Comparison of 1-sided and 2 sided Michaelis-Menten transporters in a two compartment model without flow.

## Description

Figure3: Determining Vmax and Km from initial velocity: The quantity, VmaxEstB = V2*B2/t.max is plotted (Black Lines) against B1+B2. The uppermost point of each nearly vertical line is an estimate of the velocity of the transporter between 0 and 1 second. VmaxEstB equals approximately V2*dB2/dt = PSeffective*(B1-B2).

As the Michaelis-Menten transporter becomes saturated (increasing values of B1+B2 ranging over 6 orders of magnitude), the uppermost points of the vertical lines asymptotically approach Vmax (Green Line). Half of the value, Vmax/2 (Red line) intersects the upper outline of these vertical lines where B1+B2 = Km (dashed Blue line).

Two types of a saturable Michaelis-Menten transporter are considered in this two compartment model without flow--a one sided transporter for solute A and a two-sided transporter for solute B. The model for solute A is cis- side driven. Concentration of A in V1, A1, determines the fractional saturation, PSa/PSmax, where PSmax is Vmax/Km, and

PSa = PSmax/(1 + A1/Km).

The model for solute B is cis-trans driven. Concentration of B in both V1 and V2, B1 and B2 respectively, determine the fractional saturation, where PSmax is Vmax/Km and

PSb = PSmax/(1 + B1/Km + B2/Km).

## Equations

#### One sided Michaelis-Menten Transporter

#### Ordinary Differential Equations

#### Initial Conditions

#### Two 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.