A mathematical concept known as Parrondo's paradox motivated the development of several novel computational models of chemical systems in which thermal cycling was explored. In these kinetics systems we compared the rates of formation of product under cycling temperature and steady-sate conditions. We found that a greater concentration of product was predicted under oscillating temperature conditions. Our computational models of thermal cycling suggest new applications in chemical and chemical engineering systems.

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Systems chemistry is a new discipline which investigates the interactions within a network of chemical reactions. We have studied several computational models of chemical systems inspired by mathematical paradoxes and have found that even simple systems may behave in a counterintuitive, nonlinear manner depending upon various conditions. In the present study, we modeled a set of reactions inspired by one such paradox, Braess' paradox, an interesting phenomenon whereby the introduction of additional capacity (e.g. pathways) in some simple network systems can lead to an unexpected reduction in the overall flow rate of "traffic" through the system. We devised several chemical systems that behaved in this counterintuitive manner; the overall rate of product formation was diminished when an additional pathway was introduced and, conversely, there was an enhancement of product formation when the same interconnecting pathway was removed. We found that, unlike a traffic model, the chemical model needed to include reversible pathways in order to mimic "congestion"-a condition necessary to produce Braess-like behavior. The model was investigated numerically, but a full analytical solution is also included. We propose that this intriguing situation may have interesting implications in chemistry, biochemistry and chemical engineering.

Computational models of chemical systems provide clues to counterintuitive interactions and insights for new applications.  We have been investigating models of chemical reaction systems under forced, thermal cycling conditions and have found that some hypothetical processes generate higher yields under thermal cycling than under single, fixed temperature conditions.  A simple kinetic model of an actual process, the two-temperature polymerase chain reaction that replicates DNA, is used to simulate the important features of a chemical system operating under thermal cycling.  This model provides insights into the design of other chemical systems that may have important applications in chemistry, biochemistry and chemical engineering. 

Explaining the evolution of a predominantly homochiral environment on the early Earth remains an outstanding challenge in chemistry. We explore here the mathematical features of a simple chemical model system that simulates chiral symmetry breaking and amplification towards homochirality. The model simulates the reaction of a prochiral molecule to yield enantiomers via interaction with an achiral surface. Kinetically, the reactions and rate constants are chosen so as to treat the two enantiomeric forms symmetrically. The system, however, incorporates a mechanism whereby a random event might trigger chiral symmetry breaking and the formation of a dominant enantiomer; the non-linear dynamics of the chemical system are such that small perturbations may be amplified to near homochirality. Mathematical analysis of the behavior of the chemical system is verified by both deterministic and stochastic numerical simulations. Kinetic description of the model system will facilitate exploration of experimental validation. Our model system also supports the notion that one dominant enantiomeric structure might be a template for other critical molecules.