THEORY OF CONTINUUM RANDOM-WALKS AND APPLICATION TO CHEMOTAXIS

We formulate the general theory of random walks in continuum, essentia l for treating a collision rate which depends smoothly upon direction of motion. We also consider a smooth probability distribution of corre lations between the directions of motion before and after collisions, as well as orientational Brownian motion between collisions. These fea tures lead to an effective Smoluchowski equation. Such random walks in volving an infinite number of distinct directions of motion cannot be, treated on a lattice, which permits only a finite number of direction s of motion, nor by Langevin methods, which make no reference to indiv idual collisions. The effective Smoluchowski equation enables a descri ption of the biased random walk of the bacterium Escherichia coli duri ng chemotaxis, its search for food. The chemotactic responses of cells which perform temporal comparsions of the concentration of a chemical attractant are predicted to be strongly positive, whereas those of ce lls which measure averages of the ambient attractant concentration are predicted to be negative. The former prediction explains the observed behavior of wild-type (naturally occurring) cells; however, the latte r behavior has yet to be observed, even in cells defective in adaption .