where k is the rate constant. The stochastic approach to chemical kinetics is concerned with modeling chemical reactions in situations where the assumptions underlying equations of this type break down. In order to illustrate this, suppose that the reaction above is occuring in a drop of water of volume V , which contains only a very small number, say 3, of molecules of I. The kinetic equation ...

We outline our perspective on stochastic chemical kinetics, paying particular attention to numerical simulation algorithms. We first focus on dilute, well-mixed systems, whose description using ordinary differential equations has served as the basis for traditional chemical kinetics for the past 150 years. For such systems, we review the physical and mathematical rationale for a discrete-stocha...

We present a new microfluidic platform for the study of enzymtatic reactions using static droplets on demand. This allows us to monitor both fast and slow reactions with the same device and minute amounts of reagents. The droplets are produced and displaced using confinement gradients, which allows the experiments to be performed without having any mean flow of the external phase. Our device is...

In cell biology, cell signaling pathway problems are often tackled with deterministic temporal models, well mixed stochastic simulators, and/or hybrid methods. But, in fact, three dimensional stochastic spatial modeling of reactions happening inside the cell is needed in order to fully understand these cell signaling pathways. This is because noise effects, low molecular concentrations, and spa...

The conventional methods of simplified kinetics modeling through the use of partial-equilibrium and quasi-steady approximations are reviewed and critiqued. The method of computational singular perturbation (CSP) is then presented with special emphasis on the interpretation of CSP data to obtain physical insights on massively complex reaction systems. A simple example is used to demonstrate how ...

Chemical clocks are often used as exciting classroom experiments, where an induction time is followed by rapidly changing colours that expose oscillating concentration patterns. This type of reaction belongs to a class of nonlinear chemical kinetics also linked to chaos, wave propagation and Turing patterns. Despite its vastness in occurrence and applicability, the clock reaction is only well u...

The following are interesting questions for any chemical reaction system of interest: in any time epoch, which reactions are already exhausted, and which reactions are currently dormant? Which reactions are currently rate-controlling? For each reaction, which chemical species are the major participants and which are the minor participants? Are there chain-branching processes going on? What happ...