Equatorial X-ray intensities and isometric force levels in frog sartorius muscle

J. Mol.

Biol.

(1979) 132, 53-67

Equatorial

X-ray Intensities and Isometric Force Levels in Frog Sartorius Muscle

LEEPO C. Yu, JACQUELINE

National

Institute

E. HARTT~

AND RICHARD

J. PODOLSKY

Laboratory of Physical Biology of Arthritis, Metabolism, and Digestive National Institutes of Health Bethesda, Md 20014, U.S.A. (Received

16’ November

Diseases

1978)

Isometric

force levels, ranging between 0 and 100% of maximal force P, at 2 to 3”C, were elicited in frog sartorius muscle by means of rapidly cooling a Ringer solution containing 1.25 to 2.0 mM-caffeine. Equatorial X-ray diffraction patterns were obtained in the resting state and during contraction. The rabio of the with force almost linearly, with a slight upward intensities I, I/Ilo increased curvature. The individual intensities for the contracting state were normalized relative to both the intensity of the undiffracted beam and the intensity of each reflection in the resting state. These normalized intensities were found to Vary in a reciprocal way : Ilo decreased while I, 1 increased throughout the range of forces studied. The gradual change in I,,/I 11, with force level indicates that this ratio is a sensitive measure of the number of cross-bridges in the isometric stat,e. A twostat’e model in which myosin projections are either in a resting or attached state and in which force is proportional to the fraction of projections in the attached state was applied to the experimental data of the individual reflections. Ilo deviates from this model in a way that suggests that formation of the first few cross-bridges may decrease the regularity of the remaining unattached myosin projections.

1. Introduction X-ray diffraction patterns from striated vertebrate muscle change in a characteristic way with various physiological states. In particular, the intensities of the two prominent equatorial reflections 10 and 11 have been found to vary, depending on whether the muscle is at rest, contracting or in rigor. These equatorial reflections arise from the hexagonal arrays of myofilaments in the region of overlap (Huxley, 1953,1957). Within the filament lattice, the myosin-containing filaments are situated at’ the corners of the unit cell with two act’in-containing filaments at the trigonal positions. For frog sartorius muscle at rest the 10 reflection is at least twice as intense as 11. t Present addre~a: (‘alif. 94143, U.S.A.

Cardiovascular

Research

Institute.

University

of California,

Aen Francisco,

53 Q 1979 Academic

Press Inc.

(London)

Ltd

54

L.

C. YU,

.J. F.

HAKTT

AND

13,. J.

PODOI,SKY

The intensity ratio I,,/I, I decreases by two- t#o threefold during fully activat.ccl isometric contraction (Haselgrove & Huxley, 1973) and further decrease was observetl in rigor (Huxley, 1968). In addition, it was found t)hat changes in the ratio I,,,:/, , were due to nearly equal but opposit’e changes in thcl individual intensitiw f,(, a~1 I, 1 when the muscle was fully activat,ed : I, O decreased by about one-half while I,, increased by twofold (Podolsky et al., 1976 ; Haselgrove et al.. 1976). The int,ensity ratio changes associated with act,ivitjy and rigor have bctw int.wpreted in terms of redistribution of mass between the filaments (Huxley. 1968 : Haselgrove & Huxley, 1973 : Haselgrove et ul., 1976: L-mn. 1978). A decreaw of mass originally associated with the mgosin filaments in the relaxed statci is ~CCOIIIpanied by a simultaneous increase of material associated \\-ith t~hr: actin filament. It. n-as suggested that t)he amount of mass moved might’ represent the number of crossbridges formed, namely the attachment of the mywin projrations (mainly t,hth tn~wsin subfragment-1) t,o the actin filaments, during some phaw of t’hrk wnt,raction (my&:. How-ever, there is no evidence thet the observed changes in intcnsitirs arc sensit,irrx measures of the number of cross-bridges formed, since thtl suggestions mw~tionrti above were based on ?(-ray data associated with transitions from thtl relaxed to thcb fully activated states only. If the gross mass movement ~wre R st’ronglq’ co-opwativc effect associated with tho formaCon of A small numhw of cross-bridges. relating intensity to cross-bridge number would become extremely difficult. This possibility should be considered beceuw subthreshold conwnt,rations of caffeim at’ room ttwperature induct changes in the short range’ elastic componcnt~ of fibctrs (I,anriwgrt~~l. 1971), which suggests that structural rhangcs involving myosi n pro,iwt~ions may Itts dissociated from force development. The relation between cross-bridge number and tyuatorial intJcwitirq has becornt~ even mow relevant in light of result s obtained from actively shortening niiiwlr* (Podolsky et aZ., 1976). In that cast. a smell. almost insignificant. change in thf\ ratio was associated wit’h a large decrease in force to as litt,ln as 0.2 of isornc+rica IlIP,” value. In addition. both /,O and I,, showed a slight increase during short,ening. ‘l’hc~ lack of significant, change in the S-ray paStterns with decrease in force raise:: the. question of whether those intjensities and their ratio aw sensit ivo measures of wos~bridge number. c~xamitwd as a tiItiction 01‘ In t)he present st’udy. thtb equatorial reflection, , ww force level et a fixed sarcomere length. The int’ensitics of tlw individual rrflrctions was actirat,otl 10 and 7 2 ww studied in addition to the ratio I, ,;‘lrc,. Ttic frog sartoriw by caffeine according to the rapid coolin, v method of 8akai (Sakai C%Kurihara. 1974) to give various force levels. Our purpose was to study tlw wfltwtiow from the rnuscl~ while it was in a steady state of contraction at diff&wnB tlegrtw of activation. Act ivation by thermal diffusion is preferable to activation by diffusion of’ a substanw into the muscle volume, since the thermal conductivit~~~ of musclth is roughly t,wo ortlws of magnitude greater than the diffusion coefficient of small ions and rnolccules. ‘1’11ts length was kept constant to avoid effects on inttlnsitiw due t,o changr in overlap mcl to avoid possible changes in t,he average configuratiou of tht& cross-bridges assouiatctl with motion (H. E. Huxley, 1969: A. F. Huxley. 1971; Z’odolsky it (11.. 19i6). A tlircrt correlat,ion betwrten changes in force and int8ensity ratio was obswvc~l. In addition. intensities of the individual refl&ions 10 isnd 1 I \vc‘w t~xemirwtl and found to \-ar) in an almost reciprocal way throughout, the range of forces studied. Preliminar\, accounts of this work have been reported briefly (Hartt et nl., 1977.1978).

X-RAY

INTENSITIES

ANI)

FOR,CE

IN

MUSCLE

55

2. Methods The sartorills muscle of the frog, Rana pipiens, was activated to generate various submaximal levels of isometric tension by the rapid coolin, (I contracture method of Sakai (Sakai & Kurihara, 1974). To do this the muscle was first equilibrated in Ringer solution containing caffeine at concentrations which were subthreshold at room temperature. Then the specimen was cooled to approx. 2°C in less than 1 s, by forcing cold caffeine-containing Rillger solution tllrough the specimen holder, &rich caused contracturp. X-ray exposure bvas taken before, during, and after t’he contracturr. The tension response to electrical stimulatiofl was taken as the maximal force PO. (a) (i)

Specimen,

E’hysiological

procedures

preparation

Frogs (body length 6 to 7.5 cm) were obtained weekly (Mogul-Ed, Oshkosh, Wise.). Sartorius muscles were used throughout. Extreme care was exercised in the dissection, which was similar to that described by Haselgrove (1970). Ringer composition, pH 7.1. was 115 mM-NaCl, 2.5 mM-KCl, I.8 rnnf-CaCl,, 3.0 mM-phosphate buffer. The muscle (-3 cm in length and -600 to 800 pm in thickness) was positioned in an acrylic cell with the pelvic end fixed to a stationary pin P (Fig. 1). The tibia1 end, tied to a wire, was suspended from a force transducer. The center of the muscle passed between two X-ray windows. An acrylic spacer containing a center channel (8 mm wide, 1 mm deep. and 15 mm long) which enclosed the muscle was mounted on one of the windows. Thr purpose of the spacer was to ensure that tile cold Ringer solution passed through the cell close to the muscle. The sarcomere length, 2.3 pm in this series of experiments, was measured by optical diffraction using a helium/neon laser. X-ray exposure was limited to the center of the with lead tapcJs. specimen (3 x 3 mm2 in area) by definin g the bearn at t,he ccl1 window (ii)

Pre-contracture

procedure

With the specimen still in normal Ringer solution at room temperature, the optimlun conditions for electrical stimulation were determined. Electrical stimuli were applied by platinum electrodes built into the cell near the pelvic end of the muscle. Generally a 0.5 to I s train of 1-ms pulses at 50 Hz, 25 to 40 V was applied. These conditions were then used to elicit maximum isometric force at low temperature, except that the frequency was reduced to 15 Hz because of the change in temperature. Force response was measured by a double leaf spring transducer (Thames et al., 1974) and recorded on a storage oscilloscopra. Prior to the addition of caffeine to the Ringer solution, a rest pattern was recorded at. room temperature, typically for 200 s, as a control on lattice spacings and reflection intonsities. Room temperature caffeine/Ringer solution was then added and allowed to equilibrate for 15 to 30 min. Caffeine concentration ranged from 1.25 to 2.0 mM, which is subthreshold for contracture at room temperature. For the later two-thirds of the experiments, resting patterns in room temperature caffeine/Ringer solution wore taken for approximately 100 s, immediately before and after each activation. (iii)

Contracture

The caffeine activation method was adapted for X-ray experimentation by devising a flow system which permitted rapid and constant cold fluid exchange while maintaining reasonable X-ray path length (Fig. 1). After the room temperature caffeine/Ringer solution was withdrawn, cold caffeine/Ringer, propelled by Nz gas, entered through the bottom of the cell, passed through the channel surrounding the muscle, and overflowed int,o a collecting beaker. The speed of the flow was between 15 and 25 cm3/s initially ; after about 10 s the flow was reduced to less than 10 cm3/s, which maintained the low temperature in the cell. Any flow less than 15 cm3/s initially did not elicit uniform activation along the muscle. The temperature of the bathing solution, monitored by a thermistor probe positioned near the X-ray window, dropped from room temperature (20°C) to 2 to 3°C in 0.5 to 1 s, and the low temperature was maintained throughout the duration of the flow. In t,he init,ial experiments, before the gas propulsion systern was adopted, a srnallcr

56

L.

c.

YU,

J.

E.

HARTT

Cold

ANI)

in

Warm

R.

,J.

I’OI)OLSK~

in/out

FIG. 1. Specimen holder. The pelvic bone of the sar’torius muscle was h&i fixed by pin 1’; thv tibia1 tendon was tied to a stainless steel wire U’ and attached to the force transducer. Y-rays were transmitted through the Mylar windows covering the central portion of the muscle with total X-ray path equal to 1 mm. The muscle was first equilibrated in 1.35 to 24 rn>l-cafleinc/ Ringer solution for 15 to 30 min at room temperature. For each activation the room tjemperaturtx solution was first withdrawn through one of the outlets (warm in/out). Then cold caffeine/Ringer solution (OY!), propelled by N, gas, was forced to pass through the channel surrounding the PUS& at, approx. 15 cm3/s. The overflow was collected by $1,beaker. The t~c~mperature, monitored by the thermistor, fell from 20 to 2°C in less than 1 s and rvmainod strady during the course of t,he flow. X-ray exposure was taken during resulting contract,urr. ;Ictivation generally lastjet 30 to 100 s. At the end of the cycle, cold caffeine/Ringer solution was drained through the, cold-in inlrt, an(l warm caffeine/Ringer solution was immedintcly injcct~rtl through warm in/out,.

volume of cold fluid was delivered by a 50 ml syringe. The final trmpcaraturr in these C~R(Y was higher (4 t,o 6°C) and tile solution began t.o warm up in abollt 15 R; tterrcr tile relativr forces were lower and the X-ray exposure times were shorter than in later PIUIS. The data points shown in Fig. 3 from these expcrirncmts (kangle symbols) arc a\.erapes (in forcv and in intensity ratio) of several exposures. An activation cycle began when the cold caffeinr/Ringr~r solution was lrltrodncc~d into the cell. The contracture force was characterized by a smootll rise which reached a platearl in approx. 2 s (Fig. 2). Peak isometric force u’as ttren determined by stimnlatitlg tiles muscle electrically. In the initial experiments this was performed immodiatoly hefow relaxation began, hut it was follnd t,o he more convrtkient t,o st,imulate t+ctrically at tlrv beginning. There was no difference in the values of I’, measured thlls. force ret,urrretl to the contractlIrc~ lv\~el, alld di:t,il Following the electrical stimulation, collection began. Data collection time vrrrerally ” _ ranged between 30 and 100 s, unirss therms was a.pparent fatigue of the muscle as judged by a fall in force of about CO”b. During ttlcs course of X-ray exposures, force le\-els Ilsuall,y stay& cotlst,ant,; most of ttrr data rrpclrtf~tl in Fig. 3 showed less than 1094 variation. Immediat,ely after tllo X-ray data were collectc>d. the cold solution was replaced wit,h room tempemture solution and tension WtUrJlPd to t,iltL baseline level. Contractures were repeat4 after a 15 t,o X0-tnin rest. ‘I’trr tlighr~t~ ttrcs relative force, the longer the wait. The contracture force in ttle X-ray cell was roughly rrxlatcd to ttlc cafC>~nc conccvltratiott in the range employed (1.25 to 2.0 mnl). Generally, onr caffeinr: conccnt8ratiort was nnpd OIL maximal isometric force I’, from vlect,ric~ each preparation. With repeat,etf activations, (IO stimuli generally remained constant8 to witllin 20’?&. rrt a few instances I 1 I’, incrwtscc~ to 20%) after the initial contra,ctures. The contra,cture force sornet~inxs fell progresslvel> from one activation cycle to thr next, while ~&hi?2 ca(atl cycle it rwrairwd skady. l’hrwfore, for one caffeine concentration the preparation 0ftc~11 ga\x> il. ran$t’ of relat-ivc> forWs. The callse of the progressive, tlecrrwsc~ in colltractjllrc force was trot stlltiic~tl. A slimlnilrj

X-RAY

INTENSITlES

AND

FORCE

IN

MUSCLE

57

of the activation sequences and the relative force levels produced by the preparations used in the present paper is given in Table 1. Activation cycles were repeated until one of the following occurred: (1) contra&me force fell rapidly during activation; (2) isometric P, fell to two-thirds the initial level; OI (3) although the force levels stayed stable, diffuse X-ray patterns appeared several times in succession and could not be corrected by increasing the flow rate of cold caffeine/Ringer solution. If t,he initial contracture force levels were higher than 700/6 P,, a series of 4 to 5 contractures could be produced before noticeable deterioration occurred. As many as 10 contractures were obtained if the force levels were kept below 50% P,. (b)

Optical

diffmction~

I&fore the X-ray experiments were made, the rapid cooling contracture method was examined on an apparatus designed to monitor force and optical diffraction patterns. All initial high level contractures elicited from muscles of fresh frogs (stored in the cold room for less than 1 week) gave sharp diffraction patterns. Upon repeated exposures to high concentration of cold caffeine/Ringer solution, the diffraction lines became diffuse during force generation, or the entire diffraction pattern disappeared, with definition returning in the resting state. In contrast, at low relative forces (<50% PO) the optical diffraction patterns remained relatively well defined as compared with that seen during electrical activation. (c) (i)

Data

collection

and

X-ray

d{ffraction,

reduction

Tlie camera consisted of a single bent quartz crystal (7” cut) coupled with 2 pairs of slits. The specimen-to-detector center distance ranged between 44 and 53 cm, so that the dist,ance between the 10 reflections was about 3 mm. Tlie generator was an Elliott GX-6 rotating anode, operated at 40 kV and 23 mA. Equatorial patterns were recorded by a one-dimensional position-sensitive detector (Podolsky et al., 1976). The detector anode was operated at 2975 V, with 90% Ar and 10% methane (prepurified grade ; Matheson Gas Products, East Rutherford, N. J.) pressurized to 100 lb/in2. Conversion gain was between 12.5 and 14 channels/mm. Data were collected with a pulse height analyzer (TP 5000; Tennecomp Systems, Oak Ridge, Tenn.) and stored on floppy disks. The data were smoothed by calculating the 1,2,1 running average. The background under a peak was assumed to be linear. The software provided two ways of estimating peak intensities : ( 1) cursor stripping, which was used for 10 and center peak areas; (2) light pen stripping, which was used for 11 peak areas. B’or method (l), two vertical cursors on the cathode ray tube display intersected the pattern at two data points on either side of the peak of interest. The area above the straight line connecting the two points was taken as the peak intensity. To measure the 11 peak area, a straight line approximating the background under the peak was drawn directly on the cathode ray tube screen with a light pen and the area above the line was computed. This method was preferred over cursor stripping because the Z-reflection (Yu et a/., 1977) and the 20 were close to, and sometimes overlapped, the 11 peak. In such cases t,he background level was below the st,raight line connecting the two valley points on t,he data curve, given by the cursor stripping method. For each peak, the area, position of centroid, and width were calculated. The integrated intensity of a reflection was taken as the average of the intensities from the 2 sides of the patt,ern. When analyzing the intensities of individual reflections, the central peak was used as the normalization factor. The cursor stripping method was used for the central peak with cursors fixed at the same channels around the center (20 channels apart) for all experiments. The central beam transmitted through the backstop was 120 to 150 pm (full width at half maximum) as recorded by the detector, and it contained approximately twice tlie number of counts as 20 in the rcst,ing state. (ii)

Data selection

The tions.

present paper (1) Frequently,

contains all the data in caffeine-activated

that were muscles

collected with the the 11 peaks were

following excepvery broad and

L.

58

c’.

YG,

.J. E.

HARTT

;\NI)

H.

.I.

l’OI)OLSKY

barely discernable above the background. On occasion, both tile IO and the II peaks IVC’I‘E~ diffuse. Such patterns, which were probably t,he results of prolonged caffeine activatiotl, non-uniform activation or misorientation, were seen in approximat,rly one-thirtl of tllv a.ctivation cycles, and these results were discarded. (2) There were cases wllwo thr ac%i\.atcd patterns were fairty, clear, and the forcr levels stayed X-wy fla,t, but, one reflection approximat,ely at the posltlon of t.he Z-reflection (Yn et al., 1977) on OIW side or botll sides of t,tle pattern was wry intense, sometimes as intcnsr as II. Upon examination, t.lw nctiv;rtwi bct8wrrn 1 (yO and 3O/,, (an cvl~~ivalt=nt of z?(‘~, I (I 10 spacing d, O was fourld to have decreased Ci”;b stretch in sarcomere length if constant volume is mainta~incd) a,nd reversed back tt B its original T-alue wit11 the int,roductiorr of warm solntion. Sllc>lr “ilrtolna,lorls” Z;-pc-irks correlated wit11 the decrease in d,, a sufficient, numbt~r of’ times thilt, tllcxy ~vvrv IISI~~~ ;W ;I quick diagnostic procedure. The most likely cause for t811e st,retclI ill tlrt: t&idle port,iotl of the muscle was nneven actjivation. Therefore. CHWS wlrerr d, O i II t tiv activated pat~tcwr decreased more than 19 were not included in the results. SIICII CBSPS occurred in 1 prepar:). tions. (3) If tile intensity ratios or individual rr+lect,ions from tlrv 2 sides of the pattern differed by more t,han 5Oq/,. tllr results wrrf: not IIRP~. Tl~rcc~ patt~c~rns ww excluded for this reason. A total of 20 frogs was used. Pour pr’eparatiolLs wrrt’ tliscardrd: 3 dur to tlifffnst~ patt~t~rris. 1 drle to tile muscle being stretched. Among the diffraction patterns frown tllo remaining 16 preparations (Table 1). approximately ‘iOq,i wew used ; t*llc rc,ject,iotw ww ma.irJp tlr~ci t,o diffrrsc patt,erns, criterion (2), ahtrvt~.

1

TABLE

Summary

Preparation 110.

of activation

( ‘affoino c*oncn (m&I)

sequences und relative @ce levels elicited preparations 1’1 I’, U-20

“I)-40

it1 iudividual

( ‘l(,)

40~ 60

W

X0

x0 101)

33

, .25-2.()

37

50 51 52 54 66

1.x-1.25 2.0 1.5 1.X 1.8 1.5

70 71 72 74 76 78 79 80

1.65 1.65 1.66 1.8 1.5 2.0 2.0 2.0

Xl

I.5

(l-5,* \

;8~-11;,*

I.(:!

2 (i--IO

*

-7)* 1 ,“,:I*

1,2,3,4* ,5* , (-j* >‘i*

4*

1 2*,3*,4*

2,:s 1*

1,2* >s* >4* I,“* 1,4,6 1*

2*,3*

3,4*

:!

1*,3*

1>2* , 3* , 4*

1

I

2.4 I

1*.2,3* 3” z.:j*

Relative force levels are divided into 5 groups and numbers in the corresponding columns show the sequence of activation cycles. Asterisk above a sequenoe number indicates an activation that satisfied the selection crit,eria and was plot,ted in Fig. 3. Angular brackets associated with prepare tion no. 33 and no. 37 represent data avrraged over several contractions. For prrpnration no. 33, the caffeine concentration was changed from 1.25 III&I +O 2.0 rn~ after the .5th rontzact,iou; for preparation no. 37, the concentration u-as changed from 1.8 ~RI to 1.25 rn~ after t,he 7th cuntrar:tion. For other preparations only 1 caffeine concentration was used for each experiment.

X-RAY

INTENSITIES

AND

FORCE

IN

MUSCLE

(iii) Correction GOT shortening against th,e tendon At the outset of each experiment, the sarcomere length was set at 2.3 pm. d,, in the activated pattern was generally within 1 or 2% of that in the resting pattern. However, in several runs where the force levels were greater than 0.5 P,, dlo increased upon act’ivation. Part of the increase did not reverse itself after the muscle returned to the resting state. This will be discussed later. The part that did reverse was considered to be caused by the internal sllortening against the tendon during contraction. The maximum increase in dl,j was 30/b, hence a 6 “/ decrease in sarcomere length. For those cases that showed more than 2q4, increase in d,,, an approximate correction in 1,,/11, was made, based on t’he regression line reported in Podolsky et al. (1976). The 2 data points at nearly 1OO”h P, gave corrected values close to those (II, /I, O = 2.1 at 2.3 pm) found by Podolsky et al. (1976). For submaximal contraction, t’he correction was made proportional to tile force love1 as a first approximation. The 5 cases that were corrected are shown by open circles in Figh’ 3.

3. Results (a) General A series of typical equatorial patterns from muscles developing various levels of forces is shown in Figure 2. The four patterns were obtained from three different muscles. The resting pattern (a) was taken with the muscle still in normal Ringer solution. After equilibrating in 1.8 mm-caffeine/Ringer solution for 30 minutes at room temperature, contracture was produced equal to P, (2.5 x lo4 dynes). Pattern (d) was obtained during activation. Pattern (b) was obtained from a muscle generating 0.12 P, in 1.8 mM-caffeine/Ringer solution. The muscle had undergone six activation cycles previously. The maximal force P, was higher (-20%) than that at the outset of the experiment, whereas the caffeine contracture force has decreased from 1.5 x lo4 dynes to 0.3 x lo4 dynes. Pattern (c) was obtained from a muscle during its third cycle of activation. The state of the muscle throughout each experiment was monitored by both the electrically stimulated force measurements and by the resting patterns. The intensity ratio Ill/I,, remained constant in the resting state, even after several cycles of high level contractures. The mean value of I,, 11, 0 of the resting state was 0.39 (n = 32, S.D. = O-06), a composite result of patterns mostly taken immediately before each activation. This agrees well with that observed by Podolsky et al. (1976) at 4°C (I, I /I, 0 ranged from 0.37 to 0.47 at 2.3 pm) but is lower than that found by Yu et al. (1977) where t,he resting ratio ranged from 0.38 to 0.6, obtained at room temperature. (i) Peak width The widths (S.D., u) of the 10 and II peaks during activation increased slightly relative to the resting values. g1 0 (s.D. of 10) of the 32 data points was approximately 10% greater than the resting o10 ; and oII increased roughly 20% for low force levels (<5Oo/o P,) and as much as 50% at close to lOOo/o P, levels. (ii) Changes in d,, Comparisons of spacing d,, were made for muscles resting initially in normal Ringer solution and the same muscles after 15 to 30 minutes equilibration in caffeine/ Ringer solution at room temperature. There was no experimentally significant change found among the resting patterns. In 11 experiments the changes in d, 0 value ranged between + 1.2% and -2*2%, and the mean was -0.3%.

I,.

(‘.

YLT,

.J.

E.

HARTT

AN11

K.

d.

I’OL)OLSKY

2250

4oo

(b)

(e) I

Lo

250

320

(9) PO

240 31s

160

H 30 20 IO

‘:-i-i

0

Fro. 2. x-my patt’erns ((a), (b), (,)c and ((I)) with corresponding forw tr’;xw ((c), (f) and (g)). The X-ray data wow smoothed by the ( 1,%,1) 3point~uvrragc. ‘There arc approximutel,y 44 chnmwl~ between the two l/40 (nm -‘) marks on thr abscissa. Force rtwwtls w:P~~ trawtl from original 2 to 3°C: sarcomere length, 2. 3 pm. Thr exposure periods a.w oscilloscope records. Trmpernturc. indicated by interval marks over the force records. Scale indicates 5 s intwwtl. (a) Resting p&tern (no. 5401) with reflection peaks as labelled. The direct beam was wttrnnatv(l by a thin platinum backstop. Exposure time was 300 s. (b) Pattern (no. 5210) recorded during a&w&on. l’jl’O, 0.12. Exposurf~ timr,, 85 5. (‘;lffci~w. 1.8 mar. Seventh contractwe induced on this preparation. At thr beginning of this rqx~rirnrlrt, Ij0 was 2.0 x 104 dynes; for this cycle, PO wits 2.4 x 104 tlynrn. 0.40. Esposwc timr, 52 5. (‘atS:mt~. (c) Patt,ern (no. 7208). r/I’,, 1~6.5 *1x1. Third cru~tr:rct~lrt~ induced for this preparation. Tnitial l’,, 4.0 x IO* tlyncs: t’, for t,his cycl11. 3.5 v 1 O4 dynes. (d) P&tern (no. 5402). Ramc prrparation as in (a). f’jf’,, 0~98. Es~mwrv tirnv, 31 H. (lilff<‘ilw. 3’M. ‘I’hv rorrwto
X-RAY

INTENSITIES

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61

The cl,, underwent changes during and after activations. As mentioned earlier, on occasion the muscle appeared to be reversibly stretched (d,, decreased) or shortened during activation (d, 0 increased). Another type of change in spacings was observed in some results : a progressive increase in d, 0 that occurred during activation cycles but was not totally reversed by rest. The phenomenon was not’ attributable to shortening against tendon, since it was not reversed. Of the 26 resting patterns that were compared with the corresponding initial resting patterns in caffeine, 16 points showed less than 1 o/o increase in d,,, whereas the remaining 10 points showed a range of 1 y. to 6% increase. However, the intensity rat’io of I,,/I, I did not show a trend of change. Since 1,0/1, 1 of the resting patterns was rather sensitive to sarcomere length changes (Haselgrove & Huxley, 1973; Podolsky et al., 1976; Yu et al., 1977), the changes in d,, found in the present study very likely originated from causes other than shortening. The swelling could be a result of salt leakage into the cells due t’o membrane deterioration. (b) Intensity

rutio T,,/I,,

Figure 2 shows how the 10 and 11 peaks vary with force. The change in intensities is a continuous function of force level. This result is also shown in Figure 3, which contains measurements of II 1/I, 0 from 16 muscles activated between 5 and 98% of P,. The data for low forces (<50”/ PO) consist of both first activations at low concentrations of caffeine and measurements taken after several activation cycles at high concentrations of caffeine. The sarcomere length was 2.3 pm at the outset of the experiments. Five points were corrected for internal shortening (open circles). Four data points in triangle symbols were experiments performed at higher final temperatures (4 to 6%). The range of contracture force associated with each data point was about lo%, except for the data in triangle symbols which had a range of contracture forces up to 30%. The relation between the intensity ratio and relative force was almost linear. It was found that a second order polynomial ga,ve a satisfactory fit using a least-squares fit algorithm. The fit WRS obtained with all the data points shown in Figure 3. No weighting function was used. The results gave the coefficients in F(x) = Ax2 + Bx + C, as A = 0.81, B = 1.04, C = 0.40, where x is the relative force. According to t’he fit’ted curve, which is drawn in Figure 3, there is an upward curvature. (c) Intensities

of individual!

rejlections

10 and 11

Using the central transmitted beam for normalization, it was possible to study the variations of the individual peaks 10 and 11 as a function of force development. To make meaningful comparisons between different preparations with parameters such as muscle mass, muscle orientation, camera alignment, etc. the normalization procedure for 1, 0 wa.3 defined as follows :

where active st’ate. taken resting

I* is the intensity of the central beam through the backstop, c designates the state and r the resting state immediately (less than 1 min) before the active R,, is similarly defined for II. Resting patterns used in normalization were at room temperature. This is a reasonable procedure, since we found that, patterns at 4, 11, 15, and 20°C were indistinguishable. The data reported here

I,.

62

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2.3

I-

2.c

I-

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.I.

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tL.

.I.

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I .5 ,2 \ +

1.c I-

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I 20

I 40 Relative

I 60 force

I 80

I 10

W

FIG. 3. Relation betwvcten intensity ratio, f,, /r, ,,, :iIltl Wl>Ltl\rt~ li)lTlL ( /‘/I’“). I ntcnsil y I’;~~LII IS 2 sides of t)hc pattern. (‘ontract,ure forcr 1’ in thrs :~rt~r:tg~t ,,f thtb the average of the ratios from range of the force rocordrd during t*he exposure period. (0) l’rrparations notivat,ed by :t (-olt~t:lIlt flow of cold caffeine/Ringer solution. Each data point was obtained by a singltr ;tctivati,,o c,yctc.. (A) Preparations cooled to 4 to 6°C by flow of 50 ml of cold caffeino/Ringw solution, Each &tgl, point was the average (in force and in intensity ratio) of sweral rxposwes. (i ~‘) Values of eolltrit(:. ture forces were corrected for shortening against t,he t,rntlon. Increase in 10 spacing W~LS b&wceo 2% and 3%. The correction w&s based on the regression lint (I,,/I,, !mwus sarcomerr length) reported by Podolsky et al. (1976). ( n ) Mean VU~UC of the putsterns of the wsting stat,e obtaincrl immediately before each activat,ion. The solitl line is :I Icast-squares fit 1o thv data point,s. ‘J’hwt? i;; an upward curvature.

are from nine preparations with 22 data points, all of which satisfied the same selection criteria as applied to the intensity ratio I, l/1,,. Ko correction was made fol internal shortening. The normalized 10 peak intensity K,, decreased from 1 to approximately 0.4, while R,, increased from 1 to approximately 2.5 (Fig. 4). Although the data a,re limited. it is reasonable to say that I,, decreased quickly in the low force region (up to approx. 50% P,) and the change turned gradual as the force increased. In contrast, t,he rise in R,, value was slow up to 5Oo/o of PO, and became steeper between the 50 and 907; PO region. It is interesting to note that the intensity ratio /,0/J,, in the low force region is a measure of changes in I, o ; whereas in high force region t,he ratio T, l /1, n is an approximate measure of the increase in I,,

4. Discussion Caffeine is known to cause calcium release from sarcoplasmic reticulum in mus& fibers (Endo et al., 1970; Stephenson, 1976). It was demonstrated i,r, z&w that, thtb Ca-accumulating capacity of fragmented reticulum was reduced in a graded waJ+ with caffeine concentration and with lowering of temperature (Weber & Herz, 1968). Therefore, activations elicited by the rapid cooling method in conjunction with the relatively low concentrations of caffeine used in the present experiments presumably caused various amounts of calcium release into the myofilament) space (Sakai & Kurihara, 1974). Calcium has been shown in skinned fibers to modulate isometric force by controlling the number of cross-bridges but not affecting their kinotic or mechanical properties

S-RAY

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63

r(a) i*oot

O-25 -

3 l l

0

I 20

I 40 Relowe

I 60 force (%)

I 80

l

IC

Fro. 4. Intensities of 10 and 11 normalized with respect to the undiffracted beam and the values in t,he resting stat,e. R,, = (I,o/I*),/(I~o/I*),, where I* is the attenuated intensity of the direct beam; c designates the contracting state, and T the resting state immediately before the active state. R,, is similarly defined for 11. The broken lines represent the best theoretical fit for data based on eqn (3), with the maximum fraction of attached myosin heads assumed to be 1 when force is PO. F*/P in this case is 0.57 for R, o and 1.55 for RI I.

(Hellam & Podolsky, 1969; Podolsky & Teichholz, 1970; Gulati $ Podolsky, 1978). In the present study, the observed intensity changes are associated with various force levels, presumably modulated by calcium ion concentrations. If in the intact fibers isometric force level is affected by calcium concentration in the same manner as found in the skinned fibers, our results show that changes in the intensities I,, and I, I and their ratio are correlated with the number of cross-bridges in the isometric state. Theoretically, I, 0 and I, I may also be affected by the attachment configurations of cross-bridges (Lymn, 1978). However, while there is probably a distribution of attachment configurations for bridges formed between the two filaments (H. E. Huxley, 1969; A. F. Huxley, 1974; Podolsky et al., 1976), this distribut’ion probably remains t’he same at different levels of isometric contraction, in which case changes in I 1o and III would reflect changes in cross-bridge number alone. The reciprocal changes in the individual reflections are another indication that an increase in isometric force is associated with an increasing redistribution of mass. This provides further evidence that the intensity ratio and the individual reflections are sensitive primarily to structural changes involved in cross-bridge formation. Before t’he present result had been obtained, it was conceivable that the structural changes involved in activation and force generation were strongly co-operative. The format’ion of a few cross-bridges might cause an “all or none” type of active movement of projections toward t’he thin filaments without generating force, such that the

64

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intensity ratio I,, /I,, would rise steeply at low force level and show no further change* as force was raised to higher levels. In this case: relat’ing intensibv ratio to number of cross-bridges would be extremely difficult. However. the present, data providti c,vidence that this “all or none” t’ype of projection movement does not occur. With Dhe undiffracted beam as t,he normalization factor. ones is a:blc to study t hc behavior of the inbensities I,, and I,, individuall)r. The reciprocal change of the two reflections is consistent with the idea that t)he fract*ion of t’hr mass originally associated with myosin-cont,aining filaments is shifted toward the a&in-containing filaments a+ force is generated. At the present tirnct. direct comparison b&b\ een t~xperirnc~ntal results and detailed calculations such as reported by Lymn (19%) is difficult b~eu~~ the exact structure and the absolute number of cross-bridgf,s arc not, known. HOW~VW. one can determine lvhether the expc+mental data can ht> ~~xplrinetl within the g~~r~~~al formalism of a tlvo-state model in which the projections arc cGt,tler in attached or in rest,ing configurations. For such a system. assuming that the attached projections a~ evenly distributed among the thin filaments. one oa,n tlescribc~ thtb structure factor. of t!le structural factors for ttlc> F: of the reflection (hlc) by a linear combination resting configuration, FR, and for t,he at’tachcd configurat)ion. E‘* : fqhk) where n is the fraction fraction in t’he relaxed

=-: t7Iyt.k)

-+ (1 --. ,?)E”(hk).

(1)

of the population in t,he attached position and (1 - tt) is the: position. Hence the intensity of tho reflection (hk) is

I(hk) - (nF*(hk) + (1 --- ,l)F”(hk))”

(3

and

A curve-fitting routine was used to find the best fit based on equation (3) for ttltl data R,,, and R,, in Figure 4. The maximum value of n that corresponds to P, jvas chosen successively between 0.35 to 1. A corresponding value of FA/FR was dctermined by the least-squares fit. Although t’he value of this pararneter depended on the number chosen for n at P,, the theoretical curveh of K,, an& R,, cerm.s force were in each case similar. Typical theoretical curves are shown in Figure 4 (broken lines). For this particulat case, the maximum fraction of projections attached at P, is assumed to be 1. The resulting FAIFR is 0.57 for R,, and 1.55 for R, , , which arc reasonable for t,hr vrrtebrate myofilament structure (Lymn, 1978). Approximately. the experimental data appear to follow t,he trend of t)he theoretical prediction of a two-state model. Howt~c~~, the experimental R,, deviates from the theoretical curve, regardless of bhe choice of parameters. The deviation is significant because all t’he data up to 0% P, lie b&JW the theoretical curve. The experimental R, , appears to be fitted fairIy well by rqu::tion (3). However, in the low force region (up to 6OOb PO). t,hc data are more scattered curve. If one assumes than R,,. and, on average, seem to fall below the theoreticel that the intensities I, ,, and 1, , are the sums of intensities from a,n inhomogeneous population of maximally activated and resting fibers, the depmdencr of the individutll intensities on force level would appear t,o be linear, which would give a poorer fit to the data than equation (3). A likely explanation for the deviations from the bt:st theoretical fit for both reflections seems to be that more than ?A simple two-st’att:

X-RAY

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65

some degree of disorder within the system is involved in cross-bridge formation: filament lattice accompanies the low level of attachment of projections. One source of disorder may be related to the double headedness of the heavy meromyosin. If we assume that the two heads of heavy meromyosin can attach to actin independently of one another (Offer & Elliott, 1978), then at low levels of calcium it is very likely that only one of the heads becomes attached to actin. The associated unattached Sl moieties, no longer in the regular resting position or immobilized by attachment, could then produce a degree of disorder to the lattice. The second possibility is the presence of long range interaction between projections as suggested by Huxley (1973). The equilibrium position of the projection may well be sensitive to the positions of neighboring projections. The movement of a small fraction of the population toward t’he thin filaments might perturb the regularity of the arrangement of the neighboring projections not involved in the cross-bridge formation, which would also introduce disorder at low force levels. It should be added that disorder in the regularit’y of the positions of the thick filament backbone is also consistent wit,h the results. Experiments of the type as described in this paper are complicated by the possibility of uneven activation in either the axial or transverse sense. It is unlikely that’ data which satisfied the selection rules originated from a heterogeneous sarcomere population, since the X-ray patterns were well defined, and the force levels were stable. The rapid flow of cold caffeine/Ringer solution surrounding the muscle ensured a quick and uniform temperature drop across the cross-sectional area of the preparation. The range of the thickness of the preparations was estimated from the muscle dimensions and weight to be between 600 and 800 pm. Since the muscle consis& of 80% of water, one may assume that the thermal conductivity of the muscle is the same as that of water (1.4~ 10m3 Cal/(x) ( cm2) (“C/cm) at 20%). Applying calculations of heat flow through a slab with the heat conductivity the same as that of water, with Dhe thickness being 600 to 800 pm and held at constant surface temperat’ure, one can show that the center and average temperatures of the slab reach within 10% of the surface temperature in less than one second, and within 20/ in less than 1.5 seconds (Carslaw 85 Jaeger, 1959). The fact that the contracture force levels were stable after reaching a plateau in approximately two seconds (Fig. 2) is another indication that the activat,ion due to the temperature jump method was most likely uniform. Axial inhomogeneity would result in force gradient’s along the length of the fibers, which would produce local motion and sarcomere length dispersion; this appears to be ruled out by the sharp reflection peaks and the stable force levels in the activated preparations. Transverse inhomogeneity within individual fibers seems unlikely because caffeine is allowed to diffuse into the preparation for at least’ 15 minutes before activation and the temperature drop was uniform. Inhomogeneity among fibers is another possible complication which cannot be ruled out completely. The contracture force levels frequently fell progressively from one cycle to the next. This could be due to a decreasing number of active fibers rather t’han a uniform decrease in tension at the sarcomere level. However, caffeine concentrations and the temperature drop are believed to be uniform throughout the preparations and the electrically stimulated force stayed almost, constant. As shown in Table 1. the intensity data were obtained from different preparations, and from early and late act,ivation cycles at various caffeine concentrations. Yet, the intensity rat’io I, ,/I,, appears to be a function of relative force only (Fig. 3). This consistency of

1,.

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data indicates that effects shown in Figures 3 and 4 are due primarily to phenomena that take place at the sarcomere level. Clearer evidence that this is the case could be obtained from experiments with skinned muscle fibers in which the intracellular calcium ion concentration is controlled directly with an EGTA-/- buffer system. Caffeine (0.25 to 2 mM) has been reported to produce local asynchronous sarcomeric oscillations in frog sartorius (Marco & Nastuk, 1968). Such local non-uniform asynchronous activities might not produce measurable tension at, tendon ends. but might, influence the X-ray patterns. However, according to the report, oscillations did not appear to occur below 4°C. Such oscillat,ions at) room temperature were probably not, sufficiently extensive t,o affect’ our results, since the resting patterns obtained while the muscle was in normal Ringer and in caffeine-containing Ringer solutions wer( indistinguishable. The present dat,a bear on the results obtained previously on actively shortening muscle under tetanic stimulation (Podolsky et nl., 1976). There. bhc force decreased as much as 850,/, during isotonic shortening, but, the ratio l,,/f, , was essent,iall> unchanged. The present results on t,he intensity ratio (Fig. 3) rule out, the possibility that the intensity ratio is insensitive to cross-bridge number. Therefore the simplest interpretation of the isotonic data remains that motion causes very little change in cross-bridge number (Podolsky rt al., 1976). Another possible explanation of t’hch isotonic data is that motion causes the number of bridges to change, but t#hat the distribution of configurations of bridges in shortening muscle is diRerent, from that, in isometric contraction. Model calculations (Lymn, 1978) showed that, the lack of change in the intensity ratio could arise from a compensatory effect of changing th(: cross-bridge number and cross-bridge configuration. However. the actual influenw of configurat,ional effects on the equatorial diffraction pa,tt’crn is not known. and it remains to be seen whether it, is significant compared with the influence of crowbridge number observed in the present study. IVe present

are gratefill exprrimcrrts,

to C%arlrs Grist for and to Paul Sand

constructjinp for assistance

mucll with

of tlrc cscjuipment Iwed computer tcchnictues.

nr t.hc

REFERENC:ES H. S. & Jaegrr, tJ. c. (1959). Conduction of Heat in Solids, pp. LOI-~101, University Press, London. Endo, M., Tanaka, M. & Ogawa, Y. (1970). LVature (Loradon), 228, 34 36. Gulati, J. & Podolsky, R. J. (1978). J. Gen. Physiol. 72, 701- 716. Hartt, J. E., Yu, L. C. & Podolsky, R. J. (1977). Rio@ys. J. 17, 171a Ha.rtt, J. E., Yu, L. C. & Podolsky, R. J. (1978). Hio@ys. J. 21, 87a. Haselgrove, CJ. (1970). Ph.D. thesis, University of C!ambridge. Haselgrove, ,I. & Huxley. H. E. (1973). J. Mol. Uiol. 77, 84!+ 568. Haselgrovc, .J., Stewart, M. C% Huxley, H. E. (1976). ~Yature(I,ondon), 261, 606 Hellam, D. C. & Podolsky, R. ,J. (1969). ./. I’hysiol. 200, 807~ 819. Huxley, A. F. (1974). J. Fhysiol. 243, 1 43. Huxley, H. E. (1953). Proc. Roy. Xoc. ser. B, 141, 59. 62. Huxley, H. E. (1957). .J. Biophys. Bioch. Cytol. 3, 631- 649. Huxley, H. E. (1968). J. fiIoZ. Biob. 37, 507.-520. Huxley, H. E. (1969). Science, 164, 13561366. Huxley. H. El. (1973). Cold Spring Harbor Symp. Quant. Hiol. 37, 361 37G. Lannergren, J. (1971). J. Cen. Ph,ysiol. 58, 145 162. Carslaw,

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Lymn, R. W. (1978). Biophys. J. 21, 93-98. Marco, L. A. & Nastuk, W. L. (1968). Science, 161, 1357-1358. Offer, G. & Elliot’t, A. (1978). Nature (London), 271, 325329. Podolsky. R. J. & Teichholz, L. E. (1970). J. Phylsiol. 211, 19--35. Podolsky. R. J., St. Onge, R.. Yu, L. B Lymn, R. W. (1976). Proc. Nat. Acad. 73, 813-817. Sakai, T. & Kurihara, S. (1974). Jikei Med. J. 21, 47-88. Stephenson, E. W. (1976). Fed. Proc. Fed. Amer. Sot. Exp. Biol. 35, 377. Thames, M. D., Teichholz, L. E. & Podolsky, R. J. (1974). J. Gen. Physiol. Weber. A. & Herz, R. (1968). J. Gen. Phyaiol. 52, 750-759. Yu, L. C.. Lymn, R. W. & Podolsky, R. J. (1977). J. Mol. Riol. 115, 455-464.

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