Working file for parameterizing a series of rate constants from King and Altman notation representing Hexokinase (E.C. 184.108.40.206) 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.
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 220.127.116.11 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’.
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.
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wREFERASS Program: Garcia -Sevilla F,Arribas E, Bisswanger H,Garcia -Moreno M, Garcia -Canovas F, Guevara RG -Lde , Duggleby R, Yago J,Varon R. WREFERASS:Rate equations for enzyme reactions at steady state under under ms -windows. Commun Math Comput Chem 63 :553 - 571 ,2010 . Data obtained from: Lueck Lueck JD ,Fromm HJ . Kinetics, mechanism, and regulation of rat skeletal muscle hexokinase. Journal of Biological Chemistry 249 :1341-1347 ,1974 . Alternative equations for Hexokinase: Segel, Irwin H. Enzyme kinetics :behavior and analysis of rapid equilibrium and steady state enzyme systems. New York : Wiley,1975 . Wu, Fan, et al ."Computer modeling of mitochondrial tricarboxylic acid cycle, oxidative phosphorylation, metabolite transport, and electrophysiology. "Journal of Biological Chemistry 282 .34 (2007):24525 -24537.
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Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.