Alterations of myocardial dynamic stiffness implicating abnormal crossbridge function in human mitral regurgitation heart failure.

Mitral regurgitation (MR) causes ventricular dilation, a blunted myocardial force-frequency relation, and increased crossbridge force-time integral (FTI). The mechanism of FTI increase was investigated using sinusoidal length perturbation analysis to compare crossbridge function in skinned left ventricular (LV) epicardial muscle strips from 5 MR and 5 nonfailing (NF) control hearts. Myocardial dynamic stiffness was modeled as 3 parallel viscoelastic processes. Two processes characterize intermediate crossbridge cycle transitions, B (work producing) and C (work absorbing) with Q(10)s of 4 to 5. No significant differences in moduli or kinetic constants of these processes were observed between MR and NF. The third process, A, characterizes a nonenzymatic (Q(10)=0.9) work-absorbing viscoelasticity, whose modulus increases sigmoidally with [Ca(2+)]. Effects of temperature, crossbridge inhibition, or variation in [MgATP] support associating the calcium-dependent portion of A with the structural "backbone" of the myosin crossbridge. Extension of the conventional sinusoidal length perturbation analysis allowed using the A modulus to index the lifetime of the prerigor, AMADP crossbridge. This index was 75% greater in MR than in NF (P=0.02), suggesting a mechanism for the previously observed increase in crossbridge FTI. Notably, the A-process modulus was inversely correlated (r(2)=0.84, P=0.03) with in vivo LV ejection fraction in MR patients. The longer prerigor dwell time in MR may be clinically relevant not only for its potential role as a compensatory mechanism (increased economy of tension maintenance and increased resistance to ventricular dilation) but also for a potentially deleterious effect (reduced elastance and ejection fraction).

Radial forces within muscle fibers in rigor.

Considering the widely accepted cross-bridge model of muscle contraction (Huxley. 1969. Science [Wash. D. C.]. 164:1356-1366), one would expect that attachment of angled cross-bridges would give rise to radial as well as longitudinal forces in the muscle fiber. These forces would tend, in most instances, to draw the myofilaments together and to cause the fiber to decrease in width. Using optical techniques, we have observed significant changes in the width of mechanically skinned frog muscle fibers when the fibers are put into rigor by deleting ATP from the bathing medium. Using a high molecular weight polymer polyvinylpyrrolidone (PVP-40; number average mol. wt. (Mn) = 40,000) in the bathing solution, we were able to estimate the magnitude of the radial forces by shrinking the relaxed fiber to the width observed with rigor induction. With rigor, fiber widths decreased up to approximately 10%, with shrinking being greater at shorter sarcomere spacing and at lower PVP concentrations. At higher PVP concentrations, some fibers actually swelled slightly. Radial pressures seen with rigor in 2 and 4% PVP ranged up to 8.9 x 10(3) N/m2. Upon rigor induction, fibers exerted a longitudinal force of approximately 1 x 10(5) N/m2 that was inhibited by high PVP concentrations (greater than or equal to 13%). In very high PVP concentrations (greater than or equal to 20%), fibers exerted an anomalous force, independent of ATP, which ranged up to 6 x 10(4) N/m2 at 60% PVP. Assuming that all the radial force is the result of cross-bridge attachment, we calculated that rigor cross-bridges exert a radial force of 0.2 x 1.2 x 10(-9) N per thick filament in sarcomeres near rest length. This force is of roughly the same order of magnitude as the longitudinal force per thick filament in rigor contraction or in maximal (calcium-activated) contraction of skinned fibers in ATP-containing solutions. Inasmuch as widths of fibers stretched well beyond overlap of thick and thin filaments decreased with rigor, other radially directed forces may be operating in parallel with cross-bridge forces.

Ion-specific and general ionic effects on contraction of skinned fast-twitch skeletal muscle from the rabbit.

We used single fibers from rabbit psoas muscle, chemically skinned with Triton X-100 nonionic detergent, to determine the salts best suited for adjusting ionic strength of bathing solutions for skinned fibers. As criteria we measured maximal calcium-activated force (Fmax), fiber swelling estimated optically, and protein extraction from single fibers determined by polyacrylamide gel electrophoresis with ultrasensitive silver staining. All things considered, the best uni-univalent salt was potassium methanesulfonate, while a number of uni-divalent potassium salts of phosphocreatine, hexamethylenediamine N,N,N',N'-tetraacetic acid, sulfate, and succinate were equally acceptable. Using these salts, we determined that changes in Fmax correlated best with variations of ionic strength (1/2 sigma ci z2i, where ci is the concentration of ion i, and zi is its valence) rather than ionic equivalents (1/2 sigma ci magnitude of zi). Our data indicate that increased ionic strength per sc decreases Fmax, probably by destabilizing the cross-bridge structure in addition to increasing electrostatic shielding of actomyosin interactions.

Isometric force development, isotonic shortening, and elasticity measurements from Ca2+-activated ventricular muscle of the guinea pig.

Isometric tension and isotonic shortening were measured at constant levels of calcium activation of varying magnitude in mechanically disrupted EGTA-treated ventricular bundles from guinea pigs. The results were as follows: (a) The effect of creatine phosphate (CP) on peak tension and rate of shortening saturated at a CP concentration more than 10 mM; below that level tension was increased and shortening velocity decreased. We interpreted this to mean that CP above 10 mM was sufficient to buffer MgATP(2-) intracellularly. (b) The activated bundles exhibited an exponential stress-strain relationship and the series elastic properties did not vary appreciably with degree of activation or creatine phosphate level. (c) At a muscle length 20 percent beyond just taut, peak tension increased with Ca(2+) concentration over the range slightly below 10(-6) to slightly above 10(-4)M. (d) By releasing the muscle length-active tension curves were constructed. Force declined to 20 percent peak tension with a decrease in muscle length (after the recoil) of only 11 percent at 10(-4)M Ca(2+) and 6 percent at 4x10(-6)M Ca(2+). (e) The rate of shortening after a release was greater at lower loads. At identical loads (relative to maximum force at a given Ca(2+) level), velocity at a given time after the release was less at lower Ca(2+) concentrations; at 10 M(-5), velocity was 72 percent of that at 10(-4)M, and at 4x10(-6)M, active shortening was usually delayed and was 40 percent of the velocity at 10(-4) M. Thus, under the conditions of these experiments, both velocity and peak tension depend on the level of Ca(2+) activation over a similar range of Ca(2+) concentration.

Force response to width and length perturbations in compressed skinned skeletal muscle fibers.

Previous studies have shown that radial compression of calcium-activated skinned skeletal muscle fibers, with attendant reduction of filament lattice spacing, reduces isometric force generation. In relaxed skinned fibers, radial compression produces a marked increase in axial elastic modulus, and the response to a small amplitude length perturbation resembles that of a muscle in rigor. We interpret these results as indicating that radial compression of the myofilament lattice produces "hindered" cross-bridges which are load bearing but not force generating. The experiments reported here were designed to study the effect(s) of "hindered" cross-bridges on both the time course of isometric force responses following Ca2+ activation and fiber width and length perturbations. The experiments were carried out at room temperature on radially compressed skinned single rabbit soleus fibers. Force development following step-wise Ca2+ activation and step-wise changes of fiber width was "slow" (60-90 sec) compared to that in normal width fibers (approximately 1 sec), and could be approximated by a single exponential curve. Force redevelopment following a length release in compressed fibers was both more rapid and more complicated than force development following activation and width steps, and required a double exponential curve for an adequate description. The results are consistent with the notion that hindered cross-bridges form as a result of lattice compression, and that the hindered bridges affect the force responses following width and length perturbations.

Role of the elastic protein projectin in stretch activation and work output of Drosophila flight muscles.

We examine how the stretch activation response of the Drosophila indirect flight muscles (IFM) is affected by the projectin mutation bentDominant. IFM from flies heterozygous for this mutation (bentD/+) produce approximately 85% full length projectin and approximately 15% truncated projectin lacking the kinase domain and more C-terminal sequences. Passive stiffness and power output of mutant fibers is similar to that of wild-type (+/+) fibers, but the amplitude of the stretch activation response (delayed tension rise) was significantly reduced. Measurement of actomyosin kinetics by sinusoidal analysis revealed that the apparent rate constant of the delayed tension rise (2 pi b) increased in proportion to the decrease in amplitude, accounting for the near wild-type levels of power output and nearly normal flight ability. These results suggest that projectin plays a crucial role in stretch activation, possibly through its protein kinase activity, by modulating crossbridge recruitment and kinetics.

Potassium movement during hyperpolarization of cardiac muscle.

When a bundle of cardiac muscle cells is hyperpolarized, membrane current declines with time. Voltage clamp experiments on sheep and cat ventricular bundles showed that the magnitude of inward current depended on the external K+ concentration. Following prolonged hyperpolarization, membrane current near the resting potential was generally outward. The half-time of decay of this outward current was approximately 2.5 sec at -60mV. The potential measured in the absence of externally supplied current was generally more negative than it would have been without conditioning hyperpolarization. The half-time of recovery of the current response following hyperpolarization was also approximately 2.5 sec at -60 mV, a factor of approximately 3.7 slower than the preceding decline of inward current. The rate of recovery has only a slight temperature dependence (Q10 approximately equal to 1.2). The experimental results are consistent with the idea that during hyperpolarization K+ is depleted from approximately 3% of the total muscle volume, and that the replenishment of K+ occurs primarily by K+ diffusion from a much larger fraction of the extracellular space.

A quantitative analysis of elastic, entropic, electrostatic, and osmotic forces within relaxed skinned muscle fibers.

The elastic behavior of mechanically skinned skeletal muscle fibers in relaxing solution is modelled using equations developed by Flory (1953) for the elasticity of non-biological polymers. Mechanically, the relaxed skinned fiber is considered to be a semi-crystalline network of inextensible polymer chains, which are periodically cross-linked and which are bathed in an aqueous medium. We consider (1) configurational elastic forces in the network, (2) entropic forces due to mixing of polymer and water, (3) electrostatic forces due to fixed charges on the muscle proteins and mobile charges in the bathing solution, and (4) compressive forces due to large colloids in the bathing solution. Van der Waals forces are not considered since calculations show that they are probably negligible under our conditions. We derive an expression which relates known quantities (ionic strength, osmotic compressive pressure, and fiber width), experimentally estimated quantities (fixed charge density and volume fraction of muscle proteins), and derived quantities (concentration of cross-links and a parameter reflecting the interaction energy between protein and water). The model was tested by comparison with observed changes in skinned fiber width under a variety of experimental conditions which included changes in osmotic compressive pressure, pH, sarcomere length, and ionic strength. Over a wide range of compressive pressure (0-36 atm) the theory predicted the nonlinear relation between fiber width and logarithm of pressure. The direction and magnitude of the decrease in width when pH was decreased to 4 could be modelled assuming the fixed charge density on the protein network was 0.34 moles of electrons per liter protein, a value in accordance with the estimates of others. The relation between width and sarcomere length over the complete range of compressive pressures could be modelled with the assumption that the number of cross-links increases somewhat with sarcomere length. Changes of width with ionic strength were modelled assuming that increasing salt concentration both increased the electrostatic shielding of fixed charges and decreased the number of cross-links. The decrease of fiber width in 1% glutaraldehyde was modelled by assuming that the concentration of crosslinks increased by some 10%. The theory predicted the order of magnitude but not the detailed shape of the passive tension-length relation which may indicate that, as with non-biological polymers, the theory does not adequately describe the behavior of semi-crystalline networks at high degrees of deformation. In summary, the theory provides a semiquantitative approach to an understanding of the nature and relative magnitudes of the forces underlying the mechanical behavior of relaxed skinned fibers. It indicates, for instance, that when fibers are returned to near their in vivo size with 3% PVP, the forces in order of their importance are: (elastic forces) approximately (entropic forces) greater than (electrostatic forces) approximately (osmotic compressive forces).

On the composition of the cytosol of relaxed skeletal muscle of the frog.

This review summarizes a variety of estimates for the concentrations of the principal cytosolic constituents in frog skeletal muscle. From these estimates (listed in the APPENDIX), we chose representative values and used electroneutrality and osmotic considerations to ensure that all major constituents have been considered. Given total cytosolic concentrations of these constituents from the literature, we employed a computer program to calculate the concentrations of all the major ionic species in the cytosol. In relaxed muscle, electroneutrality and osmotic constraints are fulfilled if, in addition to diffusible species, the charge contribution of the myofilaments is considered. Mean buffer power of the diffusible cytosolic species is calculated to be less than one-third of that experimentally determined for whole muscle. Computations indicate that recent estimates of intracellular free magnesium concentration approximately 1 mM are likely to be correct.

Fourier analysis of wing beat signals: assessing the effects of genetic alterations of flight muscle structure in Diptera.

A method for determining and analyzing the wing beat frequency in Diptera is presented. This method uses an optical tachometer to measure Diptera wing movement during flight. The resulting signal from the optical measurement is analyzed using a Fast Fourier Transform (FFT) technique, and the dominant frequency peak in the Fourier spectrum is selected as the wing beat frequency. Also described is a method for determining quantitatively the degree of variability of the wing beat frequency about the dominant frequency. This method is based on determination of a quantity called the Hindex, which is derived using data from the FFT analysis. Calculation of the H index allows computer-based selection of the most suitable segment of recorded data for determination of the representative wing beat frequency. Experimental data suggest that the H index can also prove useful in examining wing beat frequency variability in Diptera whose flight muscle structure has been genetically altered. Examples from Drosophila indirect flight muscle studies as well as examples of artificial data are presented to illustrate the method. This method fulfills a need for a standardized method for determining wing beat frequencies and examining wing beat frequency variability in insects whose flight muscles have been altered by protein engineering methods.

Protein osmotic pressure and the state of water in frog myoplasm.

We measured the osmotic pressure of diffusible myoplasmic proteins in frog (Rana temporaria) skeletal muscle fibers by using single Sephadex beads as osmometers and dialysis membranes as protein filters. The state of the myoplasmic water was probed by determining the osmotic coefficient of parvalbumin, a small, abundant diffusible protein distributed throughout the fluid myoplasm. Tiny sections of membrane (3.5- and 12-14-kDa cutoffs) were juxtaposed between the Sephadex beads and skinned semitendinosus muscle fibers under oil. After equilibration, the beads were removed and calibrated by comparing the diameter of each bead to its diameter measured in solutions containing 3-12% Dextran T500 (a long-chain polymer). The method was validated using 4% agarose cylinders loaded with bovine serum albumin (BSA) or parvalbumin. The measured osmotic pressures for 1.5 and 3.0 mM BSA were similar to those calculated by others. The mean osmotic pressure produced by the myoplasmic proteins was 9.7 mOsm (4 degrees C). The osmotic pressure attributable to parvalbumin was estimated to be 3.4 mOsm. The osmotic coefficient of the parvalbumin in fibers is approximately 3.7 mOsm mM(-1), i.e., roughly the same as obtained from parvalbumin-loaded agarose cylinders under comparable conditions, suggesting that the fluid interior of muscle resembles a simple salt solution as in a 4% agarose gel.

Active force as a function of filament spacing in crayfish skinned muscle fibers.

Filament spacing is shown to have a pronounced effect on active force in skinned striated muscle fibers of crayfish. At constant filament overlap and constant ionic strength, the separation between the myofilaments (measured by low-angle X-ray diffraction) was adjusted by application of osmotic pressure. Force was induced by a calcium-containing activating solution. In the absence of compression, calcium-activated force in skinned fibers was approximately 80% of that in normal intact fibers. In fibers compressed somewhat beyond the dimension of intact fibers, force was maximal. With further compression, force was reduced and then abolished. The filament spacing-force relation reported here suggests that, at any instant, the distance between the myosin filaments and actin filaments affects either the axial force per cross bridge or, more likely, the number of cross bridges in the force-generating state.

Equilibrium distribution of ions in a muscle fiber.

We have developed a mathematical description of the equilibrium (Donnan) distribution of mobile ions between two phases containing fixed charges. This differs from the classical Donnan derivation by including mobile polyvalent ions such as those present in intact muscle fibers and in solutions used with skinned muscle fibers. Given the average concentrations of ionic species present in intact frog muscle, we calculate that the myofibrillar fixed charge density (-42 meq/liter cytoplasmic fluid) is in close agreement with estimates from amino acid analysis of myofibrillar proteins. As expected, with negative fixed charges in the myofibril, anions are excluded from the myofibrillar space while cations are concentrated in this space; the ratio between the average intra- and extramyofibrillar concentrations for an ion of valence n is (1.11)n. This model allowed us to design a bathing solution for skinned muscle fibers in which the intramyofibrillar ion concentrations closely approximate those found in intact frog muscle cells. Our model, applied to the A- and I-bands of the sarcomere, suggests that likely differences in fixed charge densities in these regions accounts for only a small fraction of the extreme concentration of phosphocreatine observed in the I-bands of intact frog muscle.

In vivo x-ray diffraction of indirect flight muscle from Drosophila melanogaster.

Small-angle x-ray diffraction from isolated muscle preparations is commonly used to obtain time-resolved structural information during contraction. We extended this technique to the thoracic flight muscles of living fruit flies, at rest and during tethered flight. Precise measurements at 1-ms time resolution indicate that the myofilament lattice spacing does not change significantly during oscillatory contraction. This result is consistent with the notion that a net radial force maintains the thick filaments at an equilibrium interfilament spacing of approximately 56 nm throughout the contractile cycle. Transgenic flies with amino-acid substitutions in the conserved phosphorylation site of the myosin regulatory light chain (RLC) exhibit structural abnormalities that can explain their flight impairment. The I(20)/I(10) equatorial intensity ratio of the mutant fly is 35% less than that of wild type, supporting the hypothesis that myosin heads that lack phosphorylated RLC remain close to the thick filament backbone. This new experimental system facilitates investigation of the relation between molecular structure and muscle function in living organisms.

Morphology and transverse stiffness of Drosophila myofibrils measured by atomic force microscopy.

Atomic force microscopy was used to investigate the surface morphology and transverse stiffness of myofibrils from Drosophila indirect flight muscle exposed to different physiologic solutions. I- and A-bands were clearly observed, and thick filaments were resolved along the periphery of the myofibril. Interfilament spacings correlated well with estimates from previous x-ray diffraction studies. Transverse stiffness was measured by using a blunt tip to indent a small section of the myofibrillar surface in the region of myofilament overlap. At 10 nm indention, the effective transverse stiffness (K( perpendicular)) of myofibrils in rigor solution (ATP-free, pCa 4.5) was 10.3 +/- 5.0 pN nm(-1) (mean +/- SEM, n = 8); in activating solution (pCa 4.5), 5.9 +/- 3.1 pN nm(-1); and in relaxing solution (pCa 8), 4.4 +/- 2.0 pN nm(-1). The apparent transverse Young's modulus (E( perpendicular)) was 94 +/- 41 kPa in the rigor state and 40 +/- 17 kPa in the relaxed state. The value of E( perpendicular) for calcium-activated myofibrils (55 +/- 29 kPa) was approximately a tenth that of Young's modulus in the longitudinal direction, a difference that at least partly reflects the transverse flexibility of the myosin molecule.

Swelling of skinned muscle fibers of the frog. Experimental observations.

Frog skeletal muscle fibers, mechanically skinned under water-saturated silicone oil, swell upon transfer to aqueous relaxing medium (60 mM KCl; 3 mM MgCl(2); 3 mM ATP; 4 mM EGTA; 20 mM Tris maleate; pH = 7.0; ionic strength 0.15 M). Their cross-sectional areas, estimated with an elliptical approximation, increase 2.32-fold (+/-0.54 SD). Sarcomere spacing is unaffected by this swelling. Addition of 200 mM sucrose to relaxing medium had no effect on fiber dimensions, whereas decreasing pH to 5.0 caused fibers to shrink nearly to their original (oil) size. Decreasing MgCl(2) to 0.3 mM caused fibers to swell 10%, and increasing MgCl(2) to 9 mM led to an 8% shrinkage. Increasing ionic strength to 0.29 M with KCl caused a 26% increase in cross-sectional area; decreasing ionic strength to 0.09 M had no effect. Swelling pressure was estimated with long-chain polymers, which are probably excluded from the myofilament lattice. Shrinkage in dextran T10 (number average mol wt 6,200) was transient, indicating that this polymer may penetrate into the fibers. Shrinkage in dextran T40 (number average mol wt 28,000), polyvinylpyrrolidone (PVP) K30 (number average mol wt 40,000) and dextran T70 (number average mol wt 40,300) was not transient, indicating exclusion. Maximal calcium-activated tension is decreased by 21% in PVP solutions and by 31% in dextran T40 solutions. Fibers were shrunk to their original size with 8 x 10(-2) g/cm(3) PVP K30, a concentration which, from osmometric data, corresponds to an osmotic pressure (II/RT) of 10.5 mM. As discussed in the text, we consider this our best estimate of the swelling pressure. We find that increasing ionic strength to 0.39 M with KCl decreases swelling pressure slightly, whereas decreasing ionic strength to 0.09 M has no effect. We feel these data are consistent with the idea that swelling arises from the negatively charged nature of the myofilaments, from either mutual filamentary repulsion or a Donnan-osmotic mechanism.

Inhibition of force production in compressed skinned muscle fibers of the frog.

Calcium-activated force development in skinned frog muscle fibers is inhibited by osmotically compressing the fiber, probably owing to a decrease in spacing between the myofilaments. This inhibition depends upon sarcomere length in that fibers at long lengths must be compressed further than those at short lengths to achieve the same degree of inhibition. As a result, this length dependency of inhibition tends to compensate for the reduction of force due solely to the decrease in interfilament spacing which occurs with stretch in intact fibers.

Axial elastic modulus as a function of relative fiber width in relaxed skinned skeletal muscle fibers.

The axial elastic modulus as a function of relative fiber width was measured in relaxed skinned fiber segments from the semitendinosus muscle of the frog. Fiber width was reduced by adding the non- penetrating long-chain polymer Dextran T500 (Mm = 181,800 D) to the fiber bathing solution. The axial elastic modulus increased steeply as relative fiber width was reduced. This relationship is independent of both ionic strength and of the presence of low molecular weight fractions of dextran within the interfilament space. The observed increase in axial elastic modulus with compression may reflect an interaction between crossbridges and thin filaments, an hypothesis which is corroborated by the similarity of responses obtained from compressed fibers and from width fibers in rigor.

Influence of osmotic compression on calcium activation and tension in skinned muscle fibers of the rabbit.

Single skinned muscle fibers were osmotically compressed back to and below their in situ size by addition of a large, random-coil polymer (Deytran T500; MN = 180,000; MW = 461,000) to the bathing medium. Maximal Ca2+-activated tension in fibers swollen (zero Dextran, fiber width 21% above in situ) or near in situ size (5% Dextran, in g/100 ml final solution) was similar, but compression to 86% of in situ width with 10% Dextran decreased maximal force by 15% relative to polymer-free control. While the relative tension-pCa relation in 0 and 10% Dextran was similar, with a pCa of 6.37 required for 50% activation, that in 5% Dextran was more sensitive to Ca2+, with a pCa50 of 6.66. We feel these effects are most likely due to changes in interfilament spacing with compression and that alterations in Ca2+-sensitivity might be explained by changes in cross-bridge angle or in the concomitant attachment-detachment rate constants which would be expected to influence the troponin-Ca2+ binding equilibrium, as has been proposed by others.

Stretch and radial compression studies on relaxed skinned muscle fibers of the frog.

The influence of stretch and radial compression on the width of mechanically skinned fibers from the semitendinosus muscle of the frog (R. pipiens) was examined in relaxing solutions with high-power light microscopy. Fibers were skinned under mineral oil. We find that, after correcting for water uptake in the oil, fiber width increased by an average of 28% upon transfer from oil to relaxing medium, with some tendency for greater swelling at longer sarcomere lengths. Subsequently, fibers were compressed by addition of the long-chain polymer polyvinylpyrrolidone (PVP-40, number average molecular weight 40,000) to relaxing solutions. Sarcomere length does not appear to be affected by addition of PVP. At any PVP concentration, the inverse square of the fiber width increased smoothly and linearly with increasing stretch for sarcomere lengths between 2.10 and 4.60 micrometer. At any fixed sarcomere length, fiber width decreased linearly with the logarithm of the osmotic compressive pressure exerted by PVP (2-10% concentration). From this logarithmic relation we estimate that the swelling pressure of the intact fiber is 3.40 x 10(3) N/m2, between that of a 2 and a 3% PVP solution. The pressure giving rise to fiber swelling is not due to dilation of the sarcoplasmic reticulum (SR), since the experimental results above were not significantly different after treatment with 0.5% BRIJ-58, a nonionic detergent that disrupts the SR. Swelling may be due simply to elastic structures within the fiber that are constrained in the intact cell. Values of bulk moduli of fibers, calculated from the compression experiments, and preliminary measurements of Young's modulus from stretch experiments, are quantitatively consistent with the idea that skinned fibers behave as nonisotropic elastic bodies.