I am currently a postgraduate researcher studying the mathematical modelling of DNA replication, fork movement, and replication timing using process algebras and stochastic calculus.
DNA replication is a vital process that occurs in all living organisms, where cells produce copies of their genetic material, DNA, in order to divide and proliferate. However, the process of DNA replication is complex and not fully understood. My research aims to improve our understanding of this process through the use of different computational tools.
One aspect of my research focuses on the movement of the replication fork, which is the structure that moves along the DNA template during replication. By using process algebras and stochastic calculus, I study the main factors that influence the movement of the replication fork and how it impacts DNA replication timing.
Another aspect of my research involves the study of human DNA replication timing, which refers to the order and timing at which different regions of the genome are replicated. This process is not fully understood and can have significant implications for genetic diseases and cancer. Through the use of mathematical modelling, I aim to gain a better understanding of the factors that influence replication timing and how it is regulated, shedding light on the complex process of DNA replication and its underlying mechanisms.
During my PhD, my main interests included understanding the development of sensory organ precursor cells in several epithelial tissues of the Drosophila melanogaster fly and developing a fitting mathematical model of the crucial mechanisms and dynamics involved in such a system.
Other ongoing and more theoretical work aims to relate more generalised systems of long-range signalling and their predominant mathematical features, by performing linear stability analysis to better understand the robustness of well-established Notch-Delta models under certain parameter regions.
More generally, understanding pattern formation derived from cell-cell interactions has been a major theme in cellular biology for many years and it has motivated me to focus my research on this area. Specifically, the existence of lateral-inhibition mechanisms present in the Notch-Delta signalling pathway triggered a vast discussion among experimental biologists and applied mathematicians. Many dynamical systems and ODE models have been developed as a consequence of this discussion, some of which focus not only on juxtacrine signalling but also long-range signalling by considering cell protrusions reaching non-neighbouring cells. In the future, I plan to further extend such mechanisms and well-understood pathways to the human case and possibly trace back Notch role in cancer and other diseases.
Here’s my GitHub.
Francisco Berkemeier 