Mechanical Analysis of Cell Migration Using Hybrid Structural Optimization

Abstract

Cell migration requires the dynamic formation and dissolution of mechanical structures inside the cytoplasm. Stress fibers are made of F-actin during cell migration driven by the strategic localization of focal adhesion complexes at the cell-substrate interface. The nucleus is also strategically positioned in the cell during the migration and the stress fibers wrap around the nucleus possibly to carry the nucleus with the cell. Cell migration is energetically demanding and should require strategic utilization of resources such as the F-actin stress fiber formation at specific locations so that they generate enough force by actomyosin contraction at the cell-matrix adhesion sites for a directed movement. In this work we propose a structural optimization based biophysical model to predict the strategic localization and sizes of F-actin fibers that supports the nucleus and the cytoplasm during migration. With the use of a nonlinear controller via a Newton-Euler-based model of the generated design, we further quantified the force in the stress fibers during migration, with results close to those obtained through experimental methods such as traction force microscopy. The predicted force decreases for a cell that migrates slowly due to a pharmacological perturbation. Such quantification of forces only require the information of the trajectory of the cell that can be readily obtained from time lapse microscopy. With novel microscopy techniques emerging, such biophysical model framework can be combined with traction force microscopy data to achieve unprecedented mechanical information inside and outside cells during migration, which is otherwise not possible by experiments only. SIGNIFICANCECell migration plays a critical role in biological functions. It requires the strategic formation of F-actin stress fibers at specific locations, to generate forces by actomyosin contraction for cells to migrate in a directed manner. The present study predicts the localization and force generated by stress fibers based on the trajectory of the cell, which can be obtained via time lapse microscopy. The technique can complement other techniques such as traction force microscopy to provide mechanical information inside and outside cells during cell migration.