Diffusion-Based Noise Analysis for Molecular Communication in Nanonetworks

Statistical fluctuations limit the precision with which a microorganism can, in a given time T, determine the concentration of a chemoattractant in the surrounding medium. The best a cell can do is to monitor continually the state of occupation of receptors distributed over its surface. For nearly optimum performance only a small fraction of the surface need be specifically adsorbing. The probability that a molecule that has collided with the cell will find a receptor is Ns/(Ns + pi a), if N receptors, each with a binding site of radius s, are evenly distributed over a cell of radius a. There is ample room for many indenpendent systems of specific receptors. The adsorption rate for molecules of moderate size cannot be significantly enhanced by motion of the cell or by stirring of the medium by the cell. The least fractional error attainable in the determination of a concentration c is approximately (TcaD) - 1/2, where D is diffusion constant of the attractant. The number of specific receptors needed to attain such precision is about a/s. Data on bacteriophage absorption, bacterial chemotaxis, and chemotaxis in a cellular slime mold are evaluated. The chemotactic sensitivity of Escherichia coli approaches that of the cell of optimum design.

Many crucial biological processes operate with surprisingly small numbers of molecules, and there is renewed interest in analyzing the impact of noise associated with these small numbers. Twenty-five years ago, Berg and Purcell showed that bacterial chemotaxis, where a single-celled organism must respond to small changes in concentration of chemicals outside the cell, is limited directly by molecule counting noise and that aspects of the bacteria's behavioral and computational strategies must be chosen to minimize the effects of this noise. Here, we revisit and generalize their arguments to estimate the physical limits to signaling processes within the cell and argue that recent experiments are consistent with performance approaching these limits.