Introduction

The description of order and function in biological systems has been a challenge to scientists for many decades. The overwhelming majority of biological order is functional order, often representing self-organized dynamical states in living matter. These states include spatial, temporal and spatiotemporal structures, and all of them are ubiquitous in living as well in nonliving matter. Prominent examples are patterns (representing static functions), oscillatory states (rhythmic processes), travelling and spiraling waves (nonlinear phenomena evolving in space and time).

From a fundamental point of view, biological function must be treated in terms of dynamic properties. Biological systems exhibit a relative stability for some modes of behavior. In the living state, these modes remain very far from thermal equilibrium, and their stabilization is achieved by nonlinear interactions between the relevant biological subunits. The functional complexity of biological materials requires the application of macroscopic concepts and theories, the consideration of the motion of individual particles (e.g., atoms, ions, molecules) is either meaningless or not applicable in most cases.

The existence and stabilization of far-from-equilibrium states by nonlinear interactions within at least some subunits of a physical, chemical or biological system are intimately linked with cooperative processes. Besides the well- known strong equilibrium cooperativity, thermodynamically metastable states and nonequilibrium transitions in cooperatively stabilized systems can occur, provided a certain energy input is present.