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Department of Environmental Health, Harvard School of Public Health, Boston, Massachsetts 02115; and Department of Anesthesiology and Department of Physiology and Biophysics, Mayo Clinic, Rochester, Minnesota 55905
ABSTRACT
INTRODUCTION
A HYPOTHESIS FOR THE MOLECULAR BASIS OF FRICTION
METHODS
RESULTS AND DISCUSSION
ACKNOWLEDGEMENTS
FOOTNOTES
REFERENCES
ABSTRACT 
Fredberg, J. J., K. A. Jones, M. Nathan, S. Raboudi,
Y. S. Prakash, S. A. Shore, J. P. Butler, and G. C. Sieck. Friction in airway smooth muscle: mechanism, latch, and
implications in asthma. J. Appl.
Physiol. 81(6): 2703-2712, 1996.
In muscle,
active force and stiffness reflect numbers of actin-myosin interactions and shortening velocity reflects their turnover rates, but the molecular basis of mechanical friction is somewhat less clear. To
better characterize molecular mechanisms that govern mechanical friction, we measured the rate of mechanical energy dissipation and the
rate of actomyosin ATP utilization simultaneously in activated canine
airway smooth muscle subjected to small periodic stretches as occur in
breathing. The amplitude of the frictional stress is proportional to
E, where E is the tissue stiffness defined by the slope of the
resulting force vs. displacement loop and is the hysteresivity
defined by the fatness of that loop. From contractile stimulus onset,
the time course of frictional stress amplitude followed a biphasic
pattern that tracked that of the rate of actomyosin ATP consumption.
The time course of hysteresivity, however, followed a different
biphasic pattern that tracked that of shortening velocity. Taken
together with an analysis of mechanical energy storage and dissipation
in the cross-bridge cycle, these results indicate, first, that like
shortening velocity and the rate of actomyosin ATP utilization,
mechanical friction in airway smooth muscle is also governed by the
rate of cross-bridge cycling; second, that changes in cycling rate
associated with conversion of rapidly cycling cross bridges to slowly
cycling latch bridges can be assessed from changes of hysteresivity of
the force vs. displacement loop; and third, that steady-state force
maintenance (latch) is a low-friction contractile state. This last
finding may account for the unique inability of asthmatic patients to reverse spontaneous airways obstruction with a deep inspiration.
hysteresis; resistance; shortening velocity; cross bridge
INTRODUCTION IN MUSCLE, ACTIVE FORCE AND STIFFNESS reflect numbers
of actin-myosin interactions and shortening velocity reflects their turnover rates (18), but the molecular basis of mechanical friction is
a good deal less clear (25, 33, 41, 43, 45, 51). Before 1938, it was
accepted that there exists within biological tissues a classic viscous
behavior, in which the frictional stress depends on the shear rate
(implying a rate-dependent microscale viscous stress) with the
coefficient of proportionality being a tissue viscous
resistance (R); all other factors being equal, the greater the shear
rate, the greater would be the frictional stress. Hill (19) and Bayliss
and Robertson (3), however, demonstrated that friction in skeletal
muscle and in lung tissue does not fit the classic notion of a viscous
stress in any simple sense. This was not meant to imply
that the viscous description is wrong but only that such a viscosity
would have to exhibit characteristics that depart markedly from the
classic Newtonian viscosity and that are yet to be accounted for on the
grounds of mechanism.
More recently, these and other observations that conform only with
difficulty to the classic viscous concept were shown to conform rather
naturally to an empirical approach called structural damping, in which
the frictional stress is taken to depend on the magnitude of the
elastic stress with the coefficient of proportionality being the
hysteresivity ( Even though they differ in underlying concept, the viscous and the
structural damping approaches describe the same tissue frictional
stress. As such, the amplitude of the frictional stress (per unit
strain) can be given as either
); all other factors being equal, the greater the
elastic stress, the greater would be the friction (12, 14). The
overriding simplicity with which structural damping organizes diverse
observations, particularly in the cases of connective tissues and the
contractile responses of intact lung and lung parenchymal strips (11,
28-30, 34, 37), implies that it captures some essential attribute
of mechanism (12). The specific molecular process linking the
frictional stress to the elastic stress in active contractile systems,
however, has not been identified and is the focus of this article.
R by the classic viscous approach or
E by the structural damping approach, where is the radian
frequency at which airway smooth muscle is stretched, as in breathing;
E is the tissue stiffness (or elastic modulus) defined by the slope of
an incremental force (or stress) vs. displacement (or strain) loop; and
is a nondimensional index of the fatness (hysteresis) of that loop,
which is indicative of the presence of mechanical friction (12). Thus
This identity shows
that tissue frictional stress, which is classically represented as
being proportional to frequency and the viscous character of the
tissue,
(1)
R, can be thought of instead as a fraction, , of the
elastic stress (which is proportional to E). This decomposition of
friction into the product of and E is instructive for several
reasons (11, 12, 29), not the least of which is that E in muscle is
already known to be determined primarily by the number of attached
cross bridges (4, 5, 8, 20, 35, 50). The principal thesis of this
communication is that the hysteresivity of activated airway smooth
muscle has an equally simple molecular basis, namely, the rate at which
cross bridges cycle.
A HYPOTHESIS FOR THE MOLECULAR BASIS OF FRICTION
The sliding-filament model of Huxley is generally believed to govern the mechanics of both smooth and striated muscle (8, 20, 35). Huxley's original model holds that the cross bridge cycles between two states: a force-generating state in which the myosin head is attached to the actin filament and a non-force-generating state in which the myosin head is detached from actin. Although subsequent evidence revealed numerous intermediate states of myosin binding (5, 8, 21, 35), turnover between force-generating and non-force-generating groups of states can be treated by two apparent rate constants (4) (fapp and gapp), corresponding to the original attachment and detachment rate constants f and g described by Huxley (20). With the induction of contraction of smooth muscle, rapidly cycling cross bridges convert to slowly cycling latch bridges, and, as they do, fapp, gapp, and the rate of utilization of adenosine triphosphate (ATP) decrease progressively with time (8, 35, 50).
The relationship between mechanical friction, cross-bridge cycling
rate, and utilization of ATP is developed as follows. During externally
imposed periodic stretch (as occurs with breathing for airway smooth
muscle or with the cardiac cycle for vascular smooth muscle), the
myosin head attached to the thin filament is stretched from its
equilibrium position and, like a perfect spring (20, 21), stores strain
energy in the S2 myosin subfragment on a periodic basis (Fig.
1). During periodic stretch the cross bridge can detach spontaneously or, if the yield stress is exceeded, can rupture not unlike a stretched fiber of Velcro (12), and, in either
event, the myosin head recoils to its unstretched equilibrium position
in a thermodynamically irreversible deformation. Among an ensemble of
attached myosin heads there would be a distribution of strains at any
instant, and across that ensemble the average detachment event would
entail loss of a portion of the average energy store (u)
that had been invested to bind the myosin head to actin and stretch it
from its equilibrium position (41). If so, the total macroscopic
mechanical energy dissipation (
) per period of imposed strain would
be the product of the number of myosin heads attached
(N), the fraction of those attached
heads that detach per unit time
(gapp),
the period duration [T (=
2
/)], and the average energy loss per detachment event
(
) or
|
(2) |
)
of the total internal energy content (U) invested at peak tissue
strain. Thus = U. The total internal energy at peak tissue
strain is simply u times the number of bridges attached
|
(3) |
o is /u,
then
|
(4) |
of zero, which is known already to be the case (25,
33, 41, 43, 51); similarly, if cycling rates would decrease in time as
rapidly cycling cross bridges convert progressively to slowly cycling latch bridges, then would be predicted to decrease in concert. This
constitutes a testable prediction to which we address ourselves in
RESULTS and DISCUSSION. However,
it must be noted that this prediction (Eq. 4) is not as simple as it may seem because attachment events, multiple binding states, and strain dependence of state transition rates have been hidden in
o and
gapp.
Further elaboration of these factors is of substantial interest but
will not alter the essential points highlighted by this analysis.
L, change in
length.
The implications of cross-bridge detachment for metabolic energy dissipation, as distinct from mechanical energy dissipation, are reasoned as follows. If we consider for the moment that part of ATP utilization that can be attributed to cross-bridge cycling (26, 38), as a lower bound one molecule of ATP must be hydrolyzed for each detachment event (42), and the rate of actomyosin ATP utilization (mATPase) would be
|
(5) |
|
|
(6) |
This relationship holds that the rate of metabolic energy
dissipation (mATPase) and the material moduli characterizing mechanical friction (R or ) share the cross-bridge detachment event as their common molecular basis. It leads to the second testable prediction, namely, that respective time courses of
mATPase(t) and
R(t) should be coincident
(Eq. 6).
Finally, bearing on the hypothesized relationship (Eq. 4) between and cross-bridge cycling rates is a
third and independent line of reasoning. The maximal unloaded velocity
of shortening (Vmax)
is believed to be controlled principally by the rate of cross-bridge
cycling (20, 24). This logic leads to the further prediction that (t) should
display a time course that is highly correlated with that of
Vmax(t).
METHODS
L/Lo = 0.5%)] were imposed by using a servo-controlled lever arm
(model 305B, Cambridge Technologies). Force was measured
by an independent force transducer (model FT10, Grass). After
appropriate analog signal conditioning and calibration, and with
special attention to phase errors, raw force and length signals were
digitized, stored, and used to calculate the time courses of active
development of tissue force
[F(t)], elastance
[E(t)], hysteresivity
[(t)], and resistance
[R(t)] before, during,
and after EFS by using the following definitions.
The total force in the muscle (F) is the sum of the active force
(Fa), the elastic and the
frictional forces [i.e., F = Fa + EL + R(L/t),
where L is length and
L denotes variations about the
reference length
Lo].
The strain (
) is
L/Lo.
If is the energy dissipated per period of imposed cyclic strain
(i.e., area within the force-length loop), then according to Fredberg et al. (11), E =
(F/L)cos 
, R = (F/L)sin , and = tan , where = sin
1(4/FL).
With sinusoidal length changes at radian frequency , then F() = (E + jR)L() = E(1 + j)L() where j = 
1. The frictional (imaginary) part of
the stress is proportional to R or, equivalently, E.
Equivalently, is the peak-to-peak amplitude of the frictional force
normalized by the peak-to-peak amplitude of the elastic force.
Corresponding stresses are force per unit area.
Shortening velocity.
Small sinusoidal displacements about
Lo
(L/Lo = 0.5%) were imposed at 1.0 Hz by using the servo-controlled lever arm
(model 305B, Cambridge Technologies). Muscular contraction was elicited by supramaximal EFS. At set times after stimulus onset (2, 4, 8, 15, or
30 s, in random order), the load on the lever arm was abruptly
decreased, allowing the muscle to shorten isotonically against a small
afterload. The afterload varied somewhat because of internal friction
in the servo-lever system and its attachments to the muscle strip
(150-640 mg) but was typically <2% of the maximum force and
<6% of the force at the time of release, except for the 2-s time
point, where the force developed was quite small. In that case, the
afterload was higher (60-15%, except for dog 4 where the afterload represented 26% of developed
force). After shortening was completed, EFS was turned off and the
muscle was slowly stretched back to its initial length. Five-minute
intervals were allowed between stimulations. Immediately after the
release, the length trace sometimes exhibited a brief period of
underdamped oscillations attributable to the lever arm. After these
oscillations had decayed, shortening velocity was calculated as the
slope of the length-time trace over the ensuing interval, typically
from 100 to 400 ms after the release, although this was changed
slightly between dogs to avoid the preceding underdamped oscillations. These maneuvers were performed in duplicate.
Simultaneous measurement of muscle mechanics and the rate of ATP
usage.
Canine tracheae were obtained from mongrel dogs and immersed in chilled
aerated physiological salt solution [PSS; containing (in mM): 110.5 NaCl, 25.7 NaHCO3, 5.6 dextrose,
3.4 KCl, 1.2 KH2PO4, 0.8 MgSO4, and 4.4 CaCl2]. Fat, connective tissue,
and the epithelium were removed, and small strips (3-4 mm long,
0.1-0.2 mm wide, 0.1-0.2 mm thick, 200-300 µg
approximate wet wt) of tracheal smooth muscle were mounted in a 0.1-ml
quartz cuvette that was coupled to a photometric system that measures
optical and mechanical parameters of tissue simultaneously (17). The
tissues were continuously perfused (2.5 ml/min) with PSS (37°C)
aerated with 95% O2-5%
CO2 (pH 7.4). One end of the strip
was attached to a servo-controller stepper motor via stainless steel
microforceps; the other end was attached via stainless steel
microforceps to a calibrated force transducer (model AE801,
Aksjeselskapet Mikro Elektronikk). During a 2-h equilibration period,
the length of the strip was incrementally increased after repeated
isometric contractions with 1 µM acetylcholine until the active force
reached 4 mN, at length
Lref.
The strip was then chemically skinned, and
L was set at 0.5% of
Lref.
Skinning procedure.
Strips were perfused for 20 min with 10% Triton X-100 in relaxing
solution of the following composition (25°C): 2.5 mM
Na2ATP, 7.8 mM ethylene
glycol-bis(
-aminoethyl
ether)-N,N,N
,N-tetraacetic acid, 83 mM imidazole, 5 mM phosphoenol pyruvate (PEP) 5 mM,
0.2 mM NADH, 140 units/ml lactate dehydrogenase (LDH), 100 units/ml pyruvate kinase (PK), and 5 µM calmodulin (pH 7.1 at 25°C).
Tissues were perfused with relaxing solution (without Triton X-100) to remove the detergent.
NADH-linked fluorimetry.
The rate of total ATP usage (ATPase) was measured by quantifying the
rate of NADH consumption as previously described (17); the device was
obtained commercially (Scientific Instruments). When ATP is hydrolyzed,
ATP is regenerated from ADP and PEP by the enzyme PK. This reaction is
coupled to the oxidation of NADH to
NAD+ and the reduction of pyruvate
to lactate; these reactions are catalyzed by LDH. For each mole of ADP
produced, 1 mol of NADH (the fluorescent compound) is oxidized (i.e.,
consumed) to NAD+ (a
nonfluorescent compound). Thus the rate of decrease of NADH fluorescence intensity is proportional to the rate of ATP usage. The
perfusion cuvette was flushed for 7 s with fresh solution containing
the constituents necessary to couple ATP hydrolysis to NADH
consumption. Flushing of the cuvette with fresh solution caused an
abrupt increase in NADH fluorescence. The rate of decline in NADH
fluorescence between solution changes (over an 8-s period during which
perfusion was stopped) is proportional to the rate of ATP usage during
that time. NADH fluorescence was determined for known concentrations of
NADH before each experiment so that the amount of NADH consumed during
the 8-s period can be calculated and used to quantify the rate of ATP
usage (µM of ATP used/s). Values for the rate of ATP usage were
sampled at 0.067 Hz, whereas , E, and R, were obtained at 1 Hz. The
field of focus included most of the cuvette to provide an average
measurement of NADH usage by the tissue over each 8-s interval, thus
minimizing the influence of artifacts associated with NADH diffusion;
the calibration procedure was designed to minimize these quantitative
artifacts, and relative changes are expected to be even more reliable.
Although the percentage is very much lower in intact muscle, mATPase is
believed to account for as much as 85% of total ATPase activity in
Triton X-100 chemically skinned smooth muscle (1, 26,
38). In the canine preparation used here, we found that 1) thapsigargin, ouabain,
oligomycin, lanthanam, and omeprazole had no effect on the rate of ATP
usage in unstimulated or maximally activated
(105 M free
Ca2+) skinned tissues;
2) steady-state ATPase activity was
length sensitive; and 3) transient
ATPase activity during force development was load sensitive. This
evidence suggests, similarly, that the predominant signal in this
preparation was mATPase activity.
RESULTS AND DISCUSSION
in isolated canine
tracheal smooth muscle subjected to EFS in a muscle bath (37°C) with imposed sinusoidal length changes falling within the physiological range (f of 1 Hz, amplitude
L/Lo
of 0.5%). With the onset of EFS, changes of E and F were closely
associated, as would be expected because both depend directly on the
number of cross bridges attached (50). Changes of , by contrast,
were prominently dissociated from those of E and F (Fig.
2). Both E and F increased monotonically to
sustained plateaus, whereas (the measure of fatness of the incremental force-length loop) showed a biphasic pattern in which it
increased promptly, peaked early, and then decayed slowly, even as F
and E continued to increase. E and F rose to their plateau values over
similar time scales, ~1 min, whereas rose to a peak over a time
scale that was more than fivefold faster. During steady-state force
maintenance, plateaued at values below those observed during force
development and even below those observed in unstimulated tissue,
showing that steady-state force maintenance is a low-friction contractile state.
).
Mechanics of the fully relaxed state reflects noncontractile cytoskeletal elements (50) and extracellular matrix. If these passive elements are mechanically in parallel with the contractile element, then
of the composite would be determined by the stiffness-weighted of the contractile and passive elements. Because of their relative stiffnesses, of the activated muscle would be dominated by that of
the contractile element, whereas of the relaxed muscle would be
dominated by that of the passive elements.
When EFS ended, E and F fell toward baseline values, whereas first
increased transiently above baseline and thereafter fell toward
baseline (Fig. 2). The elevation of observed during the off-transient with EFS (Fig. 2) suggests that with deactivation, rather
than detaching directly from latch, a substantial portion of bridges in
the latch state might first convert to a rapidly cycling high- state
and only then detach. This is consistent with the observation that
Vmax
of airway smooth muscle increases during deactivation (23).
We found a similar pattern of dissociation in tracheal smooth muscle of
the cow, rat, and guinea pig. Moreover, these characteristic patterns
have been demonstrated in lung parenchymal tissue-level and organ-level
responses of the dog and guinea pig (11, 22, 29, 31). These
observations support the hypothesis (Eq. 4) and its corollary that
(t) would be expected to decrease
as rapidly cycling cross bridges (high ) gradually convert to slowly
cycling latch bridges (low ); E and F increase monotonically as
bridges recruit, and, therefore, the time courses of E and F would be expected to dissociate markedly from that of . To test the
hypothesis in greater depth, we compared the time courses of mechanical
and metabolic energy dissipation.
Friction and metabolism.
Although a substantial fraction of ATP utilization during steady-state
contraction is consumed by membrane-bound pumps activated by
stimulation, these pumps are obliterated in the Triton X-100 detergent-skinned preparation used here (1, 26, 38). Simultaneously with measurement of F, E, and , we used NADH-linked fluorimetry (17)
to measure the rate of ATP utilization in detergent-skinned tracheal
smooth muscle fiber bundles maximally activated by
105 M free
Ca2+. As with the case of EFS
(Fig. 2), in this preparation changes of E and F were again closely
associated with one another, whereas changes of were prominently
dissociated from those of E and F (Fig. 3).
During activation, the time courses of
ATPase(t) and R(t) were closely similar
(r2 = 0.86) and their respective peak values were approximately coincident in time (Fig. 4,
A and
B). After the peak, both variables
exhibited closely similar rates of gradual decline to sustained plateau levels that were above those of the unstimulated tissues. When free
Ca2+ concentration was decreased
back to 109 M, ATPase
activity exhibited a slight increment and thereafter returned toward
baseline.
.
D: frictional stress per unit strain,
which is R or, equivalently, E.
E: rate of ATP utilization (ATPase). , Radian frequency at which airway smooth muscle is stretched; [Ca2],
Ca2+ concentration.
E = 2.91 ATPase 1.69;
r2 = 0.86, P = 0.0007 (Fisher's
z transform).
The observations depicted in Figs. 3 and 4 establish the existence of the temporal relationship between R(t) and ATPase(t) predicted by Eq. 6. The relative amplitudes of the predicted responses cannot be assessed because the value of the molecular scaling variable
o is
not known, and, even in the skinned muscle fiber bundles, not all of
the ATP usage can be attributed to mATPase activity. While these
uncertainties await clarification, the coincidence of these respective
time courses during muscle activation represents a critical
confirmation of this prediction.
It should come as no surprise that there were differences evident in
the mechanics of the intact vs. the skinned preparation (Fig. 2 vs.
Fig. 3). In the intact preparation, the rates of F and E development
were higher and the off-transient elevation of was more marked.
These differences may be related to the substantial differences between
the preparations in temperature (37 vs. 25°C), stimuli, the rate at
which the stimuli could be applied and removed, and the ability in the
skinned preparation for parts of the contractile machinery and
regulatory apparatus to diffuse out of the cell.
Friction and shortening velocity.
At varied times, t, after the onset of
a sustained stimulus (EFS) of canine tracheal smooth muscle, we
measured (t) immediately before
and
Vmax(t)
immediately after a quick release to a small afterload.
Vmax
peaked at 4 s after the onset of EFS and declined thereafter, which is
consistent with previous reports and with the interpretation of the
progressive conversion of rapidly cycling cross bridges to slowly
cycling latch bridges. Importantly, the time course of also peaked
at 4 s and declined thereafter (Fig. 5).
Throughout the contraction, changes of
Vmax(t)
and (t) closely tracked one
another; linear regression of
Vmax(t)
against (t) in individual animals
during force development yielded
r2 values ranging
from 0.77 to 0.94 and, for data meaned across animals, an
r2
value of 0.98 (P < 0.0001). These
data establish the existence of the predicted relationship between
Vmax(t)
and (t) and suggest that
Vmax
and convey substantially equivalent information concerning rate
processes and their temporal modulation. That being the case, it is
noteworthy that as a mechanical index of turnover rates Vmax
is the gold standard but that, technically, is far easier to
measure.
on
right y-axis (solid circles) measured as
function of time after onset of EFS in canine trachealis.
Vmax
was measured over interval from 250 to 400 ms after quick release
to a small afterload, typically 1-2% of maximum isometric force.
Inset, regression line,
Vmax = 1.91 + 0.0;
r2 = 0.98, P = 0.0001 (Fisher's
z transform).
The unification of hysteresivity with shortening velocity, actomyosin ATP metabolism, and cross-bridge kinetics implies that the time course of
(t) must at every instant
track that of cycling rate. In that case, the frictional stress per
unit strain (E or R) in activated airway smooth muscle would be
roughly approximated by the product
gappN
or, equivalently, mATPase activity (Eq. 6). Therefore, the rate of actomyosin cycling (in
contrast to classic viscosity) seems to be a major determinant of the
frictional stress developed within airway smooth muscle. Taken
together, these multiple lines of evidence lead us to the conclusion
that, like shortening velocity and the rate of actomyosin ATP
utilization (2), the hysteresivity of airway smooth muscle is governed
by the rate of cross-bridge cycling.
Friction and airways obstruction in asthma.
Asthma is an inflammatory disease, but the chain of causality linking
airway inflammation with its ultimate mechanical consequence, airways
obstruction, is multifactorial and not well defined. One attractive
feature of the synthesis explored here (Eqs.
4 and 6) is that it
lends a novel explanation to an intriguing part of this process. In
particular, the response of the pulmonary airways to a deep inspiration
has been of scientific interest because it is known to distinguish
obstruction occurring spontaneously in asthma from obstruction induced
by inhalation of nonspecific bronchoconstrictors. This has been
discerned from the ratios of maximum expiratory flow rates measured
during complete vs. partial forced expiratory maneuvers.
A deep inspiration was shown to reverse airway obstruction that is
induced in asthmatic and healthy subjects, whereas a deep inspiration
fails to reverse obstruction that occurs spontaneously in asthmatic
subjects and, most often, exacerbates the degree of obstruction (10,
27, 32, 48). Neither the severity of the obstruction nor
the neural and humoral responses to deep inspirations are able to
account for these differences, leaving only postjunctional factors to
consider. In this connection, Skloot and colleagues (44) have shown
that they could evoke in healthy volunteers a degree of airway
hyperresponsiveness indistinguishable from that in asthmatic subjects
and did so, remarkably, merely by prohibiting deep inspirations. These
studies represent the most compelling evidence presented to date of the
long-held hypothesis that excessive airway narrowing in asthma may be
caused by an intrinsic impairment of the ability of lung inflation to
stretch airway smooth muscle (6, 10, 15, 36, 44). This hypothesis is
supported by the important studies of Tepper et al. (47) and Warner and
Gunst (49), who have shown that tidal lung inflations limit
bronchoconstriction. A major drawback of this hypothesis, however, has been that a specific mechanism that might account for such
an impairment remains unclear.
The conversion of airway smooth muscle to the latch state implies small
cycling rate, and we have shown here that small cycling rate, in turn,
implies small hysteresivity. We now go on to suggest that
the small hysteresivity associated with the latch state might account
in part for the inability of lung inflation to reverse spontaneous
airway obstruction in asthma. It has been established previously that
if the hysteresivity of the airway is small in comparison with that of
the lung tissue to which it is physically tethered, then, in response
to changes in lung volume, the airway will behave nearly elastically
and, as such, will change its caliber as demanded by its own elastic
pressure-area characteristic and change in the peribronchial stress by
which it is distended (13). It has been established, also, that the
peribronchial distending stress is reduced immediately after a deep
inspiration because of the presence of the very appreciable
hysteresivity of normal lung tissues; at the same volume, lung recoil
is far less on deflation than on inflation (12, 13). We note, finally,
that in spontaneous asthmatic obstruction, the greater the degree of
spontaneous obstruction the greater is the transient exacerbation of
obstruction with a deep inspiration (27). [The constrictor
response to a deep inspiration implies that the yield force of the
muscle could not have been exceeded at peak lung inflation because, if
it had, obstruction would have been lessened rather than exacerbated; this is consistent with the notion that the yield force exceeds isometric force by almost 2-fold (20)].
As such, after a deep inspiration the airway with small hysteresivity
must recoil passively to a smaller caliber, i.e., a more obstructed
state (13, 27). Of course, the airway in which rapidly cycling cross
bridges (high ) have converted to slowly cycling latch bridges (low
) represents just such an instance (Fig. 2). Therefore, the
inability of lung inflation to reverse spontaneous airway obstruction
in asthma is seen to be consistent with the assertion that airway
smooth muscle in that circumstance is in the latch state. According to
the analysis of Froeb and Mead (13), increased lung parenchymal
hysteresivity (7, 27, 39) and decreased airway muscle hysteresivity
(i.e., latch) are not mutually exclusive in explaining failure of a
deep inspiration to reverse obstruction, but the latter by itself is
sufficient. Taken together, these observations point to a possible
causal association between the latch state of airway smooth muscle and the failure of a deep inspiration to reverse spontaneous obstruction in
asthma.
In contrast, a deep inspiration does reverse obstruction of matched
severity that is induced in healthy and asthmatic subjects. This
suggests that the hysteresivity of the activated airway smooth muscle
in induced obstruction, as distinct from spontaneous obstruction, is
increased, becoming larger than that of lung tissues to which it is
tethered. In this case the peribronchial distending stress after a deep
inspiration is lessened, as noted above, but the inward recoil of the
airway is lessened even more, producing a more dilated state
(13). Importantly, such behavior implies that in airway
smooth muscle there can exist persistent contractile states capable of
sustaining high hysteresivity and, therefore, high cross-bridge cycling
rate, much like that seen transiently early in force development (Fig.
2). The mystery is then not so much why airway smooth muscle of the
spontaneously obstructed asthmatic subject becomes latched, for it
would be expected to do so. The mystery becomes, more so, How does
maximally activated airway smooth muscle in healthy and asthmatic
subjects with induced obstruction avoid latch? The answer to this
question would have broad implications.
Compared with the asthmatic subject with peribronchial inflammation, in
the normal subject the bronchial adventitia is thinner, the smooth
muscle fiber length is longer, the load it acts against is greater, and
the change in peribronchial stress per change in transpulmonary
pressure is more (32). In addition, based on the studies of Tepper et
al. (47) and Warner and Gunst (49), we know that tidal stretches of
airway smooth muscle can limit bronchoconstriction. Therefore, there is
already good reason to suspect that tidal stretch of airway smooth
muscle and its effect on bronchoconstriction would be attenuated in
asthma. However, the specific mechanism by which tidal stretch might
influence cross-bridge kinetics and their approach to the latch state
is not known.
Speculations on a frictional airway ratchet.
These findings lead to the speculation that airway smooth muscle in the
latch state, as disposed in situ, might behave in a particularly
pernicious way. We noted above that airway smooth muscle in latch is
transiently unloaded after a deep inspiration and that, as a result,
the muscle must recoil passively to a shorter muscle
length. But muscle can also shorten actively. When
unloaded an increment below isometric force, muscle will shorten at a
certain speed. When loaded by a like increment above isometric force, it will lengthen.
The speed of shortening is about five times the speed of lengthening
(20, 46; Fig. 6). When cyclically loaded
and unloaded in the vicinity of the isometric load, muscle is strongly
biased toward shortening. It takes up slack relatively rapidly during unloading but pays out slowly during reloading; in this regard the
action of muscle is like the ratchet mechanism within a fishing reel. Therefore, when transiently unloaded after a deep
inspiration, some small fraction of that transient shortening would be
expected to be captured by this ratchetlike action. Over a complete
breathing cycle, a small net shortening displacement would have
occurred. Over successive cycles, such displacements would be expected
to accumulate until, after many such cycles, muscle had shortened appreciably. Shortening would cease only after muscle force at the
final equilibrium muscle length had come into balance with opposing
parenchymal distending forces biased strongly toward their minimum
value over the breathing cycle. There, at that reduced length, the
muscle would be stuck, as it were, until the contractile apparatus is
deactivated. Rather than being determined by a static balance of forces
(32, 52), here airway luminal narrowing is largely determined by a
dynamic balance of forces over the course of a breath, with pivotal
roles played by asymmetry of hysteresivities of airway smooth muscle
vs. lung parenchymal tissues (with each breath this asymmetry
transiently unloads muscle if it is in the latch state) and asymmetry
of muscle velocity in lengthening vs. shortening (this asymmetry
actively captures transient passive shortening). To be sure, in latch
the velocity scale of the entire Hill curve would be less, although the
Hill relationship has not been well defined in latch vs. nonlatch
contractile states or during submaximal activation. So the ratcheting
action that we postulate might be very slow indeed or may not occur at
all. But if it does occur, it would be relentless. The issue of the static vs. dynamic determinants of smooth muscle length is further called into question by the fact that optimal length, if it exists at
all in airway smooth muscle, adapts plastically to changes of operating
length (16, 40).
, change; Fo, isometric
force.
The degree and duration of unloading are augmented by excursions to low lung volume and, as such, would give a plausible and straightforward explanation for the striking findings that repetitive expirations to low lung volume precipitate persistent obstruction in healthy volunteers in whom deep inspirations are prohibited (cf. Refs. 9 and 44). We suggest that the healthy subjects in the study of Skloot et al. (44), with no history of airway inflammation, were unable to reverse induced obstruction when deep inspirations were reinstated because, although deep inspirations had been prohibited, their airway smooth muscle had progressed into latch and, as a result, ratcheted airways to excessively small caliber. In addition, this mechanism would seem to explain the widely observed phenomenon that a fit of laughter, which involves repetitive excursions to low lung volume, frequently precipitates an asthmatic attack. Interestingly, this line of reasoning does not preclude an important role for airway closure at low lung volumes (9, 44), but on these grounds it may not be necessary to postulate closure to account for persistent obstruction that is refractory to deep inspirations. Indeed, to the degree that closure does contribute, the ratcheting mechanism described here may help to explain a key factor precipitating it. Taken together, these points are sufficient grounds for speculating that airway hyperreactivity in some circumstances may rest on a ratcheting mechanism of the kind described here. However, no such ratcheting action would be expected in healthy subjects and in asthmatic subjects who are acutely challenged. Ratcheting is not expected in these cases because these subjects transiently dilate their airways in response to a deep inspiration. As such, there would be no slack to take up after a deep inspiration, as if the ratchet pawl had never been engaged. Summary. Taken together, these results indicate that like shortening velocity and mATPase, mechanical friction in airway smooth muscle is also governed by the rate of cross-bridge cycling (in contrast to a classic viscosity), that
is a continuous mechanical index of the underlying
cycling rate, and that, compared with force development, force
maintenance (latch) is a low-friction contractile state.
This last finding may account for the unique inability of asthmatic
subjects to reverse spontaneous airways obstruction with a deep
inspiration. As such, this suggests a causal association between the
latch state of airway smooth muscle and the failure of a deep
inspiration to reverse spontaneous obstruction in asthma.
ACKNOWLEDGEMENTS
We thank Brett Miller, Robert Lorenz, and Richard Brown for assistance with various aspects of these studies. We thank Mary Ellen Avery, Claire Doerschuk, Frederick Hoppin, Jr., Peter T. Macklem, Ning Wang, Stephen Loring, and Roland Ingram, Jr., for their useful criticisms.
FOOTNOTES
Address for reprint requests: J. J. Fredberg, Harvard School of Public Health, 665 Huntington Ave., Boston, MA 02115 (E-mail: jfredber{at}hsph.harvard.edu).
Received 17 April 1996; accepted in final form 9 September 1996.
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R. Brown and W. Mitzner Effects of tidal volume stretch on airway constriction in vivo J Appl Physiol, November 1, 2001; 91(5): 1995 - 1998. [Abstract] [Full Text] [PDF]
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P. V. Romero, W. A. Zin, and J. Lopez-Aguilar Frequency characteristics of lung tissue strip during passive stretch and induced pneumoconstriction J Appl Physiol, August 1, 2001; 91(2): 882 - 890. [Abstract] [Full Text] [PDF]
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C. Y. Seow and J. J. Fredberg Signal Transduction in Smooth Muscle: Historical perspective on airway smooth muscle: the saga of a frustrated cell J Appl Physiol, August 1, 2001; 91(2): 938 - 952. [Abstract] [Full Text] [PDF]
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B. Fabry, G. N. Maksym, S. A. Shore, P. E. Moore, R. A. Panettieri Jr., J. P. Butler, and J. J. Fredberg Signal Transduction in Smooth Muscle: Selected Contribution: Time course and heterogeneity of contractile responses in cultured human airway smooth muscle cells J Appl Physiol, August 1, 2001; 91(2): 986 - 994. [Abstract] [Full Text] [PDF]
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K. R. LUTCHEN, A. JENSEN, H. ATILEH, D. W. KACZKA, E. ISRAEL, B. SUKI, and E. P. INGENITO Airway Constriction Pattern Is a Central Component of Asthma Severity . The Role of Deep Inspirations Am. J. Respir. Crit. Care Med., July 15, 2001; 164(2): 207 - 215. [Abstract] [Full Text] [PDF]
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A. Jensen, H. Atileh, B. Suki, E. P. Ingenito, and K. R. Lutchen Signal Transduction in Smooth Muscle: Selected Contribution: Airway caliber in healthy and asthmatic subjects: effects of bronchial challenge and deep inspirations J Appl Physiol, July 1, 2001; 91(1): 506 - 515. [Abstract] [Full Text] [PDF]
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R. K. Lambert, P. D. Pare, and M. Okazawa Stiffness of peripheral airway folding membrane in rabbits J Appl Physiol, June 1, 2001; 90(6): 2041 - 2047. [Abstract] [Full Text] [PDF]
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M. Filippelli, R. Pellegrino, I. Iandelli, G. Misuri, J. R. Rodarte, R. Duranti, V. Brusasco, and G. Scano Respiratory dynamics during laughter J Appl Physiol, April 1, 2001; 90(4): 1441 - 1446. [Abstract] [Full Text] [PDF]
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R. D. Hubmayr Biology lessons from oscillatory cell mechanics J Appl Physiol, October 1, 2000; 89(4): 1617 - 1618. [Full Text] [PDF]
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G. N. Maksym, B. Fabry, J. P. Butler, D. Navajas, D. J. Tschumperlin, J. D. Laporte, and J. J. Fredberg Mechanical properties of cultured human airway smooth muscle cells from 0.05 to 0.4 Hz J Appl Physiol, October 1, 2000; 89(4): 1619 - 1632. [Abstract] [Full Text] [PDF]
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N. SCICHILONE, T. KAPSALI, S. PERMUTT, and A. TOGIAS Deep Inspiration-induced Bronchoprotection Is Stronger than Bronchodilation Am. J. Respir. Crit. Care Med., September 1, 2000; 162(3): 910 - 916. [Abstract] [Full Text]
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L. Wang, P. D. Pare, and C. Y. Seow Effects of length oscillation on the subsequent force development in swine tracheal smooth muscle J Appl Physiol, June 1, 2000; 88(6): 2246 - 2250. [Abstract] [Full Text] [PDF]
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J. C. C. M.i.`t VEEN, A. J. BEEKMAN, E. H. BEL, and P. J. STERK Recurrent Exacerbations in Severe Asthma Are Associated with Enhanced Airway Closure During Stable Episodes Am. J. Respir. Crit. Care Med., June 1, 2000; 161(6): 1902 - 1906. [Abstract] [Full Text]
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W. MITZNER and R. H. BROWN Potential Mechanism of Hyperresponsive Airways Am. J. Respir. Crit. Care Med., May 1, 2000; 161(5): 1619 - 1623. [Abstract] [Full Text]
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W.-L. Chan, J. Silberstein, and C.-M. Hai Mechanical strain memory in airway smooth muscle Am J Physiol Cell Physiol, May 1, 2000; 278(5): C895 - C904. [Abstract] [Full Text] [PDF]
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J. J. FREDBERG Airway Smooth Muscle in Asthma . Perturbed Equilibria of Myosin Binding Am. J. Respir. Crit. Care Med., March 1, 2000; 161(3): S158 - 160. [Full Text] [PDF]
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F. G. Salerno, N. Shinozuka, J. J. Fredberg, and M. S. Ludwig Tidal volume amplitude affects the degree of induced bronchoconstriction in dogs J Appl Physiol, November 1, 1999; 87(5): 1674 - 1677. [Abstract] [Full Text] [PDF]
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V. Brusasco, E. Crimi, G. Barisione, A. Spanevello, J. R. Rodarte, and R. Pellegrino Airway responsiveness to methacholine: effects of deep inhalations and airway inflammation J Appl Physiol, August 1, 1999; 87(2): 567 - 573. [Abstract] [Full Text] [PDF]
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J. J. FREDBERG, D. S. INOUYE, S. M. MIJAILOVICH, and J. P. BUTLER Perturbed Equilibrium of Myosin Binding in Airway Smooth Muscle and Its Implications in Bronchospasm Am. J. Respir. Crit. Care Med., March 1, 1999; 159(3): 959 - 967. [Abstract] [Full Text]
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D. W. KACZKA, E. P. INGENITO, E. ISRAEL, and K. R. LUTCHEN Airway and Lung Tissue Mechanics in Asthma . Effects of Albuterol Am. J. Respir. Crit. Care Med., January 1, 1999; 159(1): 169 - 178. [Abstract] [Full Text]
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V. Brusasco, E. Crimi, and R. Pellegrino Airway hyperresponsiveness in asthma: not just a matter of airway inflammation Thorax, November 1, 1998; 53(11): 992 - 998. [Full Text]
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C. Y. SEOW, R. R. SCHELLENBERG, and P. D. PARE Structural and Functional Changes in the Airway Smooth Muscle of Asthmatic Subjects Am. J. Respir. Crit. Care Med., November 1, 1998; 158(2007): S179 - S186. [Abstract] [Full Text] [PDF]
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F. G. Salerno and M. S. Ludwig Dissociation between hysteresivity and tension in constricted tracheal and parenchymal strips J Appl Physiol, July 1, 1998; 85(1): 91 - 97. [Abstract] [Full Text] [PDF]
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J. Fredberg, D Inouye, B Miller, M Nathan, S Jafari, S. Raboudi, J. Butler, and S. Shore Airway smooth muscle, tidal stretches, and dynamically determined contractile states Am. J. Respir. Crit. Care Med., December 1, 1997; 156(6): 1752 - 1759. [Abstract] [Full Text]
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M. Ludwig Invited Editorial on "Dynamic properties of lung parenchyma: mechanical contributions of fiber network and interstitial cells" J Appl Physiol, November 1, 1997; 83(5): 1418 - 1419. [Abstract] [Full Text]
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H. Yuan, E. P. Ingenito, and B. Suki Dynamic properties of lung parenchyma: mechanical contributions of fiber network and interstitial cells J Appl Physiol, November 1, 1997; 83(5): 1420 - 1431. [Abstract] [Full Text] [PDF]
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X. Shen, M. F. Wu, R. S. Tepper, and S. J. Gunst Pharmacological modulation of the mechanical response of airway smooth muscle to length oscillation J Appl Physiol, September 1, 1997; 83(3): 739 - 745. [Abstract] [Full Text] [PDF]
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J. Solway and J. J. Fredberg Perhaps Airway Smooth Muscle Dysfunction Contributes to Asthmatic Bronchial Hyperresponsiveness After All Am. J. Respir. Cell Mol. Biol., August 1, 1997; 17(2): 144 - 146. [Full Text]
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R. K. Lambert and P. D. Pare Lung parenchymal shear modulus, airway wall remodeling, and bronchial hyperresponsiveness J Appl Physiol, July 1, 1997; 83(1): 140 - 147. [Abstract] [Full Text] [PDF]
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Inflammation and Airway Function in Asthma . What You See Is Not Necessarily What You Get Am. J. Respir. Crit. Care Med., January 1, 1997; 157(1): 1 - 3. [Full Text]
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D. Stamenovic, Z. Liang, J. Chen, and N. Wang Effect of the cytoskeletal prestress on the mechanical impedance of cultured airway smooth muscle cells J Appl Physiol, April 1, 2002; 92(4): 1443 - 1450. [Abstract] [Full Text] [PDF]
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N. Wang, I. M. Tolic-Norrelykke, J. Chen, S. M. Mijailovich, J. P. Butler, J. J. Fredberg, and D. Stamenovic Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells Am J Physiol Cell Physiol, March 1, 2002; 282(3): C606 - C616. [Abstract] [Full Text] [PDF]
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