  Bacteria are ubiquitous in our daily lives, either as motile planktonic cells
or as immobilized surface-attached biofilms. These different phenotypic states
play key roles in agriculture, environment, industry, and medicine; hence, it
is critically important to be able to predict the conditions under which
bacteria transition from one state to the other. Unfortunately, these
transitions depend on a dizzyingly complex array of factors that are determined
by the intrinsic properties of the individual cells as well as those of their
surrounding environments, and are thus challenging to describe. To address this
issue, here, we develop a generally-applicable biophysical model of the
interplay between motility-mediated dispersal and biofilm formation under
positive quorum sensing control. Using this model, we establish a universal
rule predicting how the onset and extent of biofilm formation depend
collectively on cell concentration and motility, nutrient diffusion and
consumption, chemotactic sensing, and autoinducer production. Our work thus
provides a key step toward quantitatively predicting and controlling biofilm
formation in diverse and complex settings.
