In-silico modeling of simple enzyme kinetics: from Michaelis-Menten to microscopic rate constants

SilviaBerra

IRCCS Ospedale Policlinico San Martino, Genova, Italy

"In-silico modeling of simple enzyme kinetics: from Michaelis-Menten to microscopic rate constants"

Chemical Reaction Networks (CRNs) provide a powerful framework for modeling interactions between multiple chemical species within complex biological pathways. Their dynamics can be described by the mass-action law, representing variations over time in species concentrations through large systems of ODEs. The study of CRNs modeling signaling mechanisms within single cells has been successfully applied to provide insight into oncogenic pathways, enabling more predictive cancer models and improved therapeutic strategies [1,2,3]. Developing a CRN requires selecting the involved species, defining their interactions, and identifying key parameters such as microscopic reaction rates. This talk presents a method to retrieve these rates, particularly in the context of enzyme kinetics. We consider a simple model, where an enzyme E binds to a substrate S, forming a complex C that dissociates into a product P while regenerating E. This process is governed by four ODEs with three reaction rates: forward k_f, reverse k_r, and catalytic k_cat, typically hard to determine experimentally. A common simplification leads to the Michaelis-Menten (MM) model, where enzyme kinetics is characterized by a single ODE depending on two measurable parameters: the Michaelis constant K_M, and the maximum reaction rate V_max. These parameters may be expressed as functions of microscopic rates and are more accessible experimentally. This talk addresses the inverse problem of estimating k_f and k_r from K_M and V_max. A computational algorithm for solving this problem is presented and analyzed, along with an estimate of the reconstruction accuracy, and numerical simulations demonstrating its potential for refining kinetic models in biological and biomedical research. [1] Sommariva et al., J. Math. Biol., 82 (6): 55, 2021. [2] Berra et al., J. Optim. Theory Appl., 200 (1): 404-427, 2024. [3] Sommariva et al., Front. Syst. Biol., 3: 1207898, 2023.
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