PROGRESS IN BIOPH Y SICS - Molecular and Cellular Biophysics

PROGRESS

IN BIOPH Y SICS

A ND 8 I OV H Y SI CA L
(.,"HEMI & T R Y

Editors
J. A. V. B U T L E R

Prot'cssor ol' Physical Chemistry
University of London

Institute of Cancer Research
Roval t ancer Hospital, London

B. It' ATZ

I'rolcssor ol Biophysics
t)epartment of Biophysics
University College, London

Institttt fiir I' hys!.>IoI;ische Che
clcr I.J»ivcl.sit it 1! Iiinchen

8000 Mih)rheo 1 8 - (t<)cthcstr'18e 8
'1'< lclon 08 11/89 43 21-22

A Pergamon Press Book

T H E M A C M IL L A N C O M P A N Y

N EW YOR K

1957



MUSCLE STRUCTURE AND THEORIES OF
CONTRACTION

zl. 7 ('. IXMxtey

(' OX 'I' I(' X Y 6

I NTRODUC'I'IO)V Page
207

l. 8' I'[(UCTUItLr Ol)' 'I'[110 MYOE1B[l Il. 200
.
260
l. fnterpretation of the striations 261
".,'Itrncture of the A, I and H b an<La 206

f>[H< ussion of' the ovidoiico

l f. L r A R I I LI 'll K V I D F N C F OiV "I'fll' 1V I DT H O Y T H E A BA N D A N D I T S

C OiMPOSI T I O L V 266
I. Const ancy o f A b <LIL<I wr<llli 207
2. Localization of inyosin 270
3. The idea of sliding molecules 272

I I I. "<II(ff'I V A T I O N " AN D 'I' l l l)l 7i M V M B I I A N [)7 27'r

I. Tho link betwoen excitst ioti an<1 contraction 272
'. Tlio P~ fino 273
.'). Con t i n u i t y o f t l i o 7 i i < t c l i tb l ILrto 275
270
4. Mechanism of c o n d u c t iun a l ong 7~ntcrit[rrarteH 277
.). Loiigitudinal spread of activatiori 278
G. 'I'lro f'urictional u n i t' iii st r i a t ed r l u l s< I< 278
7(. Otln)r f u l i c t i o n s u f t l i o 7i [i ) to .

I V. A H Y P O TH ESIS VO[t T H I ' M I : (.'HANISAI OF CONTftACTION 270
I. Statement of tlio liypotliesis 281
Matlternatical formulation 284
287
( ull l [ )ILI'IH()tl l v l't 0 I I l l . f . H I ) ([ IIILtl» I I H 201
(, ( » )i s o ( f t l()11(')I.H ()f l h <' f l y [ ) <it l l (!HIH 201

[.I. I . ong t l letiilig of a Htiill illatc<l )tins«l<' ') 02
I.2. I [ ) l i o n <l()rl Hl)ul't<'.I»rig ') 03
t .;). Ac l i v a l i uri a i» l n ) l o x o l i u t i )06)
Siz» tlrr<l rlutnbor u[ <:or)(i'll(:ti()tr situs 29);
6). I. [(ange of rriover»r iit of' Hide-pieces.
20 (
Distanc(. botwcoii Hucccssivo A sites )97

. I,.[, S [ )(L('llrgH I'x[)('('t('(I ()» H( I'»('t » l'lll g l'(»» l ( I H

(i. I ) I H<'IIHHI»rr

V. ( ) ' I'I I I ):I' I ' l i [ <'NOM I ):NA I iV [ r i U)S(11.10 209

I . I' Hl'Iy (.'hrlngoH I» IL t,wit( )i 300
I. I. I,atoircy rolaxutiori 300
1.2. 1ncrease iii torsional rigidity 301
302
1.3. The "alpha process"

M IJSCJ,J: s ' I ' I < I' ( ,"I' I) I< >: h N I ) 1 ' l l K » I ,' I I ; s » I' (' » N 'I ' l l h < " I ' t r ) N

1.4. Lrarly decrease of extensibility 302
303
J.S. Early heat liberation 304
1.<i. General discussion of early changes 304
2. Decreased extractability of proteins
3. Optical changes during a twitch :) 00

3.1. S(,attering of light :J0;)
3.2. Decrease of birefringenr <
4. Tetanus tension :I0<i
4.1. Absolute valnes :I<><i
4.2. Th o h n n l t o s h u l'<(.'nnlg nl a t l 'I anus ,'I0<i
Distribution of other substances :I OS
S).1. Sarcoplasmic proteins ;<OS
S).2. Uttra-vdotet absorbing )no<,m ial 308
;I00

Vl. CONCl.llillONS ;it »

MUSCLE STRUCTURE AND THEORIES OF
CONTRACTION

.'I. E. 1Iu;t;ley

I N T Jto D It CTJO N

lt fras see»re(l natural t» al l wh o h ave studied voluntary m u scle wit h
tire r»icroscope to suppose that tire striations are an important clue to
t,he»rechanism of contraction. U n t i l t h e early y ears of this century ,
they were almost the only clue, apart from th e process of shortening
or t.ensiorl developrne»t itself, and interest was accordingly centred on
t he changes that the striations undergo during contraction. B u t n o
coherent theory o f c o n t r action emerged from t h ese studies; p e r h aps
it is for this reason that the hard-won knowledge of muscle structure
fell into neglect as rapid progress began to be made in muscle chemistry
«nd in the energetics of contraction.

Up to the outbreak of the second war, these branches of muscle
p hysiology were able t» 1>roceed successfufly w i t h ou t r e ference to t h e
d etails of structure. I t ap p e ars now t ha t t h e d i scoveries that w e r e
I<lade in rrruscle biochemistry u p t o 1 9 3 9 w er e r elevant t o r e c overy
processes rather. than to th e contraction mechanism itself. T h i s is not
t,o belittle their importance: f rom the point of view of muscle physiology
tfrey led to the discovery of ATP and to the idea that this substance is
the imr»ediate source of' energy for contraction, while in a b r oader
context they laid the fo«ndati»rrs of our understanding of the glycolytic
c ycle and. of t h e w a y s i n w l r ich e nergy i s m a d e a v a i lable fo r t h e
;Lctivities of al l k i n d s o f c ells. I t d o e s h o wever mean t ha t t h ese dis-
c overies had l i t t l e i n u nediate relevance to t h e p r o b lem o f h o w t h e
c»trtr;Lcti»tr itself i s f » x>ugftt,;Lbout ; c o t >versely t h e c h a r acteristic
features of'musclestrueture were irrelevatrt to the processes that were
bci»g (:htcirf;Lt,(;rf. 'I'itis f>»sit,io» wns brought to an end by the discovery
» f th(' Irrt('I')Lett»trs» f »I y » s » r IL ) r d A I ~ V) ILrl(I »f. tfre col» p o sit)B liat)ul'e
»f' "l»y<>sir>." I t c o « frl l>e s;Li(f t,h;Lmt, uscle chemistry had then become
ripe fori»tegration with i»formatiotr about structure, but in the mea»-
tir»c; the ktI(>wfedge tlrat i)art bec» gaine<l by th e n i n eteenth-century
»ricroscopists had beer< largely forgotten. T h i s is illustrated for example
)>y comparing tire brief acco«nts of the striations, and of their changes
during contraction, tlrat ;Lrc to be found in m odern text-books, with
tire f»11 and accurate description in say t h e 1 888 edition of M I OHAEL
I"(>s rFIL's text-book.

The chemistry of the muscle proteins did indeed retain some contact

»(

MUScn'15 STRiTUTl>BZ A N I > I."Hz o R I I<s <)I) c <)N~lRAUTi oN

with microscopical information; for example Nor,L and Wzszz {1934)
showed that the birefringence of the 2 bands could be accounted for
by the birefringence of "myosin" threads. This contact seems to have
been lost at the time when it might have been most fruitful; t h ere
was no attempt t o l ocate myosin proper and actin with respect to
the striations until more than a decade after the separation of these
proteins.

Knowledge ofthe mechanics and heat production of muscle reached
a stage at which they were ready to link up with other lines of informa-
tion on the contractile process in 1938, when A. V. Ho.z, published his
well-known analysis of the relations between tension, speed of shorten-

ing, and heat production. H o w e ver, in spite of H n . L's repeated calls
for chemical studies to parallel his analysis of the time course of energy
liberation, this work remained isolated until the recent demonstration

by F m c x z N s TziN et <Ll. (1954) and Mo MMAzRTs (1954) t hat t h e
amounts ofATP and creatine phosphate in a muscle do not falldurinigr
the contractionphase of a twitch.

As regards the processes by which the contractile mechanism is
"turned on," itwas clear by the end of the war (KUzzLzR, 1946;

KATz, 1950) that the reduction of the resting potential which occurs

on oxcitation is tho noriiial stimulus for contr;Lction, and a nurnbor ol'

physical changes were known to begin during the "latent period"
between excitation and the development of tension or shortening (see
pp. 300 —304).

Although the basic facts concerning the striations, which had been
known for 80-100 yearn, were unduly neglected at this time, it must be
admitted that our knowledge of muscle structure had not made niucli
progress since the turn of the century, and in relation to the available
techniques it was less advanced than other branches of muscle physio-
logy. Even the application of the electron microscope did little at first
beyond confirming (and restoring to respectability) the picture that

had been handed down by thenineteeth-century rnicroscopists; i»dec<i,

s everal of t h e ne w c o nclusions that w er e d r awn f r o m t h e e a rly w o r k

with th e electron m i c roscope have since ti n ned oiit t o b e u ) i f'o»)id<)<t.

<'..l5llt l i). till($ hLst f< lw $ < ))if)< )1 Ill<Ill))<)I'<)t l f » / ) <)I'tiL)lt p < )it)ts ) Ll)<)»l i l l

striations theniselves, and about the spatial distribution of the str»c-

tiir'ILl p)'otoi)is, l)ILvo c<)inc <)iit, ainl;Ls L I'<;s»lt it Is n<)w possil))o to Inak<;

7

ststeill e)it s a b o » l ' t l ) c 11 )t1)YII'lt<) sti'li<)tiII'<) <){ i)ills<:l<w) l)il l ) ,LI'<) s<IAI .
«iently d e t a i le d t o h a v e a be a r i i i g u n t he i i i t e r p r et ation ot' t li<'.

mechanical, thermal and chemical events. I t r e mains for the fut»ie
to decide how far. the views that l ani adopting here about the structure

of muscle are correct, but I do not th ink t hat they are any more likely
to be in error than are the current statements of its mechanical and
chemical behaviour.





S TR U C T U R E O F T H E M Y O F IB R I L

became less important with the improvement of section-cutting and
staining methods, and it seems nowadays not to be universally under-
stood even bythose who work with the microscope. The interpretation
is still more difficult in a thick specimen such as a frog muscle 6bre, and
it is very difficult to tell, for example, whether the dark bands seen by
8UOHTHAL et (Ll. (1936) were in fact the A b a nds as these authors

assuiiied.

I. 2. Strttcturs of the A, I urtd H bands
It was widely supposed before the second war that the high refractive
index and birefringence ofthe A bands were due to the presence there
in a more or less solid state of the "myosin" which can be extracted by
s trong salt s o l u t i on s o r d i l u t e a c id s ( K 1THNE, 1864; D ~ I Lz w s K Y ,
1881). Although this view was strongly supported, by the quantitative
work of NoI.I, and WEBER (1934), it seems to have been discarded after
the war, partly because the "myosin" had, by then been shown not to
be a single substance, but chiefly, I t hink, because it was diKcult to
reconcile this localization of what was thought to be the contractile

reyae~in Actin I a ' t) ' I sarlament

filament f ila m e nt

I» ig. l. Diagram showing the arrangement of the filaments, within s myof ibril,
which has been suggested by recentobservations desoribed in the text. The
<Jcgr<>e of stretch corresponds to the extended length in the body. T r s r(averse
dimensions sre enormously exaggerated in comysrison with longitudinal ones.
g'hen the length of the muscle is changed, the actin and myosin Bilaments slide

liest one another in each of the zones where they overlay, snd only the 8-
filaments arc actually stretched or shortened.

Hubstance with the current idea that contraction was produced by the
I 'ol(li»gy of' protein chai)is that c x t en<led throughout t h e l e ngth o f t h e

»i«H«Jo. Becently, good evidence has appeared. that these charac-
t o) IHi,ics of I ho A b Lud aro iiuleod due largely to t h e l ocalization t h er e
of tI)(', myosin (as opposed to actin )component of the old "myosin."
Ai tb( sa»)e tir»e, observations on the changes of the striations during
s tretch an d c o n t r action, )Lxul electron m i c roscope studies o f t hi n
sections of muscle, led to ideas on the structure of the myofibril that
lit i)i well with a localization of the chief materials of the fibril in ddferent
parts of the syste)n of striations.

The resulting picture of the structure of a 6bril is shown schematically
in Fig. 1. The main features of this were arrived at independently by

261

h11!s()T 'I. RT IL(r(!'I'Ir lt z ) < N » T » 1 1 « II I IIN « Y < ' « N ' I 'IC I ("I' I «V

H . E. H v x r,z Y and H)iz soz ( 1054) and by A. 1<'. HI)xi.z Y and ¹ z i ) z i ( -
ozRKz (1954), although more of its details are due to the former than
to the latter authors. F ig. 1 is in fact almost the same as the corres-
ponding diagram of HazsoN and H. E. Hvxz,zY (1955). Most ofthe
evidence on which this scheme is based has been thoroughly reviewed
by HxzsoN and H . E . H v x z z Y ( 1955): I s h all therefore do no i»<)rc
than summarize it here.

The essentials of the scheme sliow» in .Vig. I L(e ;

(1) The A b an d owes its high refractive i»dex ;L»(I. its biret'I i»g(.»c(
to a set of rods or filaments arranged alongside oue a»other. The

length of each of the rods is constant at about 1 5 p so long as the muscle

does not shorten enough to bring the ends of the rods into contact
with the Z lines.

(2) A second set of filaments extend from the Z line through the I
and into the end of A, as far as the beginning of the less dense H
region. These keep a constant length of about 1 0 p so long as the
muscle does not shorten to a sarcomere length below 2 p.

(8) When the muscle lengthens or shortens, the filaments of these
two types slide past one another.

(4) When the fibre shorteus so much that the I filaments of the two
e n<is of <»ic sarc<)merc come i n t o c o i i t a ci , t h e y s l i o r tc u f u r t he r b y
folding or crumpling near the point where they have come into contact,
and possibly at other places. Similarly, the A. rods may fold at their ends
if the fibre sliortens so much that they come into c<)ntact with the Z Ii»c.

(5) Myosin is a principal constituent of the A rodlets, a)id actin of
the I filaments.

(6) Corresponding I fil a ments of the two ends of a sarcomere are
joined by a very extensible connection, the 8 filament.

(7) In transverse section, the filaments are arranged as shown in
Fig. 2.

The chief points of the evidence which led to this picture being put
forward are asfollows:

(1) L<'xistsnce of ttr)o setsof f ilaments. ".I'he two sets ol.' Iilainents ai e

bea<ltit'»IIy sliow)i iii t l i c r «gioi). of tl)c ; I b ( L»(I wlicrc t I)ey overlap, itl

<)I(l<'I I'(»I » » c l '<)gi'!< I)I)s <)f I)»{ill l <)»g l t » ( I » »LI )L»<I { I')L»sYOI'is<' sc(!l 1«lbs <)I

II'og a»(1 r<LI)bit »illsclc (IJ. I'~. Il ( ! x l ) I'Iv ) I!)5).ja).

(2) Consfrtnr;y of length rrf A-brinell rr)rtlr.ts. (a) A. &'. HIrxr I:v ail(I
5 lzi) I )iRozRv it (195)4) sliowcd tl»Lt, in'l)L Iivi»« isolateil muscle libre fr <»»
tl)e fi'og, pliut<)graphed witII aii i n t erfere»«e » ii<;Ioscope, tlie A b i)»»I
s tays of c oustant w i d t h , w i t h i n t h e e r r ors o f » i easurement, d u r i ng

stretcli, passive shurteuiug aiul quick a»d slow coiitractious, so long as

the sarcomere'length does not fallbelow 1.!j—2 p . They also found the
Hanic 111 l)assi v(. 'st I'( ticli IL»(l 1'el<Lx(Ltio)1 Usiilg I)ola i'Ized I(gilt (Ulll)ublished;
see p. 266).

S rR(r(,"r<rRI; « I r irHi t I e V O r ! r I L R r X,

(I)) H. E. H v x LzY and H<izsoz (1954) similarly found, by phase
contrast microscopy that th e width of t h e A b a nds of fibrils from
glycerinated. muscle is independent of sarcomere length, in stretch and
in contraction induced. by ATP treatment, so long as the sarcomere
length did not fall below 1 7 p.

(c) Hs.RM)LN (1954) recorded spontaneous contraction and relaxation
of isolated fibrils by cine photography with the phase microscope, and

• 00 0

®0 0
0
eo•

0

I)
I cI

~ 4 4 OA N

I)'ig. 2. 1)iagraru sho<ving tho crraugement of the filaments in a cross-section

through the outerpart of an A band, )vhere both myosin {larger)and actin
{smaller) e)laments are present. The dimensions given are appropriate for a

muscle at its extended length in the body.

found that shortening took place by approximation of the A bands,
with obliteration of the I bands.

(3) Constancy of length of I f'Lkrnzsnts. The gap between the I f il a -
ments belonging to the two ends of any one sarcomere shows up as the

H band in the intact fibril, and as an almost completely empty region
when the A fliaments have been dissolved away. In both casesthe gap
inci eases in width as the fibre is stretched (H. E. H v x L z Y and H<L! xsoN,
, 1954), and the length of the filaments that remain after extraction of
t,hc A filaments is independent of the degree of stretch (H )LlvsoN and
.II, .I<'..IIvxzz Y, 1955, p. 247). In living muscles under the interference
uiicroscope, the H zone is conspicuous only when the fibre is moderately
stretched (neither shortened not g r eatly s t r etched), as would' be
c xl)ected. on t hi s p i c t u re, bu t t h e o p t i cal c o nditions ar e no t g o o d

« »ough to measure its width .

(4) Constancy of X-ray spacings. The 415 A period of the low-angle
X-ray diagram was found by H . E . H v x r ,zY (1952, 1958b) to be

unchanged when the muscle was stretched. A spacing ofabout this
value is seen in both A and I ba n ds under the electron microscope
(Her.r,, J<LKvs and SoHMrTT, 1946; DRmzR and Houaz, 1949), so it is

268













1<f 778 c I, E s T R U c T 7T R E h N 7) T H E o R 7 7!s 0 I' (" o N T B h (" T 7 oN

t hat the high refractive index and th e b irefringence of the A b a n d
were due to t h e p r esence there of su bmicroscopic rods in a p a r a llel
arrangement. Th e length of these rods was supposed to stay constant

(1 5 p) as the muscle shortened, their lateral separation increasing so as
to keep the volume of the whole fibril constant. K R AUsz believed that
the I bands were liquid during life, so that this fluid. was supposed to
enter the spaces between the A r o d lets as they moved away from one
another during contracti<ni. Hc did not specify the forces that produced
these movements, but suggested that the rods of each A band attracted
those ofthe neighbouring A' s.

In recent years, however, it has been. generally believed that con-
traction takes place inthe A band (e.g. FULToN, 1055, p. 120). How

then has a universal and, itnow appears, well-founded opinion been
reversed, in spite of having been embodied in a theory of contraction by
one of the most distinguished of the nineteenth-century microscopists 1

The most important factors in t his change seem to have been two
theoretical points r aised by E N GELMANN. I n t h e fi r s t p l a ce, he di s-
missed KRAUSE's theory on t h e g r o und t h a t m u s c les can shorten far
beyond the pointat which the A bands of adjacent sarcomeres would
come int o c o n t ac t i f t h e y s t a y e d o f c o n s t ali t w i d t h (E N O ELMANN,
1873b, p. 161). 'J'his is admitt edly (L dilliculty, t h(>ugli it shoul<l have
been clear, independently of any theory, that thc shortening process
changes in some way a t t i l e st age where contraction bands begin t o
fol'l», T i l e s ( c(>rl(I 411C<>retie(Ll 1>o»rt I s 41>ILt J>JN( ElzMANN cl l u i l cl<Ltcd
the principle that all formed contractile elements are birefringent (see
for example ENGELMANN (1006), which is largely a review of his own
w ork on m u scle). F r o m t h i s gerielalizatiori, which is pr obably v a l id
as it st Ln<ls, on(1 is clearly of great sigriilicancc, 1)c c<>ricluded t1);it t1ie
birefringent parts of a striated fibre must be the contractile parts, and
hence that they must bc the parts which shorten during contraction.
He thus seems to have persuaded himself of the reverse of what he had
fo»)i<i by <lire<!4»l<>ILs(»<',r»<:I>4; »I 1»s >Lr'ti<:I<o: l 10(>(i 1><', I'<;I<:Is <>»ly»I
the most cursory way to l iis paper of 1880. Jt i s w o rtli iioting tw<>
f<IL4(rr'cs of 41>is angl>»i(,ril,: l i rs4, 11>ILt Lri <>x1><;Ii»I<>»t;Ll <>l>s<;I'v;Lti<>»
1>ILS 1><icn OV<>l'ril>l'OW» <>» 41><><>l'<>4l<l>l I gl'<>»»<1S> >L»<l See»»<1, 411>L4tile
ILI'gUII>(>fit »lv<>l v<'s tll<' 4>L»ll >L s»»>1>4><>I>41>IL4»I»s<>l(> c<>»4<L>lrs «L sl»glc

(lo»tl'Iri<ltll() sr(i>s1>Ln(>(> wl»(>ll sir<>I'1(>ns (IIII'Ing co» t l ' ILetlori. 1> (>tll» 1

these points will t u rl i »1> Ig;Lin iri a <lifl'cre»t con»ection (p. 271).

14 is those upi»i(>lie <>fEr«>EI.MANN 's t liat sce»i 4<> JIILvc boon ge»er;L11y
a ccepted, but it i s d ifficult t o say how far t his was due to his authorit y
an(l how .I'ILr 4<> 41(c well-l<»<>Nil 1>ll1>(ll' 1lllLlw(Ls pllblisllcd l>y J10IL I' ill,IL
in 1000. H e o b 4 ained cine-ph<>tographs of spontaneous contractions
in i»sect muscle libr<>s, ni<>stly with p o l(Lrixcd light, and c l aimed t h a t,
his results both confirmed ENGEI,MANN's claim that the shortening

268

E A R L I E R E V I 7) E N C E ON i V I D T ' I I O lr T H E A R AN D

occurs in the A band, arid contradicted the generally accepted view
t hat a " r eversal of striations" (development of dense bands in t h e
regions where I's had been in the resting Gbre) takes place when muscles
shorten greatly. But th e difference between his and. his predecessors'
results seems in fact to lie in the condition of his fibres in the resting
state. HisI bands appear to have been about $ the width of his A
bands, while the usual figures given for t his r atio are $ or m o r e.
The only explanation that suggests itself for this difference is that his
f iibres, even in th e resting state, were already shortened almost to t h e
point where contraction bands are formed, and further shortening
m ust necessarily involve the A h and. S i m ilarly, lm did not find a
reversal because in t h ese fibres at rest t h e S l i n e ( w it h t h e a c com-
panyingN bands, which are composed of interstitialgranules) appeared
as the densest part of the sarcomere, this being no doubt connected
with thenarrowness ofI. He observed the formation of dense contrac-
tion bands at the level of Z (i n agreement with all other observers)
but did not regard this as constituting a reversal because they were at
t he same position as the densest part of t h e resting pattern. H i s
di6'erences from former observations are therefore more apparent
than real, and depend on some imperfectly explained di6'erence in the
initial state of t h e f i b r es; n e v ertheless, his conclusions have been
widely quoted not only as supporting ENozI.MANN's contention that
shortening takes place only inthe A bands (e.g. MEIERHoz, 1930,
p. 205)but as disproving the reality of the reversal phenomenon and

thence of theformation of contraction bands.
The other well-known work which appears to support ENozI,MANN's

view is t ha t o f SU c H THAL, KNAPPEIsand LI N D HARD ( 1936). T h e y
photographed isolatedfibres from the frog in ordinary light, and found
that theirdark bands changed. in width more than their light bands,
during bothpassive stretch and isotonic contraction. As was mentioned
011pp. 261 and 265, this is an extremely di%cult specimen from the
<>1>4ic(L1 1><>int of view, and I ca n o nly conclude, from th e disagreement
with our inteii'erence microscope results (A. I<. HvxLE)t and NI EDER-
(Ii:ILI<E, 1054 ) that they were not justified in assuming that their dark
l >a»d corr<srporidcd accurately i n w i d t h t o t h e a c t u a l h i g h r e f r a ct i v e
i»dcx barrds of tlic fibrcs. T his work w(Ls, however, generally accepted
as further evidence in support of the view that it is the A band which is
contractile. The observations of HozvATH (1052), which appear to
sliow thatt,he A and I bands of aglycerol-extracted Gbre maintain a
constant ratio during contraction, are subject to the same criticisms.

With thc s,dventof the electron microscope, these confusions ought

to have been cleared up at once, but they were not. HALL, JAKUs and
ScHMITT (1046, p. 38), in their well-known paper, do indeed. state that
the A band hardlychanged in width on passive stretch, but they also

269















A (i'i'> v A'ri (> N A N i > ' i 'n IC z >>> ICh>81(ANY'

spreads for a (listance which increases with the voltage applied. and with
the size of the pipette. The experiment does not prove conclusively
that aself-maintaining inward propagation does not occur in a perfeotly
undamaged fibre,since the fibres had ceased to give ordinary all-or-
nothing twitches by the time we managed to observe these local effects,
and it is conceivable that there is normally a propagating meohanism
which had bythen been lost. But 6bres in thisstate can give apparently
normal twitches when the membrane is depolarized. by applied. current
( Bi>owN and SicHEL, 1936; confirmed in unpublished work by D r .
R. Z. TxvLoa and myself).There istherefore no need to postulate a
self-propagating mechanism, and in any case our experiments show
t liat a graded activation can spread, quite a long way m. This seems to
excluele such mechanisms as crystallization (HiLL, 1949o) and "activated
di8'usion" (diffusion of a substance whose presence causes more of the
same substance to be liberated) which have been suggested as mech-
anisms for the rapid activation of the fibre interior in response to
surface-membrane potential changes, since they would. be expected to
be self-propagating. At t h e same time, the fact that the contraction
did notreach nearly to the centre of the 6bre would be expected.on any
mechanism that was not regenerative, since the pipette covered only
a very small sector of the edge of the Z membrane, and the udiuence
of depolarization on thissmall region was spread out over a broad.
front as it was conducted inward.

There is nothing at present to contradict the very tentative sugges-
tion that the mechanism may be an electrical one. If the Z membrane
contained.channels whose lumen was connected to the external fiuid,
and whose walls had a high resistance, then the potential difference
across the walls would follow that across the surface membrane of the
fibrewith a lag depending on the size of the channels, the capacity of

their walls,etc. Bough calculations show that the lag would be very
small even if the channels were as sinall as 100 A diameter, and were
i»sulatod from tho sarcoplasin by walls with a capacity of 1 pP /om~
such asisfound in the inembranes of many cells.

IJI. 5 . l, » wgiLN<li»aL 8prea<Jf, aocti(>ation
'I'1>e><> is also tlio question l i ow a c h a ngo spa+d i ng i n w 'ards along th e

Z membrane brings about the contractileprocess which presumably
occurs in the nearest half-A-band on either side. The striking feature
; il>»ut thi s f i nal s t age of t h e s p r ead o f a c t i v a t ion i s t h a t i t g o e s n o
further than this: no shortening was seen in the I bands on either side
<>l' tho one to which the pipette was applied. If diffusion of a substance
from Z is responsible, then there must be something that limits the
range ofdiffusion, e.g. the dMusing material might be used up in the
6rst halfof the adjacent A bands, or there might be an impermeable

277

MIISC I> l~l i8'I'I< ll<«I'll I< I'l A 8 » ' I ' l l I~l<I I<I<Is <I I' <' <IN 'I'I<A < "I'I <IN

layer at the position of ill . T h e l i m i t ation of thc spread of activation
would however be directly explained if the change was some alteration
in the actin filaments, which was conveyed along them from the Z
line, since they terminate at or b efore the middle of th e adjacent .0
bands. O t her p o i nt s w h ich suggest t h <t n c t i v at ioli ma y b e a c e»I»-
p anied by a c h ange in th e actin filaments are mentioned on pp. 30 f
and 305.

Il I. <f. 'I'he fI<II<'tioII«l I<ilit iI I, ,>(I'i«terl, nuu8<1<.

It is customary to take as the repeating unit of the striation pattern
the sarcomere, which is defined as the region bounded by two adjacent
Z lines. Th e experinients described here siiggest that th e f unctional
units are centred on the Z lines, and not separated by theni, so that the
unit consists ok'a Z line with the I b and in which it lies and the half =f
band on either side. W e n ever saw a contraction involving one-half. of
an I band only (though our pipettesmay not have been small enough
to achieve this if it is possible in principle, and it is also conceivable
that a contraction at one side only of the Z line might have been
mistaken for a weak contraction involving both sides). Also, as men-
tioned above, we never saw any shortening of the neighbouring I
bands such as woulcl have occurred ifcontraction hnd taken plac«, i»
both halves of' ca«ll of' the ~'I bali<la adjacent to thc point ot' stirnulatio».
There are, however, occasional records inthe literature of contractio»
waves in fixed preparations of insect inuscle where the degree of co»-
traction is strik i » gly di fferent in th e 1IIIlf-sarco»icres <>n cithel si<le of;I,
single Z line (HCLLETT, 180i, filg. 1<I; T r zc<n, k<)5'>, fig. 39).

III . 7 . Ot h er f'«wrtior<8fothe Z 1<'ile

It was mentioned above that t h ere are great difiicukties (BENNETI,
1955) in the idea that the Z membrane conveys the force of contraction
to the sarcolenunn,, but it reniains possible that the Z line has a mech-
a nical function as w ell a s b e ing concerned in t h e a c t i v ation o f t i l e
fibrils. W i l klili c ackI »iyofibr'ik thoro » r ust b«. So»ic struck ural lirik
which keeps the Illyosili fila»ients alongside one another in e ncl> .f
b a»d, null a » et hel l i » k w l l i «h k eeps each sct o f a c t i n fi l n m clits i »
I'<IglHI»I'. I II<) <)I«' ll I'<)»»l l <',I'<)gl'ILfIIIII <II I i<PI)<< ll{ I l)55) Hll<)w cl'oss-li»l s
between the filaments of the primary array (presumably myosin) in the
• 'l k)Ii»<l; Il>»Illy I)< I kl<'s<'I frllnf kcof) fli c » l y <Islll flhl»lcllts ILlig»ed, hilt I I
N<) Lll<<l'<< <lllll»<>l b<l «')I'I'<~nfI<)»<f»lg < ll'<Iss ll»ks b < tw «<;» t l I < I; I c t » I f l h l -
inents, or the sliding»lover»cut would be impossible: connections could
o»ly <Ixtnt at f li c kI<lsitio» <>f f1I<I 7i li»c, wflcl<c tll<ry would liot i nt o> f<;I<*,
with the movement of the myosin fila»1ents an<i l.lleir set of cross-li»ks.
I t is t h c rcf<>re Ii<lccss:lry to k eep i l l B i i i l d f h c p o ssibility t h a t t i l e Z
line hns also the function of keeping the actin fiila»ients in alignment.

278















%1 lr S('I, I.' S ' I ' u t r ( ' 'I' ll' ll I; 4 N I) 'I' ll I',() I( I lr S (> I' ('< > N 'I' ll<<> (''I' I <) N

10
n

08

V=O 06
04

02

-15 -10 -05 0 x/h 05

n 10
08

V=01 V .„ 0.6
04

02

-1.5 -10 -05 0 x/h 05
10

n
08

V=025 V 06
04

02

-15 -10 — 0.5 0 x/h 0" 10
10

n
08

V= V 06
04 -

02

-15 -10 -05 x/h 05 10

1"ig. 7. V a r i a t i o n <>f rr (1>rnl><»tio«u f Hi t<a Ht w l ri< h lir>lH( I>< two<a> a< trr> <«1<I

rl)1'os«i a l ' e i l l ( ' s i s t <'n('c) vrrt I> <e (11osl t lon o f . I H l ( cn h l ( 1re I <> « Ir « I <I >r««r 1
1H>sit ion of 1]f s i t e), for Ih e st e(uly s t a te in i s o r nef ric < on(nrr ti<>r>(r(>]1) r<r><l irr

Hh<>rter)r»g Ht. I hn «' l r f f< r< 1>< HIH'«IH.

>((I))]1(),I'Iy , <><I<];).(.]<>]) (Ii) I<>]'II)< (,())H]<>)r I>« r<>r)l<H:

a<s/,' /', /<e I

"/ /' </,

I

l ht; I n r t.'(Il l ) I I I) ) 6 ' (>I'k (1<)I)(' ))) ) (' v( I< ; <I <>t« H I ( <! ]H /,/< /c '; ( I (» ( > I I ) )r<' f I) I H
bV I<', w('. I))tv(':

1)<s)o /] . (I (.I, 1}," r') I

./,,'

A I I V I ' O ' I ' 111'lg I S I " ( ) I'. 'I' ll l l i <1 I':(! ll A N I','(ill O l r ( 'O N T R A C T I ON

tltd the rate of eloing mechanical work is

'1'he. late of libe l'atio» of heat is E — P 1'.

f V. 3. Comparison nri thHil l 's equations
To fittd out whether equations of these forms can represent the actual
b ehaviour of m u scle, we may see how closely they can be m ade to f i t
the relationships shown by A. 1>r. Hrf.f. (1938) to be obeyed by frog muscle
<luri]tg tetanic stimul at ion at O'C. T h ese are:

(1) The rate of l i beration of heat i n creases linearly w it h speed of
HI)ol tening (constancy of shortening heat).

10

08

L

<)> 06

0

D 04
<r)

02

02 04 06 08 10
Tension

I'ig. f(. .Relationshif> l]etweon sl>ee<1 of shortening and t ension. C o ntinuous
l ir)c: I l l ] . 1.'s chara<>tcristic o<fuation w i t h II/Po = $. Circles: equation (11).

()nlrr>at<'., Hl>(>c<l <>I' Hlr<>rt('r«>rg HH a f r n <'.lier> Of V a l u o «l . « n l o a d o d t o ( a n u s
r lhsc>HHH,, to«R>on HH rl f>'a(',tie>1 of val«c i n i s o l n o t r i c t e t a n u s .

( 2) Tile t o t a l r a t e ol' eltergy l i b eration ( l i eat+ work) increases
linearly as the load is reduced below the isometric tension.

By combining these relationships Hn.z, obtained his "characteristic
equation," (I' + a) (V -}-/)) = constant , w h i c h h e f ou n d t o agr e e

') 87

A 1 t<S(" I( I.' S'I' I( t> ("I' I( I< I; A N » 'I' ll I;<) I> I I: S () I' ('() S 'I' i(A ( ' ' I' I <) Iv

excellently w i t h t h e d i r e c tl y d e t e r»>i»ed I'orce-velocity c u r v e . T h e

apprxoimatelyc onstant (t was f o und t o b e one-quarter of Y< ),t h e

isometric tension; /) is necessarily equal tu a/Pe >»ultiplied by the speerl

of shortening under zero load.

Inspection of equations (g) and ( 12) shows tl>at Lve have only t )>u
adjustable constants left f o r f i t t i n g o>» equations (o H TRT(s. relation-
ships (with a /Ye = ~t ). They are

><',/ > I —!/ ('1 ,/, , '!/,
( (>»( I
(/„

032

028

0

L. 024

>, 020

016

((-

0

0 12

0

008

0

004

02 04 06 10
Tension

1( ig. 9. I t c l a t i onship bctvv«r 0 total rate of energy lib( ('n(ion (bent, + <vorl<) nnd
tension. Straight line, fro>u 11»,>. s equations with « //', ) —,' sud mainternun «
heat rate = <((). Cir(.I«s: f r nn> equations (9) nnd (11). On abscissa, scale. unit>

is 8», th e i s om<'.tri( t e n sion ; o n o r d i n n t e scale, un it y i s t h ( p n ) <lu( t / ' » 1~»„„.

I he I'atto !/>//I l»>s also tu l )c cl>us(>» so (Ls I u g>v('. I I>(', »>(Ll» t('n(lt>c(> I>("LI
>;Lte:L v(>l»(, c<>r ><;sl)o»<li»g to I I»:(, I'<>t»><l <;x»<;I i»><.»(,;>lly; HI>,I, I'<»»><I
I I»t(, il, was »,I)u»I, (><I»n,l (,u «/).

'V»',ll at><l <'»'>'<»' sl>uw(',<I tl»ll, I;L>r;L«>'«,:»><',» I <,u»l<l I>c ul>I>l»>c<l. I>y

»»LI(>l>g 'I('/<' ) 7• () </I/(/> ' ,'/() , 'I/ I (i, ; L» d < //9(/> -I- </>)

' .I'hes(> «ive I ' u u„ . - -I (1. (/>, s<> t I»: t (/) is <)<I»:>I t<> Hlr,l,'s /); (1 > (y ; > I so
»>>Lk(; t l>c 1»alr>t<;»>L»c<'. I><.;a( I'(Llc b(.'>L>' tl>(: <(o>'I'cc( pr'upo>'(>o>l (I/I b) I <)
the I)roduct P o V mn~. 'I.'h(> 'dcg>ce (>I' success ir> l» at cl>i>tg H t b t ,'s
t clationsl>ips c>L>t bc scc>t I'>o»> I>'igs. S, !), IO. ;Lud I I . 'J'h(> der i>ltiot>s
I 'tor» l>yperl)olac i» I ('igs. 8 ; L»d 1 1 , ; L»(l I' n»» s!,»; igl>t li»cs in I('igs. !)
and fO, ar(. probably ru)t >>tuel> g>(utt<;I I I»:r> I hc cxper i>ru,»(>tl e> rur OI
the obser vatiuns o» which I-ill ,l. I>as(.<l 1>is >(,Iatio»ships.

A I ! Y T(01'l l I: s rs F o lt ' I ' Tl I : T > I:(' ll A N T s l>t O F C O N T R A C T I ON
032

028 0
oc 0 24

020

0
L0

0'16

0

0 12

008

0 04

02 04 06 08
Speed of shortening

I'ig. 10. Relationship bet,ween rate of heat production and speed of short-
(,ning. Straight line corresponds to a constant heat of shortening (as found by
H<»..) vvith ((/V» .= $ and maintenance heat rate = ar); ci r c les from equations
(!>) nnd (I' ) . O r d i nate scale as in 1'ig. 9; u n it y o n abscissa scale is Vm(>„, the

speed of shortening in an unloaded tetanus.

032

c 028

0

L 024

o 020

0 16

((-

0

0 12

0

0 008

0

004

02 04 06 OB 10
Speed of shortening,fraction of V<n«

I 'ig. I I. I u (al <i«»ship I>( tw«<n( t«tnl n<te of energy l i b eration an d speed of

s h«(tr ning. ( . 'ont i n uuus «u r v ( (hyperbola) d<nived f>om Hrrl ' s relationships,

<vl< h «// » ( nu(I n>nint( nnnc(> beat, r n t « = <6; < ircl«s f>om <.quation (9).
(>rdinnt«scale ns in I ("ig. 9.

) q()

M lr«<CJ« I«) STR I ? ( ' T I ? 1L1«: h N 13 T r f l «l (I R 1 KH ( ) I«' ('!( ) N T R A C T J C N

Although only tw o c onstants were available for fi t t ing H i d ' s
equations, and one for fitting the amount of maintenance heat,

arbitrary assumptions had been made at an earlierstage in making f

and g vary with x in the ways shown in Fig. 6. One or two other forms
o f these relationships were also tried. Wi t h f and g constant (instead
of increasing linearly w it h x ) in t h e r a nge 0 ( x ( /L ,H JJ.L's equations
could be fitted about as well as with the system discussed here, but the
ratio (v /e had to be given a value of about unity. T his is not plausible,
as the three reactions that are postulated cannot all go spontaneously
in the forward direction unless tv is considerably less than e (which is
a ssumed to be derived wholly front a change in free energy). T h i s
result was not much altered when the change-over from high f to high
g was shiftedfrom the point x = 0 to x = A/5. It can be seen intuitively
that, for agiven value of L%, the eSciency will be lower in t h ese
systems with constant f than in the one developed. here with f propor-
t ional to x , b e cause during shortening a h i gher p r oportion of t h e
attachments will be formed at small values of x (therefore contributing
little to the work done) in the former system than in the latter.

Another system, within the same general framework, which is of
interest, is one in w hich f a n d g v a r y e x ponentially with x . Th e
equations are:

e(L — h)/i

c(s — I«)/i

Force in elastic eleinent = p = p » (L „

1 — 0(

x ) h: f = 0, so that no c ombination occurs during shortening;
g and p therefore need not be specified.

The interesting joint about this system is that it satisfies Hrr.r.'s
equations exactly. U n f ortunately it gives about 5 times too high a
value for the maintenance heat, because of the great overlap betweett
the functions defining f and g. M a t l t em(Ltically, this can, be overcotnc
if g is allowed to become negative when x has values near tn h, lnlt th is

ls 1101«p rll llHHI1)1(') «Lt ally I ' ILt«! (wllill()Ill«('xl I'IL «Lisisll Ill f)tl()lls, ILH ll I l t l p l l ( ! H
I«llc Hlt(till (LI I(l(tl(H I'(lV(tl'HlLI (Il I L I ' ('ILcti(Ill. wit icll g ( I C H ill 1 II (: f u t w Ll (I

dilcction will> lll« r elease of a large alnounl (>f ft.ee cltergy. F o r t ilia
I'CILH(Ill> I 1alll(lvc l lla«l« ll« IH Il tl lit'()lll«ll,blcl«()He«LI<cll fill'tllcl' lor' Hc) teltt((H,

witliin the framework of the general hypothesis th Lt is under discuasio»,
whicll obey l i t t .t.'H cqualiutis exactly, since l ltiH p(Lrliculal Hystetttis

probably unique ingiving an exact agreement, apart from a "family"
of systctns th Lt ca» lie <Ibt;Litic<i froln i t 1)y t t lhnsforluations in w l t i clt

the r a t i os 13etweellj, < /, ILtl(11) al'0 (lit(lit'Lrtged;Ll, ea<;11 v;Llue of'. I,,; L ll<1

whicll lc(L(l to l « llc «s«LIIlc I'cl«ltl()IIH 1)(ll«w(l('ll Hpe(l(1()1 Hll()l'lcnlllg, t ( lttHI(III>

and rate ofliberation of heat.

«3)(1 )









A ir YFOTH E S I a F O R T H E M MO H A N IaM O F C O N T R A C T I ON

be several times longer than the time constant for forming them at
activation ( 1/f). In a n i sometric twitch, this two-stage relaxation
would show up by the active state (detected. for instance.by the ability
of the muscle to redevelop tension after a quick release) falling to zero
while there waa still considerable tension remaining. This point does not
seem to have been submit t ed. to direct experimental teat, bu t s everal
p ublished results suggest that muscles do behave in this way. F o r
example, inthe contraction shown in flg.1 (top curve) of a paper by
HITGHIE and WILKIE (1955)the degree of activation has fallen to 7 per
cent of its maximum value at 330 mace after the stimulus, while the
tension is still 90 per cent of ita value at the peak of the twitch, and
74 per cent of the isometric tetanus tension.

lt also seems di6icult to explain some of the quick stretch phenomena
described by KATz (1939) without distinguishing between two steps
in. the activation process (cf. pp. 291 and 308).

IV. 5. Size and nrjrnber focontraction aitea

IV. 5. 1. Range fomor>enrent of aide-pieces

A rough estimate of the value of (rr, the largest displacement at which a
side-piececan become attached to an actin flament, may be obtained

as follows. On p. 288 it waa shown that the quantity $(= (ffr + gr)I>/a)

caine outto be equal to HE'LL's b; hence

k — ba/(fr q gr), (13)

Now gr/(fr + gr) waa set at 3/10, in order to give the right amount
of maintenance heat ; h e n c e 1'=r 3ba/16gr. b and e a re known (for

frog muscle atO'C), and an estimate for g~ can be obtained from the

decay of tension at th e end of an isometric twitch, accepting pro-

visionally the interpretation given in the last section. The same curve

in RnrHrE and WnaUE's paperthat was referred to in that connection

givesthe time constant of decay of tension as about 150 msec at about

,>00 msec after the stimulus, when the degree of activation appears to

have fallen to zero. This time constant should be of the order of 1/g,;

t liis is not an e x act equality b ecause g varies with z ( s o t hat t h e

tlicorct,ical limo course ia not, exponential ), and only reaches gr when

x = h. H ence 1/gr is likely to be less than 150 mace; we might take
100msec, making gr = 10 aec-r. No w H xr,L (1938) found that b i s

about dI acc-', and a is about 2 5 p.; i n serting these values in the above

equationw<' obtail>

3x ( x 2- 5 p = 156A.

h= - -
10 X 10

This figure is subject to considerable uncertainties. Thus, the values
taken for b and for g, were obtained from difFerent frogs, and the

Mrrs(>LM sTRrr<'.TITRIL AN I> Ttrz<>nr>'.s <>I «'>N I'RA( ' T l <>N

estimateofgi w as in a r sy case very t o u g h; al s o t h e v a l u e f or t i l e

ratio f,/g, was obtained on the somewhat arbitrary assumptions ((L)

that the whole of the maintenance heat is derived from the breaking
of A3f links at values ofx between 0 and 1>, and (1>) that no links are
broken by a reversal of reaction. (1). None the less, the value is one
that would fit i n w ell with the attractive possibility that the side-
pieces are placed at intervals along the filaments equal to the 415-A
period which has been observed with X - r ays (BzAR, 1 945; H. E .
HUxLzY, 1952, 1953b) and in t h e electron mici'oscope(HALL, JAKUs

and SOHMlTT, 1946; DRAPzR and Hor>oz, 1949).

IV. 5 . 2 . D i s t ance 1>etu>een snccesaL>>eA sites

On p. 286, a formula for the tension during tetanic stimulation was

derived (equation 11). P u t t ing V = 0 , w e obtain for th e isometric
tetanus tension

2na>U fr ...(14)

2l (fi + gi)

>o was set at $e, and f,/(f, + gi) at 13 /16, so that

1 = 0 305>2>>se/P„. ...(15)

Valiles foi' the quar>titles oil tire 1'Ighti-h;>nd s>de of this eqilatioil nlay'

be obtained as follows, s i s 2 5 p or 2.5 X 1 0 4 cm; Po for f r og muscle
is about 2 kg/cmm, or 2 X 10~ dyne/cm~. 2n, the number of JI si t es per
c ubic centimetre of m u scle, may b e p r o visionally identified wit h t h e
number of myosin molecules in the same volume; this may be calcu-
lated from a concentration of 8 g /100 ml. and a molecular weight of
8 40,000 (Wzrrzz, 1950) to be 5 7 X 1 01%. 0. If the heat of hydrolysis
of the high-energy phosphate group is taken as 10 kcal /mole, then e is
7 X 10 13erg/ molecule. Inserting these values, we obtain l = 153 A .

The interpretation of this result is complicated by the fact that it is
close to the estimate we have just obtained for h. Equation (6), froni
which equations (11) and (15) were derived, assumes tacitly that I i s
consi<lcrabty greater t1»L» h„H<> l,l>at; 0>Lol> 2V Hit o is >Llways free 1'><>ni it,»

1>L>>t>) Lttr>Lot>I>10» ti to >» I .'1 l>010f0 ll>0 »0><tA 1>1'08011ts>liscll 101' co>nb» i>L-

tion. I f l wa s r e a 11y smaller t h n n h , t h c ( » L1ir(b. Lti<>I> wo have gone
through would probably give the value of /e, not of. l; the relationsitips
l>et woon force, velocity and 1>0>Lt productio>i would also be modified it'

lwas not appreciably greater than h. We may conclude either that 1

is c<lual to or sinai lci l,ll>L>i 1>,Ill whlcli 0>Ls<> i>lie ligure we have obtainc(1
i s <L confirmation of.' tl>c otl>or ostimat>o of 1> but the for>nulae for t l i c
force-velocity relation, etc. are no longer exactly appropriate, or else
that 1.is about 150 A and h, is appreciably less, say 100 A, which woukl

29t>

A II Y I'AT>i >;srs I<o I< 'I' ll ll M z(lriA NISM o l ' o o N T R A ( >TI o r <

probably not betoo small a value to confiict seriouslywith the earlier

estimate.

I V. 5>. 3. 8p<rcr',2>gs expected on st>'2<ctu>'nl g>ou>L<ls

I<:stimates of th e spacings of m y osin and a c ti n m o l ecules along t h eir
r espective filaments can be obt ained from t h e q u ant i t ies of th e p r o -
teins present, their molecular weights, and the arrangement and spacing
of. the filaments deduced from H . E . H U X L z Y's X - ray and e lectron-
>nicroscope observations. These calculations have been made by
HANsoN and H, E . H U XLzv (1955, p. 253). For the myosin filaments,
a ssuming that t h ere are six m o lecules abreast (one facing each of t h e
s ix actin fi laments which surround th e m y osin fi l ament), t hey f i nd
that th e l ongitudinal spacing comes out t o a b ou t 4 0 0 A., agreeing
remarkably with the well-known 415-A period seen with X-rays and
the electron microscope. Each actin filament is surrounded by three

myosinfilaments; assumingtherefore three actin m olecules abreast,

they calculate a longitudinal spacing of about 130 A. This is close to
the upper limit that was obtained in the last section for the distance
between successive A sites with which any one M site can combine;
it, would be very natural to identify this with the spacing of actin
>nolecules <Llong a filainent.

IV. 6. DL scrrssLon

At the outset, it, must be emphasized that the agreement which has
been achieved with some aspects of the known behaviour of muscle
is not to be regarded as grounds for accepting the scheme which has
been put forward. There islittle doubt that equally good agreement
could be reached on very different sets of assumptions, all equally
consistent with the structural, physical, and. chemical data to which
this set has been fitted. The agreement does however show that this
t ypo of mechanism deserves to be seriously considered, and that it i s
worth looking for direct evidence of the side-pieces, and of the localiza-
tion of enzymic activity, which have been postulated.

()uite apart from the possible value of. this scheme as a working
l >yt>othosts, several ol' th o r e sults are o f m o r e g eneral i n t erest. T h e
1>ruposed mechanism may be described as cyclic, in the sense that the
riumbor of sites in a given condition is not affected by shortening:
Oacli side-piece goes through cycles in which it combines with the actin
filament by one reaction and isseparated from it by another. The
final states of the side-piece and of the site to which it was attached are
the same as their initial states; the only changes are that the muscle
has shortened, an energy-rich phosphate bond has been split and. work
may have been done. The mechanism may be contrasted in this respect
with any of the theories that postulate folding links in series: in these

297' 't