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Cell-to-cell variations in protein abundance in clonal cell populations areubiquitous in living systems. Since protein composition determines responses inindividual cells, it stands to reason that the variations themselves aresubject to selective pressures. But the functional role of these cell-to-celldifferences is not well understood. One way to tackle questions regardingrelationships between form and function is to perturb the form (e.g., changethe protein abundances) and observe the resulting changes in some function.Here we take on the form-function relationship from the inverse perspective,asking instead what specific constraints on cell-to-cell variations in proteinabundance are imposed by a given functional phenotype. We develop a maximumentropy (MaxEnt) based approach to posing questions of this type, andillustrate the method by application to the well characterized chemotacticresponse in Escherichia coli (E. coli). We find that full determination ofobserved cell-to-cell variations in protein abundances is not inherent inchemotaxis itself, but in fact appears to be jointly imposed by the chemotaxisprogram in conjunction with other factors, e.g., the protein synthesismachinery and/or additional non-chemotactic cell functions such as cellmetabolism. These results illustrate the power of MaxEnt as a tool for theinvestigation of relationships between biological form and function.

Cell responses only partially shape cell-to-cell variations in protein abundances in Escherichia coli chemotaxis