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January  2012, 17(1): 271-282. doi: 10.3934/dcdsb.2012.17.271

A simple regulatory circuit that can simultaneously generate excitability of two different mechanisms

1. 

School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou 510275, China, China

2. 

Systems Engineering and Engineering Management, City University of Hong Kong, China

Received  April 2011 Revised  May 2011 Published  October 2011

Coupled positive and negative feedback loops occur in many cellular signaling systems. We show that a two-component circuit with this kind of network structure can simultaneously generate excitability of two different mechanisms that is similar to either integrator or resonator in neuroscience. Moreover, we find that there is an opposite tendency between switching frequencies in the two excitable mechanisms, and the duration and amplitude of the response spike are more resistant to noise in the integrate system than in the resonate system. In addition, we discuss, combining the Bacillis subtilis model organism, some possible biological implications of these differences.
Citation: Changhong Shi, Han-Xiong Li, Tianshou Zhou. A simple regulatory circuit that can simultaneously generate excitability of two different mechanisms. Discrete & Continuous Dynamical Systems - B, 2012, 17 (1) : 271-282. doi: 10.3934/dcdsb.2012.17.271
References:
[1]

U. Alon, M. G. Surette, N. Barkai and S. Leibler, Robustness in bacterial chemotaxis,, Nature, 397 (1999), 168.   Google Scholar

[2]

T. M. Yi, Y. Huang, M. I. Simon and J. Doyle, Robust perfect adaptation in bacterial chemotaxis through integral feedback control,, Proc. Natl. Acad. Sci. USA., 97 (2000), 4649.   Google Scholar

[3]

N. T. Ingolia, Topology and robustness in the drosophila segment polarity network,, PLoS Biol., 2 (2004).   Google Scholar

[4]

T. S. Gardner, C. R. Cantor and J. J. Collins, Construction of a genetic toggle switch in Escherichia coli,, Nature, 403 (2000), 339.   Google Scholar

[5]

V. Shahrezaei and P. S. Swain, Analytical distributions for stochastic gene expression,, Proc. Natl. Acad. Sci. USA, 105 (2008), 17256.   Google Scholar

[6]

G. M. Suel, J. Garcia-Ojalvo, L. M. Liberman and M. B. Elowitz, An excitable gene regulatory circuit induces transient cellular differentiation,, Nature, 440 (2006), 545.   Google Scholar

[7]

G. M. Suel, R. P. Kulkaryni, J. Dworkin, J. Garcia-Ojalvo and M. B. Elowitz, Tunability and noise dependence in differentiation dynamics,, Science, 315 (2007), 1716.   Google Scholar

[8]

T. Cagatay, M. Turcotte, M. B. Elowitz, J. Garcia-Ojalvo and G. M. Suel, Architecture-dependent noise discriminates functionally analogous differentiation circuits,, Cell, 139 (2009), 512.   Google Scholar

[9]

B. Lindner, J. Garcia-Ojalvo, A. Neiman and L. Schimansky-Geier, Effect of noise in excitable system,, Phys. Rep, 392 (2004), 321.   Google Scholar

[10]

J. W. Veening, W. K. Smits and O. P. Kuipers, Bistability, epigenetics, and bet-hedging in bacteria,, Annu. Rev. Microbiol, 4 (2008), 259.   Google Scholar

[11]

E. M. Izhikevich, Neural excitability, spiking, and bursting,, Int. J. Bifurcation Chaos, 10 (2000), 1171.   Google Scholar

[12]

T. Kalmar, C. Lim, P. Hayward, S. Munoz-Descalzo, J. Nichols, J. Garcia-Ojalvo and A. M. Arias, Regulated fluctuations in Nanog expression mediate cell fate decisions in Embryonic stem cells,, PLoS Biol, (2009).   Google Scholar

[13]

D. van Sinderen and G. Venema, comK acts as an autoregulatory control switch in the signal transduction route to competence in Bacillus subtilis,, J. Bacteriol, 176 (1994), 5762.   Google Scholar

[14]

J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations,, in, (1989), 135.   Google Scholar

[15]

E. Conrad, A. E. Mayo, A. J. Ninfa and D. B. Forger, Rate constants rather than biochemical mechanism determine behavior of genetic clocks,, J. R. Soc. Interface, 5 (2008).   Google Scholar

[16]

S. A. Oprisan and C. C. Canavier, The influence of limit cycle topology on the phase resetting curve,, Neural Comput., 14 (2002), 1027.   Google Scholar

[17]

R. Guantes and J. F. Poyatos, Dynamical principles of two-component genetic oscillators,, PLoS Comput. Biol., 2 (2006).   Google Scholar

[18]

H. Maamar, A. Raj and D. Dubnau, Noise in gene expression determines cell fate in Bacillus subtilis,, Science, 317 (2007), 526.   Google Scholar

[19]

D. Schultz, E. B. Jacob, J. N. Onuchic and P. G. Wolynes, Molecular level stochastic model for competence cycles in Bacillus subtilis,, PNAS, 1004 (2007), 17582.   Google Scholar

[20]

M. Leisner, K. Stingl, E. Frey and B. Maier, Stochastic switching to competence,, Curr. Opin. Microbiol, 11 (2008), 553.   Google Scholar

[21]

M. Leiser, J. T. Kuhr, J. O. Radler, E. Frey and B. Maier, Kinetics of genetic switching into the state of bacterial competence,, Biophys. J, 96 (2009), 1178.   Google Scholar

[22]

S. H. Dandach and M. Khammash, Analysis of stochastic strategies in bacterial competence: A master equation approach,, PLoS Comput. Biol., 6 (2010).   Google Scholar

[23]

J. Tsang and A. van Oudenaarden, Exciting fluctuations: Monitoring competence induction dynamics at the single-cell level,, Mol. Sys. Biol., (2006).   Google Scholar

[24]

M. A. Savageau, P. Coelho, R. A. Fasani, D. A. Tolla and A. Salvador, Phenotypes and tolerances in the design space of biochemical systems,, Proc. Natl. Acad. Sci. USA, 106 (2009), 6435.   Google Scholar

[25]

J. J. Zhang, Z. J. Yuan, H. X. Li and T. S. Zhou, Architecture-dependent robustness and bistability in a class of genetic circuits,, Biophys. J., 99 (2010), 1034.   Google Scholar

[26]

P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations,", Springer-Verlag, (1992).   Google Scholar

[27]

, http://indy.cs.concordia.ca/auto/., \url{http://indy.cs.concordia.ca/auto/}., ().   Google Scholar

[28]

N.Rosenfeld, J. W. Young, U. Alon, P. Swain and M. B. Elowitz, Genetic regulation at the single-cell level,, Science, 307 (2005), 1962.   Google Scholar

show all references

References:
[1]

U. Alon, M. G. Surette, N. Barkai and S. Leibler, Robustness in bacterial chemotaxis,, Nature, 397 (1999), 168.   Google Scholar

[2]

T. M. Yi, Y. Huang, M. I. Simon and J. Doyle, Robust perfect adaptation in bacterial chemotaxis through integral feedback control,, Proc. Natl. Acad. Sci. USA., 97 (2000), 4649.   Google Scholar

[3]

N. T. Ingolia, Topology and robustness in the drosophila segment polarity network,, PLoS Biol., 2 (2004).   Google Scholar

[4]

T. S. Gardner, C. R. Cantor and J. J. Collins, Construction of a genetic toggle switch in Escherichia coli,, Nature, 403 (2000), 339.   Google Scholar

[5]

V. Shahrezaei and P. S. Swain, Analytical distributions for stochastic gene expression,, Proc. Natl. Acad. Sci. USA, 105 (2008), 17256.   Google Scholar

[6]

G. M. Suel, J. Garcia-Ojalvo, L. M. Liberman and M. B. Elowitz, An excitable gene regulatory circuit induces transient cellular differentiation,, Nature, 440 (2006), 545.   Google Scholar

[7]

G. M. Suel, R. P. Kulkaryni, J. Dworkin, J. Garcia-Ojalvo and M. B. Elowitz, Tunability and noise dependence in differentiation dynamics,, Science, 315 (2007), 1716.   Google Scholar

[8]

T. Cagatay, M. Turcotte, M. B. Elowitz, J. Garcia-Ojalvo and G. M. Suel, Architecture-dependent noise discriminates functionally analogous differentiation circuits,, Cell, 139 (2009), 512.   Google Scholar

[9]

B. Lindner, J. Garcia-Ojalvo, A. Neiman and L. Schimansky-Geier, Effect of noise in excitable system,, Phys. Rep, 392 (2004), 321.   Google Scholar

[10]

J. W. Veening, W. K. Smits and O. P. Kuipers, Bistability, epigenetics, and bet-hedging in bacteria,, Annu. Rev. Microbiol, 4 (2008), 259.   Google Scholar

[11]

E. M. Izhikevich, Neural excitability, spiking, and bursting,, Int. J. Bifurcation Chaos, 10 (2000), 1171.   Google Scholar

[12]

T. Kalmar, C. Lim, P. Hayward, S. Munoz-Descalzo, J. Nichols, J. Garcia-Ojalvo and A. M. Arias, Regulated fluctuations in Nanog expression mediate cell fate decisions in Embryonic stem cells,, PLoS Biol, (2009).   Google Scholar

[13]

D. van Sinderen and G. Venema, comK acts as an autoregulatory control switch in the signal transduction route to competence in Bacillus subtilis,, J. Bacteriol, 176 (1994), 5762.   Google Scholar

[14]

J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations,, in, (1989), 135.   Google Scholar

[15]

E. Conrad, A. E. Mayo, A. J. Ninfa and D. B. Forger, Rate constants rather than biochemical mechanism determine behavior of genetic clocks,, J. R. Soc. Interface, 5 (2008).   Google Scholar

[16]

S. A. Oprisan and C. C. Canavier, The influence of limit cycle topology on the phase resetting curve,, Neural Comput., 14 (2002), 1027.   Google Scholar

[17]

R. Guantes and J. F. Poyatos, Dynamical principles of two-component genetic oscillators,, PLoS Comput. Biol., 2 (2006).   Google Scholar

[18]

H. Maamar, A. Raj and D. Dubnau, Noise in gene expression determines cell fate in Bacillus subtilis,, Science, 317 (2007), 526.   Google Scholar

[19]

D. Schultz, E. B. Jacob, J. N. Onuchic and P. G. Wolynes, Molecular level stochastic model for competence cycles in Bacillus subtilis,, PNAS, 1004 (2007), 17582.   Google Scholar

[20]

M. Leisner, K. Stingl, E. Frey and B. Maier, Stochastic switching to competence,, Curr. Opin. Microbiol, 11 (2008), 553.   Google Scholar

[21]

M. Leiser, J. T. Kuhr, J. O. Radler, E. Frey and B. Maier, Kinetics of genetic switching into the state of bacterial competence,, Biophys. J, 96 (2009), 1178.   Google Scholar

[22]

S. H. Dandach and M. Khammash, Analysis of stochastic strategies in bacterial competence: A master equation approach,, PLoS Comput. Biol., 6 (2010).   Google Scholar

[23]

J. Tsang and A. van Oudenaarden, Exciting fluctuations: Monitoring competence induction dynamics at the single-cell level,, Mol. Sys. Biol., (2006).   Google Scholar

[24]

M. A. Savageau, P. Coelho, R. A. Fasani, D. A. Tolla and A. Salvador, Phenotypes and tolerances in the design space of biochemical systems,, Proc. Natl. Acad. Sci. USA, 106 (2009), 6435.   Google Scholar

[25]

J. J. Zhang, Z. J. Yuan, H. X. Li and T. S. Zhou, Architecture-dependent robustness and bistability in a class of genetic circuits,, Biophys. J., 99 (2010), 1034.   Google Scholar

[26]

P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations,", Springer-Verlag, (1992).   Google Scholar

[27]

, http://indy.cs.concordia.ca/auto/., \url{http://indy.cs.concordia.ca/auto/}., ().   Google Scholar

[28]

N.Rosenfeld, J. W. Young, U. Alon, P. Swain and M. B. Elowitz, Genetic regulation at the single-cell level,, Science, 307 (2005), 1962.   Google Scholar

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