Biological membranes as dissipative structures

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Nuclear Physics B (Prec. Suppl.) 2 (1987) 618 North-Holland, Amsterdam

BIOLOGICAL MEMBRANES AS DISSIPATIVE STRUCTURES J. A. Tuszynski D e p a r t m e n t of Physics, Memorial University of Newfoundla~A, St. John's, NFLD., A1B 3X7, Canada In this presentation, we expand on the ideas of Frohlich 1 and Davydov 2 who envisaged molecular chains in the metabolic s t a t e of a biological cell as producing long-range order either in the f o r m of the coherence of dipolar excitations or in the f o r m of solitary waves which couple an exciton and a local deformation of the chain. We s t a r t f r o m a microscopic Hamiltonlan relevant for a membrane, discuss specific limitations, and derive the equation of motion for the individual peptide group. The resultant equation is a nonlinear differential difference equation similar to t h a t of the F e r r n i - P a s t a - U l a m problem.

However, through the dependence of the nonlinearity constants on the

dielectric constant of the whole membrane, it becomes a much m o r e complicated equation since its p a r a m e t e r s are integral transforms of the solution. We discuss several possible approximation schemes, the possibility of Bose condensation of dipolar modes and the role of external pumping. reaction-diffnsion 3 type of equations

We then m a k e c o n t a c t with phenomenological and discuss the present knowledge of their

solutions. A particular example of the rouleau f o r m a t i o n of human e r y t h r o c y t e s will be provided. REFERENCES 1. H. Frohlich, IEEE Trans. MIT 26:613 (1978). 2. A.S. Davydov, Biology and Quantttm Mechanics, Pergamon, New York (1982). 3. I. Prigogine, From Being to Becoming, Freeman, San Francisco (1980).

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