Continuum Modeling of Forces in Growing Viscoelastic Cytoskeletal Networks

Mechanical properties of the living cell are important in cell movement, cell division, cancer development and cell signaling. There is considerable interest in measuring local mechanical properties of living materials and the living cytoskeleton using micromechanical techniques. However, living materials are constantly undergoing internal dynamics such as growth and remodeling. A modeling framework that combines mechanical deformations with cytoskeletal growth dynamics is necessary to describe cellular shape changes. The present paper develops a general finite deformation modeling approach that can treat the viscoelastic cytoskeleton. Given the growth dynamics in the cytoskeletal network and the relationship between deformation and stress, the shape of the network is computed in an incremental fashion. The growth dynamics of the cytoskeleton can be modeled as stress dependent. The result is a consistent treatment of overall cell deformation. The framework is applied to a growing 1-d bundle of actin filaments against an elastic cantilever, and a 2-d cell undergoing wave-like protrusion dynamics. In the latter example, mechanical forces on the cell adhesion are examined as a function of the protrusion dynamics.