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A rigorous limit procedure is presented which links nonlocal models involvingadhesion or nonlocal chemotaxis to their local counterparts featuringhaptotaxis and classical chemotaxis, respectively. It relies on a novelreformulation of the involved nonlocalities in terms of integral operatorsapplied directly to the gradients of signal-dependent quantities. The proposedapproach handles both model types in a unified way and extends the previousmathematical framework to settings that allow for general solution-dependentcoefficient functions. The previous forms of nonlocal operators are comparedwith the new ones introduced in this paper and the advantages of the latter arehighlighted by concrete examples. Numerical simulations in 1D provide anillustration of some of the theoretical findings.

Nonlocal and local models for taxis in cell migration: a rigorous limit procedure