Part III Math Tripos: Trinity College, University of Cambridge, UK 1997
I am a theoretical physicist by upbringing. Until recently my research focused on developing renormalization group techniques applied to random matrix model formalism of (non)critical string theory. From that experience, I developed interest in complexity theory and non-equilibrium statistical mechanics. Most recently, fascinated by complexity of biological systems, my interest turned to systems biology.
I have been working on mathematical and computational modeling to explore mechanisms behind the Warburg effect and the regulation of glycolysis. Cancer cells preferentially use glycolysis in preference to oxidative phosphorylation, even when well-oxygenated (the Warburg effect). Recent discovery suggests that the switch of carbon catabolism from respiration to aerobic glycolysis could partly be explained by a simple example of plasticity that cancer cells primarily express an embryonic form of pyruvate kinase (PK) called PKM2 instead the one commonly expressed in adult tissues, namely PKM1. We believe the regulatory mechanism of this switch is distributed among several control points in the glycolytic pathway and are investigating in detail the mechanisms of phospho-fructokinase 1 and 2 (PFK1/2), and PKM1 and M2, using mathematical analysis as well as simulation using the (LISP based) little b computational infrastructure. Our analysis found that the control circuit governed by PFM2 displays a robust mechanism in its input-output relation. We have a intuitive understanding of such a precision that we believe will be important in understanding the Warburg effect in an indirect way.
There are some simpler biological examples in literature displaying somewhat similar robust mechanism. Also there are situations, where one gets more general robust mechanism revealing polynomial invariant expression among the species concentrations, that are independent of initial conditions and steady states. We are using methods from algebraic geometry, namely Groebner bases computation and the Elimination Theorem, to search for systematics that display such invariants for a given network topology.
In future the little b library modules, being developed for describing metabolic pathways (like PFK1/2 type allosteric enzymes with multiple effectors), will inter-operate with existing signal transduction library components (for instance, for multisite phosphorylation) and will be linked to receptor tyrosine kinase pathways. The PKM2 isoform has been found to be negatively regulated by tyrosine-phosphorylated proteins. We are also exploring to build kernel machine based classifier using metabolomic and protein expression data to help us learning the goal changes in glucose metabolism, such as the Warburg effect.