Thermal fluctuations of electric field and solute density in biological cells

Abstract

Thermal fluctuations of ionic densities in a biological cell’s electrolyte creates random electric fields and solute density fluctuations. Using two common models of cellular components, the capacitor-resistor membrane model and the uniform electrolyte cytoplasm model, we determine the RMS values of these random variables and their frequency and wave number spectra by including independent variations of both anion and cation densities. In the membrane, the inequality of ionic mobilities skews the frequency spectra to much lower frequencies characteristic of solute transport, rather than current transport, through the membrane. In the cytoplasm electrolyte, the electric field wave number spectrum declines approximately exponentially with increasing wave number, leading to an algebraically declining spatial correlation function; the time correlation function also declines algebraically. The cytoplasm solute density fluctuations behave normally, with exponential spatial and algebraic temporal correlation functions. The RMS electric field of the cytoplasm is estimated at $\sim 2\times {10}^7$ V/m, about a factor of ${10}^3$ higher than that of the membrane.