* Author to whom correspondence should be addressed. E-mail: subho@del3.vsnl.net.in J. theor. Biol. (1999) 200, 299 } 305 Article No. jtbi.1999.0993, available online at http://www.idealibrary.com on Evidence for Nonlinear Capacitance in Biomembrane Channel System SUBHENDU GHOSH*,AMAL K. BERA AND SUDIPTO DAS Department of Biophysics, ;niversity of Delhi South Campus, Benito Juarez Road, New Delhi 110021, India (Received on 25 June 1998, Accepted in revised form on 24 June 1999) The electrophysiological properties of voltage-dependent anion channels from mitochondrial membrane have been studied in a bilayer membrane system. It was observed that the probability of opening of the membrane channel depends on externally applied voltage and the plot is a bell-shaped curve symmetric around probability axis. A scheme of conformational energy levels under varying externally applied voltage was formulated. Assuming that the probability follows Boltzmann distribution, we arrive at an expression of change in energy containing a separate term identical to the energy of a capacitor. This fact indicates the possibility of existence of an added capacitance due to the channel protein. Further it was shown that the aforesaid channel capacitor could be a function of voltage leading to nonlin- earity. We have o!ered a general method of calculating nonlinear capacitance from the experimental data on opening probability of a membrane channel. In case of voltage- dependent anion channel the voltage dependence of the capacitor has a power 0.786. The results have been interpreted in view of the structural organization of the channel protein in the membrane. Our hypothesis is that the phenomenon of capacitor behaviour is a general one for membrane channels.  1999 Academic Press Introduction The discovery of electrical behavior of biomem- branes is a milestone in understanding complex biological phenomena. Unlike non-living objects the biological systems are #exible and dynamic in nature and this makes the physical properties more complicated. For example, the capacitance of a bilayer membrane is a complex function of the solution parameters as well as other experi- mental factors (Li et al., 1994). The root cause of the dynamicity of a biological system lies in the #exibility of the constituent macromolecules. As an example the transmembrane proteins, includ- ing channel proteins, change shape and size according to the environmental conditions lead- ing to changes in charge distribution and hence in overall electrical properties. In addition, the cooperative interactions among the channels in a membrane play an important role in the elec- trophysiological behavior of the channels (Ghosh & Mukherjee, 1993; Ghosh, 1993). The channel structure #uctuates around the minimum energy conformation. It is the collective e!ect of these #uctuations that leads to the emergence of new properties, e.g. opening and closing of channels, called gating. The process of channel gating is a highly com- plex phenomenon. Most often a channel has sev- eral substates. While changing from a closed state to an open state (or vice versa) the channel prefers 0022}5193/99/019299#07 $30.00/0  1999 Academic Press