Deterministic dynamic models with delayed feedback and state constraints arise in a variety of applications in science and engineering. There is interest in understanding what effect noise has on the behavior of such models. Here we consider a multidimensional stochastic delay differential equation with normal reflection as a noisy analogue of a deterministic system with delayed feedback and po...

We consider biochemical reaction chains and investigate how random external fluctuations, as characterised by variance and coefficient of variation, propagate down the chains. We perform such a study under the assumption that the number of molecules is high enough so that the behaviour of the concentrations of the system is well approximated by differential equations. We conclude that the varia...

In this article, Perturbation Method (PM) is employed to obtain a handy approximate solution to the steady state nonlinear reaction diffusion equation containing a nonlinear term related to Michaelis-Menten of the enzymatic reaction. Comparing graphics between the approximate and exact solutions, it will be shown that the PM method is quite efficient.

Time series data can now be routinely collected for biochemical reaction pathways, and recently, several methods have been proposed to infer reaction mechanisms for metabolic pathways and networks. In this paper we provide a survey of mathematical techniques for determining reaction mechanisms for time series data on the concentration or abundance of different reacting components, with little p...

We propose a general method for simplifying master equations by eliminating from the description rapidly evolving states. The physical recipe we impose is the suppression of these states and a renormalization of the rates of all the surviving states. In some cases, this decimation procedure can be analytically carried out and is consistent with other analytical approaches, such as in the proble...

The Michaelis-Menten equation has played a central role in our understanding of biochemical processes. It has long been understood how this equation approximates the dynamics of irreversible enzymatic reactions. However, a similar approximation in the case of networks, where the product of one reaction can act as an enzyme in another, has not been fully developed. Here we rigorously derive such...

This paper summarizes our present theoretical understanding of single-molecule kinetics associated with the Michaelis-Menten mechanism of enzymatic reactions. Single-molecule enzymatic turnover experiments typically measure the probability density f(t) of the stochastic waiting time t for individual turnovers. While f(t) can be reconciled with ensemble kinetics, it contains more information tha...

Corrugator supercilii muscle activity is considered an objective measure of valence because it increases in response to negatively valenced facial expressions (angry) and decreases to positive expressions (happy). The authors sought to determine if corrugator activity could be used as an objective measure of positivity-negativity bias. The authors recorded corrugator responses as participants r...

We address the problem of simulating biochemical reaction networks with time-dependent rates and propose a new algorithm based on our rejection-based stochastic simulation algorithm (RSSA) [Thanh et al., J. Chem. Phys. 141(13), 134116 (2014)]. The computation for selecting next reaction firings by our time-dependent RSSA (tRSSA) is computationally efficient. Furthermore, the generated trajector...

During the last two decades, scientists have developed various methods that allow the detection and manipulation of single molecules, which have also been called "in singulo" approaches. Fundamental understanding of biochemical reactions, folding of biomolecules, and the screening of drugs were achieved by using these methods. Single-molecule analysis was also performed in the field of DNA nano...