Thermal fluctuations and the minimum electrical field that can be detected by a biological membrane

Thermal electrical noise in living cells is considered to be the minimum threshold for several biological response mechanisms that pertain to electric fields. Existing models that purport to explain and interpret this phenomena yield perplexing results. The simplest model, in which the biomembrane is considered to be a linear dielectric, yields an equilibrium noise level that is several orders of magnitude larger than what is observed experimentally. An alternative approach of estimating the thermal noise as the Nyquist noise of a resistor within a finite frequency bandwidth, yields little physical insight. In this work, we argue that the nonlinear dielectric behavior must be accounted for. Using a statistical mechanics approach, we analyze the thermal fluctuations of a fully coupled electromechanical biomembrane. We develop a variational approximation to analytically obtain the benchmark results for model fluid membranes as well as physically reasonable estimates of the minimum electrical field threshold that can be detected by cells. Qualitatively, at least, our model is capable of predicting all known experimental results. The predictions of our model also suggest that further experimental work is warranted to clarify the inconsistencies in the literature.