Where and when

SMB 2023 – Society for Mathematical Biology Annual Meeting 2023. Celebrating SMB's 50th Anniversary at The Ohio State University (Columbus, Ohio) [source: https://2023.smb.org/]

The MIDA group will take part in the conference with the talk "Drug dosage in cancer: a mathematical approach for computing steady states of chemical reaction networks" presented by Silvia Berra.

abstract: During the G1-S transition phase of life of colorectal cells many proteins interact in chemical reactions, some of which are crucial since mutations altering the function of the corresponding proteins may cause cancer. The set of these interactions can be described through a properly designed Chemical Reaction Network (CRN). In turn, the latter can be represented by a mathematical model consisting in a system of autonomous ordinary differential equations. Computing the steady state of this system is a key step for understanding the global (and local) effects of each mutation and of some specific targeted drugs used to contrast the corresponding functional alterations. The most common approach for computing the steady state consists in simulating the system's dynamical evolution in time; however, this is a very time-consuming process. Here I propose a different method, consisting in recasting the steady state computation problem as a root-finding one. To solve the latter, an algorithm that combines the Newton method and the gradient descent approach is introduced, where the non-negativity constraints on the steady state concentrations are assured by defining and applying a suitable operator P at the end of every iterative step _^[1]. Such an algorithm, which is convergent under specific assumptions, turns out to be more precise and faster than the dynamic approach. Starting from a CRN previously introduced for modeling the G1-S transition phase of colorectal cells _^[2], the method is validated in simulation mimiking both physiological and mutated status and also in the presence of targeted drugs applied individually or together in a combined therapy.

^{Additional authors: Sara Sommariva, Federico Benvenuto, Giacomo Caviglia, Michele Piana – Department of Mathematics, University of Genoa, via Dodecaneso 35, 16146 Genoa, Italy
[1] Berra, Silvia, et al. 'A fast and convergent combined Newton and gradient descent method for computing steady states of chemical reaction networks.' arXiv preprint arXiv:2212.14252 (2022).
[2] Sommariva, Sara, et al. 'Computational quantification of global effects induced by mutations and drugs in signaling networks of colorectal cancer cells.' Scientific reports 11.1 (2021): 19602.}

Methods for Biological Modeling Subgroup (MFBM)

MFBM Subgroup Contributed Talks