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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

Changhong Shi 1, , Han-Xiong Li 2, and  Tianshou Zhou 1,

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.
Keywords: resonator., feedback, Excitability, integrator.
Mathematics Subject Classification: Primary: 92B05; Secondary: 93E0.
Citation: Changhong Shi, Han-Xiong Li, Tianshou Zhou. A simple regulatory circuit that can simultaneously generate excitability of two different mechanisms. Discrete and 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), 168-171.

[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), 4649-4653.

[3]

N. T. Ingolia, Topology and robustness in the drosophila segment polarity network, PLoS Biol., 2 (2004), e123.

[4]

T. S. Gardner, C. R. Cantor and J. J. Collins, Construction of a genetic toggle switch in Escherichia coli, Nature, 403 (2000), 339-342.

[5]

V. Shahrezaei and P. S. Swain, Analytical distributions for stochastic gene expression, Proc. Natl. Acad. Sci. USA, 105 (2008), 17256-17261.

[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), 545-550.

[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), 1716-1719.

[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), 512-522.

[9]

B. Lindner, J. Garcia-Ojalvo, A. Neiman and L. Schimansky-Geier, Effect of noise in excitable system, Phys. Rep, 392 (2004), 321-424.

[10]

J. W. Veening, W. K. Smits and O. P. Kuipers, Bistability, epigenetics, and bet-hedging in bacteria, Annu. Rev. Microbiol, 4 (2008), 259-271.

[11]

E. M. Izhikevich, Neural excitability, spiking, and bursting, Int. J. Bifurcation Chaos, Appl. Sci. Eng., 10 (2000), 1171-1266.

[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), 7e1000149.

[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), 5762-5770.

[14]

J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations, in "Methods in Neuronal Modeling: From Synapses to Networks" (eds C. Koch and I. Segev), MIT Press, Cambridge, MA, (1989), 135-169.

[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), S9-S15.

[16]

S. A. Oprisan and C. C. Canavier, The influence of limit cycle topology on the phase resetting curve, Neural Comput., 14 (2002), 1027-1057.

[17]

R. Guantes and J. F. Poyatos, Dynamical principles of two-component genetic oscillators, PLoS Comput. Biol., 2 (2006), e30.

[18]

H. Maamar, A. Raj and D. Dubnau, Noise in gene expression determines cell fate in Bacillus subtilis, Science, 317 (2007), 526-529.

[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), 17582-17587.

[20]

M. Leisner, K. Stingl, E. Frey and B. Maier, Stochastic switching to competence, Curr. Opin. Microbiol, 11 (2008), 553-559.

[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), 1178-1188.

[22]

S. H. Dandach and M. Khammash, Analysis of stochastic strategies in bacterial competence: A master equation approach, PLoS Comput. Biol., 6 (2010), 6e1000985.

[23]

J. Tsang and A. van Oudenaarden, Exciting fluctuations: Monitoring competence induction dynamics at the single-cell level, Mol. Sys. Biol., (2006), msb4100064-E1.

[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), 6435-6440.

[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), 1034-1042.

[26]

P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations," Springer-Verlag, Berlin, 1992.

[27]

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

[28]

N.Rosenfeld, J. W. Young, U. Alon, P. Swain and M. B. Elowitz, Genetic regulation at the single-cell level, Science, 307 (2005), 1962-1965.

show all references

References:
[1]

U. Alon, M. G. Surette, N. Barkai and S. Leibler, Robustness in bacterial chemotaxis, Nature, 397 (1999), 168-171.

[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), 4649-4653.

[3]

N. T. Ingolia, Topology and robustness in the drosophila segment polarity network, PLoS Biol., 2 (2004), e123.

[4]

T. S. Gardner, C. R. Cantor and J. J. Collins, Construction of a genetic toggle switch in Escherichia coli, Nature, 403 (2000), 339-342.

[5]

V. Shahrezaei and P. S. Swain, Analytical distributions for stochastic gene expression, Proc. Natl. Acad. Sci. USA, 105 (2008), 17256-17261.

[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), 545-550.

[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), 1716-1719.

[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), 512-522.

[9]

B. Lindner, J. Garcia-Ojalvo, A. Neiman and L. Schimansky-Geier, Effect of noise in excitable system, Phys. Rep, 392 (2004), 321-424.

[10]

J. W. Veening, W. K. Smits and O. P. Kuipers, Bistability, epigenetics, and bet-hedging in bacteria, Annu. Rev. Microbiol, 4 (2008), 259-271.

[11]

E. M. Izhikevich, Neural excitability, spiking, and bursting, Int. J. Bifurcation Chaos, Appl. Sci. Eng., 10 (2000), 1171-1266.

[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), 7e1000149.

[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), 5762-5770.

[14]

J. Rinzel and G. B. Ermentrout, Analysis of neural excitability and oscillations, in "Methods in Neuronal Modeling: From Synapses to Networks" (eds C. Koch and I. Segev), MIT Press, Cambridge, MA, (1989), 135-169.

[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), S9-S15.

[16]

S. A. Oprisan and C. C. Canavier, The influence of limit cycle topology on the phase resetting curve, Neural Comput., 14 (2002), 1027-1057.

[17]

R. Guantes and J. F. Poyatos, Dynamical principles of two-component genetic oscillators, PLoS Comput. Biol., 2 (2006), e30.

[18]

H. Maamar, A. Raj and D. Dubnau, Noise in gene expression determines cell fate in Bacillus subtilis, Science, 317 (2007), 526-529.

[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), 17582-17587.

[20]

M. Leisner, K. Stingl, E. Frey and B. Maier, Stochastic switching to competence, Curr. Opin. Microbiol, 11 (2008), 553-559.

[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), 1178-1188.

[22]

S. H. Dandach and M. Khammash, Analysis of stochastic strategies in bacterial competence: A master equation approach, PLoS Comput. Biol., 6 (2010), 6e1000985.

[23]

J. Tsang and A. van Oudenaarden, Exciting fluctuations: Monitoring competence induction dynamics at the single-cell level, Mol. Sys. Biol., (2006), msb4100064-E1.

[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), 6435-6440.

[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), 1034-1042.

[26]

P. E. Kloeden and E. Platen, "Numerical Solution of Stochastic Differential Equations," Springer-Verlag, Berlin, 1992.

[27]

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

[28]

N.Rosenfeld, J. W. Young, U. Alon, P. Swain and M. B. Elowitz, Genetic regulation at the single-cell level, Science, 307 (2005), 1962-1965.

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