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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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Comparison of twitch responses. Twitch responses - A comparison between three types of steady state twitch responses from an isolated rat ventricular myocyte viz. isosarcometric, unloaded and isometric (KSE = 2). Fixed SL in the isosarcometric case and the initial pre-contraction SL in the isometric case are chosen as 2.2 μm. Equilibrium SL in the unloaded case is 1.9 μm. (A) Traces for normalized force in each of the three cases with an overlay of normalized [Ca2 + ]myo transient responsible for the twitch and (B) Phase plots of normalized force versus the instantaneous Ca2 + concentration in the cytosol in each of the three cases. Note the overlap of ♦ and ■ in panel iii. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
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Figure 6: Comparison of twitch responses. Twitch responses - A comparison between three types of steady state twitch responses from an isolated rat ventricular myocyte viz. isosarcometric, unloaded and isometric (KSE = 2). Fixed SL in the isosarcometric case and the initial pre-contraction SL in the isometric case are chosen as 2.2 μm. Equilibrium SL in the unloaded case is 1.9 μm. (A) Traces for normalized force in each of the three cases with an overlay of normalized [Ca2 + ]myo transient responsible for the twitch and (B) Phase plots of normalized force versus the instantaneous Ca2 + concentration in the cytosol in each of the three cases. Note the overlap of ♦ and ■ in panel iii. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.

Mentions: A third type of twitch can be simulated where the cell is kept at a fixed total length, allowing it to contract in response to Ca2 + release by internal shortening of the sarcomere made possible by a non-contractile series elastic element whose stiffness (KSE value) dictates the end compliance and hence the degree of internal shortening. Increasing KSE values causes an increase in maximal plateau force in steady state F-Ca relationship as shown in Figure 6A. Figure 6B shows traces for total force (sum of both passive and active force) during an isometric twitch corresponding to KSE values increased from 1.0 to 50.0 normalized force-μm−1. With an increase in end compliance (decrease in KSE), the degree of internal shortening increases and the total force measured at the cell end decreases, showing a delayed peak and an increase in rate of relaxation (Figure 6B). The delayed peak occurs because the peak force is measured when the series elastic element is at its maximum length, which occurs with greater delay with increasing end compliance. Increasing end compliance decreases twitch duration (Figure 6B) because, as observed experimentally [28] re-lengthening hastens relaxation as a result of an increase in mean distortion of the strongly bound crossbridge states (xXB_PreR, xXB_PostR in Figure 2) which causes a decrease in the forward rotation rate of the crossbridges (Eqn. 22, Rice et al. [13]) and hence a faster force decline. Figure 6C shows the phase plots of self normalized force versus the instantaneous Ca2 + concentration in the myoplasm for increasing KSE values (traces marked ∙ to ∗) overlayed with two steady state F-Ca relationships corresponding to KSE = 1.0 (∙) and KSE = 50.0 (∗). The contraction-relaxation coupling point (∘) moves to increasing values of Ca2 + and force with increasing KSE values with the relative change in Ca2 + being smaller than force. Figure 6D shows the corresponding traces for sarcomere length during the isometric twitch. As the KSE value is increased from 1 to 50 the decreasing compliance results in a decline in cell shortening accompanied by a decrease in time to peak shortening from 122 ms to 92 ms (Figure 6D).


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

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

Comparison of twitch responses. Twitch responses - A comparison between three types of steady state twitch responses from an isolated rat ventricular myocyte viz. isosarcometric, unloaded and isometric (KSE = 2). Fixed SL in the isosarcometric case and the initial pre-contraction SL in the isometric case are chosen as 2.2 μm. Equilibrium SL in the unloaded case is 1.9 μm. (A) Traces for normalized force in each of the three cases with an overlay of normalized [Ca2 + ]myo transient responsible for the twitch and (B) Phase plots of normalized force versus the instantaneous Ca2 + concentration in the cytosol in each of the three cases. Note the overlap of ♦ and ■ in panel iii. 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 6: Comparison of twitch responses. Twitch responses - A comparison between three types of steady state twitch responses from an isolated rat ventricular myocyte viz. isosarcometric, unloaded and isometric (KSE = 2). Fixed SL in the isosarcometric case and the initial pre-contraction SL in the isometric case are chosen as 2.2 μm. Equilibrium SL in the unloaded case is 1.9 μm. (A) Traces for normalized force in each of the three cases with an overlay of normalized [Ca2 + ]myo transient responsible for the twitch and (B) Phase plots of normalized force versus the instantaneous Ca2 + concentration in the cytosol in each of the three cases. Note the overlap of ♦ and ■ in panel iii. Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
Mentions: A third type of twitch can be simulated where the cell is kept at a fixed total length, allowing it to contract in response to Ca2 + release by internal shortening of the sarcomere made possible by a non-contractile series elastic element whose stiffness (KSE value) dictates the end compliance and hence the degree of internal shortening. Increasing KSE values causes an increase in maximal plateau force in steady state F-Ca relationship as shown in Figure 6A. Figure 6B shows traces for total force (sum of both passive and active force) during an isometric twitch corresponding to KSE values increased from 1.0 to 50.0 normalized force-μm−1. With an increase in end compliance (decrease in KSE), the degree of internal shortening increases and the total force measured at the cell end decreases, showing a delayed peak and an increase in rate of relaxation (Figure 6B). The delayed peak occurs because the peak force is measured when the series elastic element is at its maximum length, which occurs with greater delay with increasing end compliance. Increasing end compliance decreases twitch duration (Figure 6B) because, as observed experimentally [28] re-lengthening hastens relaxation as a result of an increase in mean distortion of the strongly bound crossbridge states (xXB_PreR, xXB_PostR in Figure 2) which causes a decrease in the forward rotation rate of the crossbridges (Eqn. 22, Rice et al. [13]) and hence a faster force decline. Figure 6C shows the phase plots of self normalized force versus the instantaneous Ca2 + concentration in the myoplasm for increasing KSE values (traces marked ∙ to ∗) overlayed with two steady state F-Ca relationships corresponding to KSE = 1.0 (∙) and KSE = 50.0 (∗). The contraction-relaxation coupling point (∘) moves to increasing values of Ca2 + and force with increasing KSE values with the relative change in Ca2 + being smaller than force. Figure 6D shows the corresponding traces for sarcomere length during the isometric twitch. As the KSE value is increased from 1 to 50 the decreasing compliance results in a decline in cell shortening accompanied by a decrease in time to peak shortening from 122 ms to 92 ms (Figure 6D).

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