Assessing the Dynamics of Biochemical Pathways Using Continuous Boolean Approximations

The Mass Action Law is a mathematical expression that relates reaction
rates and reactant concentrations. Michaelis-Menten kinetics, derived
from the mass action law, is frequently used in modeling biochemical
pathways. Michaelis-Menten kinetics  requires knowledge on details of
the interaction between the substrates (and potential inhibitors) with
the enzymes. This information however, is often not known. Normalized
HillCube functions, characterized by continuous Boolean
approximations, provide a canonical representation of the reaction
rates that is based solely on known interactions, and not on the
kinetics of those interactions. Normalized HillCube functions thus,
can be an alternative for modeling biochemical pathways that can
address the downsides associated with Michaelis-Menten kinetics.  The
overall goal of this research is to assess whether HillCube functions
can be a good approximation for enzyme kinetics.

A simple Glycolysis pathway, for which Michaelis-Menten kinetics is
available, is used to test our research objective. We want to
determine if there are parameter values of the HillCube functions that
will produce similar dynamics to the Michaelis-Menten model. Parameter
estimation programs are developed using Matlab with this aim. These
programs return the optimum parameter values of the HillCube functions
to approximate the given dynamics of the Michaelis-Menten model, if
they exist. We hope that with the results obtained thus far, the
HillCube functions can reproduce dynamics similar to those shown by
the Michaelis-Menten model for the Glycolysis pathway, and hence be
able to approximate the enzyme kinetics as well.