E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for DRD2 are 2.6302E + 04, 2.63553E + 05, 5.0953E + 04 and 9.2533E + 04. The sebs and sebssiwa exponential function pair for DRD2 is 1.10192E+05 e4E-07x and 7.2871E+04 e4E-06x. The bsebs/bsebssiwa linearization quotient for DRD2 is1.51. The sebs - sebssiwa residual for DRD2 is 52,605, 527,106, 50,953 and 92,533. The uppesebssiwaa and dppesebssiwaa for DRD2 are 3.8628E + 04 and 1.78043E + 05. The esebssiwaagoTQ for DRD2 is 0.217. DRD2 is positioned at angle ϴA = 63.80 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for RBFOX3 are 7.7745E + 04, 7.99501E + 05, 2.15712E + 05 and 5.04325E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for RBFOX3 are 1.2957E + 04, 1.33250E + 05, 3.0816E + 04 and 7.2046E + 04. The sebs and sebssiwa exponential function pair for RBFOX3 is 1.10192E+05 e4E-07x and 7.2871E+04 e4E-06x. The bsebs/bsebssiwa linearization quotient for RBFOX3 is 4.80. The sebs - sebssiwa residual for RBFOX3 is 64,787, 666,251, 184,896 and 432,278. The uppesebssiwaa and dppesebssiwaa for RBFOX3 are 2.1887E + 04 and 1.02648E + 05. The esebssiwaagoTQ for RBFOX3 is 0.213. RBFOX3 is positioned at angle ϴA = 64.30 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for RGS18 are 1.53005E + 05, 1.438692E + 06, 3.78343E + 05 and 1.008303E + 06. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for RGS18 are 3.0601E + 04, 2.87738E + 05, 6.3057E + 04 and 1.68050E + 05. The sebs and sebssiwa exponential function pair for RGS18 is 2.0E+06 e2E-06x and 4.77757E+05 e2E-05x. The bsebs/bsebssiwa linearization quotient for RGS18 is 4.19. The sebs - sebssiwa residual for RGS18 is 122,404, 1,150,953, 315,285 and 840,252. The uppesebssiwaa and dppesebssiwaa for RGS18 are 4.6829E + 05 and 2.27894E + 05. The esebssiwaagoTQ for RGS18 is 0.205. RGS18 is positioned at angle ϴA = 65.20 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for GRIN1 are 1.7024E + 04, 1.79509E + 05, 6.2241E + 04 and 1.62947E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for GRIN1 are 8.512E + 03, 8.9755E + 04, 2.0747E + 04 and 5.4316E + 04. The sebs and sebssiwa exponential function pair for GRIN1 is 1.86172E+05 e2E-06x and 1.27295E+05 e4E-05x. The bsebs/bsebssiwa linearization quotient for GRIN1 is 1.46.

The sebs - sebssiwa residual for GRIN1 is 8,512, 89,755, 41,494 and 108,632. The uppesebssiwaa and dppesebssiwaa for GRIN1 are 1.4630E + 04 and 7.2035E + 04. The esebssiwaagoTQ for GRIN1 is 0.203. GRIN1 is positioned at angle ϴA = 65.50 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

The uppasebs, dppasebs, uppmsebs and dppasebs for DRD3 are 7.8218E + 04, 6.57108E + 05, 6.6128E + 04 and 1.08626E + 05. The uppasebssiwa, dppasebssiwa, uppmsebssiwa and dppasebssiwa for DRD3 are 1.5644E + 04, 1.31422E + 05, 1.6532E + 04 and 2.7157E + 04. The sebs and sebssiwa exponential function pair for DRD3 is 6.3965E+04 e3E-07x and 1.6772E+04 e5E-07x. The bsebs/bsebssiwa linearization quotient for DRD3 is 3.81. The sebs - sebssiwa residual for DRD3 is 62,574, 525,686, 49,596 and 81,470. The uppesebssiwaa and dppesebssiwaa for DRD3 are 1.6088E + 04 and 7.9289E + 04. The esebssiwaagoTQ for DRD3 is 0.203. DRD3 is positioned at angle ϴA = 65.50 in the z, y-axis vertical plane (Table 4; Additional file 1: Table S1).

Discussion

Linear normalized determination of gene positioning angulation in the z, y-plane by the esebssiwaagoT Q method effective intracellular pressure unit

The bsebs/bsebssiwa sebs intercept-to-sebssiwa intercept quotient and residual adjustments have been determined in this study by x-, y- or hybrid intercept exponential function plotting for specific detection of the predominant paired linearization effect as either the dppasebs, dppmsebs, uppasebs, uppmsebs, or dual uppasebs, uppmsebs, dppasebs, dppmsebs due to normalizing primary weighted averaging. Since the bsebs/bsebssiwa linearization quotient for tier 1 sub-group analysis genes within the Peff stratum ≤ 0.200 is 3.143 ± 0.688 (n = 11), and that for tier 3 sub-group analysis genes within the Peff stratum > 0.300 is 3.670 ± 1.393 (n = 8; p = 0.145 vs tier 1), whereas that for tier 2 sub-group analysis genes within the Peff stratum > 0.200 ≤ 0.300 is 2.240 ± 0.463 (n = 6; p = 0.006 vs tier 1); these pairwise comparisons are consistent with primary linearization of the dppasebs, dppmsebs anisotropy effect for tier 1 ≤ 0.200 Peff genes and of the uppasebs, uppamsebs mesotropy effect for tier 3 > 0.300 Peff genes, in contrast to dual linearization for tier 2 intermediate Peff stratum genes due to the presence of downstream and upstream tropy effects of equivalence. The pairwise statistical significance of the subtractive sebs, sebssiwa residual comparisons between tier 2 and tier 1 genes (p = 0.098, p = 0.006, p = 0.486, p = 0.477), and between tier 3 and tier 1 genes (p = 0.308, p = 0.002, p = 0.057, p = 0.068) is further consistent with the primary weighted averaging linearization due to uppmsebs and dppmsebs normalizing of the uppasebs and uppmsebs effects in tier 3 > 0.300 Peff genes as probability for significance approaches alpha (α = 0.05). Therefore, primary linearization adheres to the rule of split-integrated averaging to linearization of mutually exclusive upstream (upp-) and downstream (dpp-) parts within the respective anisotropic or mesotropic gene category inclusive of SEB interconversions; in which case, normalization of the dppasebs, dppmsebs effect predominates in anisotropic gene MYC (bsebs/bsebssiwa: 3.63), the uppasebs, uppmsebs effect predominates in mesotropic gene PRDM1 (bsebs/bsebssiwa: 3.45), while both the dppasebs, dppmsebs and uppasebs, uppmsebs effects are linear normalized in PRKCH (bsebs/bsebssiwa: 3.17).

Secondary linearization of the anisotropic effect for both types of genes is by the mesotropic effect at the second weighted averaging stage of the uppesebssiwaa and dppesebssiwaa; as in the example of mesotropic gene INSL3 (bsebs/bsebssiwa: 5.06) in which there is further linearization of the split-integrated final anisotropic effect of 1.0921E + 04 (uppasebssiwa) and 8.2893E + 04 intergene bases (dppmsebssiwa) by the mesotropic effect of 3.7099E + 04 (dppasebssiwa) and 6.6603E + 04 (dppmsebssiwa), which results in an uppasebssiwaa, dppesebssiwaa of 2.4010E + 04 and 7.4748E + 04 (Peff, 0.321) for horizontal alignment from the z, y-plane (θM = 51.20); and as another example, anisotropic gene CCN2 (bsebs/bsebssiwa: 4.00) in which there is the further linearization of the split-integrated final anisotropic effect of 3.0356E + 04 and 2.79275E + 05 with a mesotropic effect of 4.2913E + 04 and 1.13936E + 05 intergene bases that results in an uppasebssiwaa, dppesebssiwaa of 30293E + 04 and 1.82468E + 05 (Peff, 0.166) for z, x-plane transcriptive alignment (θA = 70.00).

Therefore, since the esebssiwaagoTQ method is based on the normalization of the anisotropy effect at two distinct stages and predicts the temporality of gene expression in linear normal effective intracellular pressure units (Peff) at which eukaryotic heterochromatin strand segments of DNA horizontally align for transcription with respect to the gene it can be applied to study gene positioning angulation in linear normal 2-D space, which implies that the process of horizontal z, x-plane alignment of a gene is linear normalized in the nucleoplasm of an eukaryotic cell.

Arrangement of genes in native positions is pressurotopic by heterochromatin gene loop segments of differing nano-compliance

The upstream 5’ end intergene and downstream 3’ end intergene base segments with respect a gene are subject to peptide, microRNA and functional pseudogene RNA affinity binding viscosity weighting effects in both forward transcribing and reverse anti-transcribing directions that are asymmetric [25], in which case each gene exists at angulation with reference to the z, x-axis horizontal plane at the line of unity (θH) as a result of forward paired point tropy fulcrum weighting (prpTQ) with underlying baseline reverse anisotropy.

The segmentation of strand heterochromatin for positive strand (+) native configuration genes of human 1q22 located between position -12 and +15 in reference to LMNA (pos 0) has been studied by the determinations of the esebssiwaagoTQ of sequentially situated genes. As it has been determined herein, the gene loop segment structure for the LMNA gene (Peff, 0.184; θA = 68.40)-containing forward strand (+) from 5’ to 3’ has been determined is: 5’-0.234-(a-12)-0.272 (m-11)-0.229 (a-10)-0.211 (a-9)-0.269 (m-8)-0.144 (a-7)-0.314 (m-6)-0.268 (m-5)-0.176 (a-4)-0.260 (m-3)-0.259 (m-2)-0.270 (m-1)-0.184 (a0)-0.135 (m+1)-0.395 (m+2)-0.146 (a+3)-0.212 (a+4)-0.336 (m+5)-0.287 (m+6)-0.153 (a+7)-0.283 (m+8)-0.193 (a+9)-0.269 (m+10)-0.199 (a+11)-0.146 (a+12)-0.190 (a+13)-0.188 (a+14)-0.243 (a+15)-3’, which begins at the 5’ end with DAP3 (Peff 0.234) in the form of a 9-in series anisotropy alternating mesotropy amorphous loop segment (a-m-a-a-m-a-m-m-a) followed by a 3-in series mesotropy loop segment (m), and then a 11-in series anisotropy alternating anisotropy amorphous loop segment (a-m-m-a-a-m-m-a-m-a-m) with LMNA followed by a 5-in series anisotropy loop segment (a) with 3’ end BCAN (Peff 0.234). These findings of the study are further supported by the retrospective analysis of micro-segmentation of negative strand (-) human 14q32.3 B-cell heavy chain immunoglobin locus genes in native positions (n = 42) [26, 27], in which there are two instances of sequential alternating tropy in-series amorphousity (n = 5, n = 4), two instances of sequential mesotropy in-series (n = 8, n = 3), as well as several instances of sequential microstructural anisotropy (n = 5, n = 3, 3, 3).

Therefore, based on the findings of this study on the micro-segmentation of a 0.73-mm length plus (+) strand LMNA gene-containing heterochromatin strand loop segment and a 0.25 mm length minus (-) strand IGH_ locus-containing DNA strand loop segment, there is segmental difference in DNA strand nano-compliance, in which case intergene tropy loop segments with differences nano-compliance overlap as there exists micron (μm) scale segmentation of alternating mesotropy and anisotropy; as such, heterochromatin DNA strand loops can be characterized as anisotropy, mesotropy or amorphousity loop forms with micro-segmentation perceiving various grades of the asymmetric tropy viscosity effect for genes in juxtaposition separated by intergene base distance of between 11.6 and 14 nanometers (nm; 13 - 15 bases), if two nucleic acid bases and a primed half-phosphodiester bond in-tandem is considered to be ~1.75 nm in length.

Anglemetry of gene positioning angulation in the z, y-plane and vectormetry for z, x-plane horizontal alignment in two-dimensional linear space

Gene intergene tropy anglemetry is performed in 2-D linear angulation space utilizing the strand specific effective intracellular pressure unit (Peff)-to-angle regression conversion, based on which it has been determined that anisotropic genes are situated between 60.5 and 82.30 in the z, y-vertical plane and mesotropic genes are situated between 60.4 and 11.70 in the z, y-vertical axis plane; in which case the initial momentum vector for anisotropic gene alignment, mch tropy, from origination is between 82.3 and 60.50 in the z, y-vertical, whereas the initial momentum vector for mesotropic gene alignment, mch tropy + mch nmn tropy (mM), from origination is 60.4 and 11.70 from above the z, x-horizontal plane. Therefore, the effective momentum (meff; mA, mM) for gene transcription is inversely proportional to the effective cell pressure (Peff) required for horizontal alignment of gene intergene loop segment tropy (Fig. 4).
Fig. 4

Vectormetry for horizontal alignment of anisotropic and mesotropic genes by heterochromatin strand structural pressurotopy. Anisotropic gene loci are positioned between angles 82.3 and 60.50 in the z, y-vertical plane encounter the chromatin-associated protein viscosity effect at intergene segments. The effective momentum (meff) in anisotropic gene alignment to the z, x-horizontal plane is mA = mch tropy (- mpro-grav ch tropy) as indicated by the left bracket. Mesotropic gene loci are positioned between angles 60.4 and 11.70 in the z, y-vertical plane encounter dual chromatin-associated protein viscosity effect at intergene segments and the nuclear membrane nucleoplasm chromatin-associated protein viscosity effect at intergene segments. The effective momentum (meff) in mesotropic gene alignment to the z, x-horizontal plane is mM = mch tropy + mch nmn tropy (- mpro-grav ch tropy) as indicated by the right bracket. The effective momentum (meff) in gene transcription will be inversely proportional to the effective cell pressure (Peff) required for horizontal alignment of gene intergene loop segment tropy, Peff (0.064 ≥ x < 0.245) · mA = Peff (0.245 ≥ x ≤ 0.648) · mM. The initial momentum vector for anisotropic gene alignment, mch tropy, will be greater as the origination point of anisotropic genes is 7.7 degrees (0) from the z, y-vertical, which require lesser applied pressure for horizontal alignment; whereas, the initial momentum vector for mesotropic gene alignment, mch tropy + mch nmn tropy (mM), will be lesser as the origination point of mesotropic genes is between 29.60 and 78.3 degrees (0) to the z, y-vertical plane, which require lesser applied pressure for horizontal alignment. Therefore, the effective momentum (meff; mA, mM) for gene transcription is inversely proportional to the effective cell pressure (Peff) required for horizontal alignment of gene intergene loop segment tropy. Legend. mch tropy, left bracket; mch tropy + mch nmn tropy, right bracket; mpro-grav ch tropy, pro-gravitational momentum vector (not shown); Peffective intracellular pressure (Peff) = Peffective intranuclear pressure

Based on these findings of the study, sequentially located anisotropic genes in a gene intergene tropy segment of the same will transition into the z, x-horizontal plane reading frame for gene transcription from between origination angulations of between 60.5 and 82.30 in the z, y-vertical plane where the originating momentum vector (mch tropy) will encounter a singular viscosity effect at intergene base tropy segments, in comparison to mesotropic genes situated between 60.4 and 11.70 in the z, y-vertical axis plane that will align within the inner nuclear membrane (INM) nucleoplasm where dual viscosity effects are encountered at intergene base tropy segments, in which case the additional inner nuclear membrane nucleoplasm chromatin viscosity tropy effect for mesotropic gene alignment is attributable to the additive effect of nuclear pore traffic-related to peptide synthesis rough endoplasmic reticular network of the inner nuclear envelope. Therefore, the pressurotopic model for a binomial always-on heteroeuchromatin transcription is proposed in which mesotropic DNA loop segments of supra-pressuromodulated genes are transcriptionally active at the inner nuclear membrane (INM), while anisotropic DNA loop segments of infra-pressuromodulated genes are transcriptionally active at the at the nucleolar peripheral nucleoplasm interface. The pressurotopic loop segment-dependent eukaryotic gene transcription builds on the static heterochromatin-dynamic euchromatin model in which chromatin is inactive at the nuclear envelope and active in the nucleoplasm in proximity to mobile nuclear pore complex subunits [11, 14, 15, 16] (Fig. 5).
Fig. 5

Pressurotopic model for binomial always-on heterochromatin gene transcription by anisotropic or mesotropic DNA strand loop micro-structural segmentation. In the binomial always-on model of gene transcription by micro-structural segmentation pressurotopy, mesotropy and amorphousity loop form heterochromatin loop tropy strand genes positioned between 11.7 and 60.40 degrees in the z, y-vertical plane perceiving asymmetric viscosity effects of the same align for transcription during increases of Peff to between 0.245 and 0.648 esebssiwaagoTQ units within inner nuclear membrane (INM)-associated heterochromatin; whereas, anisotropy and amorphousity loop form heterochromatin loop tropy strand genes positioned between 60.5 and 82.30 in the z, y-vertical plane perceiving lesser grade asymmetric viscosity effects of the same align for transcription during decreases in Peff to between 0.064 and 0.2445 esebssiwaagoTQ units within peripheral nucleoplasm heterochromatin in association with un-limiting nuclear pore subunits. Heterochromatin shifts towards the inner nuclear envelope margin following the transcription of EMD (Peff, 0.234; θA = 61.70) during which positive pressuromodulation at the cell membrane regulates mechanotransduction apparatus sensitivity for linear increases in nuclear effective pressure (Peff) and resultant mesotropic gene transcription; whereas, heterochromatin shifts towards the central peripheral nucleoplasm edge due to negative pressuromodulation at the cell membrane and mitochondrial oxidative challenge-exothermy, during which transcription of inner nuclear envelope peptide-coding genes LMNB1 (Peff, 0.197; θA = 66.20) → LMNA (Peff, 0.184; θA = 67.80) to LMNB2 (Peff, 0.167; θA = 69.80) regulates sensitivity for linear increases (or decreases) in mechanotransduction pressure esebssiwaagoTQ units. Legend. Cyan oval, complete nuclear pore complex with all subunits; light cyan oval, partial nuclear pore complex with some subunits; dark blue triangle, lamin and lamin-associated proteins; light blue triangle, lamin and lamin-associated proteins; transparent ovals, nucleosome with histone proteins; solid gold rectangle, anisotropic chromatin strand loop segment DNA with transcription ready infra-pressuromodulated genes; bright green rectangle, mesotropic chromatin strand loop segment DNA with transcription ready supra-pressuromodulated genes; solid bracket, nuclear membrane nucleoplasm chromatin; dashed bracket, central peripheral edge nucleoplasm chromatin

There exists significant variance of Σ intergene base segment loop tropy, although genes are positioned at similar angulation in the z, y-vertical plane as has been determined in the study; for example, the Σ intergene base segment loop tropy for CYGB is 4.11804E + 05 (Peff 0.248), whereas that for DRD1 is 2.041819E + 06 intergene bases (Peff 0.249), which align to θH = 00 from angulations of 60.00 and 59.90. Therefore, based on such determinations gene angulation distances to the z, x-horizontal plane line of unity can be determined from the hypotenusal tropy inclusive of the interposed gene bases, as in the example of MIR4537, a 3 A 7 gene positioned at an angle of 82.30 (Peff 0.064), for which the hypotenusal tropy length inclusive of intervening genes is 3.55373E + 05 bases, and thus the reverse extrapolated arc tropy distance from angulation to the z, x-horizontal plane (Ho) is 2.465E + 02 microns. Therefore, study findings are applicable to further study of heteroeuchromatin loop segment z, x-plane alignment kinetics when the inverse relationship between effective pressure and momentum, Peff (0.064 ≥ x < 0.245) · mA = Peff (0.245 ≥ x ≤ 0.648) · mM (Peff · mch tropy = Peff · mch tropy + mch nmn tropy) for DNA strand loop alignment in nuclear protoplasm.

Differentiated neuron cell sub-types differ in the range of effective cell pressures for neuroaxis gene expression in reference to tissue macro-compliance

During retinoic acid-mediated neural differentiation of NT2/D1embryonal lineage pluripotent cells (SOX1+/SOX14-) in vitro [42], it has been shown that SOX1 (Peff 0.318; θM = 51.60), expression re-increases at 2-weeks in response to RA, while SOX14 (Peff 0.219; θA = 63.50) expression increases over the same 4-week period, which is plasmid-expressed in HeLa cells at anisotropic pressure. Since SOX1 determines neuronal lineage analogous to SOX2, and SOX14 determines neural differentiation state analogous to homolog TUBB3 in differentiated radial pre-cursor cells (RPs) [43], the Peff interval for differentiating neural cells can be delineated as being between 0.219 and 0.318 esebssiwaagoTQ units, in which case the Peff interval for differentiated neuron sub-types from distal to proximal in the neuroaxis is between a Peff of 0.434 to 0.203 esebssiwaagoTQ units based on pressuromodulation mapping. Furthermore, since glial cell marker, BCAN (Peff 0.243, θA = 60.60) [44, 45], and neuronal markers, SOX14 and RBFOX3 (Peff 0.213; θM = 59.70; NeuN), are differentially expressed in symbiotic cell types; brain-specific protein of the Aggrecan class, Brevican (BCAN, Peff 0.243; θA = 60.60), is proposed to be the CNS hyaluronic acid-stabilizing chondroitin sulfate proteoglycan that increases the Peff interval for certain differentiated neuronal cell types (ie hippocampal/Papez circuit).

The upper limit of effective intracellular pressure for proprioceptive afferent lower motor neuron [lmn (a)] gene expression is at that of gene UNC13A (Peff 0.434; θM = 37.60); ortholog, munc13-1), a nuclear membrane-associated heterochromatinized gene required for presynaptic vesicle docking exocytosis, which has been shown to be under-expressed following application of sodium channel blocker tetrodotoxin (TTX) in a standard in vitro culture model for study of pre-to-post synaptic neuronal activity [46]. In addition, post-synaptic scaffold protein SHANK2 (Peff ≤ 0.301; θM = 53.60) has been shown to be over-expressed in the model, and represents the effective intracellular pressure upper limit for gene expression in secondary upper motor neurons [umn (asc)] to thalamic nuclei. Furthermore, since it has been shown in a murine model of regulator of G protein signaling gene differential expression in the corpus striatum basal ganglia nigral mesencephalic dopaminergic circuit (bgnc) in response to D1R antagonist/D2R agonist pharmacological modulation in vivo [47], and RGS2 (Peff 0.298; θM = 54.00) shown to be differentially expressed by high density array following synaptogenesis of plated neuronal precursors in vitro [46], the effective cellular pressure interval range for gene expression in basal ganglia nigral circuit deep brain nuclei neurons includes genes RGS2 and RGS16 (Peff 0.251; θM = 59.70), which implies that RGS4 (Peff 0.118; θM = 75.80) is the murine paralog for the human RGS16 gene based on the findings of this study. Dopamine receptor 1 gene DRD1 (Peff 0.249; θM = 59.70) co-expresses with RGS16, and DRD2 is expressed at a Peff of 0.217 (θA = 63.80)], the effective intracellular pressure range for basal ganglia nigral neuronal circuit neuronal gene expression is delineable as being between 0.217 and 0.298 esebssiwaagoTQ units, which are overexpressed on spiny neurons of the basal ganglia circuit by the late telencephalic development stage [48].

Neuronal nuclei protein (NeuN; RBFOX3, Peff 0.213) has been shown to be expressed in pyramidal neuron layers (I-VI) of the cerebrum [bral, pyr umn (arc)], granule cell layer neurons (gr) of the cerebellum (bell) and 3-layered hippocampal formation Papez circuit (capc) by high affinity antibody histochemistry [49]. In the murine Sox1lacz/+ model, early neuronal differentiation gene SOX1 (Peff 0.318; θM = 51.60) is maximally expressed in the periventricular zone and hippocampal Papez circuit [50], but does not appear to be expressed in the cerebral cortex (bral), while NGB (Peff 0.305; θM = 53.20) globin is minimally expressed in human brain cortex and CYGB (Peff 0.248; θM = 600) globin shows positive expression in the hippocampus [51]. Thus, the effective intracellular pressure interval for cortical telencephalon neuronal gene expression is determined to range between 0.213 and 0.305 esebssiwaagoTQ units (bral); whereas, the Peff range for hippocampal formation Papez circuit (capc) neuronal gene expression is delineated as being between a Peff of 0.318 and the effective cell pressure for expression of dopaminergic receptor DRD3 (Peff 0.203; θA = 65.20) [52], which is also the Peff for expression of GRIN1 (Peff 0.203; θA = 65.20), a NFE2L2 (Peff 0.331; θM = 50.20) target gene, as has been shown by DNA complex/transcription factor to NRF-1 antibody by electromobility super-shift assay [53]. Furthermore, since NUMA1 (Peff 0.311; θM = 52.40) is shown to be differentially upregulated in cryptorchidism by qRT-PCR [54, 55], and ovarian theca cell origin INSL3 (Peff 0.321; θM = 51.20) is shown to be expressed in the hypothalamic neuron projections to the posterior pituitary by in situ hybridization [56], the upper limit of the Peff range for gene transcription for peri-ventricular thalamic deep nuclei neurons will be in-between a Peff of 0.305 and 0.311, whereas that for the hypothalamic pituitary axis (pituit) will be inclusive to 0.331 Peff esebssiwaagoTQ units.

Based on the pressuromapping findings of the study, the upper limit interval for peripheral lower motor neuron (lmn) gene expression is definable as being between a Peff of 0.434 and 0.311 (> 0.305); whereas, the range for gene expression is between a Peff of 0.305 and 0.213 for cerebrocortical upper motor neurons, between a Peff of 0.318 and 0.203 for hippocampocortical neurons, and between a Peff of 0.298 and 0.217 for basal ganglia spiny neurons. Therefore, there exists an inverse relationship between effective range of whole cell compliance and tissue macro-compliance (Reffective whole cell compliance ˑTmacro-compliance = k), which is attributable to differences in regional negative macro-pressuromodulation in a tissue with cell populations arranged in the form of nuclear groups (ie hyaluronate matrix), and attributable to differences in the same across tissue types with differences in stromal stiffness (ie calcified matrix). In corollary, the effective cell pressure range for mesenchymal stem cell (MSC) gene expression is delineable as being between a Peff of 0.648 and <= 0.118, in which case the upper limit is attraibutable to cell-to-cell focal adhesion formation within myeloid bone caverns. Furthermore, based on the study findings, RGS18 (Peff 0.205; θM = 65.20), RGS16 (Peff 0.251; θM = 59.70; human paralog of murine RGS4), lnc-RXFP4-5 (Peff, 0.314; θM = 52.10; pituit), RGS13 (Peff; 0.360, θM = 46.50), CEACAM1 (Peff, 0.384; θM = 43.60), SLC25A44 (Peff, 0.395; θM = 42.30) and RGS21 (Peff, 0.413; θM = 40.10) are expressed within the lower motor neuron (lmn)-upper motor neuron (umn) neural cell axis; and TSACC (Peff, 0.336; θM = 49.40) and JUND (Peff, 0.344; θM = 48.40) are non-cell specific developmental biomarkers.

Expression of inner nuclear envelope and anti-apoptosis pathway genes in response to dynamic strain-mediated alterations in cellular compliance

Micropipette aspiration studies on nuclear envelope elasticity utilizing fluorescent nuclear protein expression plasmid transfectants to study rates of DNA displacement over time and resultant changes in the surface area expansion alpha power (α) as a measure of alterations in nuclear envelope deformability [29, 30, 31]. Study of nuclear stress response to tonicity in TC7 renal epithelial cell transfectants in which sub-nuclear displacement rates of GFP-lamin B1 during constant aspiration pressure application (J, creep compliance; kPa-1· sec-1) [30] has shown more significant heterochromatin displacement in hypertonic and isotonic nuclei (α = 0.28-0.32) in comparison to hypotonic nuclei (α = 0.21), in which case shrunken and unswollen nuclei are less deformable at the onset (Jinitial = 0.1) in comparison to swollen nuclei (Jinitial = 1, kPa-1) with a greater initial elastic dilation modulus (K, mN/m), implying that hypo-osmolar nuclear swelling increases cell membrane compliance. And, subsequent study of sub-nuclear GFP-fibrillarin (or upstream binding factor 1, UBF1-GFP) displacement in which whole cells, Saos-2 carcinoma, HeLa and human venous endothelial (HuVec), exposed to shear stress from 10 to 40 dyn/cm2 (1 to 4 Pa) or to compressive stress of 0.1 MPa over 60 minutes [31] have shown discordant results in alpha power (α) response to 10 dyn/cm2 physiologic shear strain for HeLa cells as compared to in HuVec cells in which there is a parabolic comparative increase in mean standard displacement (MSD) alpha power at 40 dyn/cm2, as the equivalently-increased alpha response due to 10 dyn/cm2 of shear stress in HeLa cells or 100 kPa of compressive stress in the same will be a result of mitochondrial challenge oxidative stress-exothermy due to differences in the initial effective cell pressure (Peff) setpoints of Hela carcinoma cells and HuVec endothelial cells. Furthermore, by the study of nucleus mechanical properties in EMD gene-deficient (-/y) differentiated embryonic fibroblasts, it has been determined that sex-linked deficient MEFs have a lower nuclear membrane dilation modulus (K)-to shear modulus (μ) ratio than wild-type (WT) fibroblasts, 2.1 as compared to 5.1 [32], in which case it has been shown that EMD gene-deficient cell nuclear envelope is more rigid in mechanical stain-free conditions, as it has a more significant decay exponential (e-a│K) than that for the wild-type fibroblast (WT), -0.21 and -0.04, based on nuclear GFP-lamin A/C signal intensity. Therefore, since EMD gene-deficient fibroblasts are less sensitive to mechanotransduction in comparison to wild-type MEFs, and the EMD+/y wild-type fibroblast gene Peff is 0.234 (EMD, θA = 61.70), the cellular effective pressure in EMD-/y is predictable as being relatively constant at a Peff of ≤ 0.234 esebssiwaagoTQ units during mitochondrially-mediated apoptosis.

Cell nucleus deformability in dynamic strain conditions has been studied in LMNA gene (-/-)- or EMD gene (-/y)-deficient fibroblasts as compared to wildtype (WT) fibroblasts, in which anti-apoptosis pathway-related gene expression has been studied in MEFs subject to low-frequency (1 Hz) low-grade biaxial mechanical strain (4 to 10%) at for one to 24 hours and [33, 34, 35]. Based on the findings of studies considered altogether, both LMNA gene- and EMD gene-deficient MEFs are mechanotransduction-impaired [34]; however, in the former due to increased nuclear envelope deformability as nuclear envelope perceived mechanical strain correlates with applied strain in lamin A/C-deficient cells, whereas in wildtype MEFs applied strain is cell membrane perceived and mechanotranduced to comparatively less deformable nucleus of WT fibroblasts. Furthermore, based on cells studied over in mechanical strain-free conditions by phase contrast time-lapse [33], of the two inner nuclear envelope protein deficient cell types with discordant nuclear envelope rigidity, lamin A/C-deficient cells show increased nuclear dynamics as early as 1 hour, during which neither LMNA gene-deficient nor WT fibroblasts express immediate early response 3 (IER3, IEX-1 homolog; Peff 0.204, θA = 65.40) or early growth response-1 (EGR1; Peff 0.199, θA = 66.00), whereas emerin (EMD)-deficient fibroblasts express IER3 as they must transcribe at a Peff of between 0.204 and 0.199 at baseline. In fibroblasts subject to between 2 to 4 hours of 4% biaxial cyclic strain, qRT-PCR shows significantly increased expression of both NF-κB pathway genes IER3 and EGR1 in WT MEFs [33], which indicates that mechanical strain decreases Peff from > 0.234 to in-between 0.199 and 0.204 units in mechanotransduction-sensitive EMD+/y/LMNA+/+ fibroblasts at which IER3 and EGR1 gene transcription occurs; whereas, LMNA gene (Peff 0.184; θA = 67.80)-deficient fibroblasts transcribe at a relatively constant Peff ≤ 0.184 units during which neither IER3 nor EGR1 is transcribed similar to WT fibroblasts. Since LMNA-/- fibroblasts become qRT-PCR positive for IER3 and EGR1 in response to mechanical strain, then it can be supposed that cellular pressure initially is around a Peff of 0.167 with applied dynamic stain during which LMNB2 (θA = 69.80) is expressed in the mechanotransduction in-sensitive interval, followed by an increase in Peff into the 0.197 – 0.204 units range in which LMNB1 (Peff, 0.197; θA = 66.20) is expressed, due to which the mechanotransduction sensitivity of the LMNA gene-deficient fibroblast nuclear envelope is maintained within the same. Based on these findings considered together, the Peff interval between 0.172 - 0.184 esebssiwaagoTQ units would be the mechanotransduction insensitive range for cellular gene expression.

Expression of inner nuclear envelope and extracellular matrix pathway genes in response to substrate stiffness

The effect of gel stiffness on cell morphology has been studied in vitro for contrasting cells grown on collagen I or fibronectin-coated 3 to 7.5% poly-acrylamide gels varying with shear elastic moduli for cross-linked stiffness (G’, Pa) ranging between 0.002 to 55 kPa, in which it has been determined that actin stress fibers begin to develop in GFP-actin expressing fibroblasts (MEFs) at a stiffness of between 1.6 and 3.6 kPa or in synergism with EGFP-actin wildtype (WT) transfectants of the same [36]. Based on these findings on altered cellular phenotype as a result of gel stiffness mechanotransduction force (G’), it can be inferred that the physiologic range of effective cellular pressure is between 0.180 and 2.9 kPa in-between the G0 to S phase of the cell cycle during which endothelial cell (EC) sprouting occurs during formation of cytoskeletal stress fibers; and that an additional increase in cellular pressure to between 2.9 and 28.6 kPa results in progression to binucleation followed by EC diaphragmed fenestration-associated with mitogenesis multi-nucleation. Based on MMTV-Her2/neu, myc, ras mammary tumor stiffness studied in situ (E, kPa) and tensional homeostasis studied in response to applied shear force in vitro (dynes/cm2) [37], when solid tumor tissue pressure is at 4.05 kPa, then it can be inferred that 1.59 kPa of synergistic positive mechanotransduction pressure will be attributable to secreted collagen I fibril matrix if maximum concentration is 4.0 mg/mL, which will be expressed at an effective cell pressure (Peff) range of 0.235 – 0.241 for the expression of tumor tissue collagen ligand genes COL1A1 (Peff 0.241; θA = 60.90) and COL6A1 (Peff 0.235; θA = 61.60) preceded by expression of integrin receptor (ie αvβ3) that requires between 1.1 and 1.6 kPa of applied force for ectopic vector expression [36, 37]. Additionally, since an applied shear force of 140 dynes/cm2 that results in focal adhesion formation (FAK+) parallels an increase in fibronectin (FN) matrix rigidity (G’) with an increase in Ki67 proliferative index during MEK inhibitor application (ie PD98059) [37], therefore the shear force interval between 40 and 140 dynes/cm2 will be the effective intracellular pressure interval between the G2 and S cell cycle phase, which is between 0.235 to 0.283 esebssiwaagoTQ units [26, 27]. Furthermore, since during the differentiation of human adipose tissue stromal progenitor cells (HADSCs) or myeloid marrow mesenchymal stem cells (MSC) into chondroblasts results in the spatial expression of COL2A1 isoforms 1 and 2 as early day 5 as chondrocyte cell-specific marker [57, 58], then the transcriptional activation of COL2A1 (Peff, 0.118; θA = 75.80) both directly and indirectly by Sox1 and Nkx3.2 respectively [59] will be the initial positive pressuromodulation event that increases effective cell pressure in MSCs upwards and then to an Peff of around 0.184 esebssiwaagoTQ units (LMNA) with resultant chondrocyte lineage differentiation, after an initial decrease in Peff by retinoic acid (RA) pathway activation [38].

The relationship between stoichiometry of lamin A/C to lamin-B1 protein and mRNA expression across tissue cell types (ie MSC, HSCP; U251, brain) and cellular microelasticity (kPa-1) has been studied in parallel with modeling of the time constant (1/τ; sec-1) for lamin A:B expression relationship [38], in which it has been determined that the lamin A/C : lamin B1 expression ratio follows E0.6 with lamin B1 expression follows E0.2 for the spectrum of cell types, and in parallel that the lamin A:B time constant (τ) proportionality is viscosity/elasticity. Based on the findings of this study, osteo-prone human mesenchymal stem cells from marrow (MSC) express LMNA (Peff, 0.184; θA = 67.80) but at a substrate stiffness of 12 kPa, which would be due to synergistic negative macro-pressurization, which further implies that cellular focal adhesionogenesis is required for expression of toti-pluripotency marker CD34 (Peff, 0.648; θM = 11.70) in the myeloid marrow cavern [26, 27], for a cell type that is functional over a wider range of cellular compliance. Hematopoietic stem cell progenitors from marrow (HSCP), normal brain cells (unspecific) and orthotopic xenograft GBM (U251) express LMNB1 (Peff 0.197, θA = 66.20; ~ constant LMNB2, Peff 0.167) at a substrate pressure between 0.1 and 0.2 kPa; moreover, based on the correlation between application of synergistic pressure and LMNB1 gene expression across the spectrum of cell types inclusive of osteo-prone cell types (E0.2) [38], the effective intracellular pressure (Peff) at baseline is greater than extracellular stromal pressure in osteo-prone mesenchymal stem cells (MSC), whereas the effective intracellular pressure (Peff) at baseline approximates extracellular stromal pressure in the latter. Furthermore, the lamin A/C: lamin B1 expression ratio that favors (cart >) skull > femur > MSC for comparative osteo-prone cell types in response to 12 kPa of MSC equivalent applied pressure for LMNB1 expression (Peff 0.197) is attributable to a narrower functional range of cellular compliance in comparative cell types inclusive of osteocytes and chondrocytes.

Nuclear envelope mechanotransduction in response to dynamic strain and pharmacological signaling

The dynamic strain responsiveness of the cell nucleus in mesenchymal stem cells (MSCs) subject to 0.2 to 2 Hz cyclic dynamic loading (3% strain, 10 min) has been studied with the application of inhibitors of molecular signaling such as lysophosphatidic acid (LPA), myosin light chain kinase inhibitor (ML-7), F-actin inhibitor (cytochalasin D) and rho-associated protein kinase inhibitor (Y-27632); studies in which nuclear deformability has been measured with the nuclear aspect ratio and index (NAR, b/a, a/b; NDI, %) in combination with ATP exocytosis and sarcolemmal Ca2+ release measurements, and the condensation chromatin parameter (CCP, %) utilized to detect nuclear mechanotransduction sensitivity in parallel [39, 40, 41] in pluripotent stem cells (MSC) cultured on hydrogels with a substrate stiffness of between 5 and 10 kPa.

Based on the study of mechanotransduction strain transfer in load-stressed MSCs following pre-treatment with ML-7, nuclear deformability (NDI) is increased and the yes-associated protein (YAP) pathway is activated as during dynamic loading (DL), in contrast to with the application of LPA, Y-27632 or CytoD during which nuclear deformability is decreased, and in the case of lysophosphatidic acid (LPA), pERK/ERK ratio trends towards decrease between control and dynamic loading comparison groups [39] as does matrix stiffness [38]; and by the study of alteration in chromatin condensation in dynamic strain-loaded (DL) MSCs following pre-treatment ML-7 and Y27632, CCP is indifferent at 30 sec in comparison to conditioned media (CM) + DL controls however cellular traction force (nN) decreases in response to TGFβ inhibitors or Y-27632, whereas LPA + DL increases the chromatin condensation by 1.64-fold during mitochondrial ATP exocytosis, intracellular Ca2+ oscillation and increase in autocrine TGF-β [40]. Therefore, these findings considered together are consistent with the heterochromatinization of DNA effect of LPAR agonist, lysophosphatidic acid (LPA) during dynamic loafing, being towards the inner nuclear membrane due to increased rigidity of the nuclear envelope as result of the positive pressurization effect of LPA; and furthermore, the increase in nuclear envelope deformability however an indifferent heterochromatinization DNA effect of cell membrane (CM) receptor inverse agonist myosin light chain kinase inhibitor (ML-7) being a result of the negative pressurization effect of ML-7 in synergism with dynamic loading (DL) that remains in the anisotropic pressure range, Peff < 0.245.

Mechanotransduction sensitivity alterations due to dynamic loading and resultant changes in lamin A/C protein expression have been studied under during the treatment of MSCs cultured in vitro with positive pressuromodulators HDAC inhibitor trichostatin A (TSA), CytoD and D-mannitol [41], in which it has been determined that deformation of the undifferentiated MSC nucleus in response to applied dynamic strain is lessened within the lamin-A/C protein transcription interval, LMNA (Peff, 0.184; θA = 67.80), as determined in the study. Since in dynamic strain-stressed cells there is a cell membrane compliance-mediated decrease in nuclear Peff into the nadir pressure range for mesenchymal stem cells as determined by pressuromodulation mapping [24, 26], COL2A1 gene transcription occurs (Peff, 0.118; θA = 75.80) with resultant MSC origin CTGF gene CCN2 (Peff, 0.166; θA = 700) transcription within the mechanotransduction in-sensitive cellular Peff range (> 0.118 ≤ 0.167 esebssiwaagoTQ units); therefore, the Peff pressuromodulation setpoint in toti-pluripotent cells (ie MSCs) will be at that for transcription factor ESRRB gene transcription (Peff, 0.172), which is required for re-initiation of pluripotency in a differentiated cell [60, 61], from which Peff decreases to a peri-nadir Peff around 0.118 esebssiwaagoTQ units in part by mitochondrial oxidative stress-mediated exothermy, or increases to a peak at 0.648 esebssiwaagoTQ units during the expression of a MSC origin matched limiting focal adhesion component (ie integrin subunit : collagen fibril subunit).

Conclusions

In this research, heterochromatin shift during euchromatin gene transcription has been studied by parallel determinations of DNA strand loop segmentation tropy nano-compliance (esebssiwaagoTQ units, linear nl), gene positioning angulation in linear normal two-dimensional (2-D) z, y-vertical plane (anglemetry, 0), horizontal alignment to the z, x-plane (vectormetry; mA, mM, a.u.), and by pressuromodulation mapping of differentiated neuron cell sub-class operating range for neuroaxis gene expression in reference to tissue macro-compliance (Peff).

Heterochromatin strand DNA loop micro-segmentation structural nano-compliance is either amorphousity, anisotropy or mesotropy loop segment forms perceiving various grades of the asymmetric tropy viscosity effect, where between 3-to-5 and 8-to-11 genes are arranged as one or two in-tandem alternating anisotropic and mesotropic gene(s), or as in-tandem anisotropic or mesotropic genes in juxtaposition separated by intergene tropy base distance; for example, the amorphousity loop segment form between positions -12 to -4 in reference LMNA (Peff, 0.184; θA = 68.40) on human 1q22 (+) is 5’-0.234-(a-12)-0.272 (m-11)-0.229 (a-10)-0.211 (a-9)-0.269 (m-8)-0.144 (a-7)-0.314 (m-6)-0.268 (m-5)-0.176 (a-4)-3’. Based on this arrangement of stranded chromatin DNA, an always-on pressurotopic model for gene transcription is proposed, in which either mesotropy loop form genes positioned between 11.7 and 60.40 (CD34) in the z, y-vertical plane are transcriptionally active when heterochromatin shifts towards the inner nuclear envelope margin following the transcription of EMD (Peff, 0.234; θA = 61.70), during which mechanotransduction apparatus sensitivity for linear increases in nuclear effective pressure (Peff) into the expression range for collagen fibril genes COL6A1 (Peff 0.235; θA = 61.60) and COL1A1 (Peff 0.241; θA = 60.90) for focal adhesion (FA) formation and resultant cell specific increases in nuclear pressure; or, anisotropy loop form genes positioned between 60.5 and 82.30 (MIR4537) in the z, y-vertical plane are transcriptionally active when heterochromatin shifts towards the central peripheral nucleoplasm edge, during which transcription of inner nuclear envelope peptide-coding genes LMNB1 (Peff, 0.197; θA = 66.20) → LMNA (Peff, 0.184; θA = 67.80) to LMNB2 (Peff, 0.167; θA = 69.80) regulates sensitivity for linear increases (or decreases) in mechanotransduction pressure esebssiwaagoTQ units. Based on momentum vectormetry, the relationship between effective pressure and momentum is inverse proportionality, Peff (0.064 ≥ x < 0.245) · mA = Peff (0.245 ≥ x ≤ 0.648) · mM (Peff · mch tropy = Peff · mch tropy + mch nmn tropy) for DNA strand loop alignment in nuclear protoplasm, which are applicable to further study of heteroeuchromatin loop segment z, x-plane alignment kinetics.

The episodic sub-episode block sums (SEB) split-integrated weighted average-averaged gene overexpression tropy quotient is a linear normal measure of effective intracellular pressure (Peff) for determination of gene positioning anglemetry due to primary and secondary linearization effects, validation of the primary linearization effect is the sebs intercept-to-sebssiwa intercept linearization quotient (bsebs/bsebssiwa); in which case, normalization of the dppasebs, dppmsebs effect predominates in anisotropic gene MYC (bsebs/bsebssiwa: 3.63; Peff 0.157; θA = 710), the uppasebs, uppmsebs effect predominates in mesotropic gene PRDM1 (bsebs/bsebssiwa: 3.45; Peff 0.356; θM = 470), while both the dppasebs, dppmsebs and uppasebs, uppmsebs effects are linear normalized in PRKCH (bsebs/bsebssiwa: 3.17; Peff 0.200; θA = 65.80) as examples.

Based on the findings of this study considered together, the precise mechanistic basis for alterations in chromatin gene transcription eukaryotic stranded heterochromatin arranged by structural pressurotopy nano-compliance in DNA stand loop segments is effective cell pressure (Peff) regulated shifting of transcriptionally active DNA in-between the inner nuclear envelope margin and the peripheral nucleoplasm edge and the z, x-plane horizontal alignment of a gene by gene specific Peff within the cell specific effective range of whole cell compliance in reference to tissue macro-compliance. The findings of this study are therefore applicable to the further study of changes in gene transcription in response to applied mechanical strain-mediated alterations in nuclear envelope deformability in silico.

Notes

Acknowledgements

Not applicable

Authors’ contributions

HS conceptualized the research, developed the methodology, analyzed the data, and wrote the manuscript. The author read and approved the final manuscript.

Funding

No funding was applied for this research.

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable.

Competing interests

The author declares that he has no competing interests.

Supplementary material

41231_2019_45_MOESM1_ESM.doc (66 kb)
Additional file 1: Table S1. Sequential episodic sub-episode block sum split-integrated weighted average gene overexpression tropy quotients to final esebssiwaagoTQ for predicted neural axis gene overexpression 1) Gene loci sub-episode block structure variations include non-contributory anisotropy (NCA), anisotropy converted to mesotropy (ACM), and/or 0.5-factor adjusted stabilizing mesotropy or anisotropy converted to stabilizing isotropy for anisotropy or mesotropy (stIAfM, stIMfA or stIMfM) that result in an initial to final SEB conversion; and 2) previously reported episode and sub-episode block structure is applied in all cases as per reference [25], in which gene/gene loci at cusps of the delineated base intervals, SHANK2 (784,883), RBFOX3 (521,757) classify into the adjacent interval. (DOC 66 kb)

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Authors and Affiliations

  1. 1.Freelance Investigator in Translational Science and Medicine (unaffiliated)CharlestonUSA

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