In the last two decades enormous progress has been made on understanding molecular details in a number of cellular processes such as signal transduction and gene control, but frequently the objective in modeling is to understand the population-level behavior of cells. This gives rise to the problem of how to incorporate sufficient microscopic-level information into macroscopic-level descriptions. In this talk we will discuss two systems that involve chemotaxis, one for which this has problem has been more-or-less solved, and one for which a great deal remains to be done.

Chemotaxis in the bacterium E. coli is widely-studied because of its accessibility and because it incorporates processes that are important in the response of numerous sensory systems to stimuli: signal detection and transduction, excitation, adaptation, and a change in behavior. Quantitative data on the change in behavior is available for this system, and the major biochemical steps in the signal transduction/processing pathway have been identified. We will discuss a mathematical model of single cells that can reproduce many of the major features of signal transduction, adaptation and aggregation, and which incorporates the interaction of the chemotactic protein CheY_p with the flagellar motor. We shall then address the problem of how to obtain macroscopic equations for population-level behavior that incorporate certain features of the microscopic model.

Many cells such leukocytes (cells of the immune system) also respond chemotactically to external signals, but the process by which they determine directional information and alter their pattern of movement is much more complex than in bacteria, and the micro-to-macro step is much more difficult. In the remainder of the talk we will discuss recent progress and open questions in this area.