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Cardiac Physiome Society workshop: November 6-9, 2017 , Toronto

# CaATPase

Model number: 0054

Uptake and transport of calcium from the cytosol across the sarcoplasmic reticulum membrane, aided by ATP.

## Detailed Description

This a model of the uptake of calcium from the cytosol, aided by ATP, across the sarcoplasmic reticulum membrane.

The model is taken from Lauger (1991) page 241, and is based on Inesi and de Meis (1989) (hereafter referred to as IdM). The reaction numbers r01 through r12 have been arbitrarily assigned to the reaction diagram in Lauger, page 241.

This model is similar to IdM, with some important differences. IdM uses slightly different nomenclature to emphasize that there is always a phosphate group on the transporter. The IdM reactions are listed with the corresponding reactions of this model below. IdM has an additional reaction path parallel to reactions 5 and 6 (r05 and r06). Idm also has a leakage reaction of calcium between reactions 4 and 5 (r04 and r05) which IdM label ”(E')” which should not be confused with a conformational state of the transporter which is labelled “E'”. The complexing of the transporter with ATP is no longer reaction 12 (r12), but occurs between reactions 3 and 4 (r03 and r04).

In reference to the diagram displayed in the JSim Model: PI (all in caps) is the irrational number, 3.1415926… . Pi is the chemical species, inorganic phosphate.

A leak of calcium from the SR to the cytosol has been included.

Foward reaction direction is clockwise.

## Relevant Equations

The following complete equations are derived from annotated equations in the JSim model. $\large {\frac {d}{dt}E_{\text{\small{1}}} = k_{\text{\small{f11}}}Pi \cdot E_{\text{\small{2}}} - k_{\text{\small{b11}}}Pi \cdot E_{\text{\small{1}}} k_{\text{\small{f12}}}E_{\text{\small{1}}}ATP + k_{\text{\small{b12}}}E_{\text{\small{1}}}ATP$

$\large {\frac {d}{dt}}ATP(t) = -(k_{\text{\small{f12}}}E_{\text{\small{1}}}ATP - k_{\text{\small{b12}}}E_{\text{\small{1}}}ATP) \frac {{Surf}_{\text{\small{SR}}}}{V_{\text{\small{cyt}}}}$

$\large {\frac {d}{dt}}{\it E_1ATP} \left( t \right) = -k_{\text{\small{f01}}} Ca_{\text{\small{cyt}}} E_{\text{\small{1}}} ATP + k_{\text{\small{b01}}} Ca E_{\text{\small{1}}} ATP + k_{\text{\small{f12}}} E_{\text{\small{1}}} ATP - k_{\text{\small{b12}}} E_{\text{\small{1}}} ATP$

$\large {\frac {d}{dt}}{\it Ca_{\text{\small{cyt}}}} \left( t \right) = ( - k_{\text{\small{f01}}} Ca_{\text{\small{cyt}}} E_{\text{\small{1}}} ATP + k_{\text{\small{b01}}} Ca E_{\text{\small{1}}} ATP - k_{\text{\small{f03}}} Ca_{\text{\small{cyt}}} Ca E_{\text{\small{1}}} ATP + k_{\text{\small{b03}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} ATP) \frac {Surf_{\text{\small{SR}}}}{V_{\text{\small{cyt}}}}$

$\large {\frac {d}{dt}}Ca E_{\text{\small{1}}} ATP(t) = k_{\text{\small{f01}}} Ca_{\text{\small{cyt}}} E_{\text{\small{1}}} ATP - k_{\text{\small{b01}}} Ca E_{\text{\small{1}}} ATP - k_{\text{\small{f02}}} Ca E_{\text{\small{1}}} ATP + k_{\text{\small{b02}}} Ca E_{\text{\small{1}}} ATP$

$\large {\frac {d}{dt}} Ca E_{\text{\small{1}}} ATP (t) = k_{\text{\small{f02}}} Ca E_{\text{\small{1}}} ATP - k_{\text{\small{b02}}} Ca E_{\text{\small{1}}} ATP - k_{\text{\small{f03}}} Ca_{\text{\small{cyt}}} Ca E_{\text{\small{1}}} ATP + k_{\text{\small{b03}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} ATP$

$\large {\frac {d}{dt}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} ATP (t) = k_{\text{\small{f03}}} Ca_{\text{\small{cyt}}} Ca E_{\text{\small{1}}} ATP - k_{\text{\small{b03}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} ATP - k_{\text{\small{f04}}} Ca_{\text{\small{4}}} E_{\text{\small{1}}} ATP + k_{\text{\small{b04}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} P \cdot ADP$

$\large {\frac {d}{dt}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} P \cdot ADP (t) = k_{\text{\small{f04}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} ATP - k_{\text{\small{b04}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} P \cdot ADP - k_{\text{\small{f05}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} P \cdot ADP + k_{\text{\small{b05}}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}}$

$\large {\frac {d}{dt}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} (t) = k_{\text{\small{f05}}} Ca_{\text{\small{2}}} E_{\text{\small{1}}} P \cdot ADP - k_{\text{\small{b05}}} ADP \cdot P \cdot E_{\text{\small{2}}} - k_{\text{\small{f06}}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} + k_{\text{\small{b06}}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}}$

$\large {\frac {d}{dt}} P \cdot E_{\text{\small{2}}} Ca (t) k_{\text{\small{f07}}} P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} - k_{\text{\small{b07}}} P \cdot E_{\text{\small{2}}} Ca \cdot Ca_{\text{\small{SR}}} - k_{\text{\small{f08}}} P \cdot E_{\text{\small{2}}} Ca + k_{\text{\small{b08}}} P \cdot E_{\text{\small{2}}} Ca$

$\large {\frac {d}{dt}} P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} (t) = k_{\text{\small{f06}}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} - k_{\text{\small{b06}}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} - k_{\text{\small{f07}}} P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} + k_{\text{\small{b07}}} P \cdot E_{\text{\small{2}}} Ca \cdot Ca_{\text{\small{SR}}}$

$\large {\frac {d}{dt}} P \cdot E_{\text{\small{2}}} Ca (t) = k_{\text{\small{f08}}} P \cdot E_{\text{\small{2}}} Ca - k_{\text{\small{b08}}} P \cdot E_{\text{\small{2}}} Ca - k_{\text{\small{f09}}} P \cdot E_{\text{\small{2}}} Ca + k_{\text{\small{b09}}} P \cdot E_{\text{\small{2}}} Ca_{\text{\small{SR}}}$

$\large {\frac {d}{dt}}Ca_{\text{\small{SR}}}(t) = (k_{\text{\small{f07}}} P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} - k_{\text{\small{b07}}} P \cdot E_{\text{\small{2}}} Ca \cdot Ca_{\text{\small{SR}}} + k_{\text{\small{f09}}} P \cdot E_{\text{\small{2}}} Ca - k_{\text{\small{b09}}} P \cdot E_{\text{\small{2}}} Ca_{\text{\small{SR}}}) \frac {Surf_{\text{\small{SR}}}}{V_{\text{\small{SR}}}} + \frac {g_{\text{\small{leak}}}}{V_{\text{\small{cyt}}}}(Ca_{\text{\small{cyt}}} - Ca_{\text{\small{SR}}})$

$\large {\frac {d}{dt}}P \cdot E_{\text{\small{2}}} (t) = k_{\text{\small{f09}}} P \cdot E_{\text{\small{2}}} Ca - k_{\text{\small{b09}}} P \cdot E_{\text{\small{2}}} Ca_{\text{\small{SR}}} - k_{\text{\small{f10}}} P \cdot E_{\text{\small{2}}} + k_{\text{\small{b10}}} Pi \cdot E_{\text{\small{2}}}$

$\large {\frac {d}{dt}}Pi \cdot E_{\text{\small{2}}} (t) = k_{\text{\small{f10}}} P \cdot E_{\text{\small{2}}} - k_{\text{\small{b10}}} Pi \cdot E_{\text{\small{2}}} - k_{\text{\small{f11}}} Pi \cdot E_{\text{\small{2}}} - k_{\text{\small{f11}}} Pi \cdotE_{\text{\small{2}}} + k_{\text{\small{b11}}} Pi \cdot E_{\text{\small{1}}}$

$\large {\frac {d}{dt}} Pi (t) = (k_{\text{\small{f11}}} Pi \cdot E_{\text{\small{2}}} - k_{\text{\small{b11}}} Pi \cdot E_{\text{\small{1}}} ) \frac {Surf_{\text{\small{SR}}}}{V_{\text{\small{cyt}}}}$

$\large {\frac {d}{dt}}ADP (t) = (k_{\text{\small{f06}}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}} - k_{\text{\small{b06}}} ADP \cdot P \cdot E_{\text{\small{2}}} Ca_{\text{\small{2}}}) \frac {Surf_{\text{\small{SR}}}}{V_{\text{\small{cyt}}}}$

## Run JSim Model

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## References

Lauger, P., “Electrogenic Ion Pumps,” Volume 5, Distinguished Lectures of the Society of General Physiologists, 1991, Sinauer Associates, Inc., Sunderland, Massachusetts, USA.

Inesi, G. and de Meis, L., “Regulation of Steady State Filling in the Sarcoplasmic Reticulum, Roles of back-inhibition, leakage, and slippage of the calcium pump: J. Biol. Chem. vol. 264, No. 10, April 5, pp. 5929-5936, 1989.

## Key Terms

Calcium transport, sarcoplasmic reticulum, SR kinetics, pumps, ATP, Cell Physiology, Cellular biochemical systems, Data