Abstract
Theory allows studying why Evolution might select core genetic commitment circuit topologies over alternatives. The nonlinear dynamics of the underlying gene regulation together with the unescapable subtle interplay of intrinsic biochemical noise impact the range of possible evolutionary choices. The question of why certain genetic regulation circuits might present robustness to phenotype-delivery breaking over others, is therefore of high interest. Here, the behavior of systematically more complex commitment circuits is studied, in the presence of intrinsic noise, with a focus on two aspects relevant to biology: parameter asymmetry and time-scale separation. We show that phenotype delivery is broken in simple two- and three-gene circuits. In the two-gene circuit, we show how stochastic potential wells of different depths break commitment. In the three-gene circuit, we show that the onset of oscillations breaks the commitment phenotype in a systematic way. Finally, we also show that higher dimensional circuits (four-gene and five-gene circuits) may be intrinsically more robust.
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References
Waddington, C. H. (1957) The Strategy of the Genes. London: Routledge
Ferrell, J. E. Jr. (2012) Bistability, bifurcations, and Waddington’s epigenetic landscape. Curr. Biol., 22, R458–R466
Strogatz, S. H. (1994) Nonlinear Dynamics and Chaos. Cambridge: Perseus Books Publishing
Jaeger, J., Monk, N. (2014) Bioattractors: Dynamical systems theory and the evolution of regulatory processes. J. Physiol., 592, 2267–2281
Çağatay, T., Turcotte, M., Elowitz, M. B., Garcia-Ojalvo, J. and Süel, G. M. (2009) Architecture-dependent noise discriminates functionally analogous differentiation circuits. Cell, 139, 512–522
Elowitz, M. B., Levine, A. J., Siggia, E. D. and Swain, P. S. (2002) Stochastic gene expression in a single cell. Science, 297, 1183–1186
Süel, G. M., Garcia-Ojalvo, J., Liberman, L. M. and Elowitz, M. B. (2006) An excitable gene regulatory circuit induces transient cellular differentiation. Nature, 440, 545–550
Süel, G. M., Kulkarni, R. P., Dworkin, J., Garcia-Ojalvo, J. and Elowitz, M. B. (2007) Tunability and noise dependence in differentiation dynamics. Science, 315, 1716–1719
Thattai, M. and van Oudenaarden, A. (2004) Stochastic gene expression in fluctuating environments. Genetics, 167, 523–530
Turcotte, M., Garcia-Ojalvo, J. and Süel, G. M. (2008) A genetic timer through noise-induced stabilization of an unstable state. Proc. Natl. Acad. Sci. USA, 105, 15732–15737
Xi, H., Duan, L. and Turcotte, M. (2013) Point-cycle bistability and stochasticity in a regulatory circuit for Bacillus subtilis competence. Math. Biosci., 244, 135–147
Xi, H., Yang, Z. and Turcotte, M. (2013) Subtle interplay of stochasticity and deterministic dynamics pervades an evolutionary plausible genetic circuit for Bacillus subtilis competence. Math. Biosci., 246, 148–163
Li, C., Wang, E. and Wang, J. (2011) Landscape and flux decomposition for exploring global natures of non-equilibrium dynamical systems under intrinsic statistical fluctuations. Chem. Phys. Lett., 505, 75–80.
Li, C., Wang, E. and Wang, J. (2011) Landscape, flux, correlation, resonance, coherence, stability, and key network wirings of stochastic circadian oscillation. Biophys. J., 101, 1335–1344
Li, C., Wang, E. and Wang, J. (2012) Landscape topography determines global stability and robustness of a metabolic network. ACS Synth Biol, 1, 229–239
Li, C. and Wang, J. (2013) Quantifying Waddington landscapes and paths of non-adiabatic cell fate decisions for differentiation, reprogramming and transdifferentiation. J. R. Soc. Interface, 10, 20130787
Li, C. and Wang, J. (2014) Landscape and flux reveal a new global view and physical quantification of mammalian cell cycle. Proc. Natl. Acad. Sci. USA, 111, 14130–14135
Li, C. and Wang, J. (2014) Quantifying the underlying landscape and paths of cancer. J. R. Soc. Interface, 11, 20140774
Wang, J., Zhang, K., Xu, L. and Wang, E. (2011) Quantifying the Waddington landscape and biological paths for development and differentiation. Proc. Natl. Acad. Sci. USA, 108, 8257–8262
Wu, W. and Wang, J. (2013) Landscape framework and global stability for stochastic reaction diffusion and general spatially extended systems with intrinsic fluctuations. J. Phys. Chem. B, 117, 12908–12934
Wu, W. and Wang, J. (2013) Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems. J. Chem. Phys., 139, 121920
Xu, L., Zhang, F., Zhang, K., Wang, E. and Wang, J. (2014) The potential and flux landscape theory of ecology. PLoS One, 9, e86746
Zhang F., Xu L., Zhang K., Wang E., Wang J., (2012) The potential and flux landscape theory of evolution. J. Chem. Phys., 137, 065102
Beard, D. A. D., Babson, E., Curtis, E. and Qian, H. (2004) Thermodynamic constraints for biochemical networks. J. Theor. Biol., 228, 327–333
Beard, D. A. and Qian H. (2008) Chemical Biophysics, Cambridge: Cambridge University Press
Qian, H. and Cooper, J. A. (2008) Temporal cooperativity and sensitivity amplification in biological signal transduction. Biochemistry, 47, 2211–2220
Qian, H. (2007) Phosphorylation energy hypothesis: open chemical systems and their biological functions. Annu. Rev. Phys. Chem., 58, 113–142
Qian, H. and Beard, D. A. (2005) Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. Biophys. Chem., 114, 213–220
Qian, H., Beard, D. A. and Liang, S. D. (2003) Stoichiometric network theory for nonequilibrium biochemical systems. Eur. J. Biochem., 270, 415–421
Ma, W., Trusina, A., El-Samad, H., Lim, W. A. and Tang, C. (2009) Defining network topologies that can achieve biochemical adaptation. Cell, 138, 760–773
Zhang, J., Yuan, Z., Li, H. X. and Zhou, T. (2010) Architecturedependent robustness and bistability in a class of genetic circuits. Biophys. J., 99, 1034–1042
Snoussi, E. H. (1998) Necessary Conditions for Multistationarity and Stable Periodicity. J. Biol. Syst., 06, 3–9
Gardner, T. S. and Faith, J. J. (2005) Reverse-engineering transcription control networks. Phys. Life Rev., 2, 65–88
Chickarmane, V., Troein, C., Nuber, U. A., Sauro, H. M. and Peterson, C. (2006) Transcriptional dynamics of the embryonic stem cell switch. PLoS Comput. Biol., 2, e123
Gillespie, D. T. (1976) A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions. J. Comput. Phys., 22, 403–434
Gillespie, D. T. (1977) Exact Stochastic Simulation of Coupled Chemical Reactions. J. Phys. Chem., 81, 2340–2361
Gillespie Markov Processes, D. T. An Introduction for Physical Scientists, Academic Press, 1991
Gillespie, D. T. (2007) Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem., 58, 35–55
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Xi, H., Turcotte, M. Parameter asymmetry and time-scale separation in core genetic commitment circuits. Quant Biol 3, 19–45 (2015). https://doi.org/10.1007/s40484-015-0042-1
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DOI: https://doi.org/10.1007/s40484-015-0042-1