Abstract
A two dimensional biased random walk model was applied to calculate bacterial cells' distribution around an attractant chemical in a line. This model follows the properties of bacterial chemotaxis. In a uniform chemical concentration, a bacterial cell tumbles every a certain period of time and randomly changes its swimming direction. However, a bacterial cell suppresses tumbling when the cell senses that the chemical concentration around it has increased. Thus, a bacterial cell gradually approaches the highest concentration. This produces chemotaxis as a collective behavior of many bacterial cells. In the present model, a model cell moves a certain distance during one time step. When the model cell approached a line that is assumed to be a chemical attractant during the previous time step, the cell continues moving in the same direction in the current time step with probability α, or changes its direction randomly with probability 1-α. On the contrary, when the model cell receded from the line, the cell randomly changes its direction. The parameter a means the strength of bias; α = 0 corresponds to random walk and α = 1 the strongest biased motion. The calculated model cells' steady distribution around the attractant line is an exponential distribution which depends on α. The dependence on α is not such a simple one appeared in the previous one dimensional model. The effect of directivity at tumbling was also investigated. The directivity has little impact on the cells' distribution.
