Modeling microtubule-mediated forces and centrosome positioning in Caenorhabditis elegans embryos

Microtubules and associated motor proteins are the major generators and mediators of the forces that organize the functional positioning of intracellular structures. The positioning of the centrosomes is a primary target for microtubule-mediated organization. The positioning of the centrosomes further defines the positionings of nucleus, mitotic spindles, and other organelles. Numerical modeling is an effective means by which we can further understand the physical mechanisms underlying microtubule-mediated centrosome positioning. Here, we summarize how we formulated the biophysical properties of microtubules in order to construct a numerical model of centrosome positioning in Caenorhabditis elegans embryos. Microtubules elongate and shrink in a stochastic manner, in a process known as "dynamic instability." Upon association with the cell cortex or motor proteins, microtubules mediate pushing and pulling forces. These forces move the centrosome, which is located at the minus-end of the microtubules, to the right place with the right timing. We discuss how the modeling efforts complement experimental knowledge and allow us to evaluate the sufficiency of various candidate hypotheses.