Self-organization and information in biosystems: a case study

Eigen's original molecular evolution equations are extended in two ways. (1) By an additional nonlinear autocatalytic term leading to new stability features, their dependence on the relative size of fitness parameters and on initial conditions is discussed in detail. (2) By adding noise terms that represent the spontaneous generation of molecules by mutations of substrate molecules, these terms are taken care of by both Langevin and Fokker-Planck equations. The steady-state solution of the latter provides us with a potential landscape giving a bird's eye view on all stable states (attractors). Two different types of evolutionary processes are suggested: (a) in a fixed attractor landscape and (b) caused by a changed landscape caused by changed fitness parameters. This may be related to Gould's concept of punctuated equilibria. External signals in the form of additional molecules may generate a new initial state within a specific basin of attraction. The corresponding attractor is then reached by self-organization. This approach allows me to define pragmatic information as signals causing a specific reaction of the receiver and to use equations equivalent to (1) as model of (human) pattern recognition as substantiated by the synergetic computer.