Efficiency of Organelle Capture by Microtubules as a Function of Centrosome Nucleation Capacity: General Theory and the Special Case of Polyspermia

Transport of organelles along microtubules is essential for the cell metabolism and morphogenesis. The presented analysis derives the probability that an organelle of a given size comes in contact with the microtubule aster. The question is asked how this measure of functionality of the microtubule aster is controlled by the centrosome. A quantitative model is developed to address this question. It is shown that for the given set of cellular parameters, such as size and total tubulin content, a centrosome nucleation capacity exists that maximizes the probability of the organelle capture. The developed general model is then applied to the capture of the female pronucleus by microtubules assembled on the sperm centrosome, following physiologically polyspermic fertilization. This application highlights an unintuitive reflection of nonlinearity of the nucleated polymerization of the cellular pool of tubulin. The prediction that the sperm centrosome should lower its nucleation capacity in the face of the competition from the other sperm is a stark illustration of the new optimality principle. Overall, the model calls attention to the capabilities of the centrosomal pathway of regulation of the transport-related functionality of the microtubule cytoskeleton. It establishes a quantitative and conceptual framework that can guide experiment design and interpretation.