Journal of Theoretical Biology 231 (2004) 49–67 A mechanistic model for eukaryotic gradient sensing: Spontaneous and induced phosphoinositide polarization $ K.K. Subramanian, Atul Narang à Department of Chemical Engineering, College of Engineering, University of Florida, Gainesville, FL 32611-6005, USA Received 18 February 2004; received in revised form 11 May 2004; accepted 25 May 2004 Abstract The crawling movement of cells in response to a chemoattractant gradient is a complex process requiring coordination of various subcellular activities. Although a complete description of the mechanisms underlying cell movement remains elusive, the very first step of gradient sensing, enabling the cell to perceive the imposed gradient, is becoming more transparent. The increased understanding of this step has been driven by the discovery that within 5–10 s of applying a weak chemoattractant gradient, membrane phosphoinositides such as PIP 3 localize at the front end of the cell. It is currently believed that the gradient sensing mechanism is precisely the mechanism leading to this localization. We have formulated a reaction–diffusion model based on the phosphoinositide cycle which predicts various responses of motile cells in addition to the phosphoinositide polarization induced by chemoattractant gradients. The responses include: (a) Polarized sensitivity wherein a polarized cell responds to a change in the direction of the gradient by turning its existing front. (b) Spontaneous polarization wherein cells polarize in a random direction even if the surrounding chemoattractant concentration is uniform. (c) Unique localization which refers to the formation of a unique polarity even in the face of multiple chemoattractant sources. The above responses preclude the hypothesis that the cell merely amplifies the external signal. Our model indicates that the cell must be viewed as a system that nonlinearly processes chemoattractant inputs. We show in particular that these seemingly complex dynamics can be explained very simply in terms of the instabilities and wavefront dynamics that are characteristic of the activator–inhibitor class of models. r 2004 Elsevier Ltd. All rights reserved. Keywords: Mathematical model; Signaling pathways; Cell movement; Chemotaxis; Directional sensing 1. Introduction Most eucaryotic cells move by crawling on a surface. The crawling movement occurs in response to an external stimulus, which is frequently a chemical concentration gradient. The resultant motion propels the cells forward along the direction of highest increase in concentration. The chemical that induces the move- ment is called chemoattractant and the movement itself is called chemotaxis. Eucaryotic chemotaxis is cyclic and each cycle consists of 4 phases: (1) Extension of a protrusion (2) adhesion of the protrusion to the surface (3) contraction of the cell body and (4) retraction of the tail. Each phase of the cycle is a complex process involving the coordinated action of a large constellation of molecules (Lauffenburger and Horwitz, 1996). In this work, we confine our attention to gradient sensing, the mechanism that enables the cell to read the external gradient and extend a protrusion precisely at the leading edge, the region exposed to the highest chemoattractant concentration. The extension of the protrusion involves localized actin polymerization at the leading edge. Soon after the cells are exposed to a chemoattractant gradient, the leading edge develops fingerlike actin-based structures called filopodia. The space between the filopods then fills ARTICLE IN PRESS www.elsevier.com/locate/yjtbi 0022-5193/$-see front matter r 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jtbi.2004.05.024 $ Portions of this work were presented at the KITP workshop on Bio-Molecular networks held in March, 2003 (http://online.kitp. ucsb.edu/online/bionet03/narang/). à Corresponding author. Tel.: +1-352-392-0028; fax: +1-352-392- 9513. E-mail address: narang@che.ufl.edu (A. Narang).