東京大学教養学部体 育学紀 要 (1994)参 . lS〜 24

15

Influence of Muscle Length on Maximal
Rate of Tension Development in
Frog Skeletal Muscle
Kaoru Furuya
Dept. of Sports Sciences, Crllege of Arts and Scienc€s,
The Univeniry of Tokyo

Abslract

The effec! of muscle length on pa.ameters coocerdng the force geoerating processes alboth the early tension developme[t and the subsequent tension plaleau phase iD isometrictetanic cootractiorrs was srudied in whole-muscle preparations of frog sartorius. The maximal
rate of teosioD development (dP/dtm () aDd the peak tensioD (Po) were measured at
leogths ranging ftom 70 to I20Eo of the optimum length for tension geDeration (I-o). 'lte
length-peak tension relarioo agreed with tho6e reported for single muscle-fibers. The
lerrglh-dP/dtma( relation appeared to be similar to the length-peak teDsion relations inthat they showed a maximum at l.I), but had steeper ascending limb. Greater values of Poto{P/dtmax ratio at leogths far shorter thao In iodicated that higher peak teosioD wasproduced tha[ expected from the preceding tensioD risiog phas€ at these lengths. The
results were discussed at both macaoscopic and micrGcopic levels.

lntroduction
In isometric tetanic contractons, the force

state.

generating process consists of two phases;a.e.,
the early tension development, and theMethods

following steady state r,vith maintained tension.
To characterize the early tension risingphase, the rate of tension development hasoften been investigated. Some studies havemade an attempt to use it as a substitutional
index for the maximal velocity of shortening(V,,,)o*), while others have used it more
frequently to compare the contractile
properties of different types of muscle
fiberss,6/5), and to describe functional changesof muscles under various conditions, such as
those following fatiguerr'r7 13''zr), disuse'"''u) andexercise trainingrT).

In many of these studies, the rate of tension

Materials and Apparatus

A pair of m.sartorii of. Rana catxbeiana(270-350g body wt. ; NIPPON BIO-SUPPLYCENTER, Tokyo) was dissected out with bothtieir attachments to the pelvic bone and theinnervation of sciatic nerve left intact. Paired
muscles were fixed together vertically, with
distal tendons clamped closely to the end of
muscle fibers as possible, while t}le fragment ofpelvic bone was immobillized on a lower clamp

with a bolt. Muscle length was measured with acaliper as the distance between both ends offibers, which were visually determined. The
upper clamp was connected to a force

transducer (Model UT-IK ; SHINKOH
TSUSHIN ; natural frequency of oscilation,

development has been regarded as a parameter
representing "the contracting speed of the980H2), and the muscle length was changed bymuscle", because it presumably relates to thedisplacing &e transducer with a micrometer at

speed of motion. In the isometric contraction,a minimal step of 0.01mm.

however, what the rate of tension development
actually means is the tension generated per unit

Muscles were placed in a bath containing
Ringer solution (95.0mM NaCl, 2.5mM KCl,time, so that it would not necessary represent
the dynamic properties of muscle. Contrary, it

and 5mM glucose, pH=7.2) aerutrd atith 95%

would give important information about theforce generating processes during the earlyphase of the isometric contraction.
From the early studies"l''37), the phenomenon
that peak tetanic tension measured during a
steady phase of isometric contraction varies asa function of muscle length is well known as thelength-tension relationship. In contrast. there
have been few studiesla"''7) which examined thetension generating capacity during the earlytension rising phase over a wide range ofmuscle length.

The purpose of this studey is to learn theeffect of muscle length on t}le rate of isometrictension development during the early tension
development and to compare it to t}lat on thepeak tension attained in the following steady

20.0mM NaHCOa, 1.0mM CaCL, 1.0mM MgCL,
Oz-S%COz. The temperature of tlle solution wasmaintained at 12.010.5'C. Trunks of sciatec
nerves were hung gently above the solution by
hook-shaped Ag:AgCl electrodes and kept wet

throughout the experiment by dripping thesolution on them.
Stimulation

Electrical stimulations with the trains ofrectangllar pulses of 0.1-0.2ms duration were
given at a supramaimal intensity by anelectronic stimulator (Model SEN-7203 ;NIHON KOHDEN) via sciatic nerve atintervals of 15 to 30min. Muscles wererepeatedly stimulated at a frequency of 50Hz
for 800-1,000ms until reproducible isometriccontractions were observed. At this frequency,
both tension and tension differentiatedIDfluen.. of M!*le l-engrh on M.nmrl Rate oI Tt'nsion Dereiopmetrl in FroB Skeletal Mus{['lj

tension development (dP/dt'!r) was also
obtained from the positive peak ofdi fferentiated tension (Fig.l)-TensionDifferentiatedTensionFig.l Recording parameters.
recordings did not show any visible ripple.

For normalizing Po and the dP/dt,.,, muscle
cross-sectional area (CSA) was estimated by
dividing the murle weight with the product ofmuscle fiber length at Lo''''?) and density. Fiber
length was determined by multiplying Lo byfiber-to-muscle length ratio of 0.9'), and thedensity was assumed to be 1.056'3).

--'-

muscle weisht
muscle fiber length x density

In each series of experiments, several
contractions before being fully equilibrated
were excluded from analysis, and the first
analyzed record was used as a control for
fatigue.

Muscle lengths were normalized for Lo.
The values in text and table are expressed as

meantSE.

The ef{ect of fatigue was carefully examinedby stimulating the musle at the initial length
every seven contractions to compare tension
with that of the control. If there appeared any
sign of fatigue such as the reductions in peaktension, rate of tension development and/or
rate of relaxation, the period of time to rest themuscles was prolonged and the control

Results

The frog used in the present study, Razt
calesbeiana, had large sartorius muscles (744.
3l:46.3mg), which therefore, exerted the five totenfold greater Po (4.41+0.21 N) at Lo than inotler species of frog. When normalized, Po anddP/dt,* at Lo were 32-6610.61 N/cm" andcontraction was re-examined. When the decayof the peak tension reached 5% of the initial
peak tension, the preparation was discarded.

456.34 + 23.68N/cm'ls, respectively.

Data Recording

25N/cm' Io''s're''?!r), with a large deviation'!).
Furthermore, the normalized Po values inwhole muscle preparations appear to deviate agreater deal (e.g., ranging from 439 to 831
g/gwt in'control' muscles in ref. 36) and our
datawere all within this range. Values for Po
similar to ours r{ere reported in frog sartorius

Measurements at various lengths vrere madein a random order but data at near the optimum
length of tension generation (Lo) were obtained

precedently than at other lengths to avoid

irreversible damage of the muscle (dalta
state3T)). Data from 12 preparations wereanalyzed. Tension records from individual
tetanus were amplified and digitized with A/Dconverter (Model DM-7000 ; IWATSU) at asampling rate of 0.5ms, and stored on disk.
Stimulation signals were also digitized andstored simultaneously. A custom software wasused to measure the peak tetanic tension (Po) ineach digitized tetanus. The maximum rate of

The values of mean Po per unit CSA thus far
reported for muscle or muscle fiber are around(3.325+ 0.265kg/ cm'J 3), frog semitendinosus(3.?kg/cm')n) and mouse foot muscle (375156kPa) 'ze).

There are few reported values of dP/dtn",
which can be used for the comparison with ours
because it is sensitive to temperaturer''33'3r'rr)

and pH3,,13). The dP/dto.r value of 43.88t
Z.8lkg/cm'/ s for toad sartoriusr3) under thesimilar condition (at 15C, pH=7.0) was smallerwasthan ours by about 15%. When dP/dt",
expressed as relative to peak tension"), thepresent study gave l.39fuPo/ms, which was

r00
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EDL at 15"C ( ref.12, Fig 1).
Fig. 2A shows the len8th-tension (L- %Po)
relations obtained from 12 muscles in which Po
were normalized v/ith respect to the maximal
tension in each preparation. The shape of the

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similar to the value previously reported for rat

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L-%Po c\rye was similar to those reported
for whole skeletal muscles of frog'?'I').
The relation between length and %dP /dt^ *(L- %dP / dt^,,) obtained from the same
preparations is shown in Fig.2B, in which
dP/dt,", were normalized with respect to the
maximal rate of tension development in each
preparation. o/PP/dt
was also a function of^*

Iength as did tension, and exhibited the highest

value at Lo.

The optimum length for %dP/dt,". waswithin t3% of Lo determined from the L'%Po for each preparation. No significant
difference was shown between these two

０４■

optima by the paired t-test (p)0.05).
Fig. 2A and B showed that the L- %dP/dt."-

curve is steeper at both sides of Lo than L-'%Po cur.ve. Since no difference in length
dependency was observed between Po anddP/dt.", in twitch contractions?3''5), theMuscle Length (7,)

difference observed in the present results could

be derived from the repetitive stimulation in
Fig.z (A) length-peak tensior and (B) lengthmaximal rate of tension development
relations from 12 muscles. Values of peaktension (O) and the maximal rate of
tension development (l) have beennormalized in each preparation to theirtetanic contractions.
To quantify their length dependency, both thehighest values, respectiyely, obtained atwhere y is %dP /dt^,, or ftPo, x is normalized

Lo. Lines are regression curves for all
d712 (1=97).

L-%Po and the L-%dP /dt,* relationships
were subjected to least-squares regressions to
the following polynomial equation :y=Ax'*Bx*C (1)muscle length, and A, B and C are constants.

The values of constant A, index for thecurvature, f.or the L-%dP/dt.", and the L%Po curves were -0.100t0.007 and -0.0681

Itrfluen.e of Muele l-eogrh otr Mdimal Rate ot TeNion Developmenl itr Fog Srelerat Mu&.te

19

Table l. Values of the constants of A, B, and C for regression curves of L-?odpldt*,and, L-gop..

leng血 ―
%dP/dttax

A

B

C

‑01∞

20.33
+1.33

‑938.66+0.007
lcngth―%R‑0.068

13.68
+0.49

+0.003+63.59‑585.91R2
0.7932 (n‐ 97)

0.9160 (n=97)+23.32

Values are means + standard error of the mean (SE).
0.003, respectively (Table 1). Two-sample test

for the equality of the regression coefficients
revealed that the constant A of regression

curve n'as significantly greater in the L%dP/dt.,, curve than in the L-fuPo curve(p< 0.005). This implies that dPldt,", depends

Discussion
When the length of muscle fibers (LJ is lessthan the overall length of muscle (L.), a lengthchange in whole muscle would cause a greater
length change in muscle fibers with a inverse

factor of L,/I^. For example, 10.0% length

more strongly on muscle length than does Po.

change from Lo in a whole muscle would cause

When the ratio between Po and dP/dt'"' inthe same contraction was plotted againstmuscle length, it was smallest aroutd Lo andll.l% Iength change in muxle fibers, assuming
the mean LJL- rutio is 0.9 (Fig. 4). Thus,
relative muscle lengths in the present study

inereased at lengths distant from Lo, especiallycould be re-calculated into relative muscle fiber

at shorter lene$s (Fig.3).

lengths (LJ by dividing the length changes from
Lo by 0.$3r. TheL,-ftPo crtme obtained in thisway was found to be in good accordance withal. ; 1966)'olwhen their sarcomere lengths werenormalized to the midst among ttte range of
optimal lengths, 2.125rm (Fig. 5).

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In most of previous studies which
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t}}e sarcomere length- tension curve (Gordon et1101207080901∞
Muscle tength(7・Of Lo)

Fig 3 Ratios of peak tension and maximal rateof tension development at various lengths

in 12 muscles
greaterat

Note that the ratiO is

distant

opumum lengul(Lo)lengthsfromtheinvestigated the influence of muscle length on
the mechanical properties of isometric tetanic
contractions, only peak tension values havebeen focused on. The present results indicatedthat the muscle length also affects the maximal
rate of tension development.
A few studies have observed the length
dependence of dP/dt,., of isometric tetanic
contraction in a single motor unit'r)and in awhole muscle stimulated by either directr'?) or
indirect'a'7) stimulation. On the other hand,

Julian and Morgan (1979)'z6) reported that thel瑯

地thn,3● ■8い ml
1,5
20 22S

25

275

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‐(1● ●■∞lL● くい●Lo・ (1● ,月 mR)Lr︵゛ ︶ ●盪 ３ Ｆ

r,- 9-"*".,...-

16

８

witch the lengths of non'fib€r components(s,, s,, and S as a total) and the muscle

fiber to the overall muscle length ratio嘔螢Ｅ 饉ド ● Ｚ

Fig.4 Schematic diagram illustrating lengthchange of muscle fiber within a muscle.
A), The standard muscle length (L') at

一

0COmm et.(1獅%POMPan

0

s0

70

$

ll0

130

M!!cL Flb.r LaSth (* ot L)(R) are defined. B), A new muscle length

Fig.s Length-tension diagram replotted on theaxis corrected for the muscle fiber lengt}.

(L',) with a relative length change x in
L,, assuming length change in non'fiber

Symbols are meantSE obtained in thepresent study. Line is the length-tension

area is much smaller than in muscle fiber
length and negligible. Note that it is also

diagram for single fibers based on

valid when tie muscle shortens withnegative x in the equation.

Gordon et al. (1966)'0'.

L-, overall muscle length ; L., muscle

in a motor unit). There may be morphologicaleffects to be considered (e.g., fiber-to-muscle

fiber lengti ; x, relative length change in
L,, L'represents a new length changed
from the standard.

surrounding the fibers).

Iength ratio, and the elastic component

The difference between the curvature of
L-%dP/dt^,, and that of L-/sPo rclalion

initial rate of rise of tension in a fixed-md

implies that muscle length affects differently on

tetanic contraction of a single muscle fiber was

the tension rising and the plateau phases. We{ound that the effect was greater on the former

constantover a range of sarcomere lengths froml.7pm to beyond 3.0rm. In the results byRamsey and Street (1940;in their fig.8)'?),

than on the latter. For example, dP/dt"",aparameter for tension rising phase, could exert

however, there seems to be differences in therate of tension development at the lengths of 82,

only 521 of its maximum capacity achieved at
Lo, while Po, a parameter for plateau phase,

100 and 136% of Lo.

exerled 71% of its maximum at 80% Lo ;8L%
and 93)( lor dPldt,." and Po, respectively, at
110%Lo (Fig. 2A and 2B). Fig. 3 indicates thatat lengths more distant from Lo, ttle greater
tension is generated than expected from theIt is not clear whether the lengtl dependenceof the dP/dt'i, does exist in a single muscle
fiber, since dP,/dt.., values were not shown inrelation to lengths in those studies made on asingle muscle fiber. If dP/dtm", is held constantagainst the fiber length change, the length
dependence of dP/dt.., observed in the present
study is the property of a whole muscle ormuscle fibers placed within a muscle (r'.e., those

preceding tension-rising phase.

It is considered that inward spread ofactivation along the transverse tubular(T)system is interrupted at short fiber lengths(Huxley and Taylor, 1958"). Taylor andInnuene of Musle l-etrStl oD MdiDal Rate of Telsion Devetopoeor in Frog Skelerat Musle

co-workers found inactivated wayy myofibrils
in the core of the fibet'.) and the decrease in therelease of Ca,* from sarcomplasmic reticulumr)

when a muscle fiber was allowed to shorten up

21

Po, the difference of the length dependency
between dP/dts* and Po might consequently
appear lead in a whole muscle.

For above optimum length, one might be able

to 1.61m of sarcomere spacing- Such a

to explain this phenomenon, at least partly, by

structure-related inactivation, however, doesa mechanism called 'creep'. In fixed-end tetanic
contractions at higher lengths above Lo, initial

not seem to recover through a contraction, thus
the similar effects should work on Po. In fact,

especially at shorter lengtls and that it

rapid tension rise is followed by a slower'creeping' rise of temion described for the firsttime by Hill (1953)'z3t. 11l;. creep tension has
been considered to be correlated with thedevelopment of non-uniformities in sarcomere

recovered by adding the potentiating agent.o).

lengths2r.t0,33).

Since the L1-)(Po relation (Fig. 5) in thepresent study did not show such a tension

sarcomeres in series interact to each otier with

Rome et al. (1985) indicated that the insufficient

activation of the muscle fiber with a low-rate

stimulation made the tension depressed

That is, during a creep,a small proportion of sarcomeres near ends ofdepression at shorter lengths, insufficient levelthe fiber shorten, increasing their tensionof intercellular calcium does not seem toexplain the depression occurred only in
dP/dt..,, hence, the difference of length

generating capacity, and stretching the rest,

dependency between dP/dt,"" and Po.

relationship"). Such phenomenon occurring inindividual fiber will be added in whole muscle.
Thus, the greater is the total creep tension, thegreater would become the Po to dP/dt,,,., ratio.

If sartorius muscle contains, as is thought todo, parallel and same sized fibers running fromtendon to tendon, the mechanical properties ofwhich bear the extra tension in accord withthe stretch part of the force-velocity

a whole muscle could be obtained by simply
summing those of individual muscle fibers.
There should be, however, a variation oflengths among murle fibers and shorter muscle

Furtlermore, polyneuronal innervations often
seen in lrog sartorius muscle fiberss4 might
promote tle growth of non-uniformities among

Iibers would be more sensitive to muscle lengthchanges- Julian and Morgan (1978) havereported a delay prior to the tension rise at

onset of contraction along the same fiber. In
addition, if there are fiberc arranged in series'),sarcomere lengths below 2.04m"). Such a

gradually longer extra force as the sarcomeres

length would correspond to 94%Lo in thepresent study. Below this muscle length,
therefore, the retarded tension rise in someshorter fibers may be responsible for the lower
rate of tension development. Furthermore, thedecrease in the initial rate of tension riseobserved below sarcomere length of 1..6pm'6)(corresponding to approximately 75%Lo h ourin series within a fiber do during 'creep'. Indeed,in Fig.S, Po above Lo seems to slightly exceed
the sarcomere length-tension curve predictedpreparations) would accelerate the decrease in

information about the feature of isometriccontraction when the muscular actiity in uiuo
is to be described. That is, isometriccontractions performed at various muscle

dP/dt,", of a v,/hole muscle at the shortest
length in our experiment. Since such retards
would be reflected on only dP/dtou and not on

sarcomeres by causing a subtle mismatch in theinteractions among fibers might generatefrom Gordon et al.'o).

It could not be known whether the differenceof the length dependency between dP/dt.- andPo is an intrinsic property of individual muscle
fiber. However, it Tyould give an importantFuruyr

lengths are differ not only in their peak tension
but also in their rate of tension development.
This indicates that the time course of tension
generating processes itself is greatly affectedby length, giving consequently different shapesof contraction curves at different lengths evenafter normalization.
In recent biochemicat studies, Brenner(198?)') and Metzger et al.(1989)3') havesuggested that the peak dP/dt reflects the rateof transition in actomyosin binding from aweakly bormd lovt-force-state to a strongly
bound high-force-state. On the other hand,

Calcium transisrts in isolated amphibianskeletal muscle fibers:detection witl aequorin.
J. Physiol. 2?7 t29l'323, 1978.

4. Brenner,B. Mechanical and structural
approaches to correlation of cross-bridge action

in muscle with actomyosin ATPase in solution.
Ann. Rev. Physiol. 49t655'672, 1987.

5. Buller, A. J. and D. M. Lewis. The rate of
tension development in isometric tetanic
contractions of mammalian fast aod slow
skeletal muscle. J. Physiol. U6:337'351, 1965.
6. Close, R. Dynamic properties of fast and slow
skeletal muscles of the rat during developmenl

teision generating and maintaining capability
would depend on tlre reverse transition, so that

J. Physiol. 173:?1-95, 196{.
7. Close, R. I. Dynamic properties of mammalian

the slo\a,er is the net reaction rate represented

skeletal muscles. Physiol. Rev.52:129-197, 1972.

by dP/dt, the larger is the tension maintaining
capacity. We could not correlate directly our
results to tieirs, since their experiments werecarried out on tension re-development alter

8. Close. R. I. The relations between sarcomere

quick release in activated muscle {ibers.
However, it should be still worth to mention.

9. Deleze, J. B. The mechanical properties of theProviding tension generating capacity perunit time during the tension rising phase wasmore length dependent than tension

its length in the body. J. Physiot. i58:151-16,1,

length and characteristics of isometric twitch
co[tractions of frog sartorius muscle. J. Physiol.
2201715-762, 1972.

semitendinosus muscle at lengths gleater than1961.

10. Edman, K. A. P. The velocity of unloaded

maintaining capacity, it is suggested that theslowed net reaction rate in the transition ofcrossbridge states plays an important role inshortening and its lelation to sarcomele length"compensating" the lower rate of tension
development for achieving higher peak tension.
But such an argumentation needs further

ll. Edman, K. A. P. and F. Lou. Changes in force
and stiffness induced by fatigue andinvestigations.

and isometric force in verterbrate muscle fibers

J. Phvsiol. 291:143-159, 1979.

intracellular acidification in frog muscle fibers
J. Physiol. 424:133-149, 1990.
12. Elmubarak,

M. H. and K. W, Ranatunga.

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