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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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Isosarcometric contraction. Twitch response - Isosarcometric contraction (A) Modulation of sarcomere length - (i) Steady state F-Ca relationships for increasing SL. (ii) Traces for normalized force with SL varied from 1.8 (+) to 2.3 (∗) μm in increments of 0.1 μm. The Ca2 + transient responsible for each of the traces is shown in the overlay. The inset shows the rate of relaxation versus rate of contraction for increasing sarcomere length (reciprocal of RT50, time taken for 50% sarcomere relaxation versus reciprocal of TTP, time taken for peak sarcomere contraction). (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing SL overlayed with two steady state F-Ca relationships corresponding to SL = 1.8 (+) and 2.3 μm (∗). (B) Modulation of Peak [Ca2 + ]myo - (i) Steady state F-SL relationships for increasing background [Ca2 + ]myo. (ii) Sarcomere length is held constant at 2.3 μm while the peak [Ca2 + ]myo transient is scaled down by decreasing the voltage clamp pulse duration. The traces show the contractile response corresponding to myoplasmic Ca2 + transients with peak values 1.1(∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM. The inset shows the relationship between TD50 (time taken from 50% activation to 50% relaxation) and activator Ca2 + . (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing peak [Ca2 + ]myo overlayed with a steady state F-Ca relationships corresponding to SL = 2.3 μm (∗). Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
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Figure 3: Isosarcometric contraction. Twitch response - Isosarcometric contraction (A) Modulation of sarcomere length - (i) Steady state F-Ca relationships for increasing SL. (ii) Traces for normalized force with SL varied from 1.8 (+) to 2.3 (∗) μm in increments of 0.1 μm. The Ca2 + transient responsible for each of the traces is shown in the overlay. The inset shows the rate of relaxation versus rate of contraction for increasing sarcomere length (reciprocal of RT50, time taken for 50% sarcomere relaxation versus reciprocal of TTP, time taken for peak sarcomere contraction). (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing SL overlayed with two steady state F-Ca relationships corresponding to SL = 1.8 (+) and 2.3 μm (∗). (B) Modulation of Peak [Ca2 + ]myo - (i) Steady state F-SL relationships for increasing background [Ca2 + ]myo. (ii) Sarcomere length is held constant at 2.3 μm while the peak [Ca2 + ]myo transient is scaled down by decreasing the voltage clamp pulse duration. The traces show the contractile response corresponding to myoplasmic Ca2 + transients with peak values 1.1(∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM. The inset shows the relationship between TD50 (time taken from 50% activation to 50% relaxation) and activator Ca2 + . (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing peak [Ca2 + ]myo overlayed with a steady state F-Ca relationships corresponding to SL = 2.3 μm (∗). Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.

Mentions: (A) The steady state force-Ca2 + (F-Ca) relationship shown in Figure 3A-i exhibits a leftward shift and an increase in developed maximum plateau force as SL is clamped at increasing lengths. This leftward shift results from an increase in myofilament Ca2 + sensitivity as SL is increased. Figure 3A-ii shows the temporal course of normalized force as SL is changed in steps from 1.8 to 2.3 μm. The waveshape of standard Ca2 + -transient is overlaid in dotted lines in this figure. Although an increase in SL (traces marked + to ∗) does not cause a large variation in the time to peak force (TTP), it does result in an increase in peak force magnitude and twitch duration as the result of an increase in myofilament Ca2 + sensitivity. These characteristics show a strong correspondence with measured data from rat ventricular myocytes tested at similar (∼ 22.5°C) temperatures [14,24,26]. The correlation coefficient of the speed of contraction and relaxation has been experimentally observed [27] to be very close (> 0.98). The inset in Figure 3A-ii is a plot of the rate of relaxation (reciprocal of time taken for 50% sarcomere relaxation (RT50)) versus rate of contraction (reciprocal of time taken for peak sarcomere contraction (TTP)) for increasing SL. This linear relationship highlights contraction-relaxation coupling, and represents a key intrinsic property of the contractile myofilaments [27]. Figure 3A-iii shows the phase plots of self normalized force versus the instantaneous Ca2 + concentration in the cytosol for increasing SL (traces marked + to ∗) overlayed with two steady state F-Ca relationships corresponding to SL = 1.8 μm (+) and SL = 2.3 μm (∗). The assessment of dynamic and steady-state Ca2 + relationships allows better analysis of the phase-plane loops of force versus Ca2 + . The active twitch curve is related to the steady-state values to determine, at what isochrone the dynamic force-Ca2 + value equals that obtained in the steady-state relationship. This point of intersection of the steady state F-Ca trace and the corresponding phase plot gives the contraction-relaxation coupling point (CRCP, marked as ∘) from initiation of stimulation [16]. Time is implicit on the phase trajectory and at time instants prior to reaching the critical coupling point for a particular trajectory, Ca2 + myo exceeds the value of Ca2 + predicted by the steady state F-Ca relationship. This excess favors continued sarcomere contraction. At later time points beyond the CRCP, the developed force is greater than that predicted by the steady state curve, which favors myofilament relaxation.


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

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

Isosarcometric contraction. Twitch response - Isosarcometric contraction (A) Modulation of sarcomere length - (i) Steady state F-Ca relationships for increasing SL. (ii) Traces for normalized force with SL varied from 1.8 (+) to 2.3 (∗) μm in increments of 0.1 μm. The Ca2 + transient responsible for each of the traces is shown in the overlay. The inset shows the rate of relaxation versus rate of contraction for increasing sarcomere length (reciprocal of RT50, time taken for 50% sarcomere relaxation versus reciprocal of TTP, time taken for peak sarcomere contraction). (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing SL overlayed with two steady state F-Ca relationships corresponding to SL = 1.8 (+) and 2.3 μm (∗). (B) Modulation of Peak [Ca2 + ]myo - (i) Steady state F-SL relationships for increasing background [Ca2 + ]myo. (ii) Sarcomere length is held constant at 2.3 μm while the peak [Ca2 + ]myo transient is scaled down by decreasing the voltage clamp pulse duration. The traces show the contractile response corresponding to myoplasmic Ca2 + transients with peak values 1.1(∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM. The inset shows the relationship between TD50 (time taken from 50% activation to 50% relaxation) and activator Ca2 + . (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing peak [Ca2 + ]myo overlayed with a steady state F-Ca relationships corresponding to SL = 2.3 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 3: Isosarcometric contraction. Twitch response - Isosarcometric contraction (A) Modulation of sarcomere length - (i) Steady state F-Ca relationships for increasing SL. (ii) Traces for normalized force with SL varied from 1.8 (+) to 2.3 (∗) μm in increments of 0.1 μm. The Ca2 + transient responsible for each of the traces is shown in the overlay. The inset shows the rate of relaxation versus rate of contraction for increasing sarcomere length (reciprocal of RT50, time taken for 50% sarcomere relaxation versus reciprocal of TTP, time taken for peak sarcomere contraction). (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing SL overlayed with two steady state F-Ca relationships corresponding to SL = 1.8 (+) and 2.3 μm (∗). (B) Modulation of Peak [Ca2 + ]myo - (i) Steady state F-SL relationships for increasing background [Ca2 + ]myo. (ii) Sarcomere length is held constant at 2.3 μm while the peak [Ca2 + ]myo transient is scaled down by decreasing the voltage clamp pulse duration. The traces show the contractile response corresponding to myoplasmic Ca2 + transients with peak values 1.1(∗), 0.9, 0.8, 0.7, 0.6, 0.5 (∙) μM. The inset shows the relationship between TD50 (time taken from 50% activation to 50% relaxation) and activator Ca2 + . (iii) Phase plots of self normalized force versus instantaneous [Ca2 + ]myo for increasing peak [Ca2 + ]myo overlayed with a steady state F-Ca relationships corresponding to SL = 2.3 μm (∗). Model generated data corresponds to an idealized rat ventricular myocyte at 22.5°C.
Mentions: (A) The steady state force-Ca2 + (F-Ca) relationship shown in Figure 3A-i exhibits a leftward shift and an increase in developed maximum plateau force as SL is clamped at increasing lengths. This leftward shift results from an increase in myofilament Ca2 + sensitivity as SL is increased. Figure 3A-ii shows the temporal course of normalized force as SL is changed in steps from 1.8 to 2.3 μm. The waveshape of standard Ca2 + -transient is overlaid in dotted lines in this figure. Although an increase in SL (traces marked + to ∗) does not cause a large variation in the time to peak force (TTP), it does result in an increase in peak force magnitude and twitch duration as the result of an increase in myofilament Ca2 + sensitivity. These characteristics show a strong correspondence with measured data from rat ventricular myocytes tested at similar (∼ 22.5°C) temperatures [14,24,26]. The correlation coefficient of the speed of contraction and relaxation has been experimentally observed [27] to be very close (> 0.98). The inset in Figure 3A-ii is a plot of the rate of relaxation (reciprocal of time taken for 50% sarcomere relaxation (RT50)) versus rate of contraction (reciprocal of time taken for peak sarcomere contraction (TTP)) for increasing SL. This linear relationship highlights contraction-relaxation coupling, and represents a key intrinsic property of the contractile myofilaments [27]. Figure 3A-iii shows the phase plots of self normalized force versus the instantaneous Ca2 + concentration in the cytosol for increasing SL (traces marked + to ∗) overlayed with two steady state F-Ca relationships corresponding to SL = 1.8 μm (+) and SL = 2.3 μm (∗). The assessment of dynamic and steady-state Ca2 + relationships allows better analysis of the phase-plane loops of force versus Ca2 + . The active twitch curve is related to the steady-state values to determine, at what isochrone the dynamic force-Ca2 + value equals that obtained in the steady-state relationship. This point of intersection of the steady state F-Ca trace and the corresponding phase plot gives the contraction-relaxation coupling point (CRCP, marked as ∘) from initiation of stimulation [16]. Time is implicit on the phase trajectory and at time instants prior to reaching the critical coupling point for a particular trajectory, Ca2 + myo exceeds the value of Ca2 + predicted by the steady state F-Ca relationship. This excess favors continued sarcomere contraction. At later time points beyond the CRCP, the developed force is greater than that predicted by the steady state curve, which favors myofilament relaxation.

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