<documentation xmlns="http://cellml.org/tmp-documentation"> Model Status This model is known to run in OpenCell and COR to reproduce the output shown in the publication. The units have been checked and they are consistent. <sect1 id="sec_structure"> Model Structure Abstract: The determinants of relaxation in cardiac muscle are poorly understood, yet compromised relaxation accompanies various pathologies and impaired pump function. In this study, we develop a model of active contraction to elucidate the relative importance of the [Ca2+]i transient magnitude, the unbinding of Ca2+ from troponin C (TnC), and the length-dependence of tension and Ca2+ sensitivity on relaxation. Using the framework proposed by one of our researchers, we extensively reviewed experimental literature, to quantitatively characterize the binding of Ca2+ to TnC, the kinetics of tropomyosin, the availability of binding sites, and the kinetics of crossbridge binding after perturbations in sarcomere length. Model parameters were determined from multiple experimental results and modalities (skinned and intact preparations) and model results were validated against data from length step, caged Ca2+, isometric twitches, and the half-time to relaxation with increasing sarcomere length experiments. A factorial analysis found that the [Ca2+]i transient and the unbinding of Ca2+ from TnC were the primary determinants of relaxation, with a fivefold greater effect than that of length-dependent maximum tension and twice the effect of tension-dependent binding of Ca2+ to TnC and length-dependent Ca2+ sensitivity. The affects of the [Ca2+]i transient and the unbinding rate of Ca2+ from TnC were tightly coupled with the effect of increasing either factor, depending on the reference [Ca2+]i transient and unbinding rate. <informalfigure float="0" id="fig_reaction_diagram"> <mediaobject> <imageobject> <objectinfo> model diagram </objectinfo> <imagedata fileref="niederer_2006.png" /> </imageobject> </mediaobject> Schematic diagram depicting the relationships of the active contraction framework proposed by Hunter et al. (11). The model is driven by SL and sarcomere velocity, and intracellular [Ca2+]i. Inputs are in bold, algebraic length dependencies are in italics, processes described by differential equations are standard font. </informalfigure> The original publication reference is cited below: A Quantitative Analysis of Cardiac Myocyte Relaxation: A Simulation Study, Steven Niederer, Peter Hunter, Nicholas Smith, 2006 Biophysical Journal , 90 1697-1722 PubMed ID: 16339881 </sect1> </documentation>
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Chemical concentration
Chemical concentration flow rate
Surface normal tensile stress
Troponin C, slow skeletal and cardiac muscles (TN-C)
calcium(2+)
Cardiac myocyte
Portion of cytosol
A physical entity that is defined by linking multiple physical entity terms with structural relations.
A mathematical and/or logical expression that determines the value of a data structure.
An element of a SemSim model that relates to the mathematical or logical representation of physical quantities or qualities.
A physical dependency defined in a specific SemSim model.
A physical entity defined in a specific SemSim model.
A physical process defined in a specific SemSim model.
A physical property defined in a specific SemSim model.
A computational element that stores numerical and/or logical information related to the model.
A data structure whose value is limited to decimals.
A data structure whose value is limited to the whole numbers.
A data structure unique to JSim's Mathematical Modeling Language (MML) used to set one or more model input values at runtime.
A quantitative relation between values of physical properties that occurs over a span of time and that determines the time-course of a physical process.
A physics analytical entity that represents the material, energy, and/or information content of material or immaterial, space-occupying continuants.
A SemSim model element used to represent, in whole or in part, the physical meaning of a computational element.
A physical processural entity that is a flow, or the control of a flow, of energy and/or information amongst physical continuants that are participants in the physical process.
A physical attribute of an instance of a physical entity, an occurrence of a physical process, or a physical dependency that has a quantitative value that is measurable by a physical device or method, or is computable from such values.
A data structure whose value is limited to the real numbers.
A physical dependency that is defined using a term in an external knowledge resource.
A physical entity that is defined using a term from an external knowledge resource.
A physical process that is defined using a term in an external knowledge resource.
A physical property that is defined using a term in an external knowledge resource.
A logical expression that constrains, but does not define, the value of a data structure. Example: x > 0.
A computational or physical element of a SemSim model.
A grouping of one or more data structures that comprise a computationally or physically distinct part of a model or submodel.
A physical quantity chosen as a standard in terms of which other physical quantities may be expressed.
Calcium (2+) bound to troponin C
Calcium (2+) ion bound to site II of troponin C
Weighting coefficient for process 1 of the crossbridge kinetics fading memory model
Weighting coefficient for process 2 of the crossbridge kinetics fading memory model
Weighting coefficient for process 3 of the crossbridge kinetics fading memory model
Sum of the three exponential processes in the crossbridge dynamics fading memory model
Exponential process 1 of the crossbridge kinetics fading memory model
Exponential process 2 of the crossbridge kinetics fading memory model
Exponential process 3 of the crossbridge kinetics fading memory model
The isometric tension at a given intracellular calcium ion concentration and sarcomere length
Active tension of cardiac myocyte
Curve-shaping constant for relationship between relative sarcomere velocity and relative tension
Exponential rate constant for process 1 of the crossbridge kinetics fading memory model
Exponential rate constant for process 2 of the crossbridge kinetics fading memory model
Exponential rate constant for process 3 of the crossbridge kinetics fading memory model
Change in ExtensionRatio with respect to time
Time
Temporal solution domain
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Dissociation of troponin C bound to calcium
In this model, the formation of troponin C comes from the dissociation of the calcium (2+) / troponin C complex
Sarcomere strain
Sarcomere strain, constrained to values between 0.8 and 1.15
Mystery variable mathematically equal to sarcomere strain
<apply> <eq /> <ci>ExtensionRatio</ci> <piecewise> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <gt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </piece> <otherwise> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </otherwise> </piecewise> </apply> <apply> <eq /> <ci>lambda_prev</ci> <ci>ExtensionRatio</ci> </apply> <apply> <eq /> <ci>dExtensionRatiodt</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="per_ms">0</cn> </apply> <apply> <eq /> <ci>lambda</ci> <piecewise> <piece> <ci>ExtensionRatio</ci> <apply> <and /> <apply> <gt /> <ci>ExtensionRatio</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.8</cn> </apply> <apply> <leq /> <ci>ExtensionRatio</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.15</cn> </apply> </apply> </piece> <piece> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.15</cn> <apply> <gt /> <ci>ExtensionRatio</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1.15</cn> </apply> </piece> <otherwise> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.8</cn> </otherwise> </piecewise> </apply>
Scaling factor (slope) for the relationship between lambda and T_0
Sarcomere strain?
Sarcomere overlap?
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The maximum concentration of calcium ions that can bind to site II on troponin C
Concentration of calcium (2+) bound to troponin C
Intracellular calcium (2+) concentration
Intracellular troponin flux
Intracellular troponin concentration
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cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.03507</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0003992</cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.356 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">10</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">15</cn> </apply> </apply> </piece> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <apply> <minus /> <apply> <plus /> <apply> <minus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.014</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.002555</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0001494</cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.428 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">15</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">55</cn> </apply> </apply> </piece> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <apply> <plus /> <apply> <minus /> <apply> <minus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.739 <sep /> -5 </cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 3.209 <sep /> -6 </cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 5.689 <sep /> -6 </cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.719 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">55</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">250</cn> </apply> </apply> </piece> <piece> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <apply> <plus /> <apply> <minus /> <apply> <plus /> <apply> <minus /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0001321</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">4</cn> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0002197</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">3</cn> </apply> </apply> </apply> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mM">0.0001374</cn> <apply> <power /> <apply> <divide /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <divide /> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 3.895 <sep /> -5 </cn> <ci>time</ci> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">1000</cn> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 4.441 <sep /> -6 </cn> </apply> </apply> <apply> <and /> <apply> <geq /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">250</cn> </apply> <apply> <lt /> <ci>time</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="ms">490</cn> </apply> </apply> </piece> <otherwise> <apply> <times /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1000</cn> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" type="e-notation" cellml:units="mM"> 1.2148 <sep /> -7 </cn> </apply> </otherwise> </piecewise> </apply>
Isometric tension of cell
<apply> <eq /> <ci>T_0</ci> <apply> <times /> <ci>T_Base</ci> <ci>overlap</ci> </apply> </apply>
Maximum tension at resting sarcomere length
The fraction of actin sites available for crossbridge binding
The fraction of actin sites available at full activation
<apply> <eq /> <ci>T_Base</ci> <apply> <divide /> <apply> <times /> <ci>T_ref</ci> <ci>z</ci> </apply> <ci>z_max</ci> </apply> </apply>
Concentration of free calcium (2+) at half-activation of maximum tension
Offset parameter for Ca_50 vs. lambda dependency
Calcium (2+) bound to TnC at half-activation of maximum tension
Linearization term for computing z_max
Fast relaxation rate parameter for computing z
The monoexponential activation rate seen in caged calcium (2+) experiments. Used to compute z.
Intermediate term for first component of varaible z's ODE (equation 9 in reference paper)
Slow relaxation rate parameter for computing z
Scaling parameter for Ca_50 vs. lambda dependency
Intermediate term for second component of variable z's ODE (equation 9 in reference paper)
A measure of the effect of tension on the unbinding rate of calcium (2+) from troponin C
Rate of calcium (2+) unbinding from Troponin C in the absence of tension
The binding rate of calcium (2+) to troponin C site II
Analogous to the Hill coefficient in the steady-state force-calcium (2+) curve (F-pCa) and provides a phenomenological rep- resentation of the high cooperativity, due to nearest-neighbor interactions between tropomyosin and/or crossbridges, seen in the activation of tension in cardiac muscle
The fraction of actin sites available for crossbridge binding as determined by thin filament kinetics
the maximum fraction of available actin sites at a given sarcomere length
Point around which the non-linear component of equation 9 in the paper (solving for dz/dt) is linearized to maintain an explicit formulation for the model
<apply> <eq /> <ci>K_2</ci> <apply> <times /> <apply> <divide /> <apply> <times /> <ci>alpha_r2</ci> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <apply> <times /> <ci>n_Rel</ci> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>K_1</ci> <apply> <divide /> <apply> <times /> <ci>alpha_r2</ci> <apply> <power /> <ci>z_p</ci> <apply> <minus /> <ci>n_Rel</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> <ci>n_Rel</ci> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci>z_p</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">2</cn> </apply> </apply> </apply> <apply> <eq /> <ci>z_max</ci> <apply> <divide /> <apply> <minus /> <apply> <divide /> <ci>alpha_0</ci> <apply> <power /> <apply> <divide /> <ci>Ca_TRPN_50</ci> <ci>Ca_TRPN_Max</ci> </apply> <ci>n_Hill</ci> </apply> </apply> <ci>K_2</ci> </apply> <apply> <plus /> <ci>alpha_r1</ci> <ci>K_1</ci> <apply> <divide /> <ci>alpha_0</ci> <apply> <power /> <apply> <divide /> <ci>Ca_TRPN_50</ci> <ci>Ca_TRPN_Max</ci> </apply> <ci>n_Hill</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>Ca_50</ci> <apply> <times /> <ci>Ca_50ref</ci> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <times /> <ci>beta_1</ci> <apply> <minus /> <ci>lambda</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>Ca_TRPN_50</ci> <apply> <divide /> <apply> <times /> <ci>Ca_50</ci> <ci>Ca_TRPN_Max</ci> </apply> <apply> <plus /> <ci>Ca_50</ci> <apply> <times /> <apply> <divide /> <ci>k_Ref_off</ci> <ci>k_on</ci> </apply> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <apply> <times /> <apply> <plus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <times /> <ci>beta_0</ci> <apply> <minus /> <ci>lambda</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.5</cn> </apply> <ci>gamma_trpn</ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci>alpha_Tm</ci> <apply> <times /> <ci>alpha_0</ci> <apply> <power /> <apply> <divide /> <ci>Ca_b</ci> <ci>Ca_TRPN_50</ci> </apply> <ci>n_Hill</ci> </apply> </apply> </apply> <apply> <eq /> <ci>beta_Tm</ci> <apply> <plus /> <ci>alpha_r1</ci> <apply> <divide /> <apply> <times /> <ci>alpha_r2</ci> <apply> <power /> <ci>z</ci> <apply> <minus /> <ci>n_Rel</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> </apply> </apply> </apply> <apply> <plus /> <apply> <power /> <ci>z</ci> <ci>n_Rel</ci> </apply> <apply> <power /> <ci>K_z</ci> <ci>n_Rel</ci> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <apply> <diff /> <bvar> <ci>time</ci> </bvar> <ci>z</ci> </apply> <apply> <minus /> <apply> <times /> <ci>alpha_Tm</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <ci>z</ci> </apply> </apply> <apply> <times /> <ci>beta_Tm</ci> <ci>z</ci> </apply> </apply> </apply>
The unbinding rate of calcium (2+) from troponin C site II
<apply> <eq /> <ci>k_off</ci> <piecewise> <piece> <apply> <times /> <ci>k_Ref_off</ci> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <ci>Tension</ci> <apply> <times /> <ci>gamma_trpn</ci> <ci>T_ref</ci> </apply> </apply> </apply> </apply> <apply> <gt /> <apply> <minus /> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn> <apply> <divide /> <ci>Tension</ci> <apply> <times /> <ci>gamma_trpn</ci> <ci>T_ref</ci> </apply> </apply> </apply> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.1</cn> </apply> </piece> <otherwise> <apply> <times /> <ci>k_Ref_off</ci> <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.1</cn> </apply> </otherwise> </piecewise> </apply> <apply> <eq /> <ci>J_TRPN</ci> <apply> <minus /> <apply> <times /> <apply> <minus /> <ci>Ca_TRPN_Max</ci> <ci>TRPN</ci> </apply> <ci>k_off</ci> </apply> <apply> <times /> <ci>Ca_i</ci> <ci>TRPN</ci> <ci>k_on</ci> </apply> </apply> </apply>