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FOR YEARS, physiologists have probed and stimulated muscles and muscle
fibres dissected from animals, in their search to understand how muscles
work. They have used electrical stimuli to make muscles contract and have
measured the forces required to prevent shortening. They have also measured
the rates at which the muscles can shorten under various loads. They have
assembled a mass of information about the properties and capabilities of
muscle, and about the differences between muscles from different animals
or from different parts of the body. But until recently, we were remarkably
ignorant of how living animals exploit their muscles. No one knew how the
dimensions and properties of muscle match the particular tasks they have
to do. Recent research, however, has discovered a fine balance between the
function of a muscle and three factors: the force that the muscle can exert,
its length and its maximum rate of contraction.

Muscles contract thanks to the interaction of two kinds of protein filaments:
thick filaments containing myosin and thin filaments containing actin. In
the skeletal muscles of vertebrates (and also in many invertebrate muscles)
the thick and thin filaments are arranged in a very regular pattern which
makes the fibres look banded under the microscope. Each unit of the repeating
pattern is called a sarcomere (see Figure 1).

The thick filaments have projections, or cross-bridges, which attach
to the thin filaments and pull on them, when the muscle is active. To shorten
the muscle, the cross-bridges make the thin filaments slide between the
thick ones by attaching, pulling and detaching, like people pulling in a
rope hand over hand. When a muscle is greatly stretched, thick and thin
filaments barely overlap, so few cross-bridges can attach, and the muscle
can exert little force. At moderate lengths, all the cross-bridges can attach,
and the muscles exert maximum force. If the muscle shortens much more than
this, however, filaments interfere with each other and thick filaments press
against the partitions (Z-discs) that separate one sarcomere from the next:
when muscles shorten to this extent, they can exert little force. The graph
showing how the force that a muscle can exert depends on the length of its
sarcomeres is known as its force-length curve.

Thick filaments in vertebrates are 1.6 micrometres (0.0016 millimetres)
long, but the thin filaments vary in length from 2.0 micrometres in fish,
frogs and chickens to 2.4 micrometres in rats and 2.6 micrometres in humans.
So different muscles exert maximum forces at slightly different sarcomere
lengths, depending on how long their thin filaments are.

Until recently, we did not know the ranges of sarcomere lengths that
muscles go through, as they lengthen and shorten as the animal goes about
its normal activities. So we did not know where along their force-length
curves the muscles of different species operate. Nicola Dimery and Alison
Cutts of the University of Leeds set out to fill this gap in our knowledge
by studying various sorts of vertebrate muscle. For example, Cutts investigated
the wing muscles of birds. She took freshly dead zebra finches and budgerigars,
spread their wings, and fixed them to boards in positions imitating the
extreme wing-up and wing-down positions seen in flight. She wanted to be
sure that the muscles were taut because a slack muscle fibre in a dead bird
may be kinked or folded, and so longer than it would be when the muscle
was active in the same wing position. She therefore left the carcasses for
a few hours to develop rigor mortis, which tightened the fibres. Then she
fixed the muscles with glutaraldehyde, leaving them in place on the skeleton
while the fixative took effect so that there was no danger of them shrinking
or being accidentally stretched. Next, she dissected out small groups of
muscle fibres and mounted them on microscope slides. She could have used
a micrometer to measure the sarcomeres, but it was easier to treat the fibres
as diffraction gratings, mounting them in a microscope and shining light
through to produce diffraction patterns. She calculated the lengths of the
sarcomeres from the spacing of the lines in the patterns.

Birds have two main wing muscles, the pectoralis, which shortens to
pull the wings down, and the supracoracoideus, which shortens to raise them.
(These two muscles together make up the flesh of the breast.) The measurements
showed that both muscles operate over a range of sarcomere lengths from
about 1.8 micrometres at one extreme of the wing beat to about 2.2 micrometres
at the other. The filaments in the muscles of birds are the same length
as those in frog muscle, and so the muscles probably show a similar relationship
between the force they generate and sarcomere length. The muscles do indeed
seem to work so that they generate maximum force: the sarcomere lengths
the researchers observed in the muscles lie at and just below the peak of
the curve (see Figure 2).

As in all experiments, there is room for error. In rigor mortis, the
forces exerted on the muscle are smaller than would be in flight. Flying
stretches tendons and bends bones slightly, altering the lengths of the
sarcomeres when the wings are in particular positions. These effects would
be small, however. The sarcomere lengths that Cutts measured must be very
close to the lengths in a flying bird.

The same principle applies to the muscles of other animals. When carp
swim at slow to moderate speeds – speeds that they could sustain for a long
time – they use red muscles working over about the same range of sarcomere
lengths as the wing muscles of the birds studied at Leeds. The jaw muscles
of rabbits work at longer sarcomere lengths, but have longer thin filaments
than fish or birds and probably develop maximum force at about 2.5 micrometres.
The muscles that close their jaws, the temporalis and masseter muscles,
work close to the peak of the force-length curve, but the range of the digastric
muscle, which opens the mouth, seems to extend a little beyond the peak
of the curve (see Figure 2).

So the skeletal muscles of vertebrates seem to work over a fairly narrow
range of sarcomere lengths, close to the length that allows the muscles
to develop maximum force. The animals could make do with shorter muscles;
that is, muscles with fewer sarcomeres in series. These muscles would have
to work over wider ranges of sarcomere length to produce the same movements,
but the forces they could exert would be reduced when the sarcomeres were
very long or very short.

Some researchers have suggested that muscles should be unstable at sarcomere
lengths greater than the length that gives maximum force. Suppose, for example,
that a rat muscle were stretched until its sarcomeres were 3 micrometres
long, and then stimulated to contract. Initially, the sarcomeres might all
be about the same length, but any that were stretched slightly more than
the others could exert less force and would be apt to be stretched more.
Sarcomeres that were slightly shorter than the others would exert more force
and would shorten more. So some of the sarcomeres would be stretched very
long and others would contract very short. Experiments on frog muscles seem
to show that this effect works too slowly to have much importance. But even
so, evolution seems to have erred on the side of caution, avoiding the danger
of instability. The measurements of sarcomere length suggest that muscles
work more often below, rather than above, the length at which they can exert
most force.

Yet the force that a muscle can exert does not depend only on the length
of the sarcomeres: it depends also on the rate at which the sarcomeres are
lengthening or shortening. A muscle fibre that is stimulated but prevented
from shortening is said to contract isometrically, and exerts a force P_o
(see Figure 3). If it is forcibly stretched it exerts more force, but if
it is allowed to shorten it exerts less force. When contracting freely,
with no opposing force, it shortens at its maximum rate Vmax.

The isometric force P_o that the fibres of the skeletal muscles of vertebrates
can exert is about proportional to the area of their cross-section: all
can exert about 300 kilonewtons per square metre (3 kilograms force per
square centimetre). Their maximum shortening rates V_max are generally expressed
in muscle lengths per second: for example, a fibre that shortens by one
tenth of its length in one twentieth of a second is shortening at two lengths
per second. A fast-contracting muscle in a frog can attain such maximum
rates of contraction but a slowly contracting muscle in a tortoise can achieve
only 0.2 lengths per second, both at 20 Degree C. The maximum rate of contraction
ranges from about 10 to about 20 lengths per second for various muscles
from a mouse at 35 Degree C.

Speed is sometimes of the essence

In some tasks, muscles must exert as much force as possible, but the
need is often for power, the rate of doing work. For example, if a fish
is to swim at top speed it must maximise the power output of its muscles.
The work done by a muscle is the force it exerts multiplied by the distance
through which it shortens, so the power is the force multiplied by the rate
of shortening. The power is zero when the shortening speed is zero and also
when the muscle is contracting as fast as it can, V_max, because the force
is then zero. A muscle generates maximum power when it shortens at an intermediate
rate. This rate depends on the precise shape of the curve that relates to
the rate of shortening, as well as on the maximum rate of shortening, V_max.
But generally it is about 0.3 V_max.

In yet other tasks, muscles should maximise efficiency: they should
consume as little metabolic energy as possible, while supplying the power
that is needed. Efficiency seems likely to be particularly important when
animals are travelling for relatively long periods at less than their maximum
speeds. Measurements of the rate at which cells cleave ATP to release energy
show that frog muscle is not very efficient when it shortens very fast or
very slowly, and is most efficient when its shortening speed is about 0.3
V_max.

So if either power or efficiency, or both, are important, muscles should
shorten at about 0.3 V_max. This has been known for many years, but until
recently no one knew whether normal shortening speeds in living animals
live up to these predictions.

Even now, we have good information only for one set of muscles, the
swimming muscles of carp. As consumers of fish will know, these muscles
lie on either side of the spinal cord, making up about half of the mass
of the fish. As in other fish, most of the swimming muscle is white with
a narrow strip of red muscle along either side of the body. The white muscle
is used for sprinting and works anaerobically, in the absence of oxygen,
building up an oxygen debt until the fish has to rest to recover. The red
muscle is used for swimming slowly and can continue working for long periods.
It works aerobically, releasing the necessary energy from foods by oxidising
them.

Fish on film

Larry Rome and I led a team of researchers, drawn from the University
of Tennessee and the University of Leeds, which investigated the muscles
of carp. We measured the maximum rate of shortening and the rates at which
the fibres shortened when the fish swam. We trained carp to swim against
a steady current in a water tunnel, matching their speed to the current
so they remained stationary relative to the laboratory. In this way we could
control their speed and obtain good quality films of steady swimming. We
also placed electrodes in the red and white muscle to discover which type
of muscle the fish used at each speed. We analysed the films, measuring
in each frame the curvature of the body at several points along the length
of the fish. We also measured the length of the sarcomeres in fish that
had been killed, bent to various curvatures and allowed to go into rigor
mortis. With these data we could calculate the rates at which the sarcomeres
lengthened and shortened as the fish beat their tails from side to side.

The researchers from Tennessee dissected bundles of muscle fibres from
carp and plotted curves relating the force generated by the muscle to its
rate of shortening. They made the measurements at 15 Degree C, which is
the temperature of the water in which the fish had swum.

The carp swam using just their red muscles at speeds of 20 to 40 centimetres
per second. In swimming at these speeds, the red muscle fibres shortened
at 0.7 to 1.7 lengths per second. The maximum rate at which the red fibres
shortened was 4.7 lengths per second, and they gave maximum power output
at about 1.7 lengths per second. At the highest swimming speed that the
red muscles could power, the muscles shortened at the rate that gave maximum
power output and probably also maximum efficiency. The red muscle is apparently
well matched to its task.

Carp startled by a noise make a sudden, sharp bend of the body as they
accelerate away. Their curvature changes much faster in this movement than
in steady swimming. If the red fibres powered it, they would have to shorten
at 20 lengths per second, which is far beyond their capability. In fact,
the carp making a quick getaway uses its white fibres, which do not have
to shorten so fast because they are arranged differently. The red fibres
run parallel to the backbone just under the skin, but the white fibres are
twisted like the strands of a rope so that a fibre near the side of the
body is connected in series with others that are close to the backbone.
This enables the white fibres to produce the same amount of bending as the
red ones but without shortening so much, and they need only shorten at a
rate of 5 lengths per second to power a fast start. Even this would be slightly
faster than a red fibre can manage, but the white fibres are faster than
the red ones with a maximum rate of contraction of 13 lengths per second.
In a fast start, they shorten at a rate of about 0.4 V_max per second, close
to the rate at which they will give most power. So the white fibres, too,
are well matched to their task. It seems likely that other muscles can contract
at speeds that match their tasks in the same way, but the only data I know
relate to the scallop, whose shells are often used as ashtrays. These molluscs
swim by clapping the two halves of their shells shut, and the muscle that
powers the movement seems to work at a maximum rate of 0.2 V_max.

Evolution seems to match muscles to their tasks, making adjustments
so that they work over appropriate ranges of sarcomere lengths and so that
they are required to shorten at appropriate rates. The match is achieved
by adjusting the lengths of the muscle fibres, their maximum rate of contraction
and the positions of their attachments on the skeleton. The dimensions and
properties of tendons also fine-tune the system.

Running mammals bend and re-extend the joints in their legs at every
footfall. The muscles of these joints have to stretch after the foot hits
the ground and shorten again before it is lifted, but the same job can be
done by tendons that stretch and then recoil elastically. The animals save
metabolic energy that would be needed to develop tension in the muscles
if they use tendons, acting passively, instead. As antelopes, deer, horses
and other specialised running mammals have evolved, they have ended up with
shorter muscle fibres but longer tendons in some of the muscles in the lower
part of their legs. Their tendons have become more slender in proportion
to the forces they have to transmit, so that they stretch more.

The most extreme adaptation is seen in the plantaris muscle of the camel:
this muscle runs from the back of the knee to the toes and measures 125
centimetres in an average, one-humped camel. This long ‘muscle’ has lost
its muscle fibres, apart from some useless rudiments about two millimetres
long. But a tendon as thick as a finger still runs from knee to toes. So
during the course of evolution the muscle has been replaced by a tendon
that serves as a passive spring. In this exceptional case, the best muscle
is no muscle at all.

R. McNeill Alexander FRS is professor of zoology in the University of
Leeds and author of Elastic Mechanisms in Animal Movement, Cambridge University
Press, 1988.