Amplified Biochemical Oscillations in Cellular Systems

McKane, Alan J.; Nagy, John D.; Newman, T. J.; Stefanini, Marianne O.

doi:10.1007/s10955-006-9221-9

Cited by 101 publications

(139 citation statements)

References 26 publications

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“…For example, we have begun simulating the Ras-Raf-MEK-ERK signal transduction pathway 30,31 and have plans to begin modeling generalized genetic regulation networks as in ref 12 and studies of starvation responses. 32 In each of these examples the system size is best described at the mesoscale, where limited numbers of molecules, and hence their fluctuations, should play a major role in the pathway's functionality.…”

Section: Resultsmentioning

confidence: 99%

Dynamic Simulations of Single-Molecule Enzyme Networks

et al. 2009

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Along with the growth of technologies allowing accurate visualization of biochemical reactions to the scale of individual molecules has arisen an appreciation of the role of statistical fluctuations in intracellular biochemistry. The stochastic nature of metabolism can no longer be ignored. It can be probed empirically, and theoretical studies have established its importance. Traditional methods for modeling stochastic biochemistry are derived from an elegant and physically satisfying theory developed by Gillespie. However, although Gillespie's algorithm and its derivatives efficiently model small-scale systems, complex networks are harder to manage on easily available computer systems. Here we present a novel method of simulating stochastic biochemical networks using discrete events simulation techniques borrowed from manufacturing production systems. The method is very general and can be mapped to an arbitrarily complex network. As an illustration, we apply the technique to the glucose phosphorylation steps of the Embden-Meyerhof-Parnas pathway in E. coli. We show that a deterministic version of the discrete event simulation reproduces the behavior of an analogous deterministic differential equation model. The stochastic version of the same model predicts that catastrophic bottlenecks in the system are more likely than one would expect from deterministic theory.

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Section: Resultsmentioning

confidence: 99%

Dynamic Simulations of Single-Molecule Enzyme Networks

et al. 2009

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“…The time evolution of the probability, P n (t), of finding the system in state n at time t is then governed by the master equation This procedure is well-established and has been applied to a number of microscopic interacting particle systems, so that we do not describe the mathematical details here, but instead refer to [13,23]. The main idea is to expand realizations n(t) of the microscopic dynamics about a deterministic trajectory, x(t),…”

Section: Analytical Description and System-size Expansionmentioning

confidence: 99%

“…Equations (6) are then recovered by setting x(t) = n(t) /N . At next-to-leading order the van Kampen expansion gives a linear Langevin equation for the fluctuations, ξ(t), about the deterministic trajectory which has the general form [13,23] …”

Section: Analytical Description and System-size Expansionmentioning

confidence: 99%

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Limit cycles, complex Floquet multipliers, and intrinsic noise

2009

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We study the effects of intrinsic noise on chemical reaction systems, which in the deterministic limit approach a limit cycle in an oscillatory manner. Previous studies of systems with an oscillatory approach to a fixed point have shown that the noise can transform the oscillatory decay into sustained coherent oscillations with a large amplitude. We show that a similar effect occurs when the stable attractors are limit cycles. We compute the correlation functions and spectral properties of the fluctuations in suitably co-moving Frenet frames for several model systems including driven and coupled Brusselators, and the Willamowski-Rössler system. Analytical results are confirmed convincingly in numerical simulations. The effect is quite general, and occurs whenever the Floquet multipliers governing the stability of the limit cycle are complex, with the amplitude of the oscillations increasing as the instability boundary is approached.

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“…Intrinsic noise is taken into account by chemical master equations (CMEs), which are exact mesoscopic descriptions of well-stirred and thermally equilibrated gas-phase chemical systems 11 and chemical reactions occurring in well-stirred dilute solutions 12 . Unfortunately, CMEs are generally analytically intractable, and many studies have therefore resorted to the linear-noise approximation (LNA) of the CME (see, for example, refs [13][14][15][16][17][18][19].…”

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confidence: 99%

Discreteness-induced concentration inversion in mesoscopic chemical systems

et al. 2012

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molecular discreteness is apparent in small-volume chemical systems, such as biological cells, leading to stochastic kinetics. Here we present a theoretical framework to understand the effects of discreteness on the steady state of a monostable chemical reaction network. We consider independent realizations of the same chemical system in compartments of different volumes. Rate equations ignore molecular discreteness and predict the same average steadystate concentrations in all compartments. However, our theory predicts that the average steady state of the system varies with volume: if a species is more abundant than another for large volumes, then the reverse occurs for volumes below a critical value, leading to a concentration inversion effect. The addition of extrinsic noise increases the size of the critical volume. We theoretically predict the critical volumes and verify, by exact stochastic simulations, that rate equations are qualitatively incorrect in sub-critical volumes.

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Amplified Biochemical Oscillations in Cellular Systems

Cited by 101 publications

References 26 publications

Dynamic Simulations of Single-Molecule Enzyme Networks

Dynamic Simulations of Single-Molecule Enzyme Networks

Limit cycles, complex Floquet multipliers, and intrinsic noise

Discreteness-induced concentration inversion in mesoscopic chemical systems

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