# Self-organization and information in biosystems: a case study

- 119 Downloads

## Abstract

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.

## Keywords

Self-organization Synergetics Evolution equations Pragmatic information## References

- Ebeling W (1991) Models of selforganization in complex systems. Akademie Verlag, BerlinGoogle Scholar
- Eigen M (1969) Lecture at the second international conference on theoretical physics and biology, Palais de congrès, Versailles 30 June–5 July 1969. In: Proceedings edited by M. Marois. Editions du Centre national de la recherche scientifique, 1971Google Scholar
- Eigen M (1971) Selforganization of matter and the evolution of biological macromolecules. Naturwiss 58:465–523CrossRefPubMedGoogle Scholar
- Eigen M (2013) From strange simplicity to complex familiarity. A treatise on matter, information, life and thought. Oxford University Press, OxfordCrossRefGoogle Scholar
- Eigen M, McCaskill J, Schuster P (1989) The molecular quasi-species. Adv Chem Phys 75:149–263Google Scholar
- Friston K (2012) A free energy principle for biological systems. Entropy 14:2100–2121CrossRefGoogle Scholar
- Gould SJ (2007) Punctuated equilibrium. Belknap Press of Harvard University Press, CambridgeGoogle Scholar
- Haken H (2000) Information and self-organization: a macroscopic approach to complex systems, 2nd edn. Springer, BerlinGoogle Scholar
- Haken H (2002) Brain dynamics. Springer, BerlinGoogle Scholar
- Haken H (2004a) Synergetic computers and cognition, 2nd edn. Springer, BerlinCrossRefGoogle Scholar
- Haken H (2004b) Synergetics. Introduction and advanced topics. Springer, BerlinGoogle Scholar
- Haken H, Portugali J (2017a) Information and self-organization: a unifying approach and applications. Entropy 18:197–254CrossRefGoogle Scholar
- Haken H, Portugali J (2017b) (ed) Information and self-organization. Entropy 19:18Google Scholar
- Haken H, Sauermann H (1963) Nonlinear interaction of laser modes. Z Phys 173:261–275CrossRefGoogle Scholar
- Haken H, Tschacher W (2017) How to modify psychopathological states? Hypotheses based on complex systems theory. Nonlinear Dyn Psychol Life Sci 21:19–34Google Scholar
- Jaynes ET (1957) Information theory and statistical mechanics. Phys Rev 106:620–630
**(Phys Rev 108:171–190)**CrossRefGoogle Scholar - Kauffman SA (1995) At home in the universe: the search for the laws of self-organization and complexity. Oxford University Press, OxfordGoogle Scholar
- Nicolis G, Nicolis C (2012) Foundations of complex systems. World Scientific, SingaporeCrossRefGoogle Scholar
- Schuster P (2011) Mathematical modeling of evolution. Solved and open problems. Theory Biosci 130:71–89CrossRefPubMedGoogle Scholar
- Schuster P (2013) The mathematics of Darwinian systems. In: Eigen M (ed) From strange simplicity to complex familiarity. A treatise on matter, information, life and thought. Appendix A4. Oxford University Press, Oxford, pp 667–700Google Scholar
- Schuster P (2016) Increase in complexity and information through molecular evolution. Entropy 18:397–434CrossRefGoogle Scholar