A two compartment one-sided Michaelis-Menten transporter.
Description
Compartmental models are based on mass balance equations. The compartment has a volume, V, and a time-varying concentration of a substance, C(t). An underlying assumption of compartmental models is that the material in the compartment is instantaneously well mixed. Compartmental models are also call well stirred tank models. This is a compartmental model for facilitated exchange between two chambers separated by a membrane. It is a closed model (no inflow or outflow), with volumes V1 and V2 for each compartment, time dependent concentrations A1(t) and A2(t) respectively, and an exchange coefficient PS. G2 is for Gulosity, the first order consumption of the solute in V2. This model assumes instantaneous solute binding to a Michaelis-Menten type transporter, with only a single site available from on the V1 side of the membrane. Fluxes are set by the concentration of A1(t) in V1. A1 determines the fractional saturation, PS/PSmax. See model TranspMM2sidedComp2.proj to compare with a transporter binding on either side of the membrane
Equations
One sided Michaelis-Menten Transporter
Ordinary Differential Equations
Initial Conditions
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Klingenberg M. Membrane protein oligomeric structure and transport function. Nature 290: 449-454, 1981. Stein WD. The Movement of Molecules across Cell Membranes. New York: Academic Press, 1967. Stein WD. Transport and Diffusion across Cell Membranes. Orlando, Florida: Academic Press Inc., 1986. Wilbrandt W and Rosenberg T. The concept of carrier transport and its corollaries in pharmacology. Pharmacol Rev 13: 109-183, 1961. Schwartz LM, Bukowski TR, Ploger JD, and Bassingthwaighte JB. Endothelial adenosin transporter characterization in perfused guinea pig hearts. Am J Physiol Heart Circ Physiol 279: H1502-H1511, 2000.
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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.