Abstract
We describe a mechanism for pronounced biochemical oscillations, relevant to microscopic systems, such as the intracellular environment. This mechanism operates for reaction schemes which, when modeled using deterministic rate equations, fail to exhibit oscillations for any values of rate constants. The mechanism relies on amplification of the underlying stochasticity of reaction kinetics within a narrow window of frequencies. This amplification means that fluctuations have a dominant effect, even though the number of molecules in the system is relatively large. The mechanism is quantitatively studied within simple models of self-regulatory gene expression, and glycolytic oscillations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Hess and A. Boiteux, Ann. Rev. Biochem. 40:237 (1971).
A. Goldbeter and S. R. Caplan, Ann Rev. Biophys. Bioeng. 5:449 (1976).
A. Goldbeter, Biochemical Oscillations and Cellular Rhythms (Cambridge University Press, 1996).
J. J. Tyson, in Computational Cell Biology, C. P. Fall, E. S. Marland, J. M. Wagner, J. J. Tyson, Eds. (Springer-Verlag, 2002) Ch. 9.
P. L. Lakin-Thomas and S. Brody, Ann. Rev. Microbiol. 58:489 (2004).
M. Nakajima, et al., Science 308:414 (2005).
P. Smolen, J. Theor. Biol. 174:137 (1995).
J. Keener and J. Sneyde, Mathematical Physiology (Springer-Verlag, 1998).
L. Meinhold and L. Schimansky-Geier, Phys. Rev. E 66:050901(R) (2002).
Z. Hou and H. Xin, J. Chem. Phys. 119:11508 (2003).
M. Falcke, Biophys. J. 84:42 (2003).
M. Falcke, Adv. Phys. 53:255 (2004).
H. Li, Z. Hou and H. Xin, Phys. Rev. E 71:061916 (2005).
U. Kummer, et al., Biophys. J. 89:1603 (2005).
M. S. Bartlett, J. Roy. Stat. Soc. A 120:37 (1957).
R. M. Nisbet and W. S. C. Gurney, Modelling Fluctuating Populations (Wiley, New York, 1982).
N. G. Van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1981).
A. J. McKane and T. J. Newman, Phys. Rev. E 70:041902 (2004).
A. J. McKane and T. J. Newman, Phys. Rev. Lett. 94:218102 (2005).
G. Kurosawa, A. Mochizuki and Y. Iwasa, J. Theor. Biol. 216:193 (2002).
D. T. Gillespie, J. Comp. Phys. 22:403 (1976).
E. Renshaw, Modelling biological populations in space and time (Cambridge University Press, Cambridge, 1991).
S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison Wesley, 1994).
E. E. Sel’kov, Eur. J. Biochem. 4:79 (1968).
G. von Dassow, E. Meir, E. M. Munro and G. M. Odell, Nature 406:188 (2000).
H. Goldstein, Classical Mechanics (Addison Wesley, Reading, MA, ed. 2, 1980).
D. Bell-Pedersen, et al., Nature Rev. Genetics 6:544 (2005).
M. Akashi and T. Takumi, Nature Struct. Biol. 12:441 (2005).
B. Alberts, et al., Molecular Biology of the Cell (Garland Publishing, New York, ed. 4, 2002).
M. F. Madsen, S. Dano and P. G. Sorensen, FEBS J. 272:2648 (2005).
B. Teusink, et al., Eur. J. Biochem. 267:1 (2000).
J. B. Hansen and C. M. Veneziale, J. Lab. Clin. Med. 95:133 (1980).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
McKane, A.J., Nagy, J.D., Newman, T.J. et al. Amplified Biochemical Oscillations in Cellular Systems. J Stat Phys 128, 165–191 (2007). https://doi.org/10.1007/s10955-006-9221-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10955-006-9221-9