The stochastic evolution of catalysts in spatially resolved molecular systems

A fully stochastic chemical modelling technique is derived which describes the influence of spatial separation and discrete population size on the evo lutionary stability of coupled amplification in biopolymers. The model is a nalytically tractable for an infinity -dimensional space (simplex geometry) , which also provides insight into evolution in normal Euclidean space. The results are compared with stochastic simulations describing the co-evoluti on of combinatorial families of molecular sequences both in the simplex geo metry and in lower (one, two and three) space dimensions. They demonstrate analytically the generic limits which exploitation place on co-evolving mul ti-component amplification systems. In particular, there is an optimal diff usion (or migration) coefficient for cooperative amplification and minimal and maximal threshold values for stable cooperation. Over a bounded range o f diffusion rates, the model also exhibits stable limit cycles. Furthermore , the co-operatively coupled system has a maximum tolerable error rate at i ntermediate rates of diffusion. A tractable model is thereby established wh ich demonstrates that spatial effects can stabilize catalytic biological in formation. The analytic behaviour in infinity -dimensional simplex space is seen to provide a reasonable guide to the spatial dependence of the error threshold in physical space. Nanoscale possibilities for the evolution of c atalysis on the basis of the model are outlined. We denote the modelling te chnique by PRESS, Probability Reduced Evolution of Spatially-discrete Speci es.