Gain and Loss of Function mutations in biological chemical reaction networks: a mathematical model with application to colorectal cancer cells

Abstract

This paper studies a system of Ordinary Differential Equations modeling a chemical reaction network and derives from it a simulation tool mimicking Loss of Function and Gain of Function mutations found in cancer cells. More specifically, from a theoretical perspective, our approach focuses on the determination of moiety conservation laws for the system and their relation with the corresponding stoichiometric surfaces. Then we show that Loss of Function mutations can be implemented in the model via modification of the initial conditions in the system, while Gain of Function mutations can be implemented by eliminating specific reactions. Finally, the model is utilized to examine in detail the G1-S phase of a colorectal cancer cell.

Computational quantification of global effects induced by mutations and drugs in signaling networks of colorectal cancer cells

“…Consider a cell affected by a number of mutations each one of them resulting in the loss or gain of function of a specific protein. As we have shown in a previous work (Sommariva et al, 2020) , our framework allows us quantifying the simultaneous effect of all mutations. Specifically, each LoF mutation entails a change in the value of the total concentrations provided to the algorithm.…”

“…The importance of conservation laws is twofold. On the one hand, we have numerically verified (Sommariva et al, 2020) that the system of ODEs (1) admits a unique equilibrium on the set…”

“…Indeed, the value of c defines a unique stoichiometric compatibility class and all initial states belonging to the same class lead to the same stationary state. Therefore, every equilibrium state corresponds to a set of 81 constants, and conversely (Sommariva et al, 2020) .…”

“…By exploiting the mathematical framework developed in our previous work (Sommariva et al, 2020) , we simulated the effect of a LoF of APC, AKT, SMAD4, and PTEN by observing that all these proteins are involved in only one conservation law. Their LoF mutations are implemented by setting to zero the total concentration at disposal of the corresponding conservation law.…”

“…The resulting mathematical model is capable of describing the behavior of healthy physiological networks, as well as the consequences of individual pathological conditions associated with specific mutations. As for mutations, we adopt the formal description of Loss of Function (LoF) and Gain of Function (GoF) that has been extensively analyzed in a previous paper (Sommariva et al, 2020) . In the present work, starting from the system of ODEs, we want to develop an efficient computational tool that can be used for an in silico analysis of mutations of the CRC-CRN and of the effects induced by targeted drugs.…”