# Comp2FlowMMExchangeReaction

Two compartment model with flow, Michaelis-Menten type exchanger, and a reversible reaction in non-flowing compartment converting C to B.

Model number: 0249

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## Description

This is a two compartmental (plasma and parenchymal cell (pc) exchange model with flow in the plasma compartment. The compartments are instantaneously well mixed. Substances C and B reversibly convert to each other by a first order process in the parenchymal cell compartment. This model has a Michaelis-Menten (MM) type of transporter of the cell membrane between the capillary plasma and the parenchymal cell, expressed in terms of Km and PSmax, for which the denominators include terms for the solute on both sides of the meembrane, as if the binding site is accessible simultaneously from either side. In this sense the transporter is acting more like a channel that a ferry boat.

Further reading:

- Understanding the Comp2FlowMMExchangeReaction Model. (PDF file)
## Equations

#### Ordinary Differential Equations

#### Initial Conditions

, , , and .The equations for this model may also 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.

## Download JSim project file

## References

Wilfred D Stein. Transport and Diffusion across Cell Membranes, 2nd Ed. Academic Press 1986

## Related Models

Single Compartment Models:

- Comp1Decay: Single Compartment with Decay,
- Comp1Flow: Single Compartment with Flow,
- Comp1FlowDecay: Single Compartment with Flow and Decay,
- Comp1Reaction: Single Compartment with One Reaction,
- Comp1FlowReaction: Single Compartment with Flow and One Reaction,
- Comp1FlowReactions2: Single Compartment with Flow and Two Reactions,

Two Compartment Models:

- Comp2Exchange: Two Compartments with Exchange,
- Comp2ExchangeReaction: Two Compartments with Exchange and One Reaction,
- Comp2FlowExchange: Two Compartments with Flow and Exchange Fit to a data set,
- Comp2FlowExchangeReaction: Two Compartments with Flow, Exchange, and One Reaction.
- Comp2FlowMMExchangeReaction: Two Compartments with Flow, Exchange using a Michaelis-Menten transporter, and One Reaction.
- Comp2FlowMRIContrast: Two Compartments with Flow, conversion of water to water spin for MRI contrast.
- Cortisol secretion: Two compartments with feedback control of precursor to cortisol and its adrenal secretion.

N>2 Compartment Models:

- Comp3FlowExch: Three compartmental model for plasma, interstitial fluid, and parenchymal cell,
- Comp6Propofol: Six compartmental model for propofol anaesthesia,
- CTEX10: N Compartments in series with Flow, emphasizes sensitivity analysis and optimization,
- CTEX10stat: CTEX10 model with statistics on inflow and outflow curves,
- CTEX20: N Compartments in series with Flow, each compartment exchanging with a compartment in parallel,
- CTEX20 5 path: Weighted sum of up to 5 paths of CTEX 20 modeled capillaries.
- CompNFlowDelay: N Compartments in series with Flow and Delay.
- Comp6_Recirc: Six compartmental recirculating model,
- Comp2x2Recirc: Dual two compartment models with recirculation and clearance,

Osmotic Exchange:

- Uncoupled fluxes of water and solute across membrane.
- Uncoupled fluxes of water and solute across membrane w/ columns for measuring pressure.
- Transport of a hard spherical solute through a cylindrical pore.

Pharmacology:

- Washout curve simulation by sum of three decaying exponentials.
- Three reactions in series with no enzymes.
- Michaelis-Menton reactions in series.
- Enzymatic reactions in series.
- Four sequential enzymatic reactions.

## Key Terms

Course, compartment, compartmental, tutorial, exchange, multiple compartments, flux, steady state, reaction, conversion, flow, plasma, parenchymal cell, Michaelis-Menten, transporter## Model Feedback

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## Model History

Get Model history in CVS.## Acknowledgements

Please cite

**www.physiome.org**in any publication for which this software is used and send one reprint to the address given below:

The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.[This page was last modified 14Mar18, 3:17 pm.]

**Model development and archiving support at physiome.org 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.