Working file for parameterizing a series of rate constants from King and Altman notation representing Hexokinase (E.C. 2.7.1.1) as a random order Bi-Bi, data from Leuck and Fromm. This model assesses the kinetic equilibrium for multiple representations of hexokinase with varying simulations with a range of pH's.

Description

A full kinetic model for enzymatic facilitation of substrate to product should account and 
provide equations for the binding for all reactants, the multiple enzyme-reactant states, 
the inherent ordered or random binding mechanisms for substrates, ions, or protons that 
modulate the kinetic activity. Kinetic models of this quality are uncommon because the 
simpler Michaelis-Menten (MM) representations have been considered adequate. MM approximations 
are for steady state conditions; they are inaccurate during transients; they cannot 
accommodate circumstances in which the concentration of reactants are close to the affinity 
or dissociation constant of the enzyme. The ease in implementing MM has simplified the 
general understanding of enzymes, biology, and stunted the exploration for better 
quantitative methods of higher accuracy in enzymology. Here we report the of an enzymatic 
tool wREFERASS (Garcia-Sevilla et al., 2010) to develop a complex kinetic model of skeletal 
muscle hexokinase (EC 2.7.1.1 using the King and Altman notation: all terms consist of 
rate constants and reactant concentrations. The wREFERASS tool derives detailed mathematical 
expressions based on an input file that describes explicitly the kinetic pathways. 
The expressions provide unitary balance, conserves mass, and require defining and 
parameterizing the dissociation constants for each binding step. Rate constants and 
dissociation constants were parameterized using enzymatic data obtained from Lueck and 
Fromm (1973) on rat skeletal muscle hexokinase II. The kinetic model accounts for all 
reactants described from the input file and has physical units for all biological elements. 
The kinetic behavior far surpasses any MM representation due to the consideration of the 
multiple enzyme states. It accounts for time delay due to binding, shifts in conformational 
states and product release. After parameterizing each dissociation and rate constant it 
becomes clear that there is a preferred kinetic pathway for phosphorylation of glucose even 
though the binding mechanism is referred to as ‘random ordered’.

Equations

The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.