# 4-State_Sarcomere_Energetics

The 4-State model of sarcomeric contraction created by Landesberg and Sideman is investigated in terms of the energy liberated by the system as a function of the rate of shortening.

Model number: 0070

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## Description

This model characterizes the energy liberation rate during steady sarcomeric contraction as developed by Tchaicheeyan and Landesberg (Am J Physiol 289:H2176-H2182, 2005). Three hypotheses are applied to the basic Landesberg 4-State model of sarcomeric function in an effort to explain the biphasic energy liberation rate - velocity relationship. They are:1) Crossbridge turnover rate from non-force generating (weak) to force generating (strong) conformation decreases as velocity increases.

2) Crossbridge kinetics is determined by the number of strong crossbridges

3) The affinity of troponin for calcium is modulated by the number of strong crossbridges.

All three hypotheses yeild biphasic energy liberation rate - velocity relationships. The equations given below show how these three hypotheses are integrated into the basic Landesberg 4-State model.

## Equations

and

where R, A, T and U are the unbound weak, bound weak, bound strong and unbound strong states of troponin, respectively. Tro is the total concentration of troponin regulatory units, SL is the sarcomere length and V is the sarcomere contraction velocity defined as positive in the case of sarcomere shortening. The three variants of the model affect the kinetics of the basic 4-State model in the following ways: Variant 1: Velocity affecting weak to strong transition rate

Variant 2: Crossbridge - crossbridge cooperativity

Variant 3: Crossbridge - calcium cooperativity

where f is the weak to strong transition rate of troponin, k

_{-l}is the calcium bound to unbound transition rate, N

_{XB}is the number of strong crossbridges, and f

_{m}and k

_{m}represent the number of strong crossbridges which represents an f or k

_{-1}, respectively, at the midpoint of its range.

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## References

Regulation of energy liberation during steady sarcomere shortening.

*American Journal of Physiology, Heart and Circulatory Physiology*

**289**:H2176-H2182, 2005.

Landesberg A and Sideman S.

Force-velocity relationship and biochemical-to-mechanical energy conversion by the sarcomere.

*American Journal of Physiology, Heart and Circulatory Physiology*

**278**:H1274-H1284, 2000.

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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 29Jan20, 1:02 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,
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