Hybrid stochastic simulations of intracellular reaction–diffusion systems

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction–diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction–diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.     

Developing Itô stochastic differential equation models for neuronal signal transduction pathways

Mathematical modeling and simulation of dynamic biochemical systems are receiving considerable attention due to the increasing availability of experimental knowledge of complex intracellular functions. In addition to deterministic approaches, several stochastic approaches have been developed for simulating the time-series behavior of biochemical systems. The problem with stochastic approaches, however, is the larger computational time compared to deterministic approaches. It is therefore necessary to study alternative ways to incorporate stochasticity and to seek approaches that reduce the computational time needed for simulations, yet preserve the characteristic behavior of the system in question. In this work, we develop a computational framework based on the It? stochastic differential equations for neuronal signal transduction networks. There are several different ways to incorporate stochasticity into deterministic differential equation models and to obtain It? stochastic differential equations. Two of the developed models are found most suitable for stochastic modeling of neuronal signal transduction. The best models give stable responses which means that the variances of the responses with time are not increasing and negative concentrations are avoided. We also make a comparative analysis of different kinds of stochastic approaches, that is the It? stochastic differential equations, the chemical Langevin equation, and the Gillespie stochastic simulation algorithm. Different kinds of stochastic approaches can be used to produce similar responses for the neuronal protein kinase C signal transduction pathway. The fine details of the responses vary slightly, depending on the approach and the parameter values. However, when simulating great numbers of chemical species, the Gillespie algorithm is computationally several orders of magnitude slower than the It? stochastic differential equations and the chemical Langevin equation. Furthermore, the chemical Langevin equation produces negative concentrations. The It? stochastic differential equations developed in this work are shown to overcome the problem of obtaining negative values.     

Simulation of noise characteristic effects on stochastic resonance in Belousov-Zhabotinsky flow reaction

A three-variable model, which was proposed to account for the stochastic resonance (SR) in Belousov-Zhabotinsky (B-Z) reaction in a continuous-flow stirred-tank reactor, is investigated when the control parameter kr, the flow rate, is modulated by noise near supercritical Hopf bifurcation point. Using the computer simulation, noise-induced oscillations are observed, and the signal-to-noise ratio (SNR) goes through a maximum with the increment of noise intensity, which means occurrence of stochastic resonance. in addition, we have also investigated the effects of correlation time of colored noise and the duration time of white noise on the system's dynamics.     

Survey of exact N-body decompositions of stochastic scalar-Jastrow–Hartree form

The quantum N-body dynamics problem with pairwise interactions can be exactly decomposed into the average of N stochastically evolving 1-body problems, thereby eliminating the usual exponential scaling of computational costs. Unfortunately, the variance in such averages can be large leading to slow Monte Carlo convergence. In addition, norm preserving decompositions are available only for identical fermions or bosons. Here we introduce a family of decompositions of scalar-Jastrow–Hartree form which can be applied to electronic structure and many molecular dynamics problems. We also discuss their convergence properties and test a few such methods on the vibrational stretching mode dynamics of CH₄. Finally, we explain how the Monte Carlo convergence problem can be completely eliminated via the introduction of a perfect control variate.     

Evaluation of stochastic global optimization methods for modeling vapor–liquid equilibrium data

Parameter estimation for vapor–liquid equilibrium (VLE) data modeling plays an important role in design, optimization and control of separation units. This optimization problem is very challenging due to the high non-linearity of thermodynamic models. Recently, several stochastic optimization methods such as Differential Evolution with Tabu List (DETL) and Particle Swarm Optimization (PSO) have evolved as alternative and reliable strategies for solving global optimization problems including parameter estimation in thermodynamic models. However, these methods have not been applied and compared with respect to other stochastic strategies such as Simulated Annealing (SA), Differential Evolution (DE) and Genetic Algorithm (GA) in the context of parameter estimation for VLE data modeling. Therefore, in this study several stochastic optimization methods are applied to solve parameter estimation problems for VLE modeling using both the classical least squares and maximum likelihood approaches. Specifically, we have tested and compared the reliability and efficiency of SA, GA, DE, DETL and PSO for modeling several binary VLE data using local composition models. These methods were also tested on benchmark problems for global optimization. Our results show that the effectiveness of these stochastic methods varies significantly between the different tested problems and also depends on the stopping criterion especially for SA, GA and PSO. Overall, DE and DETL have better performance for solving the parameter estimation problems in VLE data modeling.     

Canard explosion and internal signal stochastic bi-resonance in the CO oxidation on platinum surface

Canard explosion means a dramatic change fromsmall amplitude quasi-harmonic oscillation to largeamplitude relaxation oscillation, accompanied by anexponential increase of period, of a limit cycle withina very narrow interval of a control parameter. Thisphenomenon was first found in the Van Der Pol equa-tions[1], and later has been found also in chemical[2]and biological[3] systems. Generally speaking, it is theresult of multi-time scales in the system, and can bedealt with singular perturbati…     

Two-parameter stochastic resonance in a model of electrochemical oxidation of formic acid on Pt

Stochastic resonance (SR) is shown in a two-parameter system, a model of electrochemical oxidation of formic acid on Pt. The driving current and the saturation coverage for carbon monoxide are two control parameters in this model. Modulation of an excitable focal stable state close to a Hopf bifurcation by a weak periodic signal in one parameter and noise in the other parameter is found to give rise to SR. The results indicate that the noise can enlarge a weak periodic signal and lead the system to be ordered. The scenario and novel aspects of SR in this system are discussed.     

Non-Markovian stochastic Schrödinger equations in different temperature regimes: a study of the spin-boson model

Stochastic Schrodinger equations are used to describe the dynamics of a quantum open system in contact with a large environment, as an alternative to the commonly used master equations. We present a study of the two main types of non-Markovian stochastic Schrodinger equations, linear and nonlinear ones. We compare them both analytically and numerically, the latter for the case of a spin-boson model. We show in this paper that two linear stochastic Schrodinger equations, derived from different perspectives by Diosi, Gisin, and Strunz [Phys. Rev. A 58, 1699 (1998)], and Gaspard and Nagaoka [J. Chem. Phys. 13, 5676 (1999)], respectively, are equivalent in the relevant order of perturbation theory. Nonlinear stochastic Schrodinger equations are in principle more efficient than linear ones, as they determine solutions with a higher weight in the ensemble average which recovers the reduced density matrix of the quantum open system. However, it will be shown in this paper that for the case of a spin-boson system and weak coupling, this improvement does only occur in the case of a bath at high temperature. For low temperatures, the sampling of realizations of the nonlinear equation is practically equivalent to the sampling of the linear ones. We study further this result by analyzing, for both temperature regimes, the driving noise of the linear equations in comparison to that of the nonlinear equations.     

Non-motional narrowing effect in excitation profiles of second-order optical processes: Comparison between stochastic theory and experiments in β-carotene

Excitation spectra measured for the Raman scattering and luminescence of β-carotene in isopentane are compared with a stochastic theory of the second-order optical processes in which the non-motional narrowing effect is taken into account. The agreement between the theory and experiment is satisfactory. Analysis of these spectra gives detailed information on the intermediate-state interaction in β-carotene.