Optimal System Size for Mesoscopic Chemical Oscillation

Abstract

Size does matter: Stochastic simulations and chemical Langevin equations were used to investigate the effects of system size on the oscillatory behavior of the Brusselator model. In the region close to the deterministic oscillatory dynamics, stochastic oscillations are observed. Interestingly, an optimal system size exists for such stochastic oscillations, characterized by a clear maximum in the signal‐to‐noise ratio (SNR) as a function of system size V (see picture). This result may have interesting implications for biological rhythms and signaling processes.

System‐Size Biresonance for Intracellular Calcium Signaling

“…In our previous study, we have shown that it is convenient to use the CLE to study the effect of the internal noise caused by the small system size. [12] According to Gillespie, the CLE for the current model reads [Equations (2)]:…”

“…[9±11] In recent studies, using the Brusselator model, we have shown that the internal noise can induce stochastic oscillations in the region close to the deterministic oscillatory dynamics, and an optimal system size exists for such stochastic oscillations; this is characterized by a clear maximum in the signal-to-noise ratio (SNR) as a function of system size V. [12] Similar results were also obtained in a circadian-clock system, [13] which may have interesting implications for biological rhythms and signaling processes.…”

Double‐System‐Size Resonance for Spiking Activity of Coupled Hodgkin–Huxley Neurons

“…[4] On the other hand, for oscillating chemical reactions taking place in small-scale systems, stochastic oscillations can be observed and there is an optimal system size at which such stochastic oscillations show the best performance. [6][7][8][9][10][11][12] In such small systems, the numbers of the reactant molecules are often low and the internal noise resulting from the stochastic reaction events must be considered. It was reported that ionchannel clusters of optimal sizes can enhance the encoding of a subthreshold stimulus, [6][7] and optimal intracellular calcium signaling appears at a certain size or distribution of the ionchannel clusters.…”

Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator

“…As noted, coherence resonance (CR) has been studied earlier with intrinsic noise using exact stochastic simulations [31][32][33][34]. In this sub-section, we revisit this phenomenon to test a semi-analytical formula for normalised variance V N recently proposed [30].…”

“…The phenomenon of coherence resonance (CR) [26][27][28][29][30], where there is no input sub-threshold signal, has been studied earlier using Gillespie and CLE method [20][21][22][31][32][33][34]. To our knowledge, demonstration of PSR and ASR in a chemical system with Hopf bifurcation using exact CME approach is not well known; although this has been studied for bistable nonlinear chemical systems [35,36].…”