Third-order phase transition in random tilings.

We consider the domino tilings of an Aztec diamond with a cut-off corner of macroscopic square shape and given size and address the bulk properties of tilings as the size is varied. We observe that the free energy exhibits a third-order phase transition when the cut-off square, increasing in size, reaches the arctic ellipse-the phase separation curve of the original (unmodified) Aztec diamond. We obtain this result by studying the thermodynamic limit of a certain nonlocal correlation function of the underlying six-vertex model with domain wall boundary conditions, the so-called emptiness formation probability (EFP). We consider EFP in two different representations: as a τ function for Toda chains and as a random matrix model integral. The latter has a discrete measure and a linear potential with hard walls; the observed phase transition shares properties with both Gross-Witten-Wadia and Douglas-Kazakov phase transitions.

Characterization of the cross-bridge force-generating step using inorganic phosphate and BDM in myofibrils from rabbit skeletal muscles.

The inhibitory effects of inorganic phosphate (P(i)) on isometric force in striated muscle suggest that in the ATPase reaction P(i) release is coupled to force generation. Whether P(i) release and the power stroke are synchronous events or force is generated by an isomerization of the quaternary complex of actomyosin and ATPase products (AM.ADP.P(i)) prior to the following release of P(i) is still controversial. Examination of the dependence of isometric force on [P(i)] in rabbit fast (psoas; 5-15 degrees C) and slow (soleus; 15-20 degrees C) myofibrils was used to test the two-step hypothesis of force generation and P(i) release. Hyperbolic fits of force-[P(i)] relations obtained in fast and slow myofibrils at 15 degrees C produced an apparent asymptote as [P(i)]-->infinity of 0.07 and 0.44 maximal isometric force (i.e. force in the absence of P(i)) in psoas and soleus myofibrils, respectively, with an apparent K(d) of 4.3 mM in both. In each muscle type, the force-[P(i)] relation was independent of temperature. However, 2,3-butanedione 2-monoxime (BDM) decreased the apparent asymptote of force in both muscle types, as expected from its inhibition of the force-generating isomerization. These data lend strong support to models of cross-bridge action in which force is produced by an isomerization of the AM.ADP.P(i) complex immediately preceding the P(i) release step.

The effect of inorganic phosphate on force generation in single myofibrils from rabbit skeletal muscle.

In striated muscle, force generation and phosphate (P(i)) release are closely related. Alterations in the [P(i)] bathing skinned fibers have been used to probe key transitions of the mechanochemical coupling. Accuracy in this kind of studies is reduced, however, by diffusional barriers. A new perfusion technique is used to study the effect of [P(i)] in single or very thin bundles (1-3 microM in diameter; 5 degrees C) of rabbit psoas myofibrils. With this technique, it is possible to rapidly jump [P(i)] during contraction and observe the transient and steady-state effects on force of both an increase and a decrease in [P(i)]. Steady-state isometric force decreases linearly with an increase in log[P(i)] in the range 500 microM to 10 mM (slope -0.4/decade). Between 5 and 200 microM P(i), the slope of the relation is smaller ( approximately -0.07/decade). The rate constant of force development (k(TR)) increases with an increase in [P(i)] over the same concentration range. After rapid jumps in [P(i)], the kinetics of both the force decrease with an increase in [P(i)] (k(Pi(+))) and the force increase with a decrease in [P(i)] (k(Pi(-))) were measured. As observed in skinned fibers with caged P(i), k(Pi(+)) is about three to four times higher than k(TR), strongly dependent on final [P(i)], and scarcely modulated by the activation level. Unexpectedly, the kinetics of force increase after jumps from high to low [P(i)] is slower: k(Pi(-)) is indistinguishable from k(TR) measured at the same [P(i)] and has the same calcium sensitivity.

Force-velocity and unloaded shortening velocity during graded potassium contractures in frog skeletal muscle fibres.

Steady-state conditions of contraction, at maximal and submaximal forces, were produced in intact single muscle fibres, from Rana esculenta, using full tetani and graded K+-contractures. The uniformity in radial direction. of spreading of activation produced in K+-contractures, was checked in relation to the fibre diameters. The absolute isometric force was similar in tetani and maximal contractures, for fibres with diameters between 40 and 60 microm, but not for fibres with diameters greater than about 70 microm in which contracture force never reached tetanic force. The force [K+]o relation was similar for fibres with diameters between 40 and 60 microm. but it was right shifted and it had a minor slope for fibres with diameters greater than 65-70 microm. This suggests that only in the small diameter fibres (40-60 microm) the activation does not fail to penetrate uniformly from the surface towards the fibre core. For fibres selected in the diameter range between 40 and 60 microm, force-velocity relations and unloaded shortening velocities were determined in tetani and maximal and submaximal contractures. Data were obtained across a force range of 0.3 to 1 P0 (tetanic plateau force). Controlled velocity method was used to obtain force-velocity relations, and slack test to determine the unloaded shortening velocity (VU). The values of the parameters characterising the force velocity relation (V0 and a/P0) and VU as determined by the slack test did not differ significantly in tetani and contractures, independent of the activation level or absolute force developed by the fibre. These results show that. at least within the range of forces tested. crossbridge kinetics is independent of the number of cycling crossbridges, in agreement with the prediction of the 'recruitment' model of myofilament activation.

Crossbridge kinetics in single frog muscle fibres in presence of ethylene glycol.

Single fibres isolated from frog muscle were tetanically stimulated at 14 degrees C to produce isometric tetani at a sarcomere length of about 2.16 microm, using a striation follower device to measure the sarcomere length of a selected segment of fibre. Force-velocity data were obtained by applying ramp releases at pre-set velocity at the tetanus plateau. Sarcomere stiffness was measured at isometric plateau and during isotonic shortening by using sinusoidal length changes at 2 kHz frequency and about 1 nm per half sarcomere (hs) peak to peak amplitude. A correction method was used to compensate for the force truncation due to the quick recovery. After data collection, the bathing solution was substituted with Ringer plus ethylene glycol (EG) at 2 M (11.2% v/v). When the fibre was fully equilibrated with the new solution, the measurements were repeated. Ethylene glycol reduced the speed of the tetanus rise and tetanus relaxation without altering the isometric tension, and reduced the maximum shortening velocity by about 20%. During isotonic contraction tension and stiffness at each given shortening velocity were reduced by about the same amount, so that the stiffness/tension ratio remained almost unaltered. Force-velocity and stiffness data in both standard and EG Ringer were analysed in terms of a two state model (Huxley, 1957). The analysis showed that our results can be accounted for by assuming that EG at 2 M concentration reduces all the rate constants for crossbridges interaction by about the same amount.

Sarcomere tension-stiffness relation during the tetanus rise in single frog muscle fibres.

The sarcomere stiffness was measured in single muscle fibres during the development of tetanic tension using a method insensitive to fibre inertia and viscosity. The stiffness was calculated by measuring the ratio between tension and sarcomere length during a period of fast sarcomere elongation at constant velocity. Tension changes were corrected for force truncation by the quick recovery mechanism. The results show that the relation between force and stiffness deviates from the direct proportionality less than previously reported. If the deviation is due to the presence of a linear myofilament compliance in series with the cross-bridges, our data suggest that myofilament compliance accounts for about 30% of the sarcomere compliance. This value is significantly smaller than 50-70% determined by X-ray diffraction measurements. These two different findings, however, may be reconciled by assuming that the myofilament compliance is non-linear increasing appropriately at low tension.

Modulation by substrate concentration of maximal shortening velocity and isometric force in single myofibrils from frog and rabbit fast skeletal muscle.

1. The effects of magnesium adenosine triphosphate (MgATP; also referred to as 'substrate') concentration on maximal force and shortening velocity have been studied at 5 C in single and thin bundles of striated muscle myofibrils. The minute diameters of the preparations promote rapid diffusional equilibrium between the bathing medium and lattice space so that during contraction fine control of substrate and product concentrations is achieved. 2. Myofibrils from frog tibialis anterior and rabbit psoas fast skeletal muscles were activated maximally by rapidly (10 ms) exchanging a continuous flux of pCa 8.0 for one at pCa 4.75 at a range of substrate concentrations from 10 microM to 5 mM. At high substrate concentrations maximal isometric tension and shortening velocity of both frog and rabbit myofibrils were very close to those determined in whole fibre preparations from the same muscle types. 3. As in frog and rabbit skinned whole fibres, the maximal isometric force of the myofibril preparations decreases as MgATP concentration is increased. The maximal velocity of unloaded shortening (V0) depends hyperbolically on substrate concentration. V0 extrapolated to infinite MgATP (3.6 +/- 0.2 and 0.8 +/- 0.03 l0 s-1 in frog and rabbit myofibrils, respectively) is very close to that determined directly at high substrate concentration. The Km is 210 +/- 20 microM for frog tibialis anterior and 120 +/- 10 microM for rabbit psoas myofibrils, values about half those found in larger whole fibre preparations of the same muscle types. This implies that measurements in whole skinned fibres are perturbed by diffusional delays, even in the presence of MgATP regenerating systems. 4. In both frog and rabbit myofibrils, the Km for V0 is about one order of magnitude higher than the Km for myofibrillar MgATPase determined biochemically in the same experimental conditions. This confirms that the difference between the Km values for MgATPase and shortening velocity is a basic feature of the mechanism of chemomechanical transduction in muscle contraction.

Mechanical properties of frog muscle fibres at rest and during twitch contraction.

Data reported in the literature suggest that crossbridges in rapid equilibrium between attached and detached states (weakly binding bridges), demonstrated in relaxed skinned fibres at low ionic strength, could be present also in intact fibres under physiological conditions. In addition, it was suggested that the well known leading of stiffness over force during the tension development in stimulated muscle fibres could be due to an increased number of weakly binding bridges induced by the stimulation. The experiments reviewed in this paper were made to investigate these possibilities. Fast ramp length changes were applied to single frog muscle fibres at rest and during the early phases of activation. The corresponding force changes were analysed, searching for the components expected from the presence of weakly binding bridges. The results showed no mechanical indication for the presence of weakly binding bridges in both skinned and intact fibres, either at rest or during activation. It was also found that a portion of the fibre stiffness increase induced by stimulation leads the formation of crossbridges.

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.

Force responses to fast ramp stretches in stimulated frog skeletal muscle fibres.

Force responses to fast ramp stretches at various velocities were recorded from single muscle fibres isolated from either lumbricalis digiti IV or tibialis anterior muscle of the frog (Rana esculenta) at sarcomere length between 2.15 and 3.25 microns at 15 degrees C. Stretches were applied at rest, at tetanus plateau and during the tetanus rise. Stretches with the same velocity but different accelerations were imposed to the fibre to evaluate the effect of fibre inertia on the force responses. Length changes were measured at sarcomere level with either a laser diffractometer or a striation follower apparatus. The force response to a fast ramp stretch could be divided into two phases. The initial fast one (phase 1) lasts for the acceleration period during which the stretching velocity rises up to the steady state. The second slower phase (phase 2) lasts for the remainder of the stretch and corresponds to the well-known elastic response of the fibre. Most of this paper is concerned with phase 1. The amplitude of the initial fast phase was proportional to the stretching velocity as expected from a viscous response. This viscosity was associated with a very short (about 10 microseconds) relaxation time. The amplitude of the fast phase increased progressively with tension during the tetanus rise and scaled down with sarcomere length approximately in the same way as tetanic tension and fibre stiffness. These data suggest that activated fibres have a significant internal viscosity which may arise from crossbridge interaction.

Calcium dependence of the apparent rate of force generation in single striated muscle myofibrils activated by rapid solution changes.

Single myofibrils or small groups of myofibrils were isolated from different types of striated muscle: rabbit psoas, frog tibialis anterior, frog atrial and ventricular muscle. The Ca2+ concentration of the solution perfusing the myofibrils was changed within few milliseconds by translating the interface between two flowing streams of solution across the preparations. In all types of myofibrils tested, the time course of force rise in response to maximal activation (pCa 4.75) was approximately monoexponential and nearly superimposable on that observed after a release-restretch protocol applied to the myofibril at the plateau of maximal contractions. This suggests that the kinetics of force development following rapid myofibril activation essentially reflects the kinetics of interaction between contractile proteins. The half time of force rise in response to maximal activation varied among different myofibril types; it was shortest in frog tibialis anterior myofibrils and longest in frog ventricular myofibrils. In all types of myofibril preparations tested the half time of force rise increased with decreasing Ca2+ levels in the activating solution. The finding provides support for a kinetic mechanism of force regulation by Ca2+ in all types of striated muscle. The extent of this Ca2+ effect, however, varied among the different myofibril preparations tested; at 15 degrees C for instance, it was smaller in frog tibialis anterior myofibrils than in the other preparations.

Myofilament compliance and sarcomere tension-stiffness relation during the tetanus rise in frog muscle fibres.

The sarcomere stiffness was measured in single muscle fibres during the development of tetanic tension using a method insensitive to fibre inertia and viscosity. The stiffness was calculated as the ratio between tension changes and sarcomere length changes during a period of fast sarcomere elongation at constant velocity. The results show that, unlike previous measurements with step or sinusoidal length changes, the relation between relative force and relative stiffness on the tetanus rise is linear. Consequently, the development of stiffness upon stimulation is synchronous with the development of force. Since a substantial fraction of sarcomere compliance is localized in the myofilaments, this result can be accounted for by assuming that either myofilament compliance is highly non-linear or that crossbridges stiffness during the tetanus rise is not proportional to crossbridge tension.

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.

Crossbridge viscosity in activated frog muscle fibres.

Force responses to fast ramp stretches at various velocities were recorded in single muscle fibres isolated from tibialis anterior muscle of the frog (Rana esculenta) at a sarcomere length between 2.15 and 3.25 microns at 15 degrees C. Stretches were applied at the tetanus plateau and during tetanus rise. Length changes were recorded at the sarcomere level using either a laser diffractometer or a striation follower apparatus. The immediate force response to the stretch is not simply elastic, as is usually assumed, but is composed of the sum of at least two components: (i) elastic (force proportional to the amount of stretch); and (ii) viscous (force proportional to the rate of stretch). The viscous response is associated with a short (about 10 microseconds) relaxation time. The amplitude of the viscous component increases progressively with tension during the tetanus rise and scales down with sarcomere length approximately in the same way as the tetanic tension. These results suggest that the viscosity of activated fibres may arise from crossbridge kinetics.

Absence of mechanical evidence for attached weakly binding cross-bridges in frog relaxed muscle fibres.

1. Passive force responses to ramp stretches at various velocities were measured in intact and skinned single muscle fibres isolated from the lumbricalis muscle of the frog. Force was measured using a fast capacitance transducer and sarcomere length was measured using a laser light diffraction technique at a point very close to the fixed end so as to avoid effects of fibre inertia. Experiments were performed at 15 degrees C with sarcomere length between 2.13 and 3.27 microns under high (170 mM) and low (20 mM) ionic strength. 2. The analysis shows that the force response is the sum of at least three components: (i) elastic (force proportional to the amount of stretch), (ii) viscous (force proportional to rate of stretch), and (iii) viscoelastic (resembling the response of a pure viscous element in series with an elastic element). 3. The amplitude of all these components increased progressively with sarcomere length in the whole range measured. 4. A further component, attributable to the short-range elasticity (SREC), was present in the force response of the intact fibres. 5. The amplitude of the force response decreased substantially upon skinning at high ionic strength but increased again at low ionic strength. The SREC was completely abolished by skinning. 6. None of the components of the force response was found to have the properties expected from the previously postulated 'weakly binding bridges'.

Development of stiffness precedes cross-bridge attachment during the early tension rise in single frog muscle fibres.

1. Force responses to ramp stretches were recorded in single muscle fibres isolated from the lumbricalis muscle of the frog. Stretches were applied at rest and at progressively increasing times after a single stimulus. 2. The increase of fibre stiffness that precedes tension development has a 'static' component that accounts for the whole fibre stiffness increase during the latent period and at very low tension at the beginning of the twitch. 3. Static stiffness increase was not affected by 2,3-butanedione-2-monoxime, a drug that almost completely inhibited twitch tension. 4. Static stiffness increased approximately 5-fold as the sarcomere length was increased from 2.1 to 2.84 microns. 5. These results suggest that static fibre stiffness increase is not attributable to the formation of non-force-generating cross-bridges.

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

1. Force transients in response to step perturbations in length were recorded in intact atrial cells from frog heart at various temperatures (6-15 degrees C). Length changes of various sizes and in either direction, complete in 0.5 ms, were applied to single myocytes near slack length (initial sarcomere length 2.1-2.2 microns) just before the peak of an isometric twitch. The frequency response of the force transducers used was 2-4 kHz in Ringer solution. 2. An early quick force recovery phase was clearly observed after the elastic force response to the length step and before the start of much slower recovery processes. The quick recovery phase became progressively faster with larger shortening steps and was almost as fast as that originally described in intact frog skeletal muscle fibres (rate constants above 1000 s-1 in large releases at 10 degrees C). 3. The force-extension relation determined at the end of the length change (T1 curve) indicates that an instantaneous shortening of 0.5-0.6% of the initial cell length (L0) brings the force to zero. The force--extension relation determined at the end of the quick recovery phase (T2 curve) showed that the early recovery leads to an almost complete restoration of the original force with small stretches and releases (up to 0.3% L0) and that it becomes negligible in shortening steps of about 1.4% L0. 4. The results suggest that the mechanical properties of attached cross-bridges and the rate of transitions between attached cross-bridge states are approximately the same in frog atrial cells and fast skeletal muscle fibres.(ABSTRACT TRUNCATED AT 250 WORDS)

A force transducer and a length-ramp generator for mechanical investigations of frog-heart myocytes.

An apparatus for studying the mechanics of isolated frog heart myocytes is described. The cells are held horizontal in a through of Ringer solution by means of two suction micropipettes. Myocyte force is measured with an opto-electronic system recording the deflection of the tip of one micropipette, which acts as a cantilever force probe. The force probes are selected for compliance according to the force a myocyte is expected to develop in a given condition, so as to limit myocyte shortening during force development to no more than 1% of the slack cellular length (l0). The other micropipette, which is stiff relative to the forces measured, is mounted on an electromagnetic-loudspeaker motor by which controlled-velocity length changes, of preset size and in either direction, are imposed on myocytes. The force transducer has a sensitivity of 5-10 mV/nN, with a frequency response of 700-900 Hz in Ringer solution and a resolution of 0.5-1 nN. The motor with a suction micropipette can complete controlled-velocity length ramps within 1.5-2.0 ms, across a range of +/- 100 microns at a resolution of 8.0 nm. These values correspond, for frog-heart myocytes 200 microns and 400 microns long, to 25%-50% l0 and 0.002%-0.004% l0 respectively.

Taking the first steps in contraction mechanics of single myocytes from frog heart.

Intact or skinned atrial and ventricular myocytes from frog heart were mounted horizontally between the lever arms of a force transducer and a servo-controlled electromagnetic loud-speaker "motor" in a trough filled with Ringer or relaxing solution. The myocyte length-sarcomere length relation for intact preparations at rest is linear at least in the range from l0 (sarcomere length about 2.1 microns, resting force zero) to 1.6 l0 (resting force about 100 nN). The peak force value for control twitches (21-23 degrees C, stimulus interval 10 s, [Ca2+]o 1 mM) varies from 20 to 100 nN in atrial and ventricular intact myocytes. The effects induced by isoprenaline or changes in [Ca2+]o, stimulation pattern and bath temperature on twitch characteristics are comparable to those observed in multicellular preparations. The steady force produced by maximally Ca(2+)-activated skinned myocytes is much greater than that developed in control twitches and varies from 0.5 to 3.5 microN in different cells. The saturating pCa in the activating solution is around 5.50. The force response of a resting myocyte to slow ramp stretches shows an initial velocity- and length-dependent component during the stretch itself and, after completion of the length change, a gradual recovery towards a steady level which only depends on the stretch extent. The force response of a stimulated myocyte to length steps complete in 2 ms consists of an apparently elastic change during the step itself and then of a rapid partial recovery followed by slowering of recovery. Whether or not the force recovery includes different phases as reported for skeletal muscle remains unclear.

Force response of unstimulated intact frog muscle fibres to ramp stretches.

The possibility that weakly binding bridges are attached to actin in the absence of Ca2+ under physiological conditions was investigated by studying the force response of unstimulated intact muscle fibres of the frog to fast ramp stretches. The force response during the stretching period is divided into two phases: phase 1, coincident with the acceleration period of the sarcomere length change and phase 2, synchronous with sarcomere elongation at constant speed. The phase 1 amplitude increases linearly with the stretching speed in all the range tested, while phase 2 increases with the speed but reaches a plateau level at about 50 x 10(3) nm/half sarcomere per second. The analysis of data shows that phase 1, which corresponds to the initial 5-10 nm/half sarcomere of elongation, is very likely a pure viscous response; its amplitude increases with sarcomere length and it is not affected by the electrical stimulation of the fibre. Phase 2 is a viscoelastic response with a relaxation time of the order of 1 ms; its amplitude increases with sarcomere lengths and with the stimulation. These data suggest that weakly binding bridges are not present in a significant amount in unstimulated intact fibres.