Bacteria such as %DIFDELCMD < {\it %%% Escherichia coli move about in a series of runs and tumbles: while a run state (straight motion) entails all the flagellar motors spinning in counterclockwise (CCW) mode, a tumble is caused by a shift in the state of one or more motors to clockwise (CW) spinning. In the presence of an attractant gradient in the environment, runs in the favourable direction are extended, and this results in a net drift of URLanism in the direction of the gradient. The underlying signal transduction mechanism produces directed motion through a bilobe response function which relates the clockwise bias of the flagellar motor to temporal changes in the attractant concentration. The two lobes (positive and negative) of the response function are separated by a time interval of \sim 1s, such that the bacterium effectively compares the concentration at two different positions in space and responds accordingly. We present here a novel path-integral method which allows us to address this problem in the most general way possible, including multi-step CW-CCW transitions, directional persistence and power-law waiting time distributions. The method allows us to calculate quantities such as the effective diffusion coefficient and drift velocity, as well as the mean number of tumbles in a given time interval, in a power series expansion in the attractant gradient. Explicit results in the lowest order in the expansion are presented for specific models, which, wherever applicable, agree with the known results. The formalism is applied to gamma-distributed CW and CCW waiting time distributions in %DIFDELCMD < {\it %%% E. coli , as suggested by recent experimental observations, and used for predicting the dependence of drift velocity on clockwise bias.
Bacteria such as %DIFDELCMD < {\it %%% Escherichia coli move about in a series of runs and tumbles: while a run state (straight motion) entails all the flagellar motors spinning in counterclockwise (CCW) mode, a tumble is caused by a shift in the state of one or more motors to clockwise (CW) spinning. In the presence of an attractant gradient in the environment, runs in the favourable direction are extended, and this results in a net drift of URLanism in the direction of the gradient. The underlying signal transduction mechanism produces directed motion through a bilobe response function which relates the clockwise bias of the flagellar motor to temporal changes in the attractant concentration. The two lobes (positive and negative) of the response function are separated by a time interval of \sim 1s, such that the bacterium effectively compares the concentration at two different positions in space and responds accordingly. We present here a novel path-integral method which allows us to address this problem in the most general way possible, including multi-step CW-CCW transitions, directional persistence and power-law waiting time distributions. The method allows us to calculate quantities such as the effective diffusion coefficient and drift velocity, as well as the mean number of tumbles in a given time interval, in a power series expansion in the attractant gradient. Explicit results in the lowest order in the expansion are presented for specific models, which, wherever applicable, agree with the known results. The formalism is applied to gamma-distributed CW and CCW waiting time distributions in %DIFDELCMD < {\it %%% E. coli , as suggested by recent experimental observations, and used for predicting the dependence of drift velocity on clockwise bias.
R
Escherichia coli
Escherichia coli