Heat changes during transient tension responses to small releases in active frog muscle

Effects of Hydrostatic-Pressure on Muscle Contraction: A Look Back on Some Experimental Findings

Findings from experiments that used hydrostatic pressure changes to analyse the process of skeletal muscle contraction are re-examined. The force in resting muscle is insensitive to an increase in hydrostatic pressure from 0.1 MPa (atmospheric) to 10 MPa, as also found for force in rubber-like elastic filaments. The force in rigour muscle rises with increased pressure, as shown experimentally for normal elastic fibres (e.g., glass, collagen, keratin, etc.). In submaximal active contractions, high pressure leads to tension potentiation. The force in maximally activated muscle decreases with increased pressure: the extent of this force decrease in maximal active muscle is sensitive to the concentration of products of ATP hydrolysis (Pi-inorganic phosphate and ADP-adenosine diphosphate) in the medium. When the increased hydrostatic pressure is rapidly decreased, the force recovered to the atmospheric level in all cases. Thus, the resting muscle force remained the same: the force in the rigour muscle decreased in one phase and that in active muscle increased in two phases. The rate of rise of active force on rapid pressure release increased with the concentration of Pi in the medium, indicating that it is coupled to the Pi release step in the ATPase-driven crossbridge cycle in muscle. Pressure experiments on intact muscle illustrate possible underlying mechanisms of tension potentiation and causes of muscle fatigue.

Temperature Effects on Force and Actin⁻Myosin Interaction in Muscle: A Look Back on Some Experimental Findings

Observations made in temperature studies on mammalian muscle during force development, shortening, and lengthening, are re-examined. The isometric force in active muscle goes up substantially on warming from less than 10 °C to temperatures closer to physiological (>30 °C), and the sigmoidal temperature dependence of this force has a half-maximum at ~10 °C. During steady shortening, when force is decreased to a steady level, the sigmoidal curve is more pronounced and shifted to higher temperatures, whereas, in lengthening muscle, the curve is shifted to lower temperatures, and there is a less marked increase with temperature. Even with a small rapid temperature-jump (T-jump), force in active muscle rises in a definitive way. The rate of tension rise is slower with adenosine diphosphate (ADP) and faster with increased phosphate. Analysis showed that a T-jump enhances an early, pre-phosphate release step in the acto-myosin (crossbridge) ATPase cycle, thus inducing a force-rise. The sigmoidal dependence of steady force on temperature is due to this endothermic nature of crossbridge force generation. During shortening, the force-generating step and the ATPase cycle are accelerated, whereas during lengthening, they are inhibited. The endothermic force generation is seen in different muscle types (fast, slow, and cardiac). The underlying mechanism may involve a structural change in attached myosin heads and/or their attachments on heat absorption.

The force-generation process in active muscle is strain sensitive and endothermic: a temperature-perturbation study

In experiments on active muscle, we examined the tension decline and its temperature sensitivity at the onset of ramp shortening and at a range of velocities. A segment (∼1.5 mm long) of a skinned muscle fibre isolated from rabbit psoas muscle was held isometrically (sarcomere length ∼2.5 µm) at 8-9°C, maximally Ca²⁺-activated and a ramp shortening applied. The tension decline with a ramp shortening showed an early decrease of slope (the P₁ transition) followed by a slower decrease in slope (the P₂ transition) to the steady (isotonic) force. The tension level at the initial P₁ transition and the time to that transition decreased as the velocity was increased; the length change to this transition increased with shortening velocity to a steady value of ∼8 nm half-sarcomere^-1 A small, rapid, temperature jump (T-jump) (3-4°C, <0.2 ms) applied coincident with the onset of ramp shortening showed force enhancement by T-jump and changed the tension decline markedly. Analyses showed that the rate of T-jump-induced force rise increased linearly with increase of shortening velocity. These results provide crucial evidence that the strain-sensitive cross-bridge force generation, or a step closely coupled to it, is endothermic.

Statistical mechanics of the Huxley-Simmons model

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

Energetics of contraction

Muscles convert energy from ATP into useful work, which can be used to move limbs and to transport ions across membranes. The energy not converted into work appears as heat. At the start of contraction heat is also produced when Ca(2+) binds to troponin-C and to parvalbumin. Muscles use ATP throughout an isometric contraction at a rate that depends on duration of stimulation, muscle type, temperature and muscle length. Between 30% and 40% of the ATP used during isometric contraction fuels the pumping Ca(2+) and Na(+) out of the myoplasm. When shortening, muscles produce less force than in an isometric contraction but use ATP at a higher rate and when lengthening force output is higher than the isometric force but rate of ATP splitting is lower. Efficiency quantifies the fraction of the energy provided by ATP that is converted into external work. Each ATP molecule provides 100 zJ of energy that can potentially be converted into work. The mechanics of the myosin cross-bridge are such that at most 50 zJ of work can be done in one ATP consuming cycle; that is, the maximum efficiency of a cross-bridge is ∼50%. Cross-bridges in tortoise muscle approach this limit, producing over 90% of the possible work per cycle. Other muscles are less efficient but contract more rapidly and produce more power.

Crossbridge mechanism(s) examined by temperature perturbation studies on muscle

An overall view of the contractile process that has emerged from -temperature-studies on active muscle is outlined. In isometric muscle, a small rapid temperature-jump (T-jump) enhances an early, pre-phosphate release, step in the acto-myosin (crossbridge) ATPase cycle and induces a characteristic rise in force indicating that crossbridge force generation is endothermic (force rises when heat is absorbed). Sigmoidal temperature dependence of steady force is largely due to the endothermic nature of force generation. During shortening, when muscle force is decreased, the T-jump force generation is enhanced; conversely, when a muscle is lengthening and its force increased, the T-jump force generation is inhibited. Taking T-jump force generation as a signature of the crossbridge - ATPase cycle, the results suggest that during lengthening the ATPase cycle is truncated before endothermic force generation, whereas during shortening this step and the ATPase cycle, are accelerated; this readily provides a molecular basis for the Fenn effect.

Temperature change as a probe of muscle crossbridge kinetics: a review and discussion

Following the ideas introduced by Huxley (Huxley 1957, Prog. Biophys. Biophys. Chem. 7, 255-318), it is generally supposed that muscle contraction is produced by temporary links, called crossbridges, between myosin and actin filaments, which form and break in a cyclic process driven by ATP splitting. Here we consider the interaction of the energy in the crossbridge, in its various states, and the force exerted. We discuss experiments in which the mechanical state of the crossbridge is changed by imposed movement and the energetic consequence observed as heat output and the converse experiments in which the energy content is changed by altering temperature and the mechanical consequences are observed. The thermodynamic relationship between the experiments is explained and, at the first sight, the relationship between the results of these two types of experiment appears paradoxical. However, we describe here how both of them can be explained by a model in which mechanical and energetic changes in the crossbridges occur in separate steps in a branching cycle.

An analysis of the temperature dependence of force, during steady shortening at different velocities, in (mammalian) fast muscle fibres

We examined, over a wide range of temperatures (10–35°C), the isometric tension and tension during ramp shortening at different velocities (0.2–4 L₀/s) in tetanized intact fibre bundles from a rat fast (flexor hallucis brevis) muscle; fibre length (L₀) was 2.2 mm and sarcomere length ~2.5 μm. During a ramp shortening, the tension change showed an initial inflection of small amplitude (P₁), followed by a larger exponential decline towards an approximate steady level; the tension continued to decline slowly afterwards and the approximate steady tension at a given velocity was estimated as the tension (P₂) at the point of intersection between two linear slopes, as previously described (Roots et al. 2007). At a given temperature, the tension P₂ declined to a lower level and at a faster rate (from an exponential curve fit) as the shortening velocity was increased; the temperature sensitivity of the rate of tension decline during ramp shortening at different velocities was low (Q₁₀ 0.9–1.5). The isometric tension and the P₂ tension at a given shortening velocity increased with warming so that the relation between tension and (reciprocal) temperature was sigmoidal in both. In isometric muscle, the temperature T_0.5 for half-maximal tension was ~10°C, activation enthalpy change (∆H) was ~100 kJ mol⁻¹ and entropy change (∆S) ~350 J mol⁻¹ K⁻¹. In shortening, these were increased with increase of velocity so that at a shortening velocity (~4 L₀/s) producing maximal power at 35°C, T_0.5 was ~28°C, ∆H was ~200 kJ mol⁻¹ and ∆S ~ 700 J mol⁻¹ K⁻¹; the same trends were seen in the tension data from isotonic release experiments on intact muscle and in ramp shortening experiments on maximally Ca-activated skinned fibres. In general, our findings show that the sigmoidal relation between force and temperature can be extended from isometric to shortening muscle; the implications of the findings are discussed in relation to the crossbridge cycle. The data indicate that the endothermic, entropy driven process that underlies crossbridge force generation in isometric muscle (Zhao and Kawai 1994; Davis, 1998) is even more pronounced in shortening muscle, i.e. when doing external work.

Mechanism of tension generation in muscle: an analysis of the forward and reverse rate constants

Tension generation in muscle occurs during the attached phase of the ATP-powered cyclic interaction of myosin heads with thin filaments. The transient nature of tension-generating intermediates and the complexity of the mechanochemical cross-bridge cycle have impeded a quantitative description of tension generation. Recent experiments performed under special conditions yielded a sigmoidal dependence of fiber tension on temperature--a unique case that simplifies the system to a two-state transition. We have applied this two-state analysis to kinetic data obtained from biexponential laser temperature-jump tension transients. Here we present the forward and reverse rate constants for de novo tension generation derived from analysis of the kinetics of the fast laser temperature-jump phase tau(2) (equivalent of the length-jump phase 2(slow)). The slow phase tau(3) is temperature-independent indicating coupling to rather than a direct role in, de novo tension generation. Increasing temperature accelerates the forward, and slows the reverse, rate constant for the creation of the tension-generating state. Arrhenius behavior of the forward and anti-Arrhenius behavior of the reverse rate constant is a kinetic signature of multistate multipathway protein-folding reactions. We conclude that locally unfolded tertiary and/or secondary structure of the actomyosin cross-bridge mediates the power stroke.

The efficiency of muscle contraction

When a muscle contracts and shortens against a load, it performs work. The performance of work is fuelled by the expenditure of metabolic energy, more properly quantified as enthalpy (i.e., heat plus work). The ratio of work performed to enthalpy produced provides one measure of efficiency. However, if the primary interest is in the efficiency of the actomyosin cross-bridges, then the metabolic overheads associated with basal metabolism and excitation-contraction coupling, together with those of subsequent metabolic recovery process, must be subtracted from the total heat and work observed. By comparing the cross-bridge work component of the remainder to the Gibbs free energy of hydrolysis of ATP, a measure of thermodynamic efficiency is achieved. We describe and quantify this partitioning process, providing estimates of the efficiencies of selected steps, while discussing the errors that can arise in the process of quantification. The dependence of efficiency on animal species, fibre-type, temperature, and contractile velocity is considered. The effect of contractile velocity on energetics is further examined using a two-state, Huxley-style, mathematical model of cross-bridge cycling that incorporates filament compliance. Simulations suggest only a modest effect of filament compliance on peak efficiency, but progressively larger gains (vis-à-vis the rigid filament case) as contractile velocity approaches Vmax. This effect is attributed primarily to a reduction in the component of energy loss arising from detachment of cross-bridge heads at non-zero strain.

Force generation and temperature-jump and length-jump tension transients in muscle fibers

Muscle tension rises with increasing temperature. The kinetics that govern the tension rise of maximally Ca(2+)-activated, skinned rabbit psoas fibers over a temperature range of 0-30 degrees C was characterized in laser temperature-jump experiments. The kinetic response is simple and can be readily interpreted in terms of a basic three-step mechanism of contraction, which includes a temperature-sensitive rapid preequilibrium(a) linked to a temperature-insensitive rate-limiting step and followed by a temperature-sensitive tension-generating step. These data and mechanism are compared and contrasted with the more complex length-jump Huxley-Simmons phases in which all states that generate tension or bear tension are perturbed. The rate of the Huxley-Simmons phase 4 is temperature sensitive at low temperatures but plateaus at high temperatures, indicating a change in rate-limiting step from a temperature-sensitive (phase 4a) to a temperature-insensitive reaction (phase 4b); the latter appears to correlate with the slow, temperature-insensitive temperature-jump relaxation. Phase 3 is absent in the temperature-jump, which excludes it from tension generation. We confirm that de novo tension generation occurs as an order-disorder transition during phase 2slow and the equivalent, temperature-sensitive temperature-jump relaxation.

Kinetic and thermodynamic studies of the cross-bridge cycle in rabbit psoas muscle fibers

The effect of temperature on elementary steps of the cross-bridge cycle was investigated with sinusoidal analysis technique in skinned rabbit psoas fibers. We studied the effect of MgATP on exponential process (C) to characterize the MgATP binding step and cross-bridge detachment step at six different temperatures in the range 5-30 degrees C. Similarly, we studied the effect of MgADP on exponential process (C) to characterize the MgADP binding step. We also studied the effect of phosphate (Pi) on exponential process (B) to characterize the force generation step and Pi-release step. From the results of these studies, we deduced the temperature dependence of the kinetic constants of the elementary steps and their thermodynamic properties. We found that the MgADP association constant (K0) and the MgATP association constant (K1) significantly decreased when the temperature was increased from 5 to 20 degrees C, implying that nucleotide binding became weaker at higher temperatures. K0 and K1 did not change much in the 20-30 degree C range. The association constant of Pi to cross-bridges (K5) did not change much with temperature. We found that Q10 for the cross-bridge detachment step (k2) was 2.6, and for its reversal step (k-2) was 3.0. We found that Q10 for the force generation step (Pi-isomerization step, k4) was 6.8, and its reversal step (k-4) was 1.6. The equilibrium constant of the detachment step (K2) was not affected much by temperature, whereas the equilibrium constant of the force generation step (K4) increased significantly with temperature increase. Thus, the force generation step consists of an endothermic reaction. The rate constant of the rate-limiting step (k6) did not change much with temperature, whereas the ATP hydrolysis rate increased significantly with temperature increase. We found that the force generation step accompanies a large entropy increase and a small free energy change; hence, this step is an entropy-driven reaction. These observations are consistent with the hypothesis that the hydrophobic interaction between residues of actin and myosin underlies the mechanism of force generation. We conclude that the force generation step is the most temperature-sensitive step among elementary steps of the cross-bridge cycle, which explains increased isometric tension at high temperatures in rabbit psoas fibers.

A single order-disorder transition generates tension during the Huxley-Simmons phase 2 in muscle

Increasing temperature was used to progressively interconvert non-force-generating into force-generating states in skinned rabbit psoas muscle fibers contracting isometrically. Laser temperature-jump and length-jump experiments were used to characterize tension generation in the time domain of the Huxley-Simmons phase 2. In our experiments, phase 2 is subdivisible into two kinetic steps each with quite different physical properties. The fast kinetic component has rate constant of 950 s-1 at 1 degrees C and a Q10 of approximately 1.2. Its rate is tension insensitive and its normalized amplitude declines with rising temperature--behavior that closely parallels the instantaneous stiffness of the cross-bridge. It is likely that this kinetic step is a manifestation of a damped elastic element/s in the fiber. The slow component of phase 2 is temperature-dependent with a Q10 of approximately 3.0. Its rate is sensitive to tension. Unlike the fast component, its amplitude remains in fixed proportion to isometric tension at different temperatures indicating direct participation in tension generation. Similar T-jump studies on frog fibers are also included. The combined results (frog and rabbit) suggest that tension generation occurs in a single endothermic (entropy driven) step in phase 2.

Kinetic and physical characterization of force generation in muscle: a laser temperature-jump and length-jump study on activated and contracting rigor fibers

Experiments are presented that probe the mechanism of contraction in normal activated muscle fibers and in heated rigor fibers. In activated fibers we subdivide the partial recovery of isometric tension during the Huxley-Simmons phase 2 into temperature-independent and temperature-dependent steps termed, respectively, phase 2fast and phase 2slow. Evidence is presented to show that phase 2fast arises from the perturbation of a damped elastic element in the cross-bridge and that phase 2slow is the manifestation of an endothermic, order-disorder transition responsible for de novo tension generation. These responses are common to both frog and rabbit fibers. The only difference between animals is that the kinetics of phase 2slow appears to scale with the working temperature of the muscle and not absolute temperature. Rigor fibers heated above the working temperature of the muscle contract. Tension generation is, as with activated fibers, endothermic. Tension transients following a laser temperature-jump of activated and heated rigor fibers are virtually indistinguishable on the basis of either the form or magnitude of the response. In length-jump experiments, tension recovery by heated rigor fibers consists of three exponentials with a tension-dependent rate for the medium speed step. Preliminary data indicate that the rigor cross-bridge operates over a distance of between 13.5 and 18 nm. Collectively, these data imply that tension generation in muscle arises from accessible conformational states in the proteins of the cross-bridge alone. ATP hydrolysis in active fibers and the heating of rigor fibers simply serve to shift these intrinsic conformational equilibria towards tension generation.

Tension responses to joule temperature jump in skinned rabbit muscle fibres

1. Joule temperature jumps (T-jumps) from 5-9 degrees C up to 40 degrees C were used to study the cross-bridge kinetics and thermodynamics in skinned rabbit muscle fibres. To produce a T-jump, an alternating current pulse was passed through a fibre 5 s after removing the activating solution (pCa congruent to 4.5) from the experimental trough. The pulse frequency was congruent to 30 kHz, amplitude less than or equal to 3 kV, and duration 0.2 ms. The pulse energy liberated in the fibre was calculated using a special analog circuit and then used for estimation of the T-jump amplitude. 2. The T-jump induced a tri-exponential tension transient. Phases 1 and 2 had rate constants k1 = 450-1750 s-1 and k2 = 60-250 s-1 respectively, characterizing the tension rise, whereas phase 3 had a rate constant k3 = 5-10 s-1 representing tension recovery due to the fibre cooling. 3. An increase from 13 to 40 degrees C for the final temperature achieved by the T-jump led to an increase in the amplitudes of phases 1 and 2. After T-jumps to 30-40 degrees C during phase 1, tension increased by 50-80%. During phase 2 an approximately 2-fold tension increase continued. Rate constants k1 and k2 increased with temperature and temperature coefficients (Q10) were 1.6 and 1.7, respectively. 4. To study which processes in the cross-bridges are involved in phases 1 and 2, a series of experiments were made where step length changes of -9 to +3 nm (hs)-1 (nanometres per half-sarcomere length) were applied to the fibre 4 ms before the T-jump. 5. After the step shortening, the rate constant of phase 1 increased, whereas its amplitude decreased compared to those without a length change. This indicates that phase 1 is determined by some force-generating process in the cross-bridges attached to the thin filaments. This process is, most probably, the same as that producing the early tension recovery following the length change. The enthalpy change (delta H) associated with the reaction controlling this process was estimated to be positive (15-30 kJ mol-1). 6. Both the rate constant k2 and the maximal tension achieved at the end of phase 2 were practically independent of the preceding length changes. This means that phase 2 is accompanied by the cross-bridge detachment and reattachment to new sites on the thin filaments.(ABSTRACT TRUNCATED AT 400 WORDS)

Analysis of diffusion delay in a layered medium. Application to heat measurements from muscle

An analysis is presented of diffusional delays in one-dimensional heat flow through a medium consisting of several layers of different materials. The model specifically addresses the measurement of heat production by muscle, but diffusion of solute or conduction of charge through a layered medium will obey the same equations. The model consists of a semi-infinite medium, the muscle, in which heat production is spacially uniform but time varying. The heat diffuses through layers of solution and insulation to the center of the thermal element where heat flow is zero. Using Laplace transforms, transfer functions are derived for the temperature change in the center of the thermopile as a function of the temperature at any interface between differing materials or as a function of heat production in the muscle. From these transfer functions, approximate analytical expressions are derived for the time constants which scale the early and late changes in the central temperature. We find that the earliest temperature changes are limited by the diffusivities of the materials, whereas the approach to steady state depends on the total heat capacity of the system and the diffusivity of muscle. Hill (1937) analyzed a similar geometry by modeling the layered medium as a homogeneous system with an equivalent half thickness. We show that his analysis was accurate for the materials in his system. In general, however, and specifically with regard to modern thermopiles, a homogeneous approximation will lead to significant errors. We compare responses of different thermopiles to establish the limits of time resolution in muscle heat records and to correct them for diffusional delays. Using numerical techniques, we invert the Laplace transforms and show the time course of the temperature changes recorded by different instruments in response to different patterns of heat production.