Aspects of fluctuations in non-linear biological systems - Motion in bistable potentials and selection equations
2004 (English)In: SIMPLICITY BEHIND COMPLEXITY / [ed] Klonowski, W, LENGERICH: PABST SCIENCE PUBLISHERS , 2004, Vol. 3, 25-60 p.Conference paper (Refereed)
Two rather different topics are discussed with one common factor: they are driven by irregular influences. The first part considers the stochastic transition between potential minima over a maximum (barrier), and is treated as a Brownian motion description of reaction rates. We also discuss the related problem of "stochastic resonance", in which a small oscillating force synchronises transitions. In both these cases, the emphasis is on the formalism, and the relations between the two problems are stressed. The other type of problem considers growth and competition equations of macromolecules, relevant for early molecular evolution on the path to the first life. Selection rates are simple and straightforward as long as competition essentially concerns limited resources. The situation gets more complex, when molecules are considered co-operative, e.g. they can catalyse growth processes. This corresponds to the hypercycle concept of Eigen, and is also a scenario for a RNA world. Components that use the support from other components may thrive, but can lead to the extermination of an entire system as the supporters may decline in the competition. As in the first part, the emphasis is on the formalism. We also take up probability aspects and problems that appear together with small probabilities and possibilities of exponential growth. Finally, the possibility of saving the co-operativity by spatial structures are discussed.
Place, publisher, year, edition, pages
LENGERICH: PABST SCIENCE PUBLISHERS , 2004. Vol. 3, 25-60 p.
, FRONTIERS ON NONLINEAR DYNAMICS, 3
brownian motion, reaction rates, stochastic resonance, noise vs chaos, selection equations, error effects, hypercycles, RNA-world, parasites, spatial organisation
IdentifiersURN: urn:nbn:se:kth:diva-43980ISI: 000227037500002ISBN: 3-89967-070-1OAI: oai:DiVA.org:kth-43980DiVA: diva2:450898
3rd European Interdisciplinary School on Nonlinear Dynamics for System and Signal Analysis. Warsaw, POLAND. JUN 18-27, 2002
QC 201110242011-10-242011-10-192011-10-24Bibliographically approved