Quantitative biology (q-bio, for short) is a research meta-field that aims to better understand biological systems using quantitative ideas and methods. Q-bio researchers come from backgrounds across math, the sciences, and engineering. Investigations take place at the level of molecules, cells, organisms, populations, or some combination thereof. Large quantities of data are often involved, and they may be heterogeneous, combining sequence, structure, and systems information.

A classic example of q-bio research is the study of bacterial chemotaxis: the process by which bacteria like E. coli search for "food" in their aqueous environment. Their movement — a combination of straight runs and disorienting tumbles — is well described as a biased random walk toward areas of higher food concentration. The bacterium's displacement over time can only be described in probabilistic terms. Such stochasticity is a hallmark of biological systems. It is generally related to the thermal fluctuations (of order $$ k T $$) experienced by any system at nonzero temperature.

More recent research has elucidated the biochemical networks that tell the bacterium which direction to move. Feedback in a system of interacting proteins gives the organism a crude biochemical "memory" of food levels just experienced. Rotary flagellar "motors" powered by ion gradients allow the bacterium to corkscrew through the surrounding fluid. If food levels drop during one of its runs, it will soon switch the rotation of its flagella, thus inducing a tumble and changing directions. Biology often employs this type of nonlinear control.