Coupling between Membranes and External Fields

Cooperative Coupling between Membranes and External Fields 

Such structures by the way are consistent with the ideas proposed by Frohlich in the sense that they can be switched to a coherent mode. A nonequilibrium phase transition that manifest itself as a limit cycle is a familiar example of such a phenomenon.The possible role of these types of nonequilibrium phase transitions in governing the interaction of external electromagnetic fields with biological systems has been discussed by Kaiser. 

One of the first attempts to examine the consequences of an electric-field-induced cooperative response was by Hill/ This effort was the basis for the later work of Blumenthal, Changeux, and Lefever and subsequently the work of Hill and Chen/ Most of these efforts, however, were directed toward understanding electric-field-induced excitability in those classes of membranes commonly referred to as excitable membranes, for example as in nerve and muscle. They were not attempts to model the interaction of external time-varying electric fields with biological membranes. Most all of these formulations were based on some type of mean-field theory and the use of lattice statistics. More recently Grodsky and Denner and Kaiser performed somewhat analogous calculations with reference to a specific dipole model of an excitable membrane. Both analyses used a type of mean field theory to generate the thermodynamic expressions used to describe the behavior of the systems. 

Consider the membrane to be a two-dimensional lattice. Each lattice site is assumed to exist in one of two states, state A or state B, Also each site may be occupied by a bound ligand or it may be empty, meaning no bound ligand. For a membrane of M lattice sites, HilF has shown that the grand partition, S, is of the form 

X is the absolute activity of the ligand, and E is the electric field strength at the lattice site the characteristic thermodynamic equation takes the form 

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