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Mechanical and Biochemical Modeling of Cortical Oscillations in Spreading Cells

Maryna Kapustina ^*, Gabriel E. Weinreb ^*, Nancy Costigliola ^*, Zenon Rajfur ^*, Ken Jacobson ^*  and Timothy C. Elston 

^* Department of Cell and Developmental Biology, Lineberger Comprehensive Cancer Center, and Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina

Correspondence: Address reprint requests to Dr. T. Elston, E-mail: telston{at}amath.unc.edu; or Dr. G. Weinreb, E-mail: weinreb{at}med.unc.edu.

Actomyosin-based cortical contractility is a common feature of eukaryotic cells and is involved in cell motility, cell division, and apoptosis. In nonmuscle cells, oscillations in contractility are induced by microtubule depolymerization during cell spreading. We developed an ordinary differential equation model to describe this behavior. The computational model includes 36 parameters. The values for all but two of the model parameters were taken from experimental measurements found in the literature. Using these values, we demonstrate that the model generates oscillatory behavior consistent with current experimental observations. The rhythmic behavior occurs because of the antagonistic effects of calcium-induced contractility and stretch-activated calcium channels. The model makes several experimentally testable predictions: 1), buffering intracellular calcium increases the period and decreases the amplitude of cortical oscillations; 2), increasing the number or activity of stretch activated channels leads to an increase in period and amplitude of cortical oscillations; 3), inhibiting Ca²⁺ pump activity increases the period and amplitude of oscillations; and 4), a threshold exists for the calcium concentration below which oscillations cease.