Integrative and Comparative Biology
Integrative and Comparative Biology, pp. 1–13
doi:10.1093/icb/icy023
Society for Integrative and Comparative Biology
SYMPOSIUM
Muscle Function from Organisms to Molecules
Kiisa C. Nishikawa,1,* Jenna A. Monroy† and Uzma Tahir*
*Center for Bioengineering Innovation and Department of Biological Sciences, Northern Arizona University, Flagstaff,
AZ 86011-4185, USA; †W. M. Keck Science Center, The Claremont Colleges, Claremont, CA 91711-5916, USA
From the symposium “Spatial Scale and Structural Heterogeneity in Skeletal Muscle Performance” presented at the
annual meeting of the Society for Integrative and Comparative Biology, January 3–7, 2018 at San Francisco, California.
1
E-mail: Kiisa.Nishikawa@nau.edu
Synopsis Gaps in our understanding of muscle contraction at the molecular level limit the ability to predict in vivo
muscle forces in humans and animals during natural movements. Because muscles function as motors, springs, brakes, or
struts, it is not surprising that uncertainties remain as to how sarcomeres produce these different behaviors. Current
theories fail to explain why a single extra stimulus, added shortly after the onset of a train of stimuli, doubles the rate of
force development. When stretch and doublet stimulation are combined in a work loop, muscle force doubles and work
increases by 50% per cycle, yet no theory explains why this occurs. Current theories also fail to predict persistent
increases in force after stretch and decreases in force after shortening. Early studies suggested that all of the instantaneous
elasticity of muscle resides in the cross-bridges. Subsequent cross-bridge models explained the increase in force during
active stretch, but required ad hoc assumptions that are now thought to be unreasonable. Recent estimates suggest that
cross-bridges account for only 12% of the energy stored by muscles during active stretch. The inability of cross-bridges
to account for the increase in force that persists after active stretching led to development of the sarcomere inhomogeneity theory. Nearly all predictions of this theory fail, yet the theory persists. In stretch-shortening cycles, muscles with
similar activation and contractile properties function as motors or brakes. A change in the phase of activation relative to
the phase of length changes can convert a muscle from a motor into a spring or brake. Based on these considerations, it
is apparent that the current paradigm of muscle mechanics is incomplete. Recent advances in our understanding of giant
muscle proteins, including twitchin and titin, allow us to expand our vision beyond cross-bridges to understand how
muscles contribute to the biomechanics and control of movement.
Introduction
Most biologists believe that muscle physiology is a
mature field in which the general principles, comprising the sliding-filament and swinging crossbridge theories, have been adequately described.
However, if we take our current ability to predict
in vivo muscle forces in humans and animals as a
measure of that understanding, then we are forced to
accept the fact that we still understand relatively little
about how muscles function during dynamic movements. Recent state-of-the-art attempts using Hill
models explain only about half of the variation in
muscle force during dynamic movements (Lee et al.
2013; Dick et al. 2017).
This review seeks to critically evaluate the assumptions on which the current paradigm of muscle mechanics is based, toward the goal of improving the
predictive value of muscle models beyond the current state of the art. Muscle models have important
applications, not only for biomechanics and organismal biology, but also for human health—particularly for the development of assistive devices to
ameliorate the often devastating physical and psychological effects of neuromuscular injury and disease. Therefore, it is imperative to critically evaluate
progress in muscle research and to search for better
models that not only increase the accuracy of predictions but also provide solutions for important
clinical problems.
By evaluating the assumptions on which current
models and theories are based, and by offering potential alternative hypotheses, we seek to stimulate
progress in understanding muscle function. At the
outset, it is important to acknowledge that muscle
ß The Author(s) 2018. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology.
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is complex both structurally and functionally, and
that its component parts must work together to produce complex responses to changes in activation and
length. The thesis we present here is that there is
currently a failure to appreciate the speculative and
ad hoc nature of long-held assumptions about crossbridge properties, many of which are unsupported
by experimental evidence (i.e., speculative) and historically were invoked to explain particular observations of muscle behavior rather than emerging from
an evidence-based biophysical understanding of
cross-bridge structure and function (i.e., ad hoc).
To the extent that acceptance of speculation as fact
prevents consideration of alternative hypotheses, examination of underlying assumptions is a useful exercise to stimulate progress.
This review begins by describing Hill models typically used in biomechanics research and evaluating
whether their assumptions about the force–length
and force–velocity properties of muscle affect their
ability to predict in vivo muscle force. Next, several
aspects of muscle force production are discussed
which have defied explanation by cross-bridge theories and thus have inspired speculative and ad hoc
assumptions about cross-bridge properties. These include doublet potentiation, force enhancement, and
force depression. Failure of current theories to account for these history-dependent properties is important because they play a significant role in control
of dynamic movements (Nishikawa et al. 2013).
Finally, the review ends with a discussion of how,
in addition to cross-bridges, the giant titin protein
may help to explain the activation-, length-, and history dependence of muscle force production; and the
types of evidence that would be needed to definitively distinguish among alternative hypotheses to
explain these muscle properties.
Hill models
In contrast to cross-bridge models (Zahalak 2000)
that typically specify transition rates among a variable number of cross-bridge states, phenomenological Hill-type muscle models, popularized by Zajac
(1989), predict muscle force based on the activation,
force–length, and force–velocity properties of a contractile element, typically in series and/or in parallel
with purely elastic elements. Although there are
many variants (Thelen 2003; McGowan et al. 2013;
Millard et al. 2013), the common theme is that muscle force is proportional to activation act(t), the
muscle force–length relationship F(l) normalized to
a maximum value of 1.0, and the force–velocity relationship F(v) also normalized to the maximum
K. C. Nishikawa et al.
isometric force Fmax of the muscle (Zajac 1989).
An important limitation of these models is that
both F–L and F–V relationships can only decrease
muscle force for a given level of activation. Hill
models with this basic structure are widely used in
human and animal biomechanics, often because it is
difficult or impossible to measure the model parameters directly—in which case, model validation is
elusive if not impossible.
Several recent studies have attempted to predict
in vivo muscle forces in humans and animals during
dynamic movements. In these studies, the forces produced by individual muscles were estimated in vivo
using tendon buckles in animals (Lee et al. 2013) or
ultrasonography in humans (Dick et al. 2017).
Muscle fascicle length was measured using sonomicrometry or ultrasonography, along with electromyography (EMG) as a measure of muscle activation. Yet,
even the most comprehensive Hill models, which
take into account the different force–velocity properties of fast and slow fibers, performed surprisingly
poorly at predicting in vivo muscle forces. In a study
of the medial and lateral gastrocnemius muscles of
goats during walking and running, Lee et al. (2013)
found that Hill models explained only 26–51% of the
variation in muscle force, with lower r-squared values for faster gaits. A similar study investigated
in vivo forces of the gastrocnemius muscles in
humans during cycling over a range of cadences
and loads (Dick et al. 2017). In this study, the average r-squared value over all conditions was 0.54, but
up to 0.80 at low speed and high muscle activation.
Taken together, these studies demonstrate that the
models capture only about half of the within- and
between-cycle variation in muscle forces during natural movements.
There are likely many reasons for the relatively
poor performance of Hill models in predicting
in vivo muscle force. Sensor noise cannot be excluded
and may help to explain why Hill models have higher
accuracy in predicting muscle forces in situ than
in vivo (Dick et al. 2017). However, there are also
some theoretical reasons why Hill models might not
be expected to yield accurate predictions of muscle
force, including problems associated with applying
force–length (F–L) and force–velocity (F–V) relationships, derived under isometric and isotonic or isovelocity conditions, respectively, to dynamic movements
in which these conditions do not occur.
Force–length relationship
With a characteristic plateau in force at intermediate
sarcomere lengths and decreasing forces at both
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Muscle function from organisms to molecules
shorter (ascending limb) and longer (descending
limb) lengths, the F–L relationship of skeletal muscle
is well established and highly consistent across different muscles and preparations (Rockenfeller and
Gunther 2017). The standard procedure for producing a length–tension curve, whether in intact
muscles, fiber bundles, single muscle fibers, or even
single myofibrils or sarcomeres (Rockenfeller and
Gunther 2017), is to move the passive preparation
to a desired length, then stimulate with supramaximal voltage and frequency or high [Ca2þ] to produce maximum isometric force, and finally to allow
relaxation before the procedure is repeated at a different length (Hakim et al. 2013). Therefore, the F–L
relationship is a static, not a dynamic, property of
muscle.
It is important to understand the historical context of the early experiments that sought to determine the F–L relationship (Gordon et al. 1966). At
the time, the goal was specifically to test the prediction of the sliding filament theory that the steadystate isometric force of a muscle fiber is proportional
to the overlap between thick and thin filaments. In
spite of the relatively imprecise methods used at the
time for measuring sarcomere length and force
(Gordon et al. 1966), the measurements on skeletal
muscle sarcomeres corresponded well with predictions from sarcomere geometry (Herzog et al.
2010). Specifically, the results showed that force
was proportional to filament overlap predicted based
on the lengths of the thick and thin filaments, and
that the width of the plateau in force corresponded
to the length of the bare zone of thick filaments
between adjacent half-sarcomeres where no crossbridges are found (Huxley 1963). It remains a mystery why cardiac sarcomeres, whose geometry is similar to that of skeletal muscles, fail to exhibit a
similar F–L relationship (Allen and Kentish 1985).
The F–L relationship applies strictly only to isometric contractions at maximal activation, although
a similar relationship also holds for isotonic contractions (Gordon et al. 1966). It does not represent
muscle force during dynamic length changes, nor
was it intended to do so. When muscle length
changes during activation, muscle forces depend
not only on sarcomere length but also on contractile
history (Herzog et al. 2010). When shortening actively, forces are lower than predicted by the isometric F–L relationship, and forces are higher than
predicted during active lengthening. At a given sarcomere length, muscle forces can take on a wide
range of values during dynamic length changes,
from 0 to nearly twice the isometric value, depending on the contractile history. By applying the F–L
relationship to dynamic contractions, Hill muscle
models will consistently overestimate force during
shortening and underestimate force during
lengthening.
In addition, the F–L relationship applies strictly
only to maximum activation which seldom or never
occurs during in vivo dynamic movements. The F–L
relationship shifts leftward as activation increases
(Rack and Westbury 1969; Rassier et al. 1999). The
cause of this leftward shift is unknown. It has been
suggested that the shift might be due to the lengthdependence of calcium activation (Rassier et al.
1999). However, a recent study suggested that force,
rather than calcium concentration, may instead be
responsible (Holt and Azizi 2014). The authors further stated that “the effect of absolute force is due to
the varying effect of the internal mechanics of the
muscle at different activation levels,” but what might
constitute these internal mechanics remains unclear.
Despite the submaximal activation of muscles during
voluntary contractions, models seldom account for
this activation-dependent shift in the F–L relationship, which is not predicted on the basis of the sliding filament or cross-bridge theories.
Force–velocity relationship
Hill’s (1938) original purpose in using isotonic afterloaded contractions to investigate the F–V relationship of muscle was to elucidate properties of the
muscle motor under conditions in which contributions of series elastic elements could be excluded.
Using Hill’s method, a force–velocity curve is constructed by activating a muscle until it reaches a predetermined (“after”) load. When a given load is
reached, the muscle shortens in the absence of contributions from series elastic elements, which due to
constant force must remain at a constant length
(Caiozzo 2002). To construct a F–V curve, the load
is varied systematically, and the initial relatively linear contraction velocity at that load is plotted against
the load for which it was measured (Fig. 1). The
method itself makes it obvious that the F–V relationship fails to describe the dynamic time-varying behavior of shortening muscles even when the load is
constant (Fig. 1). Sandercock and Heckman (1997b)
demonstrated that a similar F–V curve can be
obtained from isovelocity experiments in maximally
activated muscles by taking the average force and
velocity of shortening near the muscle optimal
length, although the methods give slightly different
results in submaximally activated muscles (Holt et al.
2014b).
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K. C. Nishikawa et al.
Fig. 1 After-loaded isotonic paradigm for generating the muscle force–velocity relationship. A muscle is stimulated and contracts
isometrically until it reaches a predetermined force (A) at which it shortens (B). Note that the duration of stimulation prior to the
onset of shortening increases with the after-load. Force (A) and change in length (B) records for six after-loaded contractions are
shown. Numbers refer to corresponding length and force traces from which points on the force–velocity curve (C) were derived.
Adapted from Caiozzo (2002).
An important question is whether the F–V relationship measured under isotonic (Hill 1938) or
isovelocity (Sandercock and Heckman 1997b) conditions applies during in vivo locomotion when neither
the load nor the velocity of length changes is constant; several observations suggest not. The first
observation comes from predictions of the Hill models themselves (Lee et al. 2013; Dick et al. 2017).
Although Lee et al. (2013) and Dick et al. (2017)
claim that their two-element Hill model captures
general features of the estimated in vivo force, both
studies show the same deviation of the models from
the in vivo force estimates. In both studies, there is a
valley in the force prediction when the in vivo force
reaches its maximum value in each movement cycle,
suggesting that in vivo force is systematically underestimated. The rates of force development and relaxation are also not well characterized by the
model.
Similar results were obtained in efforts to predict
the force of ex vivo muscles during cyclical contractions (James et al. 1996; Askew and Marsh 1998).
Both studies found that forces predicted on the basis
of F–L and F–V relationships were lower than observed forces at higher cycle frequencies. Lastly, data
from the human vastus lateralis muscles during exercises that involve stretch-shortening cycles (SSCs)
also suggest that in vivo forces are larger at a given
velocity than predicted by F–V relationships
derived from isotonic or isovelocity contractions
(Finni et al. 2003). A possible explanation for the
discrepancy between the models and data is that
during SSCs, elastic energy stored during lengthening
can be recovered as kinetic energy to increase shortening speed at a given force, in contrast to isotonic
and isovelocity contractions in which there can be
no recovery of stored energy. Based on these considerations, it is clear that use of muscle models based
on static F–L and F–V properties to predict muscle
force production under dynamic conditions has serious limitations.
History-dependence of muscle force
In addition to fundamental problems with Hill models discussed above, it is also well known that they
fail to predict the length- and history-dependence of
muscle force (Herzog 1998; Perreault et al. 2003;
McGowan et al. 2010, 2013), including both enhancement of force with stretch and depression of
force with shortening. In the absence of biological
mechanisms to account for these intrinsic muscle
properties, phenomenological models have been developed to improve the accuracy of force predictions
(Forcinito et al. 1998; Cheng et al. 2000; Lin and
Crago 2002). However phenomenological models
are no substitute for a deeper understanding, not
only because they are unlikely to account for
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Muscle function from organisms to molecules
observations beyond the cases they were developed
to explain.
The length and history-dependent properties of
muscle play an important role in control of movement (Nishikawa et al. 2007, 2013). In elegant
experiments, Daley et al. (2009) demonstrated that
when naive guinea fowl step into an unexpected hole
covered by tissue paper, the force of their muscles
(estimated from tendon force buckles) changes tens
of milliseconds before any change in muscle activation is observed. These and other observations
(Daley and Biewener 2011) suggest that parameters
in addition to activation, F–L and F–V relationships
play an important role in force production during
dynamic movements.
In classic experiments, Nichols and Houk (1976)
demonstrated that not only central nervous reflexes
but also muscle intrinsic properties (“preflexes”)
provide stabilization to perturbations. During perturbations, force and length feedback from muscle
spindles and tendon organs are used to adjust muscle recruitment to match the altered load (Matthews
1959; Slager et al. 1998). Using surgery to eliminate
feedback control from the spinal cord, Nichols and
Houk (1976) demonstrated that load compensation
is due not only to sensory feedback, but also to intrinsic muscle properties. Experiments using
constant-velocity stretch and shortening illustrate
the intrinsic adaptive properties, or “preflexes,”
exhibited by active muscle (Sandercock and
Heckman 1997b). When a muscle is stretched by
an applied load, internal muscle stress increases to
resist overstretch. Likewise, during unloading,
muscles become more compliant.
Muscle force adjusts instantaneously in response
to changes in load without requiring input from
the nervous system (Monroy et al. 2007; Nishikawa
et al. 2007). These adjustments are thought to increase stability during the delay in onset of feedback
control, and at the limits of muscle recruitment
when muscle force is near its minimum or maximum and feedback is ineffective at modulating force
output (Nichols and Houk 1976). These and other
studies (Rack and Westbury 1974; Richardson et al.
2005) show that muscles behave like non-linear, selfstabilizing “springs” that adapt to perturbations long
before reflex loops can exert feedback control. Here,
we use the term “spring” to refer to any structure
that stores elastic potential energy. These considerations imply that an understanding of motor control
depends critically upon history-dependent properties
of muscle.
The function of muscles as motors has been studied extensively at levels ranging from single
molecules (Finer et al. 1995; Howard 1997) to single
sarcomeres (Leonard et al. 2010), myofibrils
(Leonard and Herzog 2010), muscle fibers (Gordon
et al. 1966; Huxley and Simmons 1971), and intact
muscles (Abbott and Aubert 1952). The sliding filament theory (Huxley and Niedergerke 1954; Huxley
and Hanson 1954) and later the cross-bridge theory
(Huxley 1957) together account for the F–L (Gordon
et al. 1966) and F–V (Hill 1938; Huxley 1957) properties of muscle. However, a critical evaluation of
cross-bridge theories demonstrates that the historydependent properties of muscle continue to elude
explanation.
A major problem is that, due to the small size and
large number of cross-bridges in muscle sarcomeres,
it is difficult or impossible to measure their properties directly. While the goal of muscle research
should be to predict the macroscopic behavior of
muscle from known cross-bridge properties, these
properties are instead deduced from the macroscopic
behavior of muscle that they seek to explain
(Marcucci and Yanagida 2012). Inductive models of
muscle contraction are not currently feasible; ad hoc
and mostly untestable assumptions about crossbridge properties are required to achieve “predictive”
models (see below for numerous examples). This fact
demonstrates the likelihood that the theory of muscle contraction is far from complete.
In the following paragraphs, several muscle properties that have proved difficult to explain based on
the sliding-filament, swinging cross-bridge theory are
discussed, including doublet potentiation, force enhancement, and force depression. Testable alternative
hypotheses based on a role for the giant titin protein
are also considered. In the intervening years between
the advent of the sliding filament and cross-bridge
theories, numerous ad hoc assumptions about crossbridge function—unsupported by experimental
evidence—became entrenched as dogma. Several
examples are discussed below. By the time, decades
later, that the giant titin protein was discovered
(Maruyama 1976), there was little room left for titin
in active muscle contraction. The giant size of titin,
1000 times larger than average-sized proteins, also
hindered progress on understanding its role in muscle function (Lindstedt and Nishikawa 2017;
Nishikawa et al. forthcoming 2018).
Doublet potentiation
When a single stimulus is added to a train of low
frequency stimuli (Fig. 2), the added stimulus (doublet) dramatically and persistently potentiates isometric force (Sandercock and Heckman 1997a).
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K. C. Nishikawa et al.
Fig. 2 Doublet potentiation in mouse soleus muscle at optimal
length. The black solid line shows unfused muscle stress at 10 Hz
stimulation with no doublet added. The gray dashed line shows
potentiated stress when a single stimulus is added 10 ms after the
first stimulus.
Burke et al. (1970, 1976) referred to this property as
“catch-like” due to its resemblance to the property,
observed in invertebrate muscles, that tension is
maintained for long periods after brief excitation
with very little energy expenditure (Hoyle 1983).
When doublet potentiation is combined with active
stretch and shortening in a work loop experiment
(Stevens 1996), muscle force doubles and work
increases by 50% per cycle, yet no theory explains
why this occurs (Fig. 3).
Despite significant attention, the underlying
mechanism(s) that produce doublet potentiation remain unexplained. Two primary mechanisms have
been proposed: increased sarcoplasmic [Ca2þ] and
increased stiffness of elastic elements (BinderMacleod and Kesar 2005). Abbate et al. (2002) demonstrated that an added stimulus transiently
increases [Ca2þ] in mammalian muscle, but the increase in force persists for a much longer time than
the transient increase in [Ca2þ]. The persistence of
force at low [Ca2þ] is not predicted by cross-bridge
theories and is also a property of invertebrate catch
(Butler and Siegman 2010). An alternative mechanism, in which [Ca2þ] persistently increases the stiffness of an elastic element such as titin in muscle
sarcomeres (Binder-Macleod and Kesar 2005), is
consistent with observations that doublet potentiation is greatest at short muscle lengths, that shortening during stimulation decreases potentiation
whereas stretch during stimulation increases potentiation (Sandercock and Heckman 1997a).
Long after the development of the sliding filament
and cross-bridge theories, giant elastic proteins were
discovered in animal muscles from Caenorhabditis to
vertebrates (Dos Remedios and Gilmour 2017;
Lindstedt and Nishikawa 2017). It is now apparent
that these giant proteins play important roles, not
Fig. 3 A single stimulus added during a stretch-shortening cycle
doubles muscle force and increases work per cycle by 50%.
Force output of mouse soleus muscle stimulated at 30 Hz (black)
and with a doublet added 10 ms after the first stimulus (gray).
only in invertebrate catch (Yamada et al. 2001) but
also in the Frank–Starling law of the heart (Ait-Mou
et al. 2016)—the association between the volume of
blood entering the ventricles and the force of ventricular contraction. A role for the giant titin protein
in muscle passive force is also now well established
(Prado et al. 2005).
For titin to contribute to force in doublet potentiation, its force and stiffness should increase with
calcium influx and remain high when [Ca2þ]
decreases between stimuli. Several observations support the idea that titin could perform these functions. The static stiffness of muscle fibers increases
during the early stages of muscle activation (Bagni
et al. 2002, 2004) and recent studies demonstrate a
role for titin (Nocella et al. 2014; Rassier et al. 2015;
Cornachione et al. 2016). Furthermore, Leonard and
Herzog (2010) demonstrated that titin stiffness
increases in active muscle. When single myofibrils
are activated by Ca2þ and stretched to a length beyond overlap of the thick and thin filaments (so that
cross-bridges per se cannot contribute directly to active force), the force increases more rapidly with
stretch than it does in passive myofibrils. When an
activated muscle is stretched and then allowed to relax without shortening back to its original length, its
titin-based passive tension (Joumaa et al. 2008)
remains elevated for up to 3 min after cessation of
stimulation (Herzog et al. 2003) perhaps because low
levels of Ca2þ remain in the sarcoplasm long after a
stimulus (Westerblad and Allen 1994). Recent studies
further demonstrate that proteolytic digestion of titin
significantly reduces isometric force (Li et al. 2018),
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Muscle function from organisms to molecules
Fig. 4 Force (above) and length (below) of mouse soleus muscle
during isovelocity stretch and shortening. The force increases
during active stretch, and decreases when stretching stops,
reaching a steady state force that is greater than the isometric
force at the stretched length. The force decreases during active
shortening and redevelops after shortening stops, reaching as
steady-state force that is lower than the isometric force at the
shorter length. Shades of gray indicate corresponding force and
length traces.
suggesting that titin force and stiffness increase upon
muscle activation.
Force enhancement with stretch
When a muscle is stretched while active, its force
first increases rapidly and then falls after stretching
stops, eventually settling to a steady-state force after
stretch that is greater than the isometric force at the
stretched length (Fig. 3). Early studies understandably assumed that all of the instantaneous elasticity
of muscle must reside in the cross-bridges (Huxley
and Simmons 1971). Cross-bridge models were developed later that explained the increase in force
during active stretch, but these required ad hoc
assumptions about both the number of attached
cross-bridges (77%; Lombardi and Piazzesi 1990)
and the reattachment rates of forcibly attached
cross-bridges (200 times higher than for crossbridges that complete a cycle without forcible detachment; Lombardi and Piazzesi 1990). These
assumptions are now thought to be unreasonable
(Linari et al. 2003), but were justified at the time
based on x-ray diffraction and other evidence
(Lombardi and Piazzesi 1990; Piazzesi and
Lombardi 1995). Recent estimates based on fewer
ad hoc assumptions and a much smaller number of
attached cross-bridges (20%) suggest that crossbridges account for only 12% of the energy stored
by muscles during active stretch (Linari et al. 2003).
It was apparent much earlier (Harry et al. 1990)
that cross-bridges were unable to account for the
history-dependent increase in force that persists after
active stretching, commonly referred to as “residual
force enhancement” (Edman et al. 1982), leading to
development of the sarcomere inhomogeneity theory
(Morgan 1990, 1994). The basic idea is that sarcomeres in series vary in their relative strength, that
lengthening of muscle on the descending limb of the
F–L relationship takes place by rapid, uncontrolled
lengthening of the weakest sarcomeres or half sarcomeres, with little or no lengthening of the strongest
sarcomeres which, due to their shorter length, account for the increased force. Nearly every prediction
of this theory fails (Herzog 2014a, 2014b; Hessel
et al. 2017), yet the theory persists.
Several studies have suggested that elastic elements
in muscle sarcomeres play a role in residual force
enhancement (Edman et al. 1982; Herzog and
Leonard 2002; Lindstedt et al. 2002; Rode et al.
2009; Leonard and Herzog 2010; Nishikawa et al.
2012; Powers et al. 2014, 2016; Schappacher-Tilp
et al. 2015). These observations led to the hypothesis
that titin may bind to actin when Ca2þ is present,
decreasing titin’s free length and increasing its stiffness (Lindstedt et al. 2002; Rode et al. 2009; Leonard
and Herzog 2010; Nishikawa et al. 2012; Powers
et al. 2014, 2016; Schappacher-Tilp et al. 2015).
Models that incorporate calcium-dependent titin-actin binding perform well at predicting residual force
enhancement (Rode et al. 2009; Nishikawa et al.
2012; Schappacher-Tilp et al. 2015), and are no
more speculative than cross-bridge models that rely
on untested assumptions to account for the same
phenomena.
Force depression with shortening
When a muscle is shortened while active, its force
first decreases rapidly and then redevelops, eventually settling to a steady-state force that is lower than
the isometric force at the same length (Fig. 3). The
amount of force depression increases with the amplitude of shortening, and decreases with the speed
of shortening so that force depression is proportional
to the work done during shortening (Edman 1975;
Marechal and Plaghki 1979). Early hypotheses
(Edman 1975; Marechal and Plaghki 1979) included
the ideas that cross-bridges are inhibited in direct
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proportion to the work done during shortening, perhaps because cross-bridges that bind to actin in the
new overlap region between myosin and actin that
forms during shortening produce less force than
those that form in regions of actin that were already
in the overlap zone.
Since 1979, many studies have added to our understanding of force depression. The hypothesis that
force depression is caused by non-uniform shortening of sarcomeres (Edman et al. 1993) was rejected
on the basis that force depression was observed even
in length-clamped segments of muscle fibers in
which shortening was compensated by a servo motor
(Granzier and Pollack 1989). The hypothesis that the
buildup of metabolic by-products, such as protons
or phosphate ions, was rejected due to the relatively
short duration of force depression (Herzog 1998)
compared with the rate at which these by-products
are metabolized. The observation in skinned muscle
fibers, that the force after shortening from sarcomere
lengths of 2.8–3.0 mm to 2.4 mm was lower than the
force before shortening, suggested that not only
cross-bridges in the newly formed overlap zone,
but also in the old overlap zone are affected
(Joumaa et al. 2012). Because fiber stiffness and
the rate of ATP hydrolysis (Joumaa et al. 2017)
were reduced after shortening, it was suggested that
the number of cross-bridges that attach to actin is
reduced during active shortening due to deformation
of the thin filaments. However, the assumption that
the number of attached cross-bridges can be inferred
from muscle fiber stiffness (Ford et al. 1981) was
later questioned (Howard 1997; Huxley 1998) by
the demonstration that most of the muscle stiffness
is due to compliance of the thick (Dobbie et al.
1998) and thin filaments (Wakabayashi et al. 1994).
Despite the success of Marechal and Plaghki’s
(1979) model of force depression at explaining
many observations (Rassier and Herzog 2004), one
consistent observation remains unexplained. Force
depression is inversely proportional to shortening
velocity, and is eliminated altogether at the fastest
shortening velocities (Marechal and Plaghki 1979).
Yet, it seems likely that deformation of thin filaments hypothesized to occur during shortening
would depend on shortening amplitude rather than
velocity. We note here that a recent X-ray diffraction
study suggests that thin filament strain actually
increases during shortening, rather than decreasing
as might have been expected based on cross-bridge
models (Joumaa et al. 2018).
An alternative hypothesis is that force depression
occurs because strain in titin that develops upon
activation (Nishikawa et al. 2012) is reduced by
K. C. Nishikawa et al.
muscle shortening. Force depression is predicted by
models in which an increase in titin stiffness upon
activation results from calcium-dependent interactions with actin (Nishikawa et al. 2012;
Schappacher-Tilp et al. 2015). This hypothesis is
also supported by the observation that a stretch before shortening reduces or eliminates force depression (Fortuna et al. 2017).
Work-loops and SSCs
The “work loop” technique was introduced by
Josephson (1985) in part to provide an experimental
system for studying muscle function that more
closely emulates in vivo dynamic conditions than
the isometric, isotonic, and isovelocity tests that are
typically used to investigate mechanisms of muscle
contraction in ex vivo experiments. It is striking that
force production by muscles is much more complex
in work loops, which are difficult or impossible to
perform in reduced preparations including skinned
fibers or fiber bundles and single myofibrils or sarcomeres due to the requirement for calcium activation rather than electrical stimulation. Some
examples are described below.
Muscles are complex machines that function not
only like motors, but also like brakes, struts, and
springs (Dickinson et al. 2000). One of the main
determinants of muscle function is the timing of stimulation relative to cyclical length changes (Ahn et al.
2003; Sponberg and Daniel 2012). When stimulated at
the onset of shortening (25% phase), toad muscles
function like motors, performing positive net work
(Ahn et al. 2003). When stimulated at the onset of
lengthening (75% phase), they function like brakes,
performing negative work and absorbing energy
(Hessel and Nishikawa 2017). When stimulated at intermediate phases, muscles function more like springs
or struts, performing relatively little net work (Ahn
et al. 2003). The results imply that the length at which
muscles are activated plays an important role in force
production. It is unclear how cross-bridges could contribute to the phase dependence of work, as their
force should depend on the amplitude of activation
and the F–L and F–V relationships, but not the phase
of length changes per se. Although length-dependent
activation and/or length-dependence of Ca2þ-sensitivity could modulate cross-bridge forces produced in
response to muscle activation at different lengths, it
has recently been suggested that titin plays a role in
these phenomena as well (Irving et al. 2011; Mateja
et al. 2013; Ait-Mou et al. 2016).
An explanation for why muscle work and force
differ among muscles even under the same
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9
Muscle function from organisms to molecules
conditions of length and activation remains elusive
(James et al. 1995). In cockroaches, one of a pair of
leg extensor muscles functions like a motor and the
other like a brake, even though these muscles experience similar length changes, are innervated by the
same nerve, have the same activation pattern, and
their twitch and force–velocity properties are similar
(Ahn and Full 2002).
On the grounds that muscle shortening is energetically expensive, it was long assumed that tendons
provide energy savings in SSCs despite the lack of
supporting evidence (Roberts et al. 1997). Yet, a recent study that measured heat production by
muscle–tendon units in SSCs compared with isometric contractions (Holt et al. 2014a) found no difference in heat production. These results imply that the
muscle itself is responsible for energy savings during
SSCs, perhaps because energy stored in the muscle
during stretch can be returned during shortening,
reducing the energy cost compared with shortening
alone (Schaeffer and Lindstedt 2013). Taken together, these examples strongly suggest that factors
other than cross-bridges must play an important role
in controlling muscle force production during SSCs.
A role for titin in active muscle
contraction
A variety of mechanism for titin’s role in active muscle contraction have become widely accepted (Linke
2018), including maintenance of the axial alignment
of thick filaments (Horowits et al. 1986) and rearrangement of thick and thin filaments associated
with length dependent regulation of cardiac muscle
(Ait-Mou et al. 2016). Yet, these functions require a
much greater titin stiffness than has been measured
in passive muscle. In fact, a recent study demonstrates that titin transmits most or all of the force
in active muscle (Li et al. 2018). Li et al. (2018)
created a transgenic mouse in which a specific proteolytic cleavage site from tobacco etch virus was
inserted into the distal I-band region of the titin
protein near the edge of the A-band. When titin
was cleaved in fiber bundles from heterozygous
transgenic mice, both the passive and active force
was decreased by 50%.
At present, it is unclear how titin stiffness can be
high enough in active muscle to account for these
high forces, although these new results are consistent
with hypotheses that titin binds to actin in active
muscle (Leonard and Herzog 2010; Nishikawa et al.
2012; Powers et al. 2014), or winds on actin due to
rotation of thin filaments (Nishikawa et al. 2012).
There is also some evidence that titin interacts
with actin at low [Ca2þ]. Kellermayer and Granzier
(1996) showed that titin fragments (T2) inhibit motility of actin and reconstituted thin filaments in an
in vitro motility assay, and the inhibition depends on
[Ca2þ]. A large decrease in actin motility occurred at
[Ca2þ] 30 times lower than the [Ca2þ] at which
cross-bridges are maximally activated (Kellermayer
and Granzier 1996).
Although these ideas are currently viewed as speculative (Linke 2018), speculation may be more useful
in achieving progress in the field than adherence to
ad hoc assumptions regarding cross-bridge properties
that have become widely held as facts in the absence
of any supporting evidence. The popularity of crossbridge explanations seems largely to be a historical
accident, and if titin had been discovered earlier
there would doubtless have been considerable speculation that it functions as a spring in active muscle
and might contribute to the length- and activationdependent muscle properties that cross-bridges alone
cannot explain without ad hoc assumptions.
In contrast to cross-bridges which are very small
(5.5 nm), titin is a giant molecule. Unlike many
speculations about cross-bridge properties, speculations about titin’s role in active muscle are testable
hypotheses that can be rejected using difficult but
feasible techniques. Dynamic force spectroscopy
(Bianco et al. 2007), cosedimentation (Linke et al.
2002), and in vitro motility assays (Kellermayer and
Granzier 1996) can be used to measure rupture
forces and binding constants of titin–actin interactions. Granzier (2010) suggested that, while difficult
technically, stretching active and passive myofibrils
labeled with fluorescent titin antibodies could potentially be used to test the hypothesis that interactions
with actin reduce or prevent the elongation of titin
upon activation, compared with purely passive
stretch. In fact, DuVall et al. (2017) recently demonstrated, using an F146 antibody that binds to titin
near the A-band, that elongation of titin segments
changes upon activation in a manner consistent with
a calcium-dependent, but not an actin-dependent
increase, in titin stiffness.
Recent studies have emphasized the absence of
evidence supporting titin–actin interactions in active
muscle (Linke 2018). However, absence of evidence
is not evidence of absence. The main problem with
titin-based hypotheses is not their testability per se,
but rather the extremely large size of the titin molecule. To definitively rule out a role for titin–actin
interactions in eccentric muscle contraction will require investigations of the N2A–PEVK border region, overlooked in previous studies, as well as
experiments using additional antibodies that bind
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10
to titin in the I-band. Until the critical tests have
been performed and the results evaluated, the inquiry into titin’s role in active muscle contraction
should be encouraged.
Recent research on molluscan muscle shows that the
mechanism of catch involves tethering of thick and
thin filaments by twitchin, an invertebrate mini-titin
(Funabara et al. 2007; Butler and Siegman 2010). In
molluscan catch, Ca2þ-influx triggers dephosphorylation of twitchin and binding of twitchin to actin. The
twitchin link responsible for molluscan catch adjusts
its stiffness during shortening to maintain catch force
at a shorter length (Butler and Siegman 2010).
Theoretically, what set of properties would titin
need in order to account for doublet potentiation,
force enhancement, force depression, and the other
length- and activation-dependent phenomena described above? To explain these properties would require a sarcomeric spring that (1) decreases its
length upon muscle activation (Monroy et al.
2017); (2) increases its stiffness with force development (Leonard and Herzog 2010); and (3) retains a
“memory” of the length at which it was activated.
While currently viewed as speculative, the winding
filament hypothesis was conceived to explain exactly
these phenomena (Nishikawa et al. 2012). It seems
likely that experiments to definitively test the predictions of the winding filament hypothesis will be
completed within the next decade(s).
Conclusion
The complexity of force production by muscles under dynamic conditions remains largely unexplained
by current models based on the sliding filament and
cross-bridge theories. It is clear that Hill models are
inadequate to predict in vivo, and even ex vivo muscle forces, under dynamic conditions when historydependent muscle properties contribute to muscle
force production. In this review, we have attempted
to identify factors that may have limited progress in
understanding muscle contraction and motor control
at molecular and organismal levels. The fields of biomechanics, movement science, and rehabilitation depend on the understanding of muscle properties
during dynamic movements. Forward progress
depends critically on recognizing the limitations of
current theories and exploring testable alternative
hypotheses, including a role for the giant titin protein in activated muscle.
Acknowledgments
We thank Anthony Hessel, Natalie Holt, and Stan
Lindstedt, for helpful comments on earlier versions
K. C. Nishikawa et al.
of this manuscript, and Stan Lindstedt for kind assistance with manuscript preparation.
Funding
This work was supported by the National Science
Foundation [IOS-0732949, IOS-1025806, IOS1456868, IIP-1237878, and IIP-1521231], the W.M.
Keck Foundation, and the Technology Research
Initiative Fund of Northern Arizona University.
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