Gen. Physiol. Biophys. (1996), 15, 65—69 65 Short communication Collective Dynamics of Ion Channels in Biological Membranes P. BABINEC and M. BABINCOVÁ Department of Biophysics and Chemical Physics, Faculty of Mathematics and Physics, Comenius University, Mlynská dolina Fl, 842 15 Bratislava, Slovakia Abstract. Master equation was used to describe the dynamics of coupled ion channels in biological membranes. From the stationary solution it was found that at a critical value of coupling strength the system undergoes phase transition of the second order, which can be of biological relevance. Key words: Biological membranes - Ion channels - Master equation - Phase transition - Collective dynamics As has been found experimentally, transmembrane ion channels are not func- tionally independent (Kiss and Nagy 1985; Iwasa et al. 1986, Yeramian et al. 1986). This arises from direct energy interactions between channels embedded in biological membranes of living cells (Houslay and Stanley 1982). A consistent description of ion channels functioning is only possible on the basis of nonlinear nonequilibrium statistical thermodynamics (Poledna 1989; Valko and Zachar 1989). In this work we use a simple model of interacting ion channels to show that nonlinear effects are important also for the description of collective dynamics. For the sake of simplicity we consider ion channels as effectively fluctuating two-state elements with one open (conducting) state and one closed (nonconduct- ing) state (Liu and Dilger 1991; French and Horn 1983; Hille 1984). Let a given configuration of ion channels in a biological membrane consist of n 0 and n c open and closed channels, respectively. If the total number of channels 2N = n 0 + n c is constant, then the only relevant variable n (order parameter) is given by n = (n 0 - n c )/2. Transition dynamics of the ion channels is determined by probabilities: ~ Pco("oi n c) - for transition from open to closed state, - Poc( n oi "c) _ for transition from closed to open state. Let us introduce further probability distribution function f(n 0 , n c \ t) = f(n; t),