Synonyms

Large-scale models of feedforward inhibition; Large-scale models of lateral inhibition; Large-scale models of odor processing; Large-scale models of glomerular layer; Models of granule cells; Models of mitral cells; Models of tufted cells

Definition

The olfactory bulb is a small and self-contained neural system of the forebrain that is pivotally involved in producing the sense of the smell. Large-scale models of the olfactory bulb reconstruct extensive portion of it, including the main neuron populations, such as mitral, tufted, and granule cells, along with their connectivity. They are constituted by four components: (i) a model of odor inputs, (ii) cell models reproducing the salient properties of the main neuron types, (iii) the organization in glomeruli, and (iv) models of the feedforward and/or feedback inhibition mediated via glomerular and granule cell layers, respectively. Therefore, large-scale models of the olfactory bulb realize powerful frameworks to simulate the overall odor response and perform analyses that are impracticable by experiments, in order to understand odor perception in relation to the basic neural mechanisms.

Detailed Description

Analyses on large portions of the olfactory bulb (OB) are essential for understanding how it creates odor representation. This is produced as specific spatiotemporal patterns of neural activity that are diffused across large neuron sets (Abraham et al. 2004; Niessing and Friedrich 2010; Vincis et al. 2012) and are sculpted by long-range inhibitory interactions among large sets of different neuron types (Yokoi et al. 1995; Aungst et al. 2003). However, experimental methods are unable to reveal the dynamic underlying odor learning and processing in the OB, as long as they cannot link the functional aspects with the basic neural mechanisms. On the one hand, the scope of the experimental procedures is often limited to small neuron set (Shusterman et al. 2011; Smear et al. 2011). On the other hand, if extending over large portions of the OB, the experimental procedures do not achieve the adequate resolution to outline the individual contribution of different neural mechanisms and cell types to the odor response (Abraham et al. 2004; Niessing and Friedrich 2010; Vincis et al. 2012). The intrinsic limitations of the experimental protocols have been recently overriden by large-scale computational modeling (Yu et al. 2013; Li and Cleland 2013; Polese et al. 2014; Gilra and Bhalla 2015; Cavarretta et al. 2018). In literature, there are various OB models, each developed with different paradigms, that capture different aspects of the real system. Here we have discussed the newest large-scale models of the OB (Li and Cleland 2013; Polese et al. 2014; Gilra and Bhalla 2015; Cavarretta et al. 2018), focusing particularly on the first 3D model of the OB (Migliore et al. 2013, 2014; Cavarretta et al. 2016, 2018).

The Large-Scale Three-Dimensional Model of the Olfactory Bulb

The three-dimensional model of the OB recreated the real organization and connectivity in a virtual three-dimensional space, including a high number of morphological and electrophysiological details, to simulate odor learning and processing in a realistic and physiologically consistent three-dimensional environment. The extreme realism of the model enabled to perform high-resolution analyses to understand the functional meaning of the individual neural mechanisms.

The model recreated the laminar organization of the OB. The OB shape was approximated as an ellipsoid wherein the neuronal elements took place at different laminae (Fig. 1a, left), in accord with the real location in the OB (Fig. 1a, right). In the dorsal part, the GL contained 127 glomeruli that reproduce the real locations mapped experimentally (Fig. 1b; Vincis et al. 2012), and thus the model covered ~10% of the entire OB surface.

Fig. 1
figure 1

The three-dimensional biophysically accurate large-scale model of the olfactory bulb. (a) The laminar structure of the olfactory bulb as reproduced in the model (left) and its neuronal elements and connectivity (right). Laminae: glomerular layer (GL), external plexiform layer (EPL), mitral cell layer (MCL), and granule cell layer (GCL). The olfactory sensory neurons (OSN) convey excitation onto the glomeruli. Each lamina contains different neuron types: the GL contains periglomerular (PG) cells; the EPL contains granule cell (GC) apical dendrites and middle tufted (mTC) and mitral (MC) cells in the superficial and deep half, respectively; the MCL contains MC somata; the GCL contains GC somata that are distinctive in superficial (sGC) and deep (dGC) granule cells. (b) The realistic map of 127 glomeruli (Vincis et al. 2012). MC and mTC lateral dendrites are highly overlapping in the EPL, reproducing their real organization in the OB. (c) The subcellular sections of GCs and MCs. mTCs are formed by the same subcellular sections as MCs (not shown), but they are smaller in size. (d) The glomerular unit (i.e., GC column) formed after learning

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Also, the model included the biggest neuron populations, which are mitral (MC), middle tufted (mTC), granule (GC), and few deep-short axon (dSAC) cells in some simulation, along with their connectivity (Fig. 1b) via glomerular (GL) and granule cell (GCL) layers. MCs and mTCs connected with separate subsets of GCs that were distincted in superficial (sGC) and deep (dGC) GCs (Geramita et al. 2016), respectively, by dendrodendritic reciprocal connections (Shepherd et al. 2004). These included long-term plasticity for odor learning simulation. The GL was implemented as a mathematical microcircuit defined by Cleland and Linster (Cleland and Sethupathy 2006; Cleland and Linster 2012; Cavarretta et al. 2016, 2018), whereas all other cell types were implemented as biophysically accurate multicompartmental single-cell models, formed by different subcellular sections (Fig. 1c). The MC and mTC morphologies were generated by a random algorithm designed ad hoc (Migliore et al. 2013, 2014) for generating an unlimited number of three-dimensional MC and mTC morphologies that included realistic full dendritic arbors. The synthetic and experimental morphologies were then statistically indistinguishable.

The three-dimensionality of the MC and mTC morphologies constituted a pivotal feature of the model. For example, the full dendritic arbors allow to inspect the local dynamic of odor learning along the MC and mTC lateral dendrites. The lateral dendrites extend throughout the EPL over realistic distance range, reproducing the glomerular receptive field of the real system. This in turn recreated the physiological level of dendritic overlap between different glomeruli, which impacts the number of GCs shared between different glomeruli. By simulating odor learning, the model generated GC column with shape, size, and spatial distribution that reproduce the same features observed in experiments (Willhite et al. 2006). This hence regulates the spatial spread of the lateral inhibition (Cavarretta et al. 2018), which impact many functional aspects of odor learning and processing in the OB (see the “Analysis of the Model”).

Technical Details

The model was implemented in NEURON (v. 7.3, Hines and Carnevale 1997) and Python. Simulations were parallelized by NEURON’s multisplit method (Hines et al. 2008). The synaptic connections required a massive inter-process message passing that was optimized by NEURON’s multisend method (Hines et al. 2011).

Electrophysiological Properties

Each single-cell model was formed by diverse subcellular sections (Fig. 1c). Each section was subdivided in compartments, in which the membrane properties were modeled by the Hodgkin-Huxley equations (Hodgkin and Huxley 1952; Hines and Carnevale 1997). The passive membrane properties were specific membrane conductance, specific membrane capacitance, resting potential, and axial resistance. The active membrane properties (i.e., ion channels) were transient sodium, delay rectifier, and A-type potassium channels. The specific membrane conductance and capacitance were constrained to the experimental values of membrane time constant (Burton and Urban 2014, 2015). For MCs and mTCs, the modeled input resistance was lower than observed by experiments in slice to take into the bias due to the amputation of the lateral dendrite (MC, 27.4 +/− 0.8 MΩ; mTC, 65.2 +/− 2.7 MΩ; GC, 603.2 +/− 36.3 MΩ; dSAC, 278.3 MΩ). The ion channel densities were tuned to reproduce the firing patterns and the curves of firing rate versus current injection observed experimentally (Burton and Urban 2014; Geramita et al. 2016). Thus, the mTCs responded with burst, whereas MCs responded with tonic firing (Cavarretta et al. 2018). In particular, the mTCs exhibit rebound bursts in response to hyperpolarizing pulse (Cavarretta et al. 2018). The numbers of MCs and mTCs were scaled to 5 and 10 per glomerulus, respectively. Each MC and mTC connected with ~700 dGCs and ~1250 sGCs, respectively, by dendrodendritic reciprocal connections (Shepherd et al. 2004). In each reciprocal connection, MC/mTC released glutamate onto GC, whereas GC released GABA onto MC/mTC.

Olfactory Sensory Neurons and Odor Inputs

Experimental recordings showed the OSN response during sniffing was characterized by a specific temporal dynamic and undergoes to desensitization with high sniffing frequency (Carey et al. 2009). These effects in the OSN response (S) were modeled as a dynamic system:

S(t) = O(t)(1 − D(t))

with\( \left\{\begin{array}{c}\frac{dO}{dt}={K}_O\left(1-C-O\right)\\ {}\frac{dC}{dt}={K}_{C_1} OC\left(1-C\right)+{K}_{C_2}\left(1-C\right)\\ {}\frac{dD}{dt}={K}_{D_1}O\left(1-D\right)+{K}_{D_2}D\left(1-O\right)\end{array}\right. \)t ∈ [0, T]

where T defines the sniffing period; the variables O, C, and D are the states open, closed, and desensitized, respectively, of the OSN receptor; the rates are KO = 0.01 ms−1, \( {K}_{C_1}=0.01\;{\mathrm{ms}}^{-1} \), \( {K}_{C_2}={10}^{-4}\;{\mathrm{ms}}^{-1} \), \( {K}_{D_1}=1.7\cdotp 1{0}^{-4}{\mathrm{ms}}^{-1} \), and \( {K}_{D_1}=0.01\;{\mathrm{ms}}^{-1} \); the initial conditions are O(0) = 0, C(0) = 1, and D(0) = 0.

The aggregate excitatory postsynaptic current in the MC and mTC tuft dendrites is calculated as:

\( {I}_{ORN}(t)=\left[\tilde{g}+{g}_{max}\;{GL}_i(c)S(t)\right]\left[{V}_m(t)-{E}_{AMPA/ NMDA}\right] \)where Vm is the membrane potential, EAMPA/NMDA(=0 mV) is the resting potential, gmax defines the synaptic conductance peak, and \( \tilde{g} \)is random term.

GLi(c) describes the overall activation of the OSNs that are functionally related to the ith glomerulus. The level of activation depends on the odor affinity of the receptor. For each odor, GLi(c) is defined as a Hill function (Cruz and Lowe 2013) of concentration that is calculated as:

\( {GL}_i(c)=\frac{F_{max}}{1+\frac{1}{\eta_i}{\left(1+\frac{K_i}{c}\right)}^n} \)

where \( \frac{F_{max}}{1+{\eta}_i} \) defines the maximum OSN response, Fmax is kept constant over all combinations of odor-glomerulus pairs, ηi depends on the odor identity, Ki drives the half value, and n is the cooperativity exponent.

Different odors corresponded to different arrays of OSN inputs that were obtained by different combinations of parameters of GLi(c). For the sake of simplicity, Fmax, Ki, and n were kept constant across all odor-glomerulus pairs, whereas ηi was inferred from an experimental data set of 19 natural odors (see Cavarretta et al. 2016). In particular, the relative dose-response peaks of the simulated odors were constrained to the glomerular responses observed experimentally (Vincis et al. 2012).

Glomerular Layer

The glomerular circuitry was implemented in the form of mathematical equations, which were previously defined by Cleland and Linster’s (Cleland and Sethupathy 2006; Linster and Cleland 2012). In particular, Cleland and Linster assumed that inhibitory PGs modulate the OSN excitation conveyed on MC and mTC tuft dendrites. They formulated the effects of the PGs as two computations that sculpt the spatial activity patterns in the GL. These are the olfactory input normalization and the non-topographical contrast enhancement (see “The Learning-Dependent Processing of Natural Odors”). Given GLi(c) defined as above, the olfactory input normalization is calculated as:

\( {GL}_i^{norm}(c)=\left\{\begin{array}{c}{GL}_i(c)-\overline{GL_i}(c), if\ {GL}_i(c)-\overline{GL_i}(c)>0\\ {}0, otherwise\end{array}\right. \)with

\( \overline{GL_i}(c)=\frac{1}{N}\sum {GL}_i(c) \)

Together, the contrast-enhanced odor input is calculated as

\( {GL}_i^{CE}(c)=\left\{\begin{array}{c}{GL}_i^{norm}- PG\left[{GL}_i^{norm}(c)\right]-\overline{GL_i}(c),\\ {} if\ {GL}_i^{norm}- PG\left[{GL}_i^{norm}(c)\right]>0\\ {}0, otherwise\end{array}\right. \)with

\( PG(x)=\left\{\begin{array}{c}\frac{0.6}{1+0.01\left(\frac{1}{x}-1\right)}, if\ x>0\\ {}0, otherwise\end{array}\right. \)where PG(x) defines the intraglomerular inhibition conveyed from PGs. The equations thus calculated the net excitation conveyed on MC and mTC tuft dendrites after the inhibitory effects of the PGs.

Three-Dimensional Morphology Generation of Mitral and Middle Tufted Cells

The three-dimensional morphologies of MCs and mTCs were generated by the following algorithm (Migliore et al. 2013, 2014):

FOR each MC/mTC:   Generate soma shape and location;   Generate # of LD and direction of first segment of LD and AD;   Create a list (L) of tip dendrites;   ITERATE N times AND while L is not empty DO;    FOR each element in L:     test extension of a dendrite for M times:      generate new segment (direction and diam);       IF inside the boundary:        update L;        break;     IF extension fails:       delete element from L;     ELSE IF can bifurcate:       generate new tips and add to L;     ELSE IF apical dend. is within GCL:       generate first segment of TDs and add to L; Abbreviations: MC, mitral cell; mTC, middle tufted cell; LD, lateral dendrites; BL, branch length; PL, path length; BO, branch order; AD, apical dendrite; GCL, granule cell layer; TD, tuft dendrites; N = 1000; M = 10.

The algorithm’s parameters were the distributions of dendritic maximal path length, dendritic branch length, and branching probability; they were estimated from full experimental reconstructions of MCs and mTCs (Igarashi et al. 2012).

For each segment of lateral dendrites, the growth direction was corrected by a driving force that dampened the centrifugal component, making the MC and mTC lateral dendrites curving as the OB surface, replicating the realistic curvature observed by anatomical studies.

The synthetic MC and mTC morphologies were validated against experimental reconstructions (Igarashi et al. 2012) by comparing the Sholl plots and the proportion of dendrites versus branch order, resulting statistically indistinguishable (Migliore et al. 2014; Cavarretta et al. 2018).

Analysis of the Model

Odor Learning and Granule Cell Column Formation

The model predicted the dynamic underlying odor learning and the consequent GC column formation in the OB (Willhite et al. 2006). In particular, odor learning relies on the long-term plasticity in the dendrodendritic reciprocal synapses between MC/mTCs and GCs, activated by backpropagating action potentials (APs) along MC/mTC lateral dendrites. The odor learning process can be summarized as follows: (i) the odor input triggers somatic APs in MCs and mTCs; if the odor input is strong enough, it triggers a high firing rate so that the excitatory synapses undergo to long-term potentiations; (ii) once the excitatory synapses are powerful enough, the backpropagating APs elicit the GC response, and thus the inhibitory synapses undergo to long-term potentiation; (iii) once the inhibitory synapses are powerful enough, the feedback inhibition blocks the AP backpropagation, decreasing the local dendritic firing rate; thus, the distal, but not the proximal, reciprocal synapses undergo to long-term depression. Therefore, the most effective reciprocal synapses are proximal to the MC/mTC somata so forming a GC column that is functionally related to their glomerulus. Therefore, all MCs, mTCs, and GCs that are functionally related to a glomerulus constitute a computational unit termed “glomerular unit” (GU).

Lateral Interactions between Glomerular Units during Column Formation

The model showed the possible consequences of the inter-glomerular interactions via GC columns during learning (Migliore et al. 2015). With regard to these interactions, the model suggested: (i) their strength depends on the inter-glomerular distance, (ii) they can promote or hinder the GC column formation in neighboring glomeruli, and (iii) they affect the breadth and definition (in terms of GC density) of the GC columns, depending on the odor learning order (non commutativity).

The Learning-Dependent Processing of Natural Odors

The model showed the learning-dependent dynamic underlying the OB processing of natural odors (Cavarretta et al. 2016), outlining the individual role of feedforward and lateral inhibition mediated via GL and GCL, respectively. In particular, the GL circuit sparsifies the odor representation in the GL, stabilizes the representation across different odor concentration, and decorrelates the spatial activity patterns evoked by different odors. Together, the lateral inhibition adds temporal processing to the odor representation, decorrelating over time the spatial activity patterns evoked by different natural odors. Importantly, the temporal processing via GCL crucially depends on the presence of well-formed GC columns.

The Parallel Signal Pathways of the Olfactory Bulb

The model characterized the two parallel pathways of the OB (Cavarretta et al. 2018), concerning of the MC and mTC outputs. In particular, the different MC and mTC intrinsic properties make different responses to lateral inhibition. Thus, mTC synchronization follows a common GC input, whereas MCs respond with firing rate variation only to a high number of GC inputs. The model then suggested that MCs and mTCs are controlled by similar computations via GL, whereas their functional separation occurs in the GCL, where they connect with separate subsets of GCs. Finally, it was hypothesized that dSACs inhibit the GCs connecting with different clusters of GUs. The dSAC inhibition may thus organize the GUs into larger learning-dependent entities termed “glomerular unit clusters,” where the inter-GU interaction via GC column occurs within but not between GU clusters.

Spine Relocation in Adult-Born Granule Cell

Experiments in vivo revealed a novel form of fast activity-dependent synaptic plasticity, in which a low percent of mature spines (3–8%) in adult-born GCs rapidly switch from inactive toward active MC dendrites (Breton-Provencher et al. 2016). This was simulated in a scaled three-dimensional OB network including three glomeruli, where GC columns were formed below each. The model suggested that spine relocation increases the synchronization between the most responsive GUs. The effect of spine relocation was substantial despite their relatively low percent (3–6%). Therefore, the model supported the hypothesis that spine relocation within GC column may realize a fast-adaptive mechanism for fast oscillation generation.

Other Models of the Olfactory Bulb

Polese and colleagues (2014) developed a model including MCs, ETs, PGs, and sSAs. Thus, they exclusively analyzed the effects of the feedforward inhibition on the OB outputs. Each cell was implemented as a ball-and-stick model in which the biophysical properties were modeled by the Izhikevich’s equations. They then suggested that odor identity and intensity are separately encoded in MCs and ETs, respectively.

Li and Cleland (2013) developed a model based on NEURON simulation environment (Hines and Carnevale 1997), including 25 glomeruli, 1 MC per glomerulus, 25 PGs, and 100 GCs. Each cell was implemented as an oligocompartmental morphology including a single section of each subcellular type. The biophysical properties were modeled by the Hodgkin-Huxley equations (Hodgkin and Huxley 1952). In particular, they dissected the individual effects of nicotinic and muscarinic modulations: (i) nicotinic modulation, which operates in the GL, sharpens the MC receptive fields by modulating the average firing rate, decorrelating the spatial representations between similar odors; (ii) muscarinic modulation affects the lateral inhibition via GCs, increasing the MC spike synchrony as well as the gamma oscillations, without substantially affecting the MC firing rate; and (iii) the combination of nicotinic and muscarinic modulations produce an even sharper odor tuning than either modulation alone.

Gilra and Bhalla (2015) developed an OB model based on Multi-scale Object-Oriented Simulation Environment, Python, and NeuroML. The model included 3 glomeruli, 2 MCs per glomerulus, 1000 PGs, and ~1200 GCs. Each cell was implemented as a biophysical multicompartmental model in which the intrinsic membrane properties were described by the Hodgkin-Huxley equations (Hodgkin and Huxley 1952). In particular, they analyzed the long-range lateral interactions between MCs, hypothesizing the occurrence of intraglomerular lateral inhibition via GCs, though experiments revealed that GCs do not make multiple synapses with sister MCs/TCs (Kim et al. 2011). Together, they suggested that the MC response to odor mixture is the linear summation of specific response time profiles to the individual odor components, suggesting that this linearization occurs only over short concentration ranges, and is due to the PG inhibition.