Chemical reaction network theory for cancer modelling: optimization techniques for studying and building signalling networks in colorectal cancer

Systems biology is an interdisciplinary field of study that applies computational and mathematical methods to analyse complex biological systems. Within this framework, Chemical Reaction Networks (CRNs) have proven to be powerful tools for modelling the signalling networks regulating information flow inside a cell. Since many cancers arise from mutations that alter the dynamics of such networks, by acting on protein activity and signalling cascades, CRNs offer an effective approach to studying cancer onset, progression, and therapy by representing cellular processes as networks of interacting proteins. By applying mass-action kinetics, these interaction networks can be translated into systems of ordinary differential equations (ODEs). This Thesis applies CRN Theory (CRNT) to oncological research, focusing on a CRN-based model of the G1-S transition phase of colorectal cancer (CRC) cells. A key computational challenge in CRN analysis is efficiently computing non-negative steady states of the network. In the first part of this Thesis we address this problem by presenting the Non-Linearly Projected Combined (NLPC) algorithm, an iterative root-finding method combining Newton’s method with gradient descent, ensuring fast and accurate equilibrium estimation. NLPC is validated both by comparing its performance to other state-of-the art algorithms and by simulating mutations and targeted therapies on the MAPK pathway, a key driver of CRC progression. The second part of this Thesis aims at extending the existing CRN for CRC by incorporating the mTOR pathway, a critical regulator of cell growth, metabolism, and therapy resistance. A major challenge in defining this CRN is that enzyme-substrate reaction rates are typically described in the literature using Michaelis-Menten (MM) parameters, which cannot be directly incorporated into a CRN model based on mass-action kinetics. To overcome this limitation, this Thesis provides an algorithmic approach for estimating the kinetic parameters of a CRN from the corresponding MM variables, ensuring greater model accuracy. By bridging computational modelling and cancer biology, this work provides new insights into the mathematical representation and analysis of oncogenic pathways, paving the way for more precise and predictive models in cancer research. These advances have the potential to help refining therapeutic strategies, optimizing drug efficacy while minimizing side effects and unintended consequences.