Modeling actin cable contraction

Extension of an epithelial membrane to close a hole is a very widespread process both in morphogenesis and in tissue repair. In many circumstances an important component driving these movements is an actomyosin contraction which consists of meshworks of actin filaments cross-linked by Myosin II molecular motors. We introduce a mathematical model to simulate the contraction of an actin cable structure attached to an external epithelial tissue and we use this curvature-type model as a basis to build other models in more general settings. This result is obtained by adding extra terms that describe the particular process we want to model (lamellipodial crawling, granulation tissue contraction, extension of actin protrusions, epithelial resistance, etc.). Finally, we concentrate on the treatment of non-homogeneous forces, i.e. non-constant boundary terms which can be associated with a non-uniform cable, internal pull or zipping force due to the non-uniformity of the biological or physical properties of the boundary cells or of the connective tissue.