Abstract
Biological functions are regulated through the interactions among genes, proteins and other molecules in a cell. Among various approaches to modeling gene regulatory networks (GRNs), Boolean networks (BNs) and its probabilistic extension, probabilistic Boolean networks (PBNs), have been effective means; in particular, PBNs consider molecular and genetic noise, so they provide significant insights into the understanding of the dynamics of GRNs. The applications of PBNs, however, are hindered by the complexities involved in the computation of the state transition matrix and steady-state distribution of a PBN. This chapter discusses stochastic logic networks as computationally efficient gene network models. Initially, stochastic Boolean networks (SBNs) are presented as a novel implementation of PBNs. SBNs are based on the notions of stochastic logic and stochastic computation. To further exploit the simplicity of logical models, a multiple-valued network employs gene states that are not limited to binary values, thus providing a finer granularity in the modeling of GRNs. Subsequently, stochastic multiple-valued networks (SMNs) are presented for modeling the effects of noise and gene perturbation in a GRN. These novel logical models provide accurate and efficient simulations of probabilistic Boolean and multiple-valued networks (PBNs and PMNs). The analysis of a p53–Mdm2 network and a WNT5A network shows that the stochastic logic networks are efficient in evaluating the network dynamics and steady state distribution of gene networks under random gene perturbation. These techniques are potentially useful in the investigation of intracellular delivery and drug discovery.
Keywords
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- GRN:
-
Gene regulatory network
- BN:
-
Boolean network
- GAP:
-
Gene activity profile
- PBN:
-
Probabilistic Boolean network
- SBN:
-
Stochastic Boolean network
- PMN:
-
Probabilistic multiple-valued networks
- SMN:
-
Stochastic multiple-valued network
- STM:
-
State transition matrix
- SSD:
-
Steady state distribution
- MCMC:
-
Markov chain Monte Carlo
- MC:
-
Monte Carlo
- FSM:
-
Finite state machine
- EL:
-
Equal or larger
- ES:
-
Equal or smaller
- TB:
-
Ternary buffer
- TI:
-
Ternary inverter
- DSBs:
-
Double strand breaks
References
Abdi A, Tahoori MB, Emamian ES (2008) Fault diagnosis engineering of digital circuits can identify vulnerable molecules in complex cellular pathways. Sci Signal 1(42):ra10
Abou-Jaoude W, Ouattara D, Kaufman M (2009) From structure to dynamics: frequency tuning in the p53–mdm2 network: I. logical approach. J Theor Biol 258(4):561–577. doi:10.1016/j.jtbi.2009.02.005
Adamatzky A (2003) On dynamically non-trivial three-valued logics: oscillatory and bifurcatory species. Chaos Solit Fract 18:917–936
Adar R, Benenson Y, Linshiz G, Rosner A, Tishby N, Shapiro E (2004) Stochastic computing with biomolecular automata. PNAS 101(27):9960–9965
Aldana M, Coopersmith S, Kadanoff LP (2003) Boolean dynamics with random couplings. http://arXiv.org/abs/adap-org/9305001
Batchelor E, Loewer A, Lahav G (2009) The ups and downs of p53: understanding protein dynamics in single cells. Nature Rev Cancer 9:371–377
Benenson Y, Gil B, Ben-Dor U, Adar R, Shapiro E (2004) An autonomous molecular computer for logical control of gene expression. Nature 429:423–429
Ching W, Zhang S, Ng M, Akutsu T (2007) An approximation method for solving the steady-state probability distribution of probabilistic Boolean networks. Bioinformatics 23:1511–1518
Ciliberto A, Novak B, Tyson JJ (2005) Steady states and oscillations in the p53–Mdm2 network. Cell Cycle 4:486–493
de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 9(1):67–103. doi:10.1089/10665270252833208
Dougherty ER, Pal R, Qian X, Bittner ML, Datta A (2010) Stationary and structural control in gene regulatory networks: basic concepts. Int J Syst Sci 41(1):5–16
Dubrova E (2006) Random multiple-valued networks: theory and applications. In: Proceedings of international symposium on multiple-valued logic (ISMVL ’06), pp 27–33, May 2006
Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297:1183–1186
Faryabi B, Vahedi G, Datta A, Chamberland JF, Dougherty ER (2009) Recent advances in intervention in Markovian regulatory networks. Curr Genomics 10(7):463–477
Gaines BR (1969) Stochastic computing systems. Adv Inf Syst Sci 2:37–172
Garg A, Mendoza L, Xenarios I, DeMicheli G (2007) Modeling of multiple valued gene regulatory networks. In: Proceedings of 29th IEEE International Conference on Engineering in Medicine and Biology Society (EMBC ’07), pp. 1398–1404, Aug 2007
Geva-Zatorsky N, Rosenfeld N, Itzkovitz S, Milo R, Sigal A, Dekel E, Yarnitzky T, Liron Y, Polak P, Lahav G, Alon U (2006) Oscillations and variability in the p53 system. Mol Syst Biol 2:0033. doi: 10.1038/msb4100068
Glass L, Kauffman S (1973) The logical analysis of continuous non-linear biochemical control networks. J Theor Biol 39:103–129
Guelzim N, Bottani S, Bourgine P, Kepes F (2002) Topological and causal structure of the yeast transcriptional regulatory network. Nat Genet 31:60–63
Han J, Chen H, Liang J, Zhu P, Yang Z, Lombardi F (2013) A stochastic computational approach for accurate and efficient reliability evaluation. IEEE Trans Comput (in press)
Harvey I, Bossomaier T (1997) Time out of joint: attractors in asynchronous random Boolean networks. In: Husbands P, Harvey I. (eds) Proceedings of 4th European conference on artificial life (ECAL97). MIT Press, New York, pp 67–75
Huang S (1999) Gene expression profiling, genetic networks, and cellular states: an integrating concept for tumorigenesis and drug discovery. J Mol Med 77:469–480
Ivanov I, Pal R, Dougherty ER (2007) Dynamics preserving size reduction mappings for probabilistic Boolean networks. IEEE Trans Signal Process 55(5):2310–2322
Karlebach G, Shamir R (2008) Modelling and analysis of gene regulatory networks. Nat Rev Mol Cell Biol 9:770–780
Karlebach G, Shamir R (2010) Minimally perturbing a gene regulatory network to avoid a disease phenotype: the glioma network as a test case. BMC Syst Biol 4:15
Kauffman SA (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. Theor Biol 22:437–467
Kervizic G, Corcos L (2008) Dynamical modeling of the cholesterol regulatory pathway with Boolean networks. BMC Syst Biol 2:99
Kim S, Li H, Dougherty ER et al (2002) Can Markov chain models mimic biological regulation? J Biol Syst 10(4):337–357
Kitano H (2001) Foundations of systems biology. MIT Press, Massachusetts
Lahav G, Rosenfeld N, Sigal A, Geva-Zatorsky N, Levine AJ, Elowitz MB, Alon U (2004) Dynamics of the p53–Mdm2 feedback loop in individual cells. Nat Genet 36:147–150
Li Z, Cheng D (2010) Algebraic approach to dynamics of multivalued networks. Int J Bifurcat Chaos 20(3):561–582
Liang J, Han J (2012) Stochastic Boolean networks: an efficient approach to modeling gene regulatory networks. BMC Syst Biol 6:113
Luo C, Wang X (2013) Dynamics of random Boolean networks under fully asynchronous stochastic update based on linear representation. PLoS ONE 8(6):e66491. doi:10.1371/journal.pone.0066491
McAdams HH, Shapiro L (1995) Circuit simulation of genetic networks. Science 269(5224):650
Morris MK, Saez-Rodriguez J, Sorger PK, Lauffenburger DA (2010) Logic-based models for the analysis of cell signaling networks. Biochemistry 49:3216–3224
Murrugarra D, Veliz-Cuba A, Aguilar B, Arat S, Laubenbacher R (2012) Modeling stochasticity and variability in gene regulatory networks. EURASIP J Bioinform Syst Biol 1:5
Pal R (2010) Context-sensitive probabilistic Boolean networks: steady-state properties, reduction, and steady-state approximation. IEEE T Signal Proces 58(2):879–890
Pandey S, Wang R, Wilson L, Li S, Zhao Z, Gookin T, Assmann S, Albert R (2010) Boolean modeling of transcriptome data reveals novel modes of heterotrimeric G-protein action. Mol Syst Biol 372. doi:10.1038/msb.2010.28
Qian X, Ivanov I, Ghaffari N, Dougherty ER (2009) Intervention in gene regulatory networks via greedy control policies based on long-run behavior. BMC Syst Biol 3:61
Qian X, Ghaffari N, Ivanov I, Dougherty ER (2010) State reduction for network intervention in probabilistic Boolean networks. Bioinformatics 26(24):3098–3104
Rosenthal JS (1995) Minorization conditions and convergence rates for Markov chain Monte Carlo. J Am Stat Assoc 90:558–566
Shmulevich I, Dougherty ER (2010) Probabilistic Boolean networks: the modeling and control of gene regulatory networks. ociety for Industrial & Applied Mathematics, U.S
Shmulevich I, Dougherty ER, Zhang W (2002a) From Boolean to probabilistic Boolean networks as models of genetic regulatory networks. In: Proceedings of IEEE, vol 90, pp 1778–1792
Shmulevich I, Dougherty ER, Kim S, Zhang W (2002b) Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18:261–274
Shmulevich I, Dougherty ER, Zhang W (2002c) Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics 18(10):1319–1331
Shmulevich I, Gluhovsky I, Hashimoto RF, Dougherty ER, Zhang W (2003) Steady-state analysis of genetic regulatory networks modelled by probabilistic Boolean networks. Comp Funct Genom 4:601–608. doi:10.1002/cfg.342
Thomas R, D’Ari R (1990) Biological feedback. CRC Press, Boca Raton
Vogelstein B, Lane D, Levine AJ (2000) Surfing the p53 network. Nature 408:307–310
Volker LG, Conrad M (1998) The role of weak interactions in biological systems: the dual dynamic model. J Theor Biol 193:287–306
von Neumann J (1956) Probabilistic logics and the synthesis of reliable organisms from unreliable components. In: Shannon CE, McCarthy J (eds) Automata studies. Princeton University Press, Princeton, pp 43–98
Weinberg RA (2006) The biology of cancer, 1st edn. Garland Science, New York
Zhang S et al (2007) Simulation study in probabilistic Boolean network models for genetic regulatory networks. Int J Data Min Bioinformatics 1:217–240
Zhu P, Han J (2013) Stochastic multiple-valued gene networks. IEEE Trans Biomed Circuits Syst 8(1):42–53
Zhu P, Han J (2014) Asynchronous stochastic boolean networks as gene network models. J Comput Biol (in press)
Zhu P, Liang J, Han J (2014) Gene perturbation and intervention in context-sensitive stochastic boolean networks. BMC Syst Biol (in press)
Acknowledgment
This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) in a Discovery Grant.
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Zhu, P., Liang, J., Han, J. (2014). Toward Intracellular Delivery and Drug Discovery: Stochastic Logic Networks as Efficient Computational Models for Gene Regulatory Networks. In: Prokop, A., Iwasaki, Y., Harada, A. (eds) Intracellular Delivery II. Fundamental Biomedical Technologies, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-8896-0_17
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