Parameter asymmetry and time-scale separation in core genetic commitment circuits

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.

[1]  Jin Wang,et al.  Quantifying the Waddington landscape and biological paths for development and differentiation , 2011, Proceedings of the National Academy of Sciences.

[2]  H. Qian,et al.  Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. , 2005, Biophysical chemistry.

[3]  El Houssine Snoussi.  Necessary Conditions for Multistationarity and Stable Periodicity , 1998 .

[4]  Hong Qian,et al.  Phosphorylation energy hypothesis: open chemical systems and their biological functions. , 2007, Annual review of physical chemistry.

[5]  Gürol M. Süel,et al.  An excitable gene regulatory circuit induces transient cellular differentiation , 2006, Nature.

[6]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[7]  Chunhe Li,et al.  Landscape and flux reveal a new global view and physical quantification of mammalian cell cycle , 2014, Proceedings of the National Academy of Sciences.

[8]  Wei Wu,et al.  Landscape framework and global stability for stochastic reaction diffusion and general spatially extended systems with intrinsic fluctuations. , 2013, The journal of physical chemistry. B.

[9]  Erkang Wang,et al.  Landscape topography determines global stability and robustness of a metabolic network. , 2012, ACS synthetic biology.

[10]  M. Thattai,et al.  Stochastic Gene Expression in Fluctuating Environments , 2004, Genetics.

[11]  H. Qian,et al.  Thermodynamic constraints for biochemical networks. , 2004, Journal of theoretical biology.

[12]  D. Gillespie.  A General Method for Numerically Simulating the Stochastic Time Evolution of Coupled Chemical Reactions , 1976 .

[13]  Carsten Peterson,et al.  Transcriptional Dynamics of the Embryonic Stem Cell Switch , 2006, PLoS Comput. Biol..

[14]  Erkang Wang,et al.  Landscape and flux decomposition for exploring global natures of non-equilibrium dynamical systems under intrinsic statistical fluctuations , 2011 .

[15]  Gürol M. Süel,et al.  A genetic timer through noise-induced stabilization of an unstable state , 2008, Proceedings of the National Academy of Sciences.

[16]  Daniel T Gillespie,et al.  Stochastic simulation of chemical kinetics. , 2007, Annual review of physical chemistry.

[17]  Rajan P Kulkarni,et al.  Tunability and Noise Dependence in Differentiation Dynamics , 2007, Science.

[18]  Erkang Wang,et al.  The Potential and Flux Landscape Theory of Ecology , 2014, PloS one.

[19]  W. Lim,et al.  Defining Network Topologies that Can Achieve Biochemical Adaptation , 2009, Cell.

[20]  N. Monk,et al.  Bioattractors: dynamical systems theory and the evolution of regulatory processes , 2014, The Journal of physiology.

[21]  F. Zhang,et al.  The potential and flux landscape theory of evolution. , 2012, The Journal of chemical physics.

[22]  Han-Xiong Li,et al.  Architecture-dependent robustness and bistability in a class of genetic circuits. , 2010, Biophysical journal.

[23]  Timothy S Gardner,et al.  Reverse-engineering transcription control networks. , 2005, Physics of life reviews.

[24]  Michael B. Elowitz,et al.  Architecture-Dependent Noise Discriminates Functionally Analogous Differentiation Circuits , 2009, Cell.

[25]  Wei Wu,et al.  Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems. , 2013, The Journal of chemical physics.

[26]  L. Duan,et al.  Point-cycle bistability and stochasticity in a regulatory circuit for Bacillus subtilis competence. , 2013, Mathematical biosciences.

[27]  Jin Wang,et al.  Quantifying Waddington landscapes and paths of non-adiabatic cell fate decisions for differentiation, reprogramming and transdifferentiation , 2013, Journal of The Royal Society Interface.

[28]  J. Ferrell.  Bistability, Bifurcations, and Waddington's Epigenetic Landscape , 2012, Current Biology.

[29]  Hong Qian,et al.  Temporal cooperativity and sensitivity amplification in biological signal transduction. , 2008, Biochemistry.

[30]  P. Swain,et al.  Stochastic Gene Expression in a Single Cell , 2002, Science.

[31]  Zhuoqin Yang,et al.  Subtle interplay of stochasticity and deterministic dynamics pervades an evolutionary plausible genetic circuit for Bacillus subtilis competence. , 2013, Mathematical biosciences.

[32]  H. Qian,et al.  Stoichiometric network theory for nonequilibrium biochemical systems. , 2003, European journal of biochemistry.

[33]  Jin Wang,et al.  Quantifying the underlying landscape and paths of cancer , 2014, Journal of The Royal Society Interface.

[34]  S. Counce.  The Strategy of the Genes , 1958, The Yale Journal of Biology and Medicine.

[35]  Landscape, flux, correlation, resonance, coherence, stability, and key network wirings of stochastic circadian oscillation. , 2011, Biophysical journal.

[36]  Steven H. Strogatz,et al.  Nonlinear Dynamics and Chaos , 2024 .