The effect of interactive noise on the driven Brusselator model

Feed rate noise modulates autocatalysis and shapes the oscillations of the Belousov–Zhabotinsky reaction in a continuous stirred tank reactor

Noise applied to a specific reactant feed rate directs the Belousov–Zhabotinsky reaction into specific pathways and results in noise-controlled oscillation shapes and features.

Regularity of beating of small clusters of embryonic chick ventricular heart-cells: experiment vs. stochastic single-channel population model

The transmembrane potential is recorded from small isopotential clusters of 2-4 embryonic chick ventricular cells spontaneously generating action potentials. We analyze the cycle-to-cycle fluctuations in the time between successive action potentials (the interbeat interval or IBI). We also convert an existing model of electrical activity in the cluster, which is formulated as a Hodgkin-Huxley-like deterministic system of nonlinear ordinary differential equations describing five individual ionic currents, into a stochastic model consisting of a population of ∼20 000 independently and randomly gating ionic channels, with the randomness being set by a real physical stochastic process (radio static). This stochastic model, implemented using the Clay-DeFelice algorithm, reproduces the fluctuations seen experimentally: e.g., the coefficient of variation (standard deviation/mean) of IBI is 4.3% in the model vs. the 3.9% average value of the 17 clusters studied. The model also replicates all but one of several other quantitative measures of the experimental results, including the power spectrum and correlation integral of the voltage, as well as the histogram, Poincaré plot, serial correlation coefficients, power spectrum, detrended fluctuation analysis, approximate entropy, and sample entropy of IBI. The channel noise from one particular ionic current (I_Ks), which has channel kinetics that are relatively slow compared to that of the other currents, makes the major contribution to the fluctuations in IBI. Reproduction of the experimental coefficient of variation of IBI by adding a Gaussian white noise-current into the deterministic model necessitates using an unrealistically high noise-current amplitude. Indeed, a major implication of the modelling results is that, given the wide range of time-scales over which the various species of channels open and close, only a cell-specific stochastic model that is formulated taking into consideration the widely different ranges in the frequency content of the channel-noise produced by the opening and closing of several different types of channels will be able to reproduce precisely the various effects due to membrane noise seen in a particular electrophysiological preparation.

DEPENDENCE OF FLUX DISTRIBUTION AND SYSTEM COORDINATION ON DYNAMICAL STATES FOR BIOCHEMICAL SYSTEMS WITH MULTIPLE COEXISTING STATES

Flux distribution and system coordination in branched biochemical systems with a source producing multiple coexisting states have been studied both theoretically and numerically. For such systems, flux distribution depends sensitively on the dynamical states and the parameter values of enzymatic kinetics at branching point. Various dynamical states including noise-induced new states can be located by superimposing noisy fluctuations on a branched biochemical system with multiple coexisting states. Once noise induces transitions or new dynamical states, the flux through a specific branch may increase, maintain or decrease, depending on parameter values of enzymatic kinetics at branching point. Furthermore, system coordination can be destroyed by noise-induced dynamical changes. When at least one state cannot be coordinated in the absence of noise, noise-induced transitions may destroy system coordination. When all coexisting states are coordinated in the absence of noise, noise-induced new states may be still able to destroy system coordination. It is revealed that destruction of system coordination is due to the interaction of enzyme saturation and noise-induced dynamical changes. Finally, control of flux distribution and maintenance of system coordination for biochemical systems with multiple coexisting states are discussed.

Transitions and new dynamical states induced by noise in a multiply regulated biochemical system

Noise-induced transitions between coexisting states, and the emergence of a new oscillatory state, are examined in a model for a multiply regulated biochemical system. For the undisturbed system, three oscillatory states, I, II, and III, coexist. It is found that noise above a critical amplitude can cause a transition between states III and II and between states III or II and state I, whereas a transition from state I to either states II or III is never observed. This indicates that the relative stability under noise perturbations is greatest for state I, and progressively less for states II and III. In addition to this transition behaviour, a purely noise-induced state is found. Under noise perturbations, the average concentration of metabolites may depend on both the time duration and amplitude of the superimposed noise. The implications of these results for understanding the in vivo behaviour of complex biochemical systems are discussed.