Mathematical model of loss and gain of function mutations in a chemical reaction network for colorectal cancer cells.

All cellular functions are regulated by a complex network of chemical reactions that translates extracellular signals into cellular responses. Most cancer diseases are induced by alterations of this signalling network due to loss or gain of function mutations that respectively reduce or enhance the activity of specific proteins. Here we present a computational tool for simulating chemical reaction networks and their alteration due to loss and gain of function mutations. By applying mass action kinetics, we first describe the concentration dynamics of the species involved in the reaction network through a system of ordinary differential equations (ODEs), whose stationary stable state describes the species concentrations in the physiological cell. We then show that loss of function mutations can be implemented in the model via modification of the initial conditions of the system while gain of function mutations can be implemented by eliminating specific reactions. Eventually our model is extended to account for the concatenation of multiple mutations. As example we consider the chemical reaction network devised by Tortolina and colleagues for the G1-S transition point in colorectal cancer cells. We validate our approach by simulating the most frequent mutations in this type of cancer and comparing the results predicted by our model with those in the literature.