Tension responses to joule temperature jump in skinned

1992;447;425-448 J. Physiol.

S Y Bershitsky and A K Tsaturyan

rabbit muscle fibres.Tension responses to joule temperature jump in skinned

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Journal of Physiology (1992), 447, pp. 425-448 425With 13 figuresPrinted in Great Britain

TENSION RESPONSES TO JOULE TEMPERATURE JUMP IN SKINNEDRABBIT MUSCLE FIBRES

BY SERGEY Y. BERSHITSKY* AND ANDREY K. TSATURYANtFrom the *Department of Biophysics, Institute of Physiology, Urals Branch of

Academy of Sciences of the USSR, Popova Street 30, 620014 Sverdlovsk, USSR andthe tDepartment ofMechanics of Nature Processes, Institute of Mechanics, M. V.Lomonosov Moscow State University, Leninsky Gory, 119899 Moscow, USSR

(Received 25 February 1991)

SUMMARY

1. Joule temperature jumps (T-jumps) from 5-9 °C up to 40 °C were used to studythe cross-bridge kinetics and thermodynamics in skinned rabbit muscle fibres. Toproduce a T-jump, an alternating current pulse was passed through a fibre 5 s afterremoving the activating solution (pCa - 4-5) from the experimental trough. Thepulse frequency was - 30 kHz, amplitude < 3 kV, and duration 0-2 ms. The pulseenergy liberated in the fibre was calculated using a special analog circuit and thenused for estimation of the T-jump amplitude.

2. The T-jump induced a tri-exponential tension transient. Phases 1 and 2 hadrate constants k1 = 450-1750 s-1 and k2 = 60-250 s-1 respectively, characterizing thetension rise, whereas phase 3 had a rate constant k3 = 5-10 s-5 representing tensionrecovery due to the fibre cooling.

3. An increase from 13 to 40 °C for the final temperature achieved by the T-jumpled to an increase in the amplitudes of phases 1 and 2. After T-jumps to 30-40 °Cduring phase 1, tension increased by 50-80 %. During phase 2 an approximately 2-fold tension increase continued. Rate constants k. and k2 increased with temperatureand temperature coefficients (Q1o) were 1P6 and 1-7, respectively.

4. To study which processes in the cross-bridges are involved in phases 1 and 2, aseries 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 beforethe T-jump.

5. After the step shortening, the rate constant of phase 1 increased, whereas itsamplitude decreased compared to those without a length change. This indicates thatphase 1 is determined by some force-generating process in the cross-bridges attachedto the thin filaments. This process is, most probably, the same as that producing theearly tension recovery following the length change. The enthalpy change (AH)associated with the reaction controlling this process was estimated to be positive(15-30 kJ mol').

*t Present address to which all correspondence and reprint requests should be sent: BiophysicsSection, King's College London, 26-29 Drury Lane, London WC2B 5RL.MS 9178



S. Y BERSHITSKY AND A. K. TSATURYAN

6. Both the rate constant k2 and the maximal tension achieved at the end of phase2 were practically independent of the preceding length changes. This means thatphase 2 is accompanied by the cross-bridge detachment and reattachment to newsites on the thin filaments.

7. A simple three-state model of the cross-bridge kinetics is proposed to explainthe experimental data.

INTRODUCTION

In 1971 Huxley and Simmons proposed a model of the force generation in muscle.They assumed that the cross-bridge can produce a reversible step movement whileit is attached to the thin filament. This model explains the kinetics of the earlypartial tension recovery following a step length change (Huxley & Simmons, 1971;Ford, Huxley & Simmons, 1977, 1981, 1985). The main postulate in the Huxley &Simmons model is that the early tension recovery is due to a process in the cross-bridges attached to the thin filament, not to the cross-bridge detachment andreattachment. Time-resolved X-ray experiments (Huxley, Simmons, Farugi, Kress,Bordas & Koch, 1983) confirmed this assumption. It was shown that the changes inthe X-ray diffraction pattern induced by quick length change can be completelyreversed by the length recovery to its initial value in 1-2 ms after the step, i.e. duringor just after the early tension recovery.However, there is no evidence that the step movement of the attached cross-bridge

can be made without a relative sliding of the filaments. So, it is not clear whether thestep movement is involved in isometric force generation (Huxley, 1980). Tosynchronize the force-generating step of the cross-bridges, we used the jouletemperature jump (T-jump) in single skinned muscle fibres (Bershitsky & Tsaturyan,1985). In this method the T-jump is induced by the joule heat liberation in a fibrewhile it is suspended in air. The method permits a temperature change of up to 35 Kwith simultaneous monitoring of the mechanical events in the fibre. The fibrestiffness measurement before and after the T-jump (Bershitsky & Tsaturyan, 1986 a,1989) showed that the stiffness drops immediately after the T-jump by about 0 5-1 %per 1 K. During a 3-4-fold tension rise initiated by the T-jump from 5-7 to 28-30 °Cthe stiffness also increases, but by only - 50% (Bershitsky & Tsaturyan, 1989).So, the tension changes initiated by the T-jump are mainly due to the change in thecross-bridge force, not stiffness.The primary version of the joule T-jump method, as well as experiments similar

to those presented here, were briefly described earlier, but were performed usingmuscle fibres from the frog (Bershitsky & Tsaturyan, 1986b, 1988; Tsaturyan &Bershitsky, 1988). At temperatures above 20 °C the tension transients in the frogfibres become too fast for their rate constants to be measured accurately. Thus a newseries of experiments was performed using rabbit psoas muscle fibres whose T-jump-induced tension transients are not as fast. Also, the isometric tension at maximalactivation is more temperature sensitive in fibres from warm-blooded animals thanthose from cold-blooded animals (Woledge, Curtin & Homsher, 1985; Stephenson &Williams, 1985).

426



JOULE TEMPERATURE JUMP IN MUSCLE FIBRE

METHODS

Principle of the methodIn order to make stepwise temperature changes in skinned muscle fibres, 0-2 ms, 30 kHz, up to

3 kV alternating current pulse was passed through the fibre segment suspended in air between twoelectrodes of the heating pulse generator. The joule heat liberated in the fibre was calculated witha special analog circuit and then used for the T-jump amplitude determination.The active electrode was fixed to the length-change generator and the ground electrode to the

force transducer. When the fibre was fully activated (pCa - 45), the activating solution wasremoved and the heating pulse applied within 5 s of the fibre being suspended in air. Tensiontransients initiated by the T-jumps from 5-9 to 13-40 °C were monitored. In some experimentsstep length changes from -9 to + 3 nm (hs)'- (nanometres per half-sarcomere) were applied 4 msbefore the T-jump to study the cross-bridge processes producing the tension transients.

Fibre preparation and solutionsMuscle fibres were obtained from European grey rabbits of either sex weighing 2-5-3-5 kg.

Animals were killed by a blow to the head. Thin fibre bundles (- 1 mm in diameter, - 3 cm long)were tied to wooden sticks and cut loose from the psoas minor muscles. Then each bundle was putinto a glass tube filled with the storage solution (Table 1) and rapidly cooled to -20 'C. After 24 hthe bundles were transferred to a fresh storage solution and stored at -20 'C for 2-6 weeks.A segment of a single fibre was separated from the bundle under a long-focus microscope MBS-9

(LOMO Inc., Leningrad, USSR) in storage solution at 3-5 'C. Then the fibre was transferred tothe experimental trough at 0-2 'C. The fibre ends were placed on dry nickel tube electrodes andmoistened by droplets (= 0 05 ,ul) of shellac dissolved in ethanol (70/30, v/v). The trough was filledwith cold relaxing solution (Table 1). As ethanol diffuses into the solution, the shellac hardensquickly providing reliable fixation and electric contact between the fibre segment (1P4-2-5 mm long)and the electrodes. The fibre glued to the nickel tube electrode is shown in the left inset in Fig. 1.The sarcomere length was adjusted to 2-5-2-6 ,um while being monitored by laser diffraction.The homogeneity of the fibre widths along the segment was inspected in two projections using

an MBS-9 microscope and the optical system described below. The sarcomere length homogeneitywas checked using laser diffraction at various fibre lengths in the relaxing solution. The fibre cross-sectional area A) was determined twice: in air (A.) and in the relaxing solution (A8). A8 was usedfor the fibre tension (force per area) calculation, while A. was necessary for determination of theheated volume of the fibre surrounded by a thin layer of solution. The cross-sectional area wascalculated using a formula A = 7Td1d2/4 (Blinks, 1965), where A is A8 or A., d4 and d2 are the fibrewidths in two perpendicular projections in solution or in air. If the variation of the area along thefibre suspended in air was more than 10%, the fibre was replaced by another one.

Before each experiment, the fibre was treated with 05-1 % (v/v) solution of non-ionic detergentTriton X-100 in the relaxing solution to ensure destruction of the sarcolemma and the membranesof the sarcoplasmic reticulum.The method of Moisescu (1976) was used for quick and homogeneous activation of the fibre. The

composition of the solutions is similar to that previously described (Bershitsky & Tsaturyan, 1989)and is shown in Table 1.

Cacodilic acid was used as a pH buffer because of the very low temperature coefficient of its pKa.This coefficient measured using an EV-74 ionometer was -00045 log units per 1 0C in the range0-35 0C. So, the T-jump of 25 'C induced a decrease in pH of only about 0-1 log units.

Mechanical instrumentationTrough. An experimental chamber with a 09 ml solution trough was made from anodized

aluminum. The lower part of the chamber was placed into the thermoelectric thermostat whichkept the chamber temperature at 0-4 'C. The trough width and depth were 4 and 8 mmrespectively. The short distances from the fibre held in the middle of the trough to the walls andbottom of the massive cold chamber provided a temperature increase of not more than 5 K whenthe solution was removed from the trough. When cold, vapour in the trough was nearly saturatedindependently of vapour pressure in the surrounding air. The uncoated transistor covered with athin layer of isolator was fixed 1 mm from the centre of the fibre and used as a thermometer in

427



428 S. Y. BERSHITSKY AND A. K. TSATURYANo~~~~~~~~ CCDC)-4

2c<



JOULE TEMPERATURE JUMP IN MUSCLE FIBRE 429

both the solution and air. Its accuracy was 0 1 °C and the time constant in solution was < 1 s. Afterremoval of a solution, the fibre temperature approaches a value close to the 'dew point' veryquickly (Ferenezi, 1985, 1986). At this temperature, there is a balance between heat diffusion andenergy flux due to evaporation or condensation and vapour diffusion. It is believed that thetemperature of the small (= 0 5 mm diameter) wet transistor also approaches this point ratherquickly. The time constant of the thermometer in air was - 3 s. Thus accuracy of the fibretemperature measurement just before a T-jump was estimated to be - 0-5 'C.

TABLE 1. Composition of the solutions used in the experiments (mM)Cacodilic

Solution Na2ATP MgCl2 EGTA HDTA CaCl2 Na2CP Imidasol acidRelaxing 5 6 10 - 15 100Pre-activating 5 6 0-2 9-8 15 - 100Activating 5 6 10 10 15 100Preparation and storage 5 6 5 - 20

All solutions contained 3 mm of NaN3. The pH of each solution was adjusted to 7 0 at 20 'C. Theionic strength for the experimental solutions was adjusted to 200 nm with KCl; the ionic strengthof the preparation solution was adjusted to 125 mm with KCl, the storage solution was preparedby mixing the preparation solution with glycerol (50%, v/v). Creatine phosphate kinase (CPK)was just added prior to each experiment (1 mg or 50-100 U ml-') in all solutions containingcreatine phosphate (Na2CP). HDTA, 1,6,diaminohexano-N,N,N',N'-tetraacetic acid (AldrichChemical Co. Ltd).

M

: | ~~DS|I~~~~~~W DPFig. 2. Scheme of the fibre dimensions and sarcomere length measurements. The He-Nelaser beam, LB, passed through the quartz 'in' window, IW, the fibre, F, placedperpendicular to the figure plane, the dividing prism, DP, onto the diffraction screen, DS.The fibre widths in two perpendicular projections were measured with the long-focusmicroscope (M) observing the direct and reflected (by the prism) fibre images.

The chamber had 'in' and 'out' quartz windows for the laser beam. The 'out' window was adividing prism for measurement of the fibre dimensions with two perpendicular projections usingthe MBS-9 long-focus stereo microscope placed under the chamber. The scheme of the opticmeasurements is shown in Fig. 2. The He-Ne 1-5 mW laser LGN-105 (LEMZ Inc., L'vov, USSR),with beam diameter 1 mm, was used without lenses. The width of the first-order diffractionmaximum on the screen (0-2 m distant from the fibre) quantified the scatter of the sarcomerelengths. The external surfaces of the windows were lubricated with a 50% glycerol solution toprevent vapour condensation. There was a glass tube in the trough bottom through which thesolutions could be removed using a syringe.



S. Y. BERSHITSKY AND A. K. TSATURYAN

Force transducer. The hybrid force transducer used for the fibre tension measurement has beendescribed previously by Bershitsky & Tsaturyan (1985). The steady-state force was registered witha mechanoelectronic valve gauge 6Mx2B (MELZ Inc., Moscow, USSR) within the frequency range0-10 Hz. The piezo-electric force transducer (similar to that described by Chiu, Karwash & Ford(1978)) was attached to the gauge. A bamboo arm was fixed to the piezo crystal with epoxy resin.The arm was tipped with a nickel tube which held the fibre (see left inset in Fig. 1) and acted asthe ground electrode for the heating pulse generator. The time constant of the electric drain fromthe piezo crystal was - 3 s.The natural frequency of the piezo transducer used in the experiments presented here was10 kHz. The piezo crystal was damped with a droplet of unhardened epoxy resin. The damped

frequency was 8-1 kHz and the damping constant was - 4 x 104 s-1. The peak-to-peak noise of thepiezo transducer was less than 2 #N.

Length-change generator. A moving-coil length-change generator with a mirror angle photodiodetransducer was similar to that described by Ford et al. 1977, but the permanent magnet wasreplaced by an electric one. A lever made of straw with epoxy resin was fixed to the moving coil.This lever was tipped with a nickel tube acting as the active electrode of the heating pulsegenerator.The step length changes of -100 to 100 ,lm were completed in - 0 35 ms with less than 5%

overshoot. The noise of the length-change transducer was less than 0-2 ,um peak to peak.

Joule T-jump apparatusThe joule T-jump method described earlier (Bershitsky & Tsaturyan, 1985, 1989) was used with

some modifications. Figure 1 shows the block diagram of the T-jump apparatus. A single musclefibre (F) was attached to the nickel tube electrodes (NTE) of the heating pulse generator. After thesolution was removed from the trough, the fibre became a single conductor between the electrodes.The heating pulse generator (HPG) consisted of a waiting sinusoidal pulse generator (= 30 kHz,

0-2 ms duration) and a power amplifier (up to 100 W). The HPG output signal was transformed intoa high-voltage (up to 3 kV) heating pulse passing through the fibre.The attenuated heating pulse was used as the voltage signal, U(t), where t is the time from the

beginning of the heating pulse. The voltage drop on a 200 Ql resistor was measured with the high-frequency pulse transformer and used as the fibre current signal, I(t). The fibre resistance was400-700 kQ. The U(t) and I(t) signals were multiplied using an analog multiplier (AM) to obtainpulse power of W(t) = I(t) U(t). Then power, W(t), was integrated with an analog integrator (Al) todetermine the energy, E, equal to the joule heat liberated in the fibre,

E=J W(r) dT. (1)

The E value at 1 ms after the T-jump was stored using the sample and hold circuit. I, U, WandE signals during the heating pulse in a fibre are shown in the right inset in Fig. 1. The error of thejoule heat determination was less than 2 %. The T-jump amplitude, AT, was calculated by dividingthe energy, E, by the fibre thermal capacity C. Thus, AT = E/C, where C = LAa cp, L is the fibresegment length, Aa is the fibre cross-sectional area in air, c = 3-65 kJ kg-'K-1 is the specific thermalcapacity of the fibre, and p = 1060 kg m-3 is the fibre density (Woledge et al. 1985). The total errorof the AT calculation was mainly determined by an error of the Aa measurement and was < 15%.

Recording and data analysisThe T-jump, length-change and tension signals were recorded with two storage oscilloscopes C8-

13 (VTZ, Vilnus, Lietuva, USSR) at different sweep speeds, and then filmed with a Zenit-M camera(LOMO Inc., Leningrad, USSR). Tension transients were then amplified and rewritten on paperusing a Microfot-1 enlarger (LOMO Inc.) and digitized with a Tektronix-4662 interactive digitalplotter. Fifty to one hundred points were collected from each transient. The exponential analysisof the transients was made using the computer program by Provencher (1976). This programpermits determination of the most probable number of exponential components in a transient, aswell as the rate constants of these components and their standard deviations. This program wasincorporated in the Graphic Interactive Management (GIM) system developed by Dr A. L.Drachev (A. N. Belozersky laboratory, Moscow State University). The GIM system was used forthe computer simulation and the data analysis.

430




ProtocolFigure 3 shows typical records of the tension and temperature changes in an experiment at slow

(Fig. 3A) and fast (Fig. 3B and C) time scales. When the pre-activating solution was removed fromthe trough, the fibre temperature increased from 3-8 to 6-3 'C. Refilling the trough with the cold

A

25Kj

5 C I- __

105 N m-2A T-J R

41 1 130 s

B C. _-----~~~~- ~~ | ~20 KI 40 nm (hs-1)

105 N m-2

01 s 10 ms

Fig. 3. Tension responses induced by a T-jump in a single fibre. A, the bottom trace is thetension response recorded with the mechanoelectronic force transducer; the middle traceis temperature in solution or in air in 1 mm of the fibre; the top trace is the T-jump (from6-4 to 27 °C). The solution around the fibre: pre-activating (P), activating (A) and relaxing(R) were changed at the time indicated by arrows, T-J is the T-jump. B and C, the tensiontransient induced by a T-jump from 6-5 to 27-5 'C and recorded with the piezo-electricforce transducer at two speeds during the next activation of the fibre. Traces from top tobottom: the T-jump; length change; tension and the tension baseline. The method usedfor baseline recording is shown in B. To produce slack, the fibre was released by40 nm (hs)-l. The tension value 1 ms after the release was stored with a sample and holdcircuit and recorded during the next trigger of the oscilloscope. Fibre dimensions in airwere: 1-63 mm x 4 70 x 10-9 M2; sarcomere length = 2-52 /tm.

activating solution induced a decrease in temperature to 3-9 'C and active tension development.The steady tension of 61 kN m-2 was achieved in - 5 s. Then the activating solution was removedfrom the trough which led to an increase in both temperature and tension to new steady-state levelsof 6-4 'C and 70 kN m-2 respectively. About 5 s after the fibre was suspended in air, the heating

431



432 S. Y. BERSHITSKY AND A. K. TSATURYAN

current pulse of 0 2 ms duration and 0 61 mJ energy was passed through the fibre. The pulseinitiated a T-jump from 6 4 to about 27 °C which induced the transient tension increase. Then thefibre was relaxed with cold relaxing solution.The amplitude of the tension response to the T-jump in Fig. 3A is truncated due to the frequency

limitation of the valve force transducer. Figure 3B and C shows the tension transient initiated bythe T-jump from 6-5 to 27 5 °C recorded using the high-frequency piezo-electric force transducer in

20

E) 313

C

10

0.E

04 II0 50 100 150

Time from the T-jump (ms)

Fig. 4. Result of computer stimulation of the fibre cooling. The continuous line is thatcalculated temperature change at the fibre surface versus time after a 20 K T-jump;squares are the experimental points for the transient shown in Fig. 3B and C normalizedto fit the theoretical curve. Simulation was made for a fibre of 75 ,um diameter.

the next activation of the same fibre. The upper traces in Fig. 3B and C are from the T-jump, themiddle traces are the fibre length changes and the two lower traces are tension and tension baseline.The method used for the baseline recording is shown in Fig. 3B. At 150 ms after the T-jump thefibre was released by 40 nm (hs)-1 to produce slack. The piezo-electric force-transducer outputat 1 ms after the release was stored using the sample and hold circuit and then recorded as thetension baseline on the oscilloscope screen during the second trigger.The fibre activation at 5-9 °C induced moderate tension development (50-90 kN m2) and did

not lead to significant sarcomere length disorder. Because the increase in temperature following theT-jump was brief (< 0 5 s), the disorder after the T-jump was also insignificant. Neither the fibreactivation at low temperature nor the T-jump of short duration induced significant fibre damage.It was possible to apply up to twenty activations and T-jumps before tension reduced by 20% andthe experiment was ended.

Fibre cooling after the T-jumpFigure 3A and B shows that the T-jump induced a fast tension rise followed by a slow recovery.

The computer simulation of fibre cooling in air was made taking into account that heat diffusionin the fibre and air, evaporation from the fibre surface, and vapour diffusion in air.The diffusion coefficient of heat in air is close to that of vapour. Therefore, a single diffusion

equation can be used for describing both heat and vapour diffusion in surrounding air. In thisgeneralized equation, sum Capa + r dn(T)/dT has been used instead of the volumetric heat capacity




of air (Ca pa) where ca and Pa are the specific thermal capacity and density of air, r is the specific heatof vaporization, and n(T) is the dependence of the saturated vapour density, n, on temperature, T.The equation has been linearized by substitution of function dn(T)/dT to a constant equal to itsaveraged value in the range 5-35 'C. Convection of the heated air surrounding the fibre wasestimated to be negligible 150 ms after the T-jump. Thus, far from the end of the fibre themathematical solution can be considered as axi-symmetrical. A solution of the problem of heatdiffusion in tube (fibre) and surrounding space (air) has been described (Lykov, 1978). This solutionwas numerically integrated using a personal computer.The calculated temperature gradient between the fibre axis and surface was calculated to be

< 3 % of the T-jump amplitude, AT. The calculated time course of the cooling of the fibre surfacefar from the ends is shown in Fig. 4 where E1 represents the tension transients shown in Fig. 3Band C. It is seen that the time course is close to that of the slow tension recovery after the T-jumpin a fibre of the same diameter. The calculated cooling was not exponential, but in the time range20-150 ms after the T-jump it could be fitted by an exponential function with the apparent rateconstant kapp - 38300/d2 s-1, where d is the fibre diameter in /Lm.

Cooling of the ends of the fibre differed from that of the middle part of the fibre due to the heatdiffusion into the cold metal electrodes. Because of the small temperature gradient across the fibreand the near exponential heat drain to air, the mathematical solution describing the cooling of theend of the fibre can be considered as one-dimensional. This solution is given by:

T(x, t) = o + V2 ATexp (-k. t) (7TDt)2f exp - D) d6, (2)

where x ant t are distance from the fibre's end and time after the T-jump, To is the initialtemperature of fibre, and D = 1-5 x 10-7 m2 S-' is the heat diffusion coefficient in a fibre. At 20 msafter the T-jump the length of the end segment where temperature differs from that of the middleof the fibre by more than 30% is - 40 ,um, i.e. at the time the length of the cooled ends is 3-6%of the fibre length. The length of the cooled end segment increases with time t and is proportionalto \It (eqn (2)).

RESULTS

General features of the tension transientsIn relaxed fibres the T-jump did not induce tension changes. A small electric

artifact similar to that without a fibre was seen on the force transducer output duringthe heating pulse.When the fibre was fully activated, the T-jump induced a fast tension rise followed

by a slow tension recovery to approximately the same tension as that before theT-jump (Fig. 3B and C). The tension transient, P(t), initiated by the T-jump couldbe fitted by a tri-exponential function of the following form:

P(t) = PO + (a'11exp (k, t)) + (aO(I1-exp (k2 t)) exp (k3 t), (3)where Po is the initial tension before the T-jump, aO and aO are the amplitudecoefficients, k1 and k2 are the rate constants of the phases 1 (fast) and 2 (slow) of thetension rise, and k3 is the rate constant of the slow tension recovery due to the fibrecooling. Figure 5 shows the fit of eqn (3) to the tension transient shown in Fig. 3Band C.The rate constant of the slow tension recovery, k3, was 5-10 s-1. For fibres of a

relatively small diameter (60-70,tm), k3 was greater than that of thick fibres(70-80 ,um). The k3 value was close to the apparent rate constant of the fibre cooling,kapp, calculated for a fibre of the same diameter (Fig. 4). Occasionally, k3 was lessthan kapp, but the difference was < 30%.

After T-jumps of a rather high amplitude (20-30 K) the biphasic character of the

433



4S. Y BERSHITSKY AND A. K. TSATURYAN

150

'E 100z

C:0Ina)

Rn

15 ms

Time

Fig. 5. Analysis of the tension transients induced by a T-jump. The same event as thatshown in Fig. 3B and C. Squares are the experimental points; continuous line is the tri-exponential fitting function (eqn (3) in the text) with the rate constants k1 = 1130 +90 s-1,k2 =166+8 s-' and the relative amplitudes al/PO = 0-32+ 0-03, a°/lP = 1-08+ 0-06;dashed line is extrapolation of phase 2 back to time of the T-jump.

8K .. -tw- 16K

*

23 K___ ____. 30 K

|105 N m-2_._.,._ , ____ j_o_N,m_ _

10 Ms

Fig. 6. Tension transients induced by T-jumps of various amplitudes in a single fibre. Thetraces in each panel are (from top to bottom): the T-jump; the length; tension, andtension baseline. The amplitude of the T-jumps are shown beside each row. The startingtemperature was 5-1-5 4 'C. Asterisk shows an initial tension drop during the T-jump.Fibre dimensions in air were: 1 23 mm x 2-83 x 10-im2; sarcomere length = 2-55 jim.

434




tension rise was observed by eye (Fig. 3). For the transient shown in Figs 3B, C and5 the rate constants for phases 1 and 2 were k, = 1130 s-1 and k2 = 166 s-1,respectively. The dashed line in Fig. 5 shows the extrapolation of phase 2 back to theheating pulse. It can be seen that during the fast phase 1, tension rose by 23 kN m2,i.e. 1-32 times. During phase 2 an additional tension rise of about 65 kN m-2 or 1P7times occurred.

A B

_~~~~~ ~~~~~1000o/ T

200 ° -

E 150 0z 0 C kC

.210 10 20 3 - - -

C 10C.210 0

50-Temperature (OC)

21.1 30.0 39-50*

0 10 20 30 3.2 3.3 3.4Temperature (OC) 1 000/T (K-1)

Fig. 7. A, variation of the maximal tension with temperature. Temperature at the timemaximal tension after the T-jump was corrected for fibre cooling. the line is the regressioncalculated for all data points. B, Arrhenius plot for two rate constants, k, (Ea) and k2 (K>).The rate constants are plotted on a logarithmic ordinate against the reciprocal absolutetemperature, T, on the abscissa. Straight lines represent the regression for each set of datapoints. Data are from four muscle fibres.

Responses to T-jumps of various amplitudeTo study the temperature dependence of the amplitudes and rate constants for

phases 1 and 2, a series of four experiments was performed where T-jumps of variousamplitudes were applied to the fibres.The records of the tension responses to the T-jumps of various amplitudes are

shown in Fig. 6 at two oscilloscope sweep speeds. The starting temperature justbefore the T-jumps was 5-1-5-4 'C. The initial tension in air, P0, at the temperaturewas 50-54 kN m-2. An increase in the final temperature reached by the T-jump ledto an increase in the maximal tension achieved during the tension transient and anacceleration of this transient.

Sometimes, after T-jumps of an intermediate amplitude, a small tension dropduring the heating pulse preceded the tension rise (Fig. 6, 16 K example). At T-jumpsof a rather high amplitude (20-35 K), the drop was not seen because of an electricartifact during the heating pulse and the fast tension rise (phase 1) which beganduring the heating pulse.

Figure 7A shows the temperature dependence of tension before (in the activatingsolution and air) and after the T-jumps from four experiments. The maximal tension

435




achieved after the T-jump is plotted in Fig. 7A against the temperature which wascorrected for fibre cooling during tension rise. The plot shows a nearly linear increasein tension from 15-40 to 170-210 kN m-2 when the temperature was increased from1-5-3 to 30-40 °C. At the initial temperature 5-1-6-3 °C tension was 50-60 kN m2.A B

1-0 1.0

,0.5- o 0 5 - o0C14

CalX

0-0 i 0-0 ~ r-0 10 20 30 + 0 20 30

T-jump amplitude (K)Fig. 8. Normalized amplitudes of phases 1, aO/lP (A), and 2, aO/(Po+aO) (B), against

the T-jump amplitude, AT. Data are from four muscle fibres.

T-jumps of a relatively high amplitude (> 15 K) induced a biexponential tensionrise. For T-jumps of lower amplitude, phase 1 was not determinable (Fig. 6, 8 K) orthe computer program (Provencher, 1976) showed that this phase was not significant.Both k1 and k2 increased with the final temperature. An Arrhenius plot for k1 and k2obtained from four experiments is shown in Fig. 7B. The Qlo values determined bythe least-squares method were 1-6 for k1 and 1-7 for k2, respectively. At any giventemperature k1 was = 5 times k2. At 20 °C k, was 400-600 s-1 and k2 was 75-120 s-'.The dependence of normalized tension rise during phase 1, al/PO, on the T-jump

amplitude, AT, is shown in Fig. 8A. The tension increment associated with phase 1was a near linear function of AT. After 25-35 K T-jumps the increment achieved was55-75% of Po. Normalized tension increment during phase 2, al(Po + a'), is plotted inFig. 8B, against AT. This increment increased quickly when AT rose to 15-20 K andthen achieved a plateau at 70-100%.

Effects of preceding length changesTo examine what cross-bridge processes are responsible for phases 1 and 2 of the

tension rise due to a T-jump, a series of five experiments was made with step lengthchanges of amplitude ranging from -9 to + 3 nm (hs)-1 applied to the fibre 4 msprior to the T-jump.

Mechanical transientsTypical records in an experiment of this series are shown in Fig. 9. In this

experiment, the tension in air just before the length step, Po, at the startingtemperature 8-7-9 °C was 80-88 kN m-2. Length steps completed within 0 35 ms

436




induced a tension transient which was similar to those described by Huxley &Simmons (1971) and Ford et al. (1977). The subsequent T-jump induced a bi-exponential tension rise followed by a slow tension recovery similar to those withoutlength change.

j....125K

+ 3nm (hs)-1

<'~~ ~~~~~0 NL

*

10 Ms

Fig. 9. Fibre tension transients induced by T-jumps from 8&7-9 0C to 31-33-5 0C after thestep length changes of various amplitudes. Traces in each panel from top to bottom are:the T-jump; the length change; tension; and tension baseline. The length step amplitudein nm (hs)'1 is shown beside each panel. Asterisk shows an initial tension drop during theT-jump. Fibre dimensions in air were: 1-36 mm x 3-12 x 109 inl; sarcomere length=2-5#m.

In the five experiments the starting temperature in air was 7-9 'C. Tension beforethe step length change and the T-jump, Po, was 65-88 kN M-2. Averaged values ofthe normalized tension at the end of the length step, P1/P0, and just before T-jump,

P2/PO,,areshown in Fig. 10 against the length-step amplitude, y. The tension valuesPO andP, correspond to the Tol and T77 values introduced by Huxley & Simmons (1971).The P2 is however different than their T2 value. In skinned rabbit fibres at 7-9 00 theearly tension recovery was followed by a slower tension recovery practically withoutpause or delay. Thus, we were unable to determine the early recovery tension, T2.Instead we used the tension value 4 ms after the length change, P2.The slope of the P1 curve was less in our experiments with rabbit muscle fibres than

that in the experiments of Ford et al. 1977 with intact frog fibres. The average yovalue (step-shortening amplitude per half-sarcomere necessary to bring tension to

437




zero) estimated from the tension responses to +3 nm (hs)-1 length changes was84 ± 17 nm (hs)-' (mean+ S.D., n = 5), i.e. about twice that described by Ford et al.(1977, 1981) with intact frog fibres at 0-2 'C. On the other hand, a similar yo valuewas obtained in experiments using skinned frog fibres (Goldman & Simmons, 1984,

1.5

P2IPo ,,

+ ,'

+ Ej ,'7- .

-10 -8 -6 -4 -2 0 2 4Length step (nm (hs)-1)

Fig. 10. Relative tension just after the length step change (Pj/IP) and 4 ms later (P2/Po)against the length step amplitude. Bars show the standard deviations in 5 experiments.

1986). Due to a difference between the tension transients in skinned and intactmuscle fibres (Blange & Stienen, 1985; Goldman & Simmons, 1986), the P2 curve inour experiments also differs from the T2 curve in the experiments of Ford et al. (1977).An exponential function did not fit the early tension recovery after the length step.

As the fast tension recovery was followed by a slow one, and the tension transientwas not complete in the 4 ms before the T-jump, this recovery could also not be fittedby a biexponential function.

T-jump effectsAt 4 ms after the length step, the T-jump was applied to increase the fibre

temperature from 7-9 to 29-5-35 'C. The tension response to the T-jump was similarto that without the length step (Fig. 9). The tension transient initiated by the T-jump applied after the length step also could be fitted with a tri-exponential functionwith a form similar to eqn (3):

P(t) = P2+ (a,(1-exp (-/k t)) + a2(1-exp (-lk2t))) exp (-k3 t), (4)

where P2 is the tension before the T-jump, a1 and a2 are the amplitude coefficients,and kl, k2 are the rate constants of phases 1 and 2, respectively. If the T-jump wasapplied after the fibre stretch, a small initial tension drop due to the thermalexpansion was seen during the T-jump (Fig. 9). After T-jumps applied during theisometric contraction or after step shortening the initial tension drop wasundetectable.Phase 1. After the step shortening the amplitude of phase 1 (a1) was less than that

in the isometric contraction (Fig. 9). Figure 11C shows (P2 + a,)/(PO+ ao), the

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normalized tension at the end of phase 1, versus the length-step amplitude, y, as wellas the P2 curve for the five experiments. Here P2 + a, and P0 + al are the tension valuesobtained by extrapolation of phase 2 to the T-jump time with and without the lengthstep, respectively (Fig. 11A and B). The larger the step release, the lower the tension

A B

T-jumpLengthstepTension

ag + a +P2-)Po 1 < P2

C0 (a, + P2)/(a° + P0) 1.5-

c0 P21PO

-10 -8 -6 -4 -2 0 2 4Length step (nm (hs)1')

Fig. 1 1. C, normalized tension just before the T-jump (K>) and at the end of phase 1 of thetension rise induced by T-jumps from 7-9 to 29-5-33-5 0C (LI) against the length stepamplitude. Bars show the standard deviations in five experiments. Nomenclature isshown in A and B.

at the end of phase 1. It is seen that the normalized dependencies on y of the tensionat the end of phase 1 and before a T-jump are very similar.The averaged dependence of the rate constant of phase 1, kl1, on the length-step

amplitude, y, is shown in Fig. 12A. Phase 1 was accelerated after fibre shortening anddecelerated after fibre stretching. After a quick release of -9 nm (hsf-', kc1 was1620 + 125 s51 (mean + S.D_, n = 5) or about twice that without a length change(910+ 145 s-1). The dependence of kc1 on y shown in Fig. 12A was similar to that forthe early tension recovery after the step length changes in the intact frog fibres(Huxley & Simmons, 1971; Ford et al. 1977). There was some difference, however,due in part to the end-compliance of the fibre in our experiments. In the experimentsof Huxley & Simmons (1971) and Ford et al. (1977) the compliance was eliminatedby using the spot-follower technique. Another reason for the difference may be adeceleration of the tension transients in the skinned fibres as compared with those inthe intact fibres (Blang. & Stienen, 1985).The data presented in Figs1s and 12A show that the rate constants and tension

achieved at the end of fast components of the tension transients initiated by thetemperature and length perturbations are similar. This indicates that thesetransients, most probably are due to the same process.Phase 2. The records in Fig. 9 show that the maximal tension after the T-jump was

essentially independent of the length-step amplitude, y. After maximal shortening

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(-9 nm (hs)-1), the maximal tension was -0-93+0-08 (means+.D., n = 5) of thatwithout the length step. For the length steps of lower amplitude, the differencebetween the maximal tension after the step and without it was even less (< 5%).Thus, tension achieved during phase 2 was independent of the preceding length

A B

ki (S-1 ) k2 (s-l )250

1500 -200

1000 15

I 1aoo-.>100500 -

50

-9 -6 -3 0 3 -9 -6 -3 0 3

Length step (nm (hs)-')Fig. 12. Variation of the rate constant of phases 1 (k,) and 2 (k2) with the length stepamplitude. Bars show the standard deviations in the five experiments presented in Figs10 and 11.

change. The amplitude of phase 2, a2, increased after fibre shortening. The increasein a2 as compared with aO (at y = 0) was significant (P < 0 02) at y values from -6to -9 nm (hs)-.

Figure 12B shows the rate constant k2 of the slow phase 2 compared to thepreceding length change, y. It can be seen that k2 is practically independent of y. Thescatter of the data was due to the variation of k2 values between fibres. Correlationbetween k2 and y was not significant for individual fibres.The fact that the rate constant and the final tension of phase 2 were independent

of the preceding length changes means that during this phase the cross-bridges'forgot' the relative sliding of the thin and thick filaments. Hence, it can beconcluded that phase 2 is accompanied by the cross-bridge detachment andreattachment to the thin filaments.

DISCUSSION

Joule T-jump methodPossible artifacts

Electric artifacts. Some possible artifacts of the joule T-jump method were brieflydescribed earlier (Bershitsky & Tsaturyan, 1985, 1989). The direct effect of the

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electric field on the fibre was, most likely, insignificant. Taking the peak electric fieldintensity, E = 2 MV m-l, charge of a cross-bridge q = 1.6 x 1018 C (ten times unitcharge), and the dielectric constant of the solution, e = 80, one can calculate themaximal electric force acting on a cross-bridge, Fe = 4 x 10-14 N. This force is only1 % of the force per cross-bridge during an isometric contraction (Huxley &Simmons, 1971). Since up to twenty activations and T-jumps were applied to a fibrewithout a significant loss of tension, it can be concluded that the heating pulse didnot harm the contractile proteins.

There was a small effect of the electric field on the ionic composition of theactivating solution due to electrolysis. Even for H+ ions, which are the most mobileions, the displacement during a half-wave of the heating pulse of maximal amplitudewas estimated to be < 5,m. This means that the thickness of a layer near theelectrodes where the solution composition was changed due to electrolysis was notthicker than two sarcomere lengths.

Changes in the solution composition in air. As the heating pulse was applied to thefibre suspended in air, possible effects of water evaporation from the fibre surface andthe ATP hydrolysis in the fibre should be discussed. The fibre temperature in the coldtrough was as low as 5-9 °C, and the evaporation was also small. Computersimulation showed that the increase in ionic strength due to evaporation was < 5%in 5 s. At room temperature this effect is more significant (Ferenczi, 1985, 1986).The ATPase rate in the rabbit fibre at 5-10 "C is less than 1-3 s-1 per myosin head

(Brenner, 1986). Taking the concentration of heads in the fibre to be 0-15 mM(Ferenczi, Homsher & Trentham, 1984), one can calculate the ATPase activity in thefibre to be < 0-2 mm s-'. This means that < 1 mM-MgATP is converted into Mg-ADP in 5 s after the fibre had been suspended in air. The computer simulation takinginto account MgATP hydrolysis and the CP/CPK regeneration system showed thatin this system the MgATP concentration in air remains practically the same as thatin the solution, and the MgADP concentration is < 0-15 mm. The inorganicphosphate (Pi) concentration increased from 0-5 mm in the solution to 1-5 mM5 s after the fibre was suspended in air.

Temperature heterogeneityPossible reasons for heterogeneity of the electric field and the temperature

distribution just after the T-jump are the 'skin-effect' and a variation of the cross-sectional area along the fibre. At the current frequency of 30 kHz and the fibreconductivity - 1 m1 2-1 the skin depth should be more than 1 m, i.e. four orders ofmagnitude greater than the fibre radius. Thus the field heterogeneity due to the'skin-effect' was negligible. Therefore, the main reason for heterogeneity in theelectric field and temperature just after the T-jump was the variation of the cross-sectional area Aa along the fibre. This variation was shown in the Methods section tobe < 15%.The temperature heterogeneity after the T-jump due to fibre cooling was

estimated using computer simulation (see Methods). The temperature gradientacross the fibre was estimated to be < 3% at any time after the T-jump. Length ofthe cooled ends increased with time. At 20-30 ms, the cooled length was 40-50,tmor 3-6% of the fibre length (see eqn (2)). The cooling of the fibre's ends after the T-

441




jump is not likely to have a major affect on the tension transients described here. Themaximal tension achieved after the T-jump (Fig. 6) was not less than the tensionat the same temperature in solution (Goldman, McCray & Ranatunga, 1987,Ranatunga, 1990). The fact that a fibre-stiffness rise accompanied tension riseinduced by the T-jump shows additionally an absence of the compliant end segmentsin the heated fibre (Bershitsky & Tsaturyan, 1989).

Comparison with other T-jump methodsThe laser T-jump method has been used by Smith, Goldman, Hibberd, Liquori,

Luttmann & McCray (1984), Smith, McCray, Hibberd & Goldman (1989) and Davis& Harrington (1987a, b). Fibre heating with microwave radiation has been used byLindley & Kuyel (1978) and Lindley & Goldthwait (1984). The time resolution of thejoule T-jump method used here is 0-2 ms, which is about the same resolution asthat of the laser T-jump methods. The time resolution of the microwave-radiationmethod is about one order of magnitude slower. On the other hand, the laser T-jumpdoes not permit a temperature change of more than 8 K, while the magnitude of thejoule heating is as much as 35 K. The main limitation of the joule T-jump methodis the relatively fast fibre cooling after the T-jump. Thus this method is only usefulfor the study of rather fast processes.The infra-red laser pulse used by Goldman et al. 1987 induced heating of not only

the fibre but also the surrounding solution and the metal hooks attached to the fibre.As we have discussed earlier (Bershitsky & Tsaturyan, 1989), the heating of thehooks led to thermal expansion. The effect of elongation of the hooks is comparablewith that of fibre thermal expansion. Thus, after the laser pulse, a tension transientwas induced by both the T-jump (of a rather small amplitude) and fibre lengthrelease due to the thermal expansion of the hooks as well as the fibre.

Comparison with earlier studiesTemperature dependence of maximal tensionTemperature dependence of isometric tension at maximal activation shown in Fig.

7A is similar to that obtained in steady-state experiments with skinned rabbit fibresat maximal activation (Goldman et al. 1987; Ranatunga, 1990). In steady-stateexperiments, a similar dependence was obtained with fibres from other warm-blooded animals (Stephenson & Williams, 1985). The only difference in thetension-temperature relation between our experiments and those of Goldman et al.(1987) is the fact that in their experiments the relation became less steep attemperatures above 20 'C. This difference can be explained by disorder of thesarcomere length reducing tension in steady-state experiments at high temperature(Brenner, 1986). Also steady-state experiments where temperature was increasedfrom 0 to 40 'C rather quickly (in about 50 s) showed a near linear tensi-on-temperature relation (Ranatunga, 1990).

T-jump de ectsA biexponential tension rise initiated by laser (Goldman et al. 1987; Davies &

Harrington, 1987a) and joule (Bershitsky & Tsaturyan, 1986b, 1988) T-jumps hasbeen described. In the laser T-jump experiments, tension rise was preceded by a

442




tension drop due to thermal expansion of the fibre and the hooks. The drop wasexpressed much less or was indeterminable after the joule T-jumps. The differencewas, most probably, due to thermal expansion of the hooks in the laser T-jumpexperiments. In the experiments presented here, a fast tension rise of high amplitudebeginning during the heating pulse masked the initial drop. That is why the drop wasseen only during T-jumps of an intermediate amplitude (Fig. 6, 16 K) or after thefibre stretch (Fig. 9, + 3 nm (hs)-1). Stretch slowed down the fast tension rise and thedrop became more evident.The rate constant k1 of the fast phase 1 of the tension rise was similar to that of

the laser T-jump experiments (Goldman et al. 1987). However, in contrast to theexperiments presented here (Fig. 7B), no temperature dependence of this rateconstant was observed. Goldman et al. (1987) used relatively small T-jumps atvarious initial temperatures. As can be seen from Fig. 6, the tension rise initiated byan 8 K T-jump (the maximal value for the laser T-jump) is rather small. The k1 valuecannot be determined accurately enough for such small T-jumps. For this reason,the data scatter in the experiments of Goldman et al. (1987) was significant (see Fig.10 in their paper) and, possibly, masked the temperature dependence of kl. In theexperiments presented here, the temperature dependence was studied using T-jumpsof various amplitudes. At T-jumps > 15 K, the rate constant of phase 1 can beestimated exactly.

In the experiments reported here, the rate constant of phase 2 was a few timesgreater than that of the laser T-jump experiments (Goldman et al. 1987; Davis &Harrington, 1987a). The difference cannot be explained by fibre cooling after thejoule T-jump, because the estimation of the rate constants was made taking intoconsideration cooling kinetics. After laser T-jumps of a small amplitude, the tensionobtained by the extrapolation of phase 2 to the T-jump moment was about the sameas tension before the T-jump (Goldman et al. 1987). After joule T-jumps of highamplitude, the extrapolated tension was - 1P5 times higher than that before the T-jump. It is possible that the cross-bridge processes controlling phase 2 in the laserand joule T-jump experiments are different due to the differences in initial conditionsfor the cross-bridges at the beginning of this phase (i.e. at the end of phase 1) afterT-jumps of different amplitudes.The rate constants k1 and k2 at 20-25 °C are very close to the rate constants of

exponential processes 'C' and 'B' in experiments with small-amplitude sinusoidallength changes in rabbit fibres at the same temperature (Kawai & Brandt, 1980). Thek2 value is also close to the rate constant of cross-bridge attachment estimated by the'Ca-jump' (Goldman & Kaplan, 1988) and the 'ATP-jump' (Goldman, Hibberd &Trentham, 1984) experiments with flash photolysis of 'caged-compounds' in therabbit muscle fibres.

Interpretation of the dataPhase 1The fast component of tension rise initiated by the T-jump (phase 1) is, probably,

induced by some forced-generating process in the cross-bridges attached to the thinfilaments. The main evidence for this conclusion is the fact that the rate constant ofphase 1 increases after fibre shortening and decreases after stretching (Fig. 12A). The

443




dependence of the rate constant on the preceding length change means that the cross-bridges involved in phase 1 'remember' filament sliding and, therefore, they wereattached to the thin filaments before the length step and T-jump. An absence of thecross-bridge reattachment during phase 1 is also indicated by measurements(Bershitsky & Tsaturyan, 1989) showing that the fibre stiffness remains practicallyconstant during phase 1.The process controlling phase 1 is, most probably, the same as that controlling the

early tension recovery following the step length change (Huxley & Simmons, 1971;Ford et al. 1977, 1981, 1985). The rate constants of these processes are similar anddepend on the length change in a similar manner (Figs 9 and 12A). For frog fibres,the rate constant of phase 1 extrapolated to 0-2 °C (Bershitsky & Tsaturyan, 1988)was the same as the rate constant of the early tension recovery interpolated to zerolength change (Ford et al. 1977). A similar conclusion was made by Goldman et al.(1987) who compared the tension responses to the T-jumps and length steps.The data presented in Fig. 11 are further evidence for identity of the processes

controlling the fast responses to length and temperature perturbations. Tensiondependencies on the length-step amplitude before the T-jump and at the end of phase1 are very similar.Tension rise during phase 1 indicates that the enthalpy change, AH, associated

with the force-generating process controlling this phase is positive. Goldman et al.(1987) have estimated it to be 9 kJ mol-1 in their laser T-jump experiments. In theexperiments presented here, tension at the end of phase 1 was much higher than intheir experiments. Therefore, our estimate of All is higher, AH = 15-30 kJ mol-1 (seebelow).

Phase 2The slow component of the tension rise initiated by the T-jump (phase 2) is

accompanied by cross-bridge detachment and reattachment because neither themaximal tension after the T-jump nor the rate constant of phase 2 depend on thepreceding length change (Figs 9 and 12B). Thus, during phase 2, the force-generatingcross-bridges 'forget' the filament sliding and, therefore, they reattach to new siteson the thin filaments.

During phase 2, the fibre stiffness increases to a lesser extent than tension(Bershitsky & Tsaturyan, 1989). Since fibre stiffness is proportional to the number ofcross-bridges attached to the thin filaments (Huxley & Simmons, 1973), an increasein the tension-to-stiffness ratio means that during phase 2 there is an increase in theforce generated by a cross-bridge.The data of the experiments presented here and earlier (Bershitsky & Tsaturyan,

1988) cannot be explained by the Huxley & Simmons (1971) model or the four-statemodels of Eisenberg, Hill & Chiu (1980) and Pate & Cooke (1989). It is difficult toexplain why the cross-bridge should reattach to the thin filament to generate moreforce. It will be shown below that the main features of the experimental data can beexplained by a rather simple model joining the models of Huxley & Simmons (1971)and Huxley (1973).

444




Kinetic modelThe tension and stiffness transients initiated by the joule T-jump have been

explained using a simple kinetic model based on a scheme of the cross-bridge cycletaken as follows

D -->N N' -- F =>DI (5)where D is the detached state of the cross-bridge, N, N' and F are the attached states.Only state F is force-generating during isometric contraction, whereas N and N' arenon-force-generating states. The cross-bridge stiffness is proposed to be equal in allthree attached states N, N' and F. In the detached state D, the stiffness is zero. Thus,normalized tension, P, and stiffness, S, are as follows:

P = [F], S = [N] + [N'] + [F], (6)

where [N], [N'] and [F] are the probabilities that the cross-bridge is in states N, N'and F, respectively.The reversible attachment D * N is followed by a reversible transition between

two stages of attachment N , N' as proposed by Huxley (1973). The transitionN = N' may be the step of the inorganic phosphate release of the cross-bridge ATPasecycle (Huxley, 1980). The rapid reversible transition N' * F is the force-generatingstep postulated by the Huxley & Simmons (1971) model. The slow irreversibledetachment F -= D is the rate-limiting step of the ATP hydrolysis and includes ADPrelease, ATP binding the cross-bridge detachment. A more detailed six-state kineticscheme and a model describing mechanical responses to temperature and concen-tration perturbations has been characterized briefly (Tsaturyan, 1991).The rate constants kDN = 80 s-1 and kND = 50 s-1 at 20 °C were estimated from the

kinetics of the stiffness transients in the experiments with the photolysis of 'cagedATP' (Goldman et al. 1984) and 'caged Ca' (Goldman & Kaplan, 1988). The kineticconstants of the transition N * N', kNN' = 130 s-1 and kN,N = 60 s-1 at 20 °C wereestimated from rigor and active stiffness measurements (Goldman et al. 1984) and thedelay between the stiffness and tension rise during an onset of contraction (Goldman& Kaplan, 1988). The rate constants kNTF = kFN' = 300 s-1 at 20 °C were estimatedfrom experiments with sinusoidal length changes (Kawai & Brandt, 1980), and kFD= 10 s-1 was chosen to provide the ATPase rate ([F]kFD) equal to that in theexperiments of Ferenezi et al. (1984).The Qlo values for the rate constants were chosen to approximate the data

presented here, the stiffness transients initiated by the T-jump (Bershitsky &Tsaturyan, 1989) and the temperature dependence of the ATPase activity in thefibres (Brenner, 1986). The Q1o values for the rate constants kDN", kN'N, kNF and kFDwere 1-5, 2, 2 and 1-5, respectively.To explain the experimental data it is necessary to accept that the enthalpy

changes, AHNN, and AHN'F, associated with the transitions N = N' and N' =>F arepositive. In this case, an increase in temperature leads to a shift of the equilibriumbetween states N, N' and N', F to the right. Phase 1 of the tension rise is due to arapid force-generating transition N' = F. Phase 2 is explained by a decrease in thenumber of cross-bridges in the predominant state N due to a shift from state N tostate N' and then to state F. Tension and stiffness rise in phase 2 is accompanied by

445




a change in the population of attached cross-bridges due to the reversibility of stepsN < N' and N' F. The enthalpy change values for the force-generating step, AHN'F= 15-30 kJ mol', and the predominant step, AHNN = 30-60 kJ mol2, provide thebest fit of the experimental data. These estimated values depend on the equilibrium

Stiffness

1.0 3cn 2

0) 1CA

.) Tension

0) ~~~~~~~~~~~~~~30 0.5 2

1

E _0z

-10 0 10 20 30 40 50Time after T-jump (ms)

Fig. 13. Simulated stiffness and tension transients from the model described in the text.The starting temperature was 7 °C; the final temperatures after the T-jump applied attime zero were: 15 °C (1), 25 °C (2) and 35 °C (3). The enthalpy change associated with theforce-generating step was AHN'F = 22-5 kJ mol-1, for the previous step AHN'N =40 kJ mol-1, and for the cross-bridge attachment AHDN = -10 kJ mol-1. For the rateconstants and their temperature coefficients see text.

constant K = kN F/kFN at 20 °C which cannot be determined accurately enough. Itshould be noted that heat measurements in frog muscle after step shortening (Gilbert& Ford, 1988) also showed a positive enthalpy change associated with a rapid force-generation step.

Three simultaneous differential equations describing non-steady kinetics inaccordance with scheme (5) were solved numerically. Figure 13 shows the results ofsimulation of tension and stiffness transients after T-jumps of various amplitudes.The main features of the experimental transients are well described by the abovemodel. After high T-jumps the biphasic character of the tension rise is easily seen(compared to Fig. 6). The stiffness increase is near exponential with the rate constantbeing close to that of the slow component of tension rise as was found in theexperiments of Bershitsky & Tsaturyan (1989).

We wish to thank Professor Sir A. F. Huxley, Professor Y. E. Goldman and Dr K. W.Ranatunga for helpful discussions. We are grateful to Dr A. L. Drachev for assistance in thecomputer simulation and the experimental data analysis. We are also grateful to Dr J. Clark forhis kind help in preparation of the manuscript.

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S Y Bershitsky and A K Tsaturyan rabbit muscle fibres.

Tension responses to joule temperature jump in skinned

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