Compartmentalized reaction-diffusion systems.

Reaction-diffusion systems consisting of a collection of reactive domains separated by chemically inactive regions are considered. The reactive dynamics is governed by a multistep reaction mechanism and each reactive domain is specific to a particular elementary step or collection of elementary steps of the global reaction mechanism. Far-from-equilibrium situations where the global kinetics can give rise to complex states such as bistability or oscillations are studied. A general method for the calculation of the average concentration on each reactive domain is presented. The effects of compartmentalization are illustrated by a study of the influence of diffusion, reactive domain size, and domain distribution on the nature of the stationary states of the Schlögl model. Compartmentalization can drive the system into and out of the bistable regime of this reactive system.

Turbulent fronts in resonantly forced oscillatory systems.

Phase fronts in the forced complex Ginzburg-Landau equation, a model of a resonantly forced oscillatory reaction-diffusion system, are studied in the 3:1 resonance regime. The focus is on the turbulent (Benjamin-Feir-unstable) regime of the corresponding unforced system; in the forced system, phase fronts between spatially uniform phase-locked states exhibit complex dynamics. In one dimension, for strong forcing, phase fronts move with constant velocity. As the forcing intensity is lowered there is a bifurcation to oscillatory motion, followed by a bifurcation to a regime in which fronts multiply via the nucleation of domains of the third homogeneous phase in the front. In two dimensional systems, rough fronts with turbulent, complex internal structure may arise. For a critical value of the forcing intensity there is a nonequilibrium phase transition in which the turbulent interface grows to occupy the entire system. The phenomena we explore can be probed by experiments on periodically forced light sensitive reaction-diffusion systems.

Dynamics of solvation-induced structural transitions in mesoscopic binary clusters

Ion solvation dynamics following collision of K+ with mesoscopic water-ammonia aggregates is investigated. Two processes determine the postcollision state of the clusters: First, a morphological transformation from a structure characterized by a solid water core and a liquid-phase ammonia sheath into a dumbbell-shaped cluster composed of a liquid water droplet attached to an ammonia subcluster containing the solvated ion. Second, evaporation cools the cluster during and after the morphological change and this evaporative cooling is quantitatively characterized by determining the size-dependent rate constants for these complex clusters.

Resonantly forced inhomogeneous reaction-diffusion systems.

The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex Ginzburg-Landau equation in the 3:1 resonance regime. Front roughening and spontaneous nucleation of target patterns are observed and characterized. Time dependent spatially varying forcing fields are studied in the 3:1 forced FitzHugh-Nagumo system. The periodic variation of the spatially random forcing amplitude breaks the symmetry among the three quasi-homogeneous states of the system, making the three types of fronts separating phases inequivalent. The resulting inequality in the front velocities leads to the formation of "compound fronts" with velocities lying between those of the individual component fronts, and "pulses" which are analogous structures arising from the combination of three fronts. Spiral wave dynamics is studied in systems with compound fronts. (c) 2000 American Institute of Physics.

Polymerase chain reaction: a Markov process approach.

A probabilistic approach to the kinetics of the polymerase chain reaction (PCR) is developed. The approach treats the primer extension step of PCR as a microscopic Markov process in which the molecules of deoxy-nucleoside triphosphate (dNTP) are bound to the 3' end of the primer strand one at a time. The binding probability rates are prescribed by combinatorial rules in accord with the microscopic chemical kinetics. As an example, a simple model based on this approach is proposed and analysed, and an exact solution for the probability distribution of lengths of synthesized DNA strands is found by analytical means. Using this solution, it is demonstrated that the model is able to reproduce the main features of PCR, such as extreme sensitivity to the variation of control parameters and the existence of an amplification plateau. A multidimensional optimization technique is used to find numerically the optimum values of control parameters which maximize the yield of the target sequence for a given PCR run while minimizing the overall run time.

Molecular Turing structures in the biochemistry of the cell.

Reactive lattice gas automata simulations show that Turing structure can form on a mesoscopic scale and are stable to molecular fluctuations in this domain. Calculations on the Sel'kov model suggest that Turing instabilities can give rise to global spatial symmetry breaking in ATP concentration within the cell cytoplasm with a mesoscopic Turing scale well within typical cell dimensions. This leads to a new mechanism for the global breaking of energy distribution in the cell. It also leads to reappraisal of the importance of the Turing effect on extended biochemical spatial structures and energy transport available to cell morphogenesis.