What is special about autocatalysis?

The single-step autocatalytic reaction A + X ↔ 2X in different environments—batch reactor, flow reactor, logistic equation—is studied by means of conventional deterministic kinetics and as a stochastic process. Self-enhancement requires an initial concentration of the autocatalyst X—at least in seeding amounts—for starting the reaction. Deterministic solution curves have sigmoid shapes. At small concentrations, three stochastic phenomena are observed: (1) thermal fluctuations, (2) stochastic delay, and (3) stochastic bifurcations and anomalous fluctuations in case of multiple final states. The introduction of heterogeneous populations containing subspecies with different fitness values gives rise to natural selection in all three environments investigated here. In large populations, survival of the fittest is observed, whereas random fluctuations may result in selection of each of the subspecies. Then, the fitness values determine only probabilities of selection. The fittest subspecies, of course, has the largest probability of selection. There is a smooth transition to neutral evolution where the probabilities of selection are the same for all subspecies.© The Author(s) 201

Molecular evolution between chemistry and biology

Biological evolution is reduced to three fundamental processes in the spirit of a minimal model: (i) Competition caused by differential fitness, (ii) cooperation of competitors in the sense of symbiosis, and (iii) variation introduced by mutation understood as error-prone reproduction. The three combinations of two fundamental processes each, (A) competition and mutation, (B) cooperation and competition, and (C) cooperation and mutation, are analyzed. Changes in population dynamics that are induced by bifurcations and threshold phenomena are discussed.© The Author(s) 201

Increase in Complexity and Information through Molecular Evolution

Biological evolution progresses by essentially three different mechanisms: (I) optimization of properties through natural selection in a population of competitors; (II) development of new capabilities through cooperation of competitors caused by catalyzed reproduction; and (III) variation of genetic information through mutation or recombination. Simplified evolutionary processes combine two out of the three mechanisms: Darwinian evolution combines competition (I) and variation (III) and is represented by the quasispecies model, major transitions involve cooperation (II) of competitors (I), and the third combination, cooperation (II) and variation (III) provides new insights in the role of mutations in evolution. A minimal kinetic model based on simple molecular mechanisms for reproduction, catalyzed reproduction and mutation is introduced, cast into ordinary differential equations (ODEs), and analyzed mathematically in form of its implementation in a flow reactor. Stochastic aspects are investigated through computer simulation of trajectories of the corresponding chemical master equations. The competition-cooperation model, mechanisms (I) and (II), gives rise to selection at low levels of resources and leads to symbiontic cooperation in case the material required is abundant. Accordingly, it provides a kind of minimal system that can undergo a (major) transition. Stochastic effects leading to extinction of the population through self-enhancing oscillations destabilize symbioses of four or more partners. Mutations (III) are not only the basis of change in phenotypic properties but can also prevent extinction provided the mutation rates are sufficiently large. Threshold phenomena are observed for all three combinations: The quasispecies model leads to an error threshold, the competition-cooperation model allows for an identification of a resource-triggered bifurcation with the transition, and for the cooperation-mutation model a kind of stochastic threshold for survival through sufficiently high mutation rates is observed. The evolutionary processes in the model are accompanied by gains in information on the environment of the evolving populations. In order to provide a useful basis for comparison, two forms of information, syntactic or Shannon information and semantic information are introduced here. Both forms of information are defined for simple evolving systems at the molecular level. Selection leads primarily to an increase in semantic information in the sense that higher fitness allows for more efficient exploitation of the environment and provides the basis for more progeny whereas understanding transitions involves characteristic contributions from both Shannon information and semantic information

Inverse bifurcation analysis: Application to simple gene systems

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