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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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Isometric contraction. Twitch response - Isometric contraction. The cell is held at a constant total length but the sarcomere is allowed to contract via a series elastic element. (A) Steady state F-Ca relationships for increasing KSE values. (B) Traces for total muscle force during an isometric twitch with KSE values of 1(∙), 1.4, 2, 3, 4, 5, 7, 10 and 50 (∗) where units of KSE are normalized force-per-micrometer extension. (C) phase plots of self normalized force versus [Ca2 + ]myo for increasing KSE values (corresponding to panel B) overlayed with two steady state F-Ca relationships corresponding to KSE = 1.0 (∙) and 50.0 (∗). (D) Sarcomere length traces showing internal shortening. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
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Figure 5: Isometric contraction. Twitch response - Isometric contraction. The cell is held at a constant total length but the sarcomere is allowed to contract via a series elastic element. (A) Steady state F-Ca relationships for increasing KSE values. (B) Traces for total muscle force during an isometric twitch with KSE values of 1(∙), 1.4, 2, 3, 4, 5, 7, 10 and 50 (∗) where units of KSE are normalized force-per-micrometer extension. (C) phase plots of self normalized force versus [Ca2 + ]myo for increasing KSE values (corresponding to panel B) overlayed with two steady state F-Ca relationships corresponding to KSE = 1.0 (∙) and 50.0 (∗). (D) Sarcomere length traces showing internal shortening. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.

Mentions: The protocol for the unloaded case is as follows. The cell is not stretched with pre-load so that the series elastic element is unattached and is therefore not in play. In the model of Rice et al. ([13]; Figure 1), the contractile element is shunted by elastic and viscous damping elements. In that figure, the nonlinear elastic element is characterized by a cubic force vs SL characteristic centered about an equilibrium point (SL0=1.9 μm; F=0). In the unloaded case without stimulation, any stored energy in the system is dissipated and SL decays to the equilibrium point on the passive force vs SL characteristic. With electrical activation and subsequent Ca2 + release, active force is developed and SL shortening occurs against the aforementioned passive restoring forces. Providing the same sequence of voltage clamp pulses as in Figure 5, an identical sequence of Ca2 + -transients is produced to drive the active contractile mechanism. Figure 5A is a plot of total developed force (active and passive) as a function of peak Ca2 + myo. This net instantaneous force can become negative when the magnitude of the passive forces exceeds that of the active component (Figure 5A). Thus, an increase in activator Ca2 + causes an increase in peak force generated, which translates into enhanced shortening. Corresponding changes in sarcomeric length as shown in Figure 5B indicate that increasing levels of activator Ca2 + result in a decrease in time to peak (TTP declined from 156.0 ms (∙) to 70.5 ms (∗)) and an increase in the rate of relaxation (RT50 computed from time of peak decreased from 183.0 ms (∙) to 157.5 ms (∗)).


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

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

Isometric contraction. Twitch response - Isometric contraction. The cell is held at a constant total length but the sarcomere is allowed to contract via a series elastic element. (A) Steady state F-Ca relationships for increasing KSE values. (B) Traces for total muscle force during an isometric twitch with KSE values of 1(∙), 1.4, 2, 3, 4, 5, 7, 10 and 50 (∗) where units of KSE are normalized force-per-micrometer extension. (C) phase plots of self normalized force versus [Ca2 + ]myo for increasing KSE values (corresponding to panel B) overlayed with two steady state F-Ca relationships corresponding to KSE = 1.0 (∙) and 50.0 (∗). (D) Sarcomere length traces showing internal shortening. 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 5: Isometric contraction. Twitch response - Isometric contraction. The cell is held at a constant total length but the sarcomere is allowed to contract via a series elastic element. (A) Steady state F-Ca relationships for increasing KSE values. (B) Traces for total muscle force during an isometric twitch with KSE values of 1(∙), 1.4, 2, 3, 4, 5, 7, 10 and 50 (∗) where units of KSE are normalized force-per-micrometer extension. (C) phase plots of self normalized force versus [Ca2 + ]myo for increasing KSE values (corresponding to panel B) overlayed with two steady state F-Ca relationships corresponding to KSE = 1.0 (∙) and 50.0 (∗). (D) Sarcomere length traces showing internal shortening. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
Mentions: The protocol for the unloaded case is as follows. The cell is not stretched with pre-load so that the series elastic element is unattached and is therefore not in play. In the model of Rice et al. ([13]; Figure 1), the contractile element is shunted by elastic and viscous damping elements. In that figure, the nonlinear elastic element is characterized by a cubic force vs SL characteristic centered about an equilibrium point (SL0=1.9 μm; F=0). In the unloaded case without stimulation, any stored energy in the system is dissipated and SL decays to the equilibrium point on the passive force vs SL characteristic. With electrical activation and subsequent Ca2 + release, active force is developed and SL shortening occurs against the aforementioned passive restoring forces. Providing the same sequence of voltage clamp pulses as in Figure 5, an identical sequence of Ca2 + -transients is produced to drive the active contractile mechanism. Figure 5A is a plot of total developed force (active and passive) as a function of peak Ca2 + myo. This net instantaneous force can become negative when the magnitude of the passive forces exceeds that of the active component (Figure 5A). Thus, an increase in activator Ca2 + causes an increase in peak force generated, which translates into enhanced shortening. Corresponding changes in sarcomeric length as shown in Figure 5B indicate that increasing levels of activator Ca2 + result in a decrease in time to peak (TTP declined from 156.0 ms (∙) to 70.5 ms (∗)) and an increase in the rate of relaxation (RT50 computed from time of peak decreased from 183.0 ms (∙) to 157.5 ms (∗)).

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