Tracer transients Slow versus fast binding. Figure 5 of "Tracers in Physiological Systems Modeling".
Two compartment model with constant volumes, V1 and V2, 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 The program test the addition of tracers "tr" and "T" both in pM, but either or both of which can be added to mM levels and thus are not "tracers", but are competing chemical species, displacing C1 from the C1B complex. Tracer "C1tr" has the same equations for binding as does C1. Tracer "C1T" hsa equation based on assuming instantaneous binding to C to B in V1. thus C1T is an approximation which becomes correct when kon is very fast. Function generator, Qintr and QinT, provide delayed step inputs to inject after SS is reached for C1
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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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The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
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.