Complex patterns predicted in an in vitro experimental model system for the evolution of molecular cooperation

From quasispecies to quasispaces: coding and cooperation in chemical and electronic systems

This contribution addresses the physical roles of spatial structures, either externally imposed or generated through self-assembly, either passive or active, on the physical chemistry of evolution. Starting with simple diffusion in closed capillaries, a one-dimensional space, it covers eight aspects of experimental and theoretical research into the interaction of evolution with spatial structures: in various dimensions, including hitherto unexplored ones, spanning from externally defined physical spaces to actively tailored spaces, assembled by the evolving components themselves. As such, it contains some original research by the author as well as tracing how other insights grew over three decades out of the mentorship of Manfred Eigen in the 1980s. Much of the early interest in spatial structures centres on its role in stabilizing higher order cooperative structures involving the coevolution of different molecules, as the genetic coding system exemplifies. Modern nanotechnology enables the design and construction of genetically encoded variants of smart components that can actively control both the proliferation of molecules and the structuring of space. A key role for this article is to show the continuity in this line of enquiry, beginning with quasispecies and projecting to autonomous microparticles with electronic genomes able to form programmable quasispaces.

Pattern selection in a cooperative biochemical in vitro amplification system: the role of parasites

Previously, numerical simulations have shown that evolving systems can be stabilized against emerging parasites by pattern formation in spatially extended flow reactors. Hence, it can be argued that pattern formation is a prerequisite for any experimental investigation of the biochemical evolution of cooperative function. Here, we study a model of an experimental biochemical system for the cooperative in vitro amplification of DNA strands and show that emerging parasites can induce a complex pattern formation even when no pattern formation occurs without parasites. In an adiabatic approximation where the cooperative amplification reaction is assumed to adapt fast to slowly emerging parasites, the parasite concentration itself acts as a Steuer parameter for the selection of various complex patterns. Without such an adiabatic approximation only transient patterns emerge. As any species can grow for very low concentrations, the parasite is able to infect the entire reactor and the system is finally diluted out. In the experimental biochemical system, however, the species are individual molecules and the growth of spatially separated, non-infected regions becomes feasible. Hence a cutoff threshold for the minimal concentration is applied. In these simulations the otherwise lethal infection by parasites induces the formation of spatiotemporal spirals, and this spatial structure help the host and parasitoid species to survive together. These theoretical results describe an inherent property of cooperative reactions and have an important impact on experimental investigations on the molecular evolution and complex function in spatially extended reactors. Since the formation of the complex pattern is restricted either to a rather large cutoff value or a special choice of the kinetic parameters, we, however, conclude that the persistence of evolving cooperative amplification is not possible in a simple reaction-diffusion reactor. Experimental set-ups with patchy environments, e.g. biomolecular amplification in coupled microstructured flow chambers or in microemulsion, are eligible candidates for the observation of such a self-organized pattern selection.

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 evolutionary stability of coupled amplification in biopolymers. The model is analytically tractable for an infinite-dimensional space (simplex geometry), which also provides insight into evolution in normal Euclidean space. The results are compared with stochastic simulations describing the co-evolution of combinatorial families of molecular sequences both in the simplex geometry and in lower (one, two and three) space dimensions. They demonstrate analytically the generic limits which exploitation place on co-evolving multi-component amplification systems. In particular, there is an optimal diffusion (or migration) coefficient for cooperative amplification and minimal and maximal threshold values for stable cooperation. Over a bounded range of diffusion rates, the model also exhibits stable limit cycles. Furthermore, the co-operatively coupled system has a maximum tolerable error rate at intermediate rates of diffusion. A tractable model is thereby established which demonstrates that spatial effects can stabilize catalytic biological information. The analytic behaviour in infinite-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 catalysis on the basis of the model are outlined. We denote the modelling technique by PRESS, Probability Reduced Evolution of Spatially-discrete Species.