Abstract
The number of studies in cell biology in which quantitative models accompany experiments has been growing steadily. Roughly, mathematical and computational techniques of these models can be classified as "differential equation based" (DE) or "agent based" (AB). Recently AB models have started to outnumber DE models, but understanding of AB philosophy and methodology is much less widespread than familiarity with DE techniques. Here we use the history of modeling a fundamental biological problem-positioning of the cleavage furrow in dividing cells-to explain how and why DE and AB models are used. We discuss differences, advantages, and shortcomings of these two approaches.