Mathematical Biology Seminar: Jesus Espinal

A crucial element for life is fertilization and for this to take place a sperm must meet an egg. The question is how does the sperm locate and swim towards the egg. Here, we consider the case of sea urchins for which fertilization is external and communication between egg and sperm is achieved by means of molecules secreted by the egg, that diffuse to the sperm. Once they reach the sperm they attach to its flagellum and trigger a biochemical signaling pathway that produces oscillations in the internal calcium concentration. These fluctuations are known to reorient the sperm navigation. Our main concern is to increase our understanding of this activation process. We achieve this by means of a network model with linked nodes representing the pathway elements and their interactions. In our approach nodes take discrete values and time evolution is dictated by regulatory tables. With this logical network we have been able to identify unforeseen elements for the regulation of the onset and periodicity of the calcium oscillations, which we have corroborated experimentally. These time evolution characteristics affect sperm navigation properties such as the presence or absence of chemotaxis. Our study also reveals that the network dynamics operates in a critical regime, this meaning that it strikes a balance between evolvability and robustness, a condition that favors the adaptation to different environments and that has probably been achieved throughout evolution. Our work hence provides a new instance for the proposition that life takes place at criticality.