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One-Dimensional Elastic Continuum Model of Enterocyte Layer Migration

Qi Mi ^*, David Swigon ^*, Béatrice Rivière ^*, Selma Cetin ^¶, Yoram Vodovotz   and David J. Hackam   ^¶

^* Department of Mathematics, Center for Inflammation and Regeneration Modeling, McGowan Institute for Regenerative Medicine, Department of Surgery, and Department of Cell Biology and Physiology, University of Pittsburgh, Pittsburgh, Pennsylvania; and ^¶ Children's Hospital of Pittsburgh, Division of Pediatric Surgery, Pittsburgh, Pennsylvania

Correspondence: Address reprint requests to David Swigon, Dept. of Mathematics, University of Pittsburgh, 301 Thackeray Hall, Pittsburgh, PA 15260. Tel.: 412-624-4689; Fax: 412-624-8397; E-mail.: swigon{at}pitt.edu.

Necrotizing enterocolitis is the leading cause of death from gastrointestinal disease in preterm infants. It results from an injury to the mucosal lining of the intestine, leading to translocation of bacteria and endotoxin into the circulation. Intestinal mucosal defects are repaired by the process of intestinal restitution, during which enterocytes migrate from healthy areas to sites of injury. In this article, we develop a mathematical model of migration of enterocytes during experimental necrotizing enterocolitis. The model is based on a novel assumption of elastic deformation of the cell layer and incorporates the following effects: i), mobility promoting force due to lamellipod formation, ii), mobility impeding adhesion to the cell matrix, and iii), enterocyte proliferation. Our model successfully reproduces the behavior observed for enterocyte migration on glass coverslips, namely the dependence of migration speed on the distance from the wound edge, and the finite propagation distance in the absence of proliferation that results in an occasional failure to close the wound. It also qualitatively reproduces the dependence of migration speed on integrin concentration. The model is applicable to the closure of a wound with a linear edge and, after calibration with experimental data, could be used to predict the effect of chemical agents on mobility, adhesion, and proliferation of enterocytes.