I am a theoretical biologist, which means that I formulate hypotheses about how biological systems work and test them using mathematical models.
The primary focus of my research involves using mathematical modeling to study cancer as an evolving ecosystem within the human body, where heterogeneous populations of cancer cells: compete for limited resources (oxygen and glucose), cooperate with each other to fight off predators (the immune system), and disperse and migrate (metastases). Thinking about the disease from an ecological perspective has the power to change how we approach cancer treatment. As conservation biology has taught us in larger ecosystems, the best way to extinguish species is not to target them directly but to target their environment – hence the intense focus on habitat preservation efforts. And so in my research, I look for ways to target the tumor environment without killing the host.
Recently, I have been applying my academic cancer research work to devising a ecological and evolutionary approaches to cancer treatment using the tools of Quantitative Systems Pharmacology (QSP), including drug Pharmacokinetics and Pharmacodynamics (PKPD). This research is ongoing, so stay tuned.
A Bit About Mathematical Modeling
As a modeler, I try to:
1) Understand a biological process or mechanism
2) Tease out key drivers of the underlying dynamics
3) Formulate assumptions about how these key drivers interact with each other and their environment
4) Translate these assumptions into equations
5) Analyze these equations using well developed mathematical tools, and
6) Translate the results back into the language of biology
If my predictions are consistent with experimental observations, then maybe I got it right! If so, then I can try to make further predictions about what will happen to a system if we change this or that aspect of the model.
And if my predictions do not match observations? Well that is even more interesting! An incomplete answer means that some of my assumptions are incorrect, implying that our understanding of biology is incomplete. The good news is that since my experimental platform is a mathematical model, I can go through my assumptions one by one and identify which one(s) are causing the discrepancy. Chances are, our model just identified a gap in knowledge which we can now try to close using both theory and experiment.