Effectiveness factor for spatial gradient sensing in living cells

We consider the steady-state pattern of messenger molecules produced in the membrane of a cell perceiving and responding to an extracellular gradient of chemoattractant, which directs cell movement towards the chemoattractant source. Specifically, we analyze the undesirable effect of lateral diffusion in blurring the intracellular messenger profile. The concept of an effectiveness factor, akin to the analysis of reactions in porous catalysts, is applied to the spatial gradient sensing problem, with the distinction that slow, not fast, diffusion is required for effective gradient sensing. Analytical effectiveness factor expressions are derived for ideal geometries and then generalized to arbitrary cell shapes. In the case of mouse fibroblasts responding to gradients of platelet-derived growth factor, we conclude that the cell morphology and orientation with respect to the gradient can dictate whether messenger diffusion obliterates gradient sensing or has very little effect. The analysis outlined here allows the effect of intracellular messenger diffusion on spatial gradient sensing to be quantified for individual cells.