Mechanism and kinetics of dithiobenzoate-mediated RAFT polymerization. I. The current situation

Investigations into the kinetics and mechanism of dithiobenzoate-mediated Reversible Addition-Fragmentation Chain Transfer (RAFT) polymerizations, which exhibit nonideal kinetic behavior, such as induction periods and rate retardation, are comprehensively reviewed. The appreciable uncertainty in the rate coefficients associated with the RAFT equilibrium is discussed and methods for obtaining RAFT-specific rate coefficients are detailed. In addition, mechanistic studies are presented, which target the elucidation of the fundamental cause of rate retarding effects. The experimental and theoretical data existing in the literature are critically evaluated and apparent discrepancies between the results of different studies into the kinetics of RAFT polymerizations are discussed. Finally, recommendations for further work are given. (c) 2006 Wiley Periodicals, Inc.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.