Force responses to rapid length changes in single intact cells from frog heart

Kinetic coupling of phosphate release, force generation and rate-limiting steps in the cross-bridge cycle

A basic goal in muscle research is to understand how the cyclic ATPase activity of cross-bridges is converted into mechanical force. A direct approach to study the chemo-mechanical coupling between P_i release and the force-generating step is provided by the kinetics of force response induced by a rapid change in [P_i]. Classical studies on fibres using caged-P_i discovered that rapid increases in [P_i] induce fast force decays dependent on final [P_i] whose kinetics were interpreted to probe a fast force-generating step prior to P_i release. However, this hypothesis was called into question by studies on skeletal and cardiac myofibrils subjected to P_i jumps in both directions (increases and decreases in [P_i]) which revealed that rapid decreases in [P_i] trigger force rises with slow kinetics, similar to those of calcium-induced force development and mechanically-induced force redevelopment at the same [P_i]. A possible explanation for this discrepancy came from imaging of individual sarcomeres in cardiac myofibrils, showing that the fast force decay upon increase in [P_i] results from so-called sarcomere 'give'. The slow force rise upon decrease in [P_i] was found to better reflect overall sarcomeres cross-bridge kinetics and its [P_i] dependence, suggesting that the force generation coupled to P_i release cannot be separated from the rate-limiting transition. The reasons for the different conclusions achieved in fibre and myofibril studies are re-examined as the recent findings on cardiac myofibrils have fundamental consequences for the coupling between P_i release, rate-limiting steps and force generation. The implications from P_i-induced force kinetics of myofibrils are discussed in combination with historical and recent models of the cross-bridge cycle.

A simple model of cardiac muscle for multiscale simulation: Passive mechanics, crossbridge kinetics and calcium regulation

A simple model of cardiac muscle was designed for multiscale simulation of heart mechanics. Relaxed cardiac muscle was described as a transversally isotropic hyperelastic material. Active tension caused by actin-myosin crossbridges depends on the ensemble averaged strain of myosin heads bound to actin. Calcium activation was modeled by Ca²⁺ binding to troponin-C. To account for the dependence of troponin affinity for Ca²⁺ on myosin heads strongly bound to actin, the kinetics of troponin binding to Ca²⁺ in the overlap zone of the thin and thick filaments and outside it were separated. The changes in the length of these zones during muscle shortening or lengthening were accounted for explicitly. Simplified version of the model contains only 5 ordinary differential equations (ODE). Model parameters were estimated from a limited set of experiments with skeletal and cardiac muscle. Simulations have shown that model reproduces qualitatively a number of experimental observations: steady-state force-velocity and stiffness-velocity relations; mechanical responses to step changes in muscle length or load; steep Ca²⁺-tension relationship and its dependence on sarcomere length tension (the Frank-Starling mechanism); tension, shortening and Ca²⁺-transients in twitch isometric and isotonic contractions, tension development and redevelopment upon fast change in Ca²⁺ concentration or muscle release followed by re-stretch. We believe that the model can be effectively used for modeling contraction and relaxation of the heart.

New Insights in Cardiac Calcium Handling and Excitation-Contraction Coupling

Excitation-contraction (EC) coupling denotes the conversion of electric stimulus in mechanic output in contractile cells. Several studies have demonstrated that calcium (Ca²⁺) plays a pivotal role in this process. Here we present a comprehensive and updated description of the main systems involved in cardiac Ca²⁺ handling that ensure a functional EC coupling and their pathological alterations, mainly related to heart failure.

Size and speed of the working stroke of cardiac myosin in situ

The power in the myocardium sarcomere is generated by two bipolar arrays of the motor protein cardiac myosin II extending from the thick filament and pulling the thin, actin-containing filaments from the opposite sides of the sarcomere. Despite the interest in the definition of myosin-based cardiomyopathies, no study has yet been able to determine the mechanokinetic properties of this motor protein in situ. Sarcomere-level mechanics recorded by a striation follower is used in electrically stimulated intact ventricular trabeculae from the rat heart to determine the isotonic velocity transient following a stepwise reduction in force from the isometric peak force TP to a value T(0.8-0.2 TP). The size and the speed of the early rapid shortening (the isotonic working stroke) increase by reducing T from ∼3 nm per half-sarcomere (hs) and 1,000 s(-1) at high load to ∼8 nm⋅hs(-1) and 6,000 s(-1) at low load. Increases in sarcomere length (1.9-2.2 μm) and external [Ca(2+)]o (1-2.5 mM), which produce an increase of TP, do not affect the dependence on T, normalized for TP, of the size and speed of the working stroke. Thus, length- and Ca(2+)-dependent increase of TP and power in the heart can solely be explained by modulation of the number of myosin motors, an emergent property of their array arrangement. The motor working stroke is similar to that of skeletal muscle myosin, whereas its speed is about three times slower. A new powerful tool for investigations and therapies of myosin-based cardiomyopathies is now within our reach.

A constitutive model for cytoskeletal contractility of smooth muscle cells

The constitutive model presented in this article aims to describe the main bio-chemo-mechanical features involved in the contractile response of smooth muscle cells, in which the biochemical response is modelled by extending the four-state Hai–Murphy model to isotonic contraction of the cells and the mechanical response is mainly modelled based on the phosphorylation-dependent hyperbolic relation between isotonic shortening strain rate and tension. The one-dimensional version of the model is used to simulate shortening-induced deactivation with good agreement with selected experimental measurements. The results suggest that the Hai–Murphy biochemical model neglects the strain rate effect on the kinetics of cross-bridge interactions with actin filaments in the isotonic contractions. The two-dimensional version and three-dimensional versions of the model are developed using the homogenization method under finite strain continuum mechanics framework. The two-dimensional constitutive model is used to simulate swine carotid media strips under electrical field stimulation, experimentally investigated by Singer and Murphy, and contraction of a hollow airway and a hollow arteriole buried in a soft matrix subjected to multiple calcium ion stimulations. It is found that the transverse deformation may have significant influence on the response of the swine carotid medium. In both cases, the orientation of the maximal value of attached myosin is aligned with the orientation of maximum principal stress.

Novel approaches to determine contractile function of the isolated adult zebrafish ventricular cardiac myocyte

The zebrafish (Danio rerio) has been used extensively in cardiovascular biology, but mainly in the study of heart development. The relative ease of its genetic manipulation may indicate the suitability of this species as a cost-effective model system for the study of cardiac contractile biology. However, whether the zebrafish heart is an appropriate model system for investigations pertaining to mammalian cardiac contractile structure-function relationships remains to be resolved. Myocytes were isolated from adult zebrafish hearts by enzymatic digestion, attached to carbon rods, and twitch force and intracellular Ca(2+) were measured. We observed the modulation of twitch force, but not of intracellular Ca(2+), by both extracellular [Ca(2+)] and sarcomere length. In permeabilized cells/myofibrils, we found robust myofilament length-dependent activation. Moreover, modulation of myofilament activation-relaxation and force redevelopment kinetics by varied Ca(2+) activation levels resembled that found previously in mammalian myofilaments. We conclude that the zebrafish is a valid model system for the study of cardiac contractile structure-function relationships.

Efficiency of cross-bridges and mitochondria in mouse cardiac muscle

The aim of this study was to make cellular-level measurements of the mechanical efficiency of mouse cardiac muscle and to use these measurements to determine (1) the work performed by a cross-bridge in one ATP-splitting cycle and (2) the fraction of the free energy available in metabolic substrates that is transferred by oxidative phosphorylation to free energy in ATP (i.e. mitochondrial thermodynamic efficiency). Experiments were performed using isolated left ventricular mouse papillary muscles (n = 9; studied at 27°C) and the myothermic technique. The production of work and heat was measured during and after 40 contractions at a contraction frequency of 2 Hz. Each contraction consisted of a brief isometric period followed by isovelocity shortening. Work output, heat output and enthalpy output were all independent of shortening velocity. Maximum initial mechanical efficiency (mean ± SEM) was 31.1 ± 1.3% and maximum net mechanical efficiency 16.9 ± 1.5%. It was calculated that the maximum work per cross-bridge cycle was 20 zJ, comparable to values for mouse skeletal muscle, and that mitochondrial thermodynamic efficiency was 72%. Analysis of data in the literature suggests that mitochondrial efficiency of cardiac muscle from other species is also likely to be between 70 and 80%.

Thin filament Ca2+ binding properties and regulatory unit interactions alter kinetics of tension development and relaxation in rabbit skeletal muscle

The influence of Ca(2+) binding properties of individual troponin versus cooperative regulatory unit interactions along thin filaments on the rate tension develops and declines was examined in demembranated rabbit psoas fibres and isolated myofibrils. Native skeletal troponin C (sTnC) was replaced with sTnC mutants having altered Ca(2+) dissociation rates (k(off)) or with mixtures of sTnC and D28A, D64A sTnC, that does not bind Ca(2+) at sites I and II (xxsTnC), to reduce near-neighbour regulatory unit (RU) interactions. At saturating Ca(2+), the rate of tension redevelopment (k(TR)) was not altered for fibres containing sTnC mutants with decreased k(off) or mixtures of sTnC:xxsTnC. We examined the influence of k(off) on maximal activation and relaxation in myofibrils because they allow rapid and large changes in [Ca(2+)]. In myofibrils with M80Q sTnC(F27W) (decreased k(off)), maximal tension, activation rate (k(ACT)), k(TR) and rates of relaxation were not altered. With I60Q sTnC(F27W) (increased k(off)), maximal tension, k(ACT) and k(TR) decreased, with no change in relaxation rates. Surprisingly, the duration of the slow phase of relaxation increased or decreased with decreased or increased k(off), respectively. For all sTnC reconstitution conditions, Ca(2+) dependence of k(TR) in fibres showed Ca(2+) sensitivity of k(TR) (pCa(50)) shifted parallel to tension and low-Ca(2+) k(TR) was elevated. Together the data suggest the Ca(2+)-dependent rate of tension development and the duration (but not rate) of relaxation can be greatly influenced by k(off) of sTnC. This influence of sTnC binding kinetics occurs primarily within individual RUs, with only minor contributions of RU interactions at low Ca(2+).

Shortening induced effects on force (re)development in pig urinary smooth muscle

INTRODUCTION

When muscle is allowed to shorten during an active contraction, the maximum force that redevelops after shortening is smaller than the isometric force at the same muscle length without prior shortening. We studied the course of force redevelopment after shortening in smooth muscle to unravel the mechanism responsible for this deactivation.

METHOD

In a first series of measurements the shortening velocity was varied resulting in different shortening amplitudes. In a second series, the duration of stimulation before shortening (shortening delay) was varied. In a third series, the stimulation was interrupted for a certain duration immediately after shortening. Force, muscle length and stimulation were continuously recorded. Time constants were calculated to describe the rate of force development before and after shortening.

RESULTS

With increasing shortening amplitude and with increasing shortening delay, force redevelopment decreased. Redevelopment increased with an increase in the interruption time. After stimulus interruption force redeveloped mono-exponentially with a time constant similar to that of isometric contractions (approximately 3s). Without the interruption of stimulation, the redevelopment of force immediately after shortening was best described by two time constants; one similar to and one about 3-5 times faster than the isometric time constant.

DISCUSSION

Force (re)development is caused by a cascade of events leading to the cycling of cross-bridges. In smooth muscle, isometric force development is described by a time constant of about 3s. Force redevelopment immediately after shortening involves a second process which takes place at a faster rate (time constant about 1s). We assume that this process is faster due to the immediate availability of cytoplasmic calcium released during active shortening. Deactivation presumably is caused by disorganization of filaments during shortening.

Initial mechanical efficiency of isolated cardiac muscle

The aim of this study was to determine whether the initial mechanical efficiency (ratio of work output to initial metabolic cost) of isolated cardiac muscle is over 60%, as has been reported previously, or whether it is approximately 30%, as suggested by an estimate based on the well-established net mechanical efficiency (ratio of work output to total, suprabasal energy cost) of 15%. Determination of initial efficiency required separation of the enthalpy output (i.e. heat + work) into initial and recovery components. The former corresponds to energy produced by reactions that use high-energy phosphates and the latter to energy produced in the regeneration of high-energy phosphates. The two components were separated mathematically. Experiments were performed in vitro (30 degrees C) using preparations dissected from rat left ventricular papillary muscles (N=13). Muscle work output and heat production were measured during a series of 40 contractions using a contraction protocol designed to mimic in vivo papillary muscle activity. Net mechanical efficiency was 13.3+/-0.7%. The total enthalpy output was 2.16 times greater than the initial enthalpy output, so that initial mechanical efficiency was 28.1+/-1.2%.

Relaxation kinetics following sudden Ca(2+) reduction in single myofibrils from skeletal muscle

To investigate the roles of cross-bridge dissociation and cross-bridge-induced thin filament activation in the time course of muscle relaxation, we initiated force relaxation in single myofibrils from skeletal muscles by rapidly (approximately 10 ms) switching from high to low [Ca(2+)] solutions. Full force decay from maximal activation occurs in two phases: a slow one followed by a rapid one. The latter is initiated by sarcomere "give" and dominated by inter-sarcomere dynamics (see the companion paper, Stehle, R., M. Krueger, and G. Pfitzer. 2002. Biophys. J. 83:2152-2161), while the former occurs under nearly isometric conditions and is sensitive to mechanical perturbations. Decreasing the Ca(2+)-activated force preceding the start of relaxation does not increase the rate of the slow isometric phase, suggesting that cycling force-generating cross-bridges do not significantly sustain activation during relaxation. This conclusion is strengthened by the finding that the rate of isometric relaxation from maximum force to any given Ca(2+)-activated force level is similar to that of Ca(2+)-activation from rest to that given force. It is likely, therefore, that the slow rate of force decay in full relaxation simply reflects the rate at which cross-bridges leave force-generating states. Because increasing [P(i)] accelerates relaxation while increasing [MgADP] slows relaxation, both forward and backward transitions of cross-bridges from force-generating to non-force-generating states contribute to muscle relaxation.

Force regulation by Ca2+ in skinned single cardiac myocytes of frog

Atrial and ventricular myocytes 200 to 300 microm long containing one to five myofibrils are isolated from frog hearts. After a cell is caught and held between two suction micropipettes the surface membrane is destroyed by briefly jetting relaxing solution containing 0.05% Triton X-100 on it from a third micropipette. Jetting buffered Ca2+ from other pipettes produces sustained contractions that relax completely on cessation. The pCa/force relationship is determined at 20 degrees C by perfusing a closely spaced sequence of pCa concentrations (pCa = -log[Ca2+]) past the skinned myocyte. At each step in the pCa series quick release of the myocyte length defines the tension baseline and quick restretch allows the kinetics of the return to steady tension to be observed. The pCa/force data fit to the Hill equation for atrial and ventricular myocytes yield, respectively, a pK (curve midpoint) of 5.86 +/- 0.03 (mean +/- SE.; n = 7) and 5.87 +/- 0.02 (n = 18) and an nH (slope) of 4.3 +/- 0.34 and 5.1 +/- 0.35. These slopes are about double those reported previously, suggesting that the cooperativity of Ca2+ activation in frog cardiac myofibrils is as strong as in fast skeletal muscle. The shape of the pCa/force relationship differs from that usually reported for skeletal muscle in that it closely follows the ideal fitted Hill plot with a single slope while that of skeletal muscle appears steeper in the lower than in the upper half. The rate of tension redevelopment following release restretch protocol increases with Ca2+ >10-fold and continues to rise after Ca2+ activated tension saturates. This finding provides support for a strong kinetic mechanism of force regulation by Ca2+ in frog cardiac muscle, at variance with previous reports on mammalian heart muscle. The maximum rate of tension redevelopment following restretch is approximately twofold faster for atrial than for ventricular myocytes, in accord with the idea that the intrinsic speed of the contractile proteins is faster in atrial than in ventricular myocardium.

Active and passive forces of isolated myofibrils from cardiac and fast skeletal muscle of the frog

1. Force measurements in isolated myofibrils (15 degrees C; sarcomere length, 2.10 microns) were used in this study to determine whether sarcomeric proteins are responsible for the large differences in the amounts of active and passive tension of cardiac versus skeletal muscle. Single myofibrils and bundles of two to four myofibrils were prepared from glycerinated tibialis anterior and sartorius muscles of the frog. Skinned frog atrial myocytes were used as a model for cardiac myofibrils. 2. Electron microscope analysis of the preparations showed that: (i) frog atrial myocytes contained a small and variable number of individual myofibrils (from 1 to 7); (ii) the mean cross-sectional area and mean number of myosin filaments of individual cardiac myofibrils did not differ significantly from those of single skeletal myofibrils; and (iii) the total myofibril cross-sectional area of atrial myocytes was on average comparable to that of bundles of two to four skeletal myofibrils. 3. In maximally activated skeletal preparations, values of active force ranged from 0.45 +/- 0.03 microN for the single myofibrils (mean +/- S.E.M.; n = 16) to 1.44 +/- 0.24 microN for the bundles of two to four myofibrils (n = 9). Maximum active force values of forty-five cardiac myocytes averaged 1.47 +/- 0.10 microN and exhibited a non-continuous distribution with peaks at intervals of about 0.5 microN. The results suggest that variation in active force among cardiac preparations mainly reflects variability in the number of myofibrils inside the myocytes and that individual cardiac myofibrils develop the same average amount of force as single skeletal myofibrils. 4. The mean sarcomere length-resting force relation of atrial myocytes could be superimposed on that of bundles of two to four skeletal myofibrils. This suggests that, for any given amount of strain, individual cardiac and skeletal sarcomeres bear essentially the same passive force. 5. The length-passive tension data of all preparations could be fitted by an exponential equation. Equation parameters obtained for both types of myofibrils were in reasonable agreement with those reported for larger preparations of frog skeletal muscle but were very different from those estimated for multicellular frog atrial preparations. It is concluded that myofibrils are the major determinant of resting tension in skeletal muscle; structures other than the myofibrils are responsible for the high passive stiffness of frog cardiac muscle.

The effects of mechanical loading and changes of length on single guinea-pig ventricular myocytes

1. The effects of mechanical loading and changes of length on the contraction of single guinea-pig ventricular myocytes has been investigated. 2. Cell shortening was monitored during isotonic contractions (in which the cell shortened freely) and after attaching carbon fibres of known compliance to the ends of the cell, so that the cell contracted auxotonically (the cell both shortened and developed force). 3. Mechanically loading the cells decreased the amount of shortening during a contraction and abbreviated the contraction. There were, however, no consistent changes in the action potential or the [Ca2+]i transient (measured with the fluorescent dye fura-2). 4. Increasing stimulation rate increased the size of the contraction and the [Ca2+]i transient in both isotonic and auxotonic conditions. The increase in the size of the contraction induced by an increase in stimulation rate was greater in auxotonic conditions but the increase in the size of the [Ca2+]i transient was not. 5. When cells were stretched, there was a step increase in the size of the contraction and a prolongation of its time course. However, neither the size nor the time course of the accompanying [Ca2+]i transient was significantly altered by this intervention. 6. When a stretch was maintained, a further, slow increase in the size of the contraction occurred during the following 3-11 min, in about half the cells studied. The probability of this slow response occurring was increased if the initial degree of activation of the cell was decreased. 7. These data suggest that the mechanisms underlying the responses to mechanical loading and changes of length are the same in both multicellular and single cell preparations of cardiac muscle.