Volume of Distribution of equilibrium binding and unsteady state. Figure 3 of "Tracers in Physiological Systems Modeling".
One compartment model with constant volumes, V1, but concentration-dependent volume of distribution. B is an uncomplexed binding site which reacts, first order, with C1 to form CB The reverse dissociation reaction converts CB to C1 and B. The dissociation const Kd = koff/kon and at equilibrium = C1*B/CB
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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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Anderson JC and Bassingthwaighte JB: "Tracers in physiological systems modeling". In: Mathematical Modeling in Nutrition and Agriculture. Proc 9th International Conf on Mathematical Modeling in Nutrition, Roanoke, VA, August 14-17, 2006, edited by Mark D. Hanigan JN and Casey L Marsteller. Virginia Polytechnic Institute and State University, Blacksburg, VA 2007, pp 125-159.
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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.