Modeling the dynamics of furrow ingression in <i>Drosophila</i> cellularization

During Drosophila cellularization, which is the first cytokinetic and tissue building event in Drosophila embryos, a membrane reservoir stored in the form of microvilli unfolds to fuel cleavage furrow ingression. Experiments have demonstrated that furrow ingression is kinetically coupled to the loss of surface area of the microvillar reservoir and that furrow ingression takes place in two kinetic phases. In this work, we developed a quantitative biophysical model of the dynamics of furrow ingression. Our model is based on principles of force balance where plasma membrane tension, cytoskeletal force generation, and force generated by motor proteins (number and force per protein) play important roles in the kinetics of furrow ingression. Each of the force generating terms is informed by known biophysical mechanisms. The resulting governing equations from the model are able to capture the key dynamics of furrow ingression as observed by experiments. In addition, we introduced in silico variations of the key biophysical parameters, including membrane tension and number of motor proteins, and found that the total membrane area available in the microvillar reservoir is a key determinant of the kinetics of furrow ingression.