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Multiphysics model of a rat ventricular myocyte: a voltage-clamp study.

Krishna A, Valderrábano M, Palade PT, Clark WJ - Theor Biol Med Model (2012)

Bottom Line: We also study the impact of temperature (22 to 38°C) on myofilament contractile response.The critical role of myofilament Ca2 + sensitivity in modulating developed force is likewise studied, as is the indirect coupling of intracellular contractile mechanism with the plasma membrane via the Na + /Ca2 + exchanger (NCX).Thus, the model provides mechanistic insights into whole-cell responses to a wide variety of testing approaches used in studies of cardiac myofilament contractility that have appeared in the literature over the past several decades.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Electrical and Computer Engineering, Rice University, 6100 Main Street, Houston, TX 77005, USA.

ABSTRACT

Background: The objective of this study is to develop a comprehensive model of the electromechanical behavior of the rat ventricular myocyte to investigate the various factors influencing its contractile response.

Methods: Here, we couple a model of Ca2 + dynamics described in our previous work, with a well-known model of contractile mechanics developed by Rice, Wang, Bers and de Tombe to develop a composite multiphysics model of excitation-contraction coupling. This comprehensive cell model is studied under voltage clamp (VC) conditions, since it allows to focus our study on the elaborate Ca2 + signaling system that controls the contractile mechanism.

Results: We examine the role of various factors influencing cellular contractile response. In particular, direct factors such as the amount of activator Ca2 + available to trigger contraction and the type of mechanical load applied (resulting in isosarcometric, isometric or unloaded contraction) are investigated. We also study the impact of temperature (22 to 38°C) on myofilament contractile response. The critical role of myofilament Ca2 + sensitivity in modulating developed force is likewise studied, as is the indirect coupling of intracellular contractile mechanism with the plasma membrane via the Na + /Ca2 + exchanger (NCX). Finally, we demonstrate a key linear relationship between the rate of contraction and relaxation, which is shown here to be intrinsically coupled over the full range of physiological perturbations.

Conclusions: Extensive testing of the composite model elucidates the importance of various direct and indirect modulatory influences on cellular twitch response with wide agreement with measured data on all accounts. Thus, the model provides mechanistic insights into whole-cell responses to a wide variety of testing approaches used in studies of cardiac myofilament contractility that have appeared in the literature over the past several decades.

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Unloaded contraction. Twitch response - Unloaded contraction. (A) The total muscle force is plotted corresponding to Ca2 + transients with peak values 1.1 (∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM as in Figure 3B. (B) Cell shortening twitches as a function of Ca2 + activation. The cell is allowed to contract from its equilibrium length of 1.9 μm against the passive elastic and viscous restoring forces in the model of Rice et al. ([13]; Figure 1). Increasing peak translating into increased amount of activator Ca2 + causes a decrease in time to peak shortening. The inset shows self-normalized sarcomere length for peak values of 1.1 (∗) and 0.5 (∙) μM. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
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Figure 4: Unloaded contraction. Twitch response - Unloaded contraction. (A) The total muscle force is plotted corresponding to Ca2 + transients with peak values 1.1 (∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM as in Figure 3B. (B) Cell shortening twitches as a function of Ca2 + activation. The cell is allowed to contract from its equilibrium length of 1.9 μm against the passive elastic and viscous restoring forces in the model of Rice et al. ([13]; Figure 1). Increasing peak translating into increased amount of activator Ca2 + causes a decrease in time to peak shortening. The inset shows self-normalized sarcomere length for peak values of 1.1 (∗) and 0.5 (∙) μM. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.

Mentions: (B) Increasing background Ca2 + myo causes a leftward shift in steady state F-SL relationship as shown in Figure 3B-i. The increase in maximal plateau force with increase in background Ca2 + myo is observed to be less prominent at higher levels of activator Ca2 + in the myoplasm. In Figure 3B-ii the activator Ca2 + is varied by modulating the peak of the Ca2 + myo transient by adjusting the voltage clamp pulse duration (an increase in pulse duration from 5 ms to 50 ms increased peak Ca2 + myo from 0.5 to 1.1 μM respectively). This protocol allows for the peak of the transient to be changed without a significant change in the duration of the transient (Krishna et al. [4] ; Figure 4). The traces correspond to increasing peak values from 0.5 (∙) to 1.1 (∗) μM. Although similar to case with increasing SL, increasing activator Ca2 + results in a relatively non-linear increase in peak force generated. As shown in Figure 3A-i, the steady state F-Ca relationship is characterized by a Hill function as experimentally observed [25]. The time-to-peak force (TTP) remains relatively unaffected by the amount of activator Ca2 + causing the twitch response. Inset in Figure 3B-ii shows the dependence of TD50 (time taken from 50% activation to 50% relaxation) on peak Ca2 + myo indicating an increase in twitch duration with increasing levels of activator Ca2 + . Figure 3B-iii shows the phase plots of self normalized force versus the instantaneous Ca2 + concentration in the myoplasm for increasing peak Ca2 + myo (traces marked ∙ to ∗) overlayed with a steady state F-Ca relationships corresponding to SL = 2.3 μm (∗). The contraction-relaxation coupling point (∘) traverses along the F-Ca relationship to increasing values of Ca2 + and force with increasing peak Ca2 + myo.


Multiphysics model of a rat ventricular myocyte: a voltage-clamp study.

Krishna A, Valderrábano M, Palade PT, Clark WJ - Theor Biol Med Model (2012)

Unloaded contraction. Twitch response - Unloaded contraction. (A) The total muscle force is plotted corresponding to Ca2 + transients with peak values 1.1 (∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM as in Figure 3B. (B) Cell shortening twitches as a function of Ca2 + activation. The cell is allowed to contract from its equilibrium length of 1.9 μm against the passive elastic and viscous restoring forces in the model of Rice et al. ([13]; Figure 1). Increasing peak translating into increased amount of activator Ca2 + causes a decrease in time to peak shortening. The inset shows self-normalized sarcomere length for peak values of 1.1 (∗) and 0.5 (∙) μM. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3585474&req=5

Figure 4: Unloaded contraction. Twitch response - Unloaded contraction. (A) The total muscle force is plotted corresponding to Ca2 + transients with peak values 1.1 (∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM as in Figure 3B. (B) Cell shortening twitches as a function of Ca2 + activation. The cell is allowed to contract from its equilibrium length of 1.9 μm against the passive elastic and viscous restoring forces in the model of Rice et al. ([13]; Figure 1). Increasing peak translating into increased amount of activator Ca2 + causes a decrease in time to peak shortening. The inset shows self-normalized sarcomere length for peak values of 1.1 (∗) and 0.5 (∙) μM. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
Mentions: (B) Increasing background Ca2 + myo causes a leftward shift in steady state F-SL relationship as shown in Figure 3B-i. The increase in maximal plateau force with increase in background Ca2 + myo is observed to be less prominent at higher levels of activator Ca2 + in the myoplasm. In Figure 3B-ii the activator Ca2 + is varied by modulating the peak of the Ca2 + myo transient by adjusting the voltage clamp pulse duration (an increase in pulse duration from 5 ms to 50 ms increased peak Ca2 + myo from 0.5 to 1.1 μM respectively). This protocol allows for the peak of the transient to be changed without a significant change in the duration of the transient (Krishna et al. [4] ; Figure 4). The traces correspond to increasing peak values from 0.5 (∙) to 1.1 (∗) μM. Although similar to case with increasing SL, increasing activator Ca2 + results in a relatively non-linear increase in peak force generated. As shown in Figure 3A-i, the steady state F-Ca relationship is characterized by a Hill function as experimentally observed [25]. The time-to-peak force (TTP) remains relatively unaffected by the amount of activator Ca2 + causing the twitch response. Inset in Figure 3B-ii shows the dependence of TD50 (time taken from 50% activation to 50% relaxation) on peak Ca2 + myo indicating an increase in twitch duration with increasing levels of activator Ca2 + . Figure 3B-iii shows the phase plots of self normalized force versus the instantaneous Ca2 + concentration in the myoplasm for increasing peak Ca2 + myo (traces marked ∙ to ∗) overlayed with a steady state F-Ca relationships corresponding to SL = 2.3 μm (∗). The contraction-relaxation coupling point (∘) traverses along the F-Ca relationship to increasing values of Ca2 + and force with increasing peak Ca2 + myo.

Bottom Line: We also study the impact of temperature (22 to 38°C) on myofilament contractile response.The critical role of myofilament Ca2 + sensitivity in modulating developed force is likewise studied, as is the indirect coupling of intracellular contractile mechanism with the plasma membrane via the Na + /Ca2 + exchanger (NCX).Thus, the model provides mechanistic insights into whole-cell responses to a wide variety of testing approaches used in studies of cardiac myofilament contractility that have appeared in the literature over the past several decades.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Electrical and Computer Engineering, Rice University, 6100 Main Street, Houston, TX 77005, USA.

ABSTRACT

Background: The objective of this study is to develop a comprehensive model of the electromechanical behavior of the rat ventricular myocyte to investigate the various factors influencing its contractile response.

Methods: Here, we couple a model of Ca2 + dynamics described in our previous work, with a well-known model of contractile mechanics developed by Rice, Wang, Bers and de Tombe to develop a composite multiphysics model of excitation-contraction coupling. This comprehensive cell model is studied under voltage clamp (VC) conditions, since it allows to focus our study on the elaborate Ca2 + signaling system that controls the contractile mechanism.

Results: We examine the role of various factors influencing cellular contractile response. In particular, direct factors such as the amount of activator Ca2 + available to trigger contraction and the type of mechanical load applied (resulting in isosarcometric, isometric or unloaded contraction) are investigated. We also study the impact of temperature (22 to 38°C) on myofilament contractile response. The critical role of myofilament Ca2 + sensitivity in modulating developed force is likewise studied, as is the indirect coupling of intracellular contractile mechanism with the plasma membrane via the Na + /Ca2 + exchanger (NCX). Finally, we demonstrate a key linear relationship between the rate of contraction and relaxation, which is shown here to be intrinsically coupled over the full range of physiological perturbations.

Conclusions: Extensive testing of the composite model elucidates the importance of various direct and indirect modulatory influences on cellular twitch response with wide agreement with measured data on all accounts. Thus, the model provides mechanistic insights into whole-cell responses to a wide variety of testing approaches used in studies of cardiac myofilament contractility that have appeared in the literature over the past several decades.

Show MeSH
Related in: MedlinePlus