Articles in PresS. Am J Physiol Cell Physiol (May 14, 2008). doi:10.1152/ajpcell.00172.2008
The effect of low pH on single skeletal muscle myosin mechanics and kinetics
E. P. Debold, S. E. Beck, D.M. Warshaw
Department of Molecular Physiology and Biophysics, University of Vermont, Burlington,
VT 05405
Running head: Low pH affects single myosin molecule kinetics
Contact information: Edward P. Debold, Department of Molecular Physiology and
Biophysics, University of Vermont, Burlington VT, 05405 e-mail:
[email protected] Phone# 802-656-3820
Fax# 802-656-0747.
Copyright © 2008 by the American Physiological Society.
Abstract:
Acidosis (low pH) is the oldest putative agent of muscular fatigue, but the
molecular mechanism underlying its depressive effect on muscular performance remains
unresolved. Therefore, the effect of low pH on the molecular mechanics and kinetics of
chicken skeletal muscle myosin was studied using in vitro motility (IVM) and single
molecule laser trap assays. Decreasing pH from 7.4 to 6.4 at saturating ATP slowed actin
filament velocity (Vactin) in the IVM by 36%. Single molecule experiments, at 1 µM
ATP, decreased the average unitary step size of myosin (d) from 10
2nm (pH 7.4) to 2
1nm (pH 6.4). Individual binding events at low pH were consistent with the presence
of a population of both productive (average d = 10nm) and non-productive (average d =
0nm) actomyosin interactions. Raising the ATP concentration from 1µM to 1mM at pH
6.4 restored d (9
3nm), suggesting that the lifetime of the non-productive interactions is
solely dependent on the [ATP]. Vactin however was not restored by raising the [ATP] (110mM) in the IVM assay, suggesting that low pH also prolongs actin strong-binding (ton).
Measurement of ton as a function of the [ATP] in the single molecule assay suggested that
acidosis prolongs ton by slowing the rate of ADP-release. Thus, in a detachment limited
model of motility (i.e. Vactin ~ d/ton) a slowed rate of ADP-release and the presence of
non-productive actomyosin interactions could account for the acidosis-induced decrease
in Vactin, suggesting a molecular explanation for this component of muscular fatigue.
Key words: acidosis, fatigue, velocity, myosin, laser trap
2
Introduction
After several minutes of intense contractile activity, skeletal muscle’s ability to
generate force and power declines precipitously (45). Despite intensive investigation for
more than 100 years the etiology of this phenomenon, known as fatigue, remains elusive.
With the increased rate of ATP utilization during such intense activity, the onset of
fatigue is believed to result, in part, from the rapid accumulation of ATP hydrolysis
products (ADP, Pi and H+) (8). Evidence from skinned single muscle fibers demonstrates
that elevated Pi significantly reduces force (28). Recent evidence suggests that acidosis
(i.e. low pH), has only a small effect on force production (31) but significantly decreases
both the shortening velocity and power generating capacity of muscle (20).
The
reduction in maximum unloaded shortening velocity (Vmax) due to intracellular acidosis
in muscle fibers has also been confirmed at the molecular level in the in vitro motility
assay, where actin filament movement generated by isolated myosin was slowed at low
pH (22). The mechanism of this depressed velocity may be due to acidosis slowing
myosin’s ATPase rate, which has been demonstrated in skinned single muscle fibers (5).
While this finding remains equivocal (33) it is likely that the acidosis-induced reduction
in shortening velocity results from an effect on one or more steps of actomyosin’s
mechanochemical cycle. In fact, based on findings from solution (2; 4) and skinned
single muscle fiber studies, Kentish (19) postulated that ATP hydrolysis and ADP-release
may be influenced by acidosis. To address this at the single molecule level the threebead laser trap assay (7) affords the ability to directly determine the molecular
mechanism by which acidosis affects the mechanics and/or the kinetics of an individual
cross-bridge.
3
In the present study, actin filament velocity (Vactin) was slowed at low pH. Based
on a detachment limited model (15), Vactin is dependent on myosin’s step size (d) and the
duration of the strongly bound state following the powerstroke (ton), i.e. Vactin~d/ton. By
characterizing skeletal muscle myosin’s molecular mechanics in the laser trap assay,
lowering pH from 7.4 to 6.4 does not appear to affect myosin’s inherent step size.
However, low pH does alter the kinetics of the cross-bridge cycle by prolonging ton. This
prolongation of ton appears to result from a 3-fold slower rate of ADP-release from
myosin.
Additionally, low pH may increase the probability of a rigor-like, non-
productive interaction between actin and myosin that may act as an internal load to
motion generation in an ATP-dependent manner, serving to further slow Vactin at low pH.
Methods
Proteins
The myosin was prepared as previously described (43) from chicken pectoralis muscle,
which expresses predominantly a fast myosin heavy chain isoform (11). Actin was
isolated from the acetone powder of the pectoralis muscle preparation (30). Isolated actin
was fluorescently labeled with an overnight incubation in 50% tetramethylrhodamine
isothiocyanate (TRITC) labeled phalloidin (Sigma-Aldrich Inc.) and 50% biotin labeled
phallodin. The myosin was further purified to remove inactive myosin molecules before
each experiment by subjecting a small aliquot (200µg/ml) to centrifugation (95K) in the
presence of an equimolar amount of filamentous actin in the presence of ATP (1mM) in
myosin buffer (see solutions). Glass microspheres (1.0 µm silica, Duke Scientific Inc.)
used in the laser trap assay were incubated overnight with N-ethylmaleimide (NEM)
4
modified skeletal muscle myosin, prepared as previously described (43), and with
neutravidin (NAV).
Solutions
Isolated myosin was diluted in Myosin Buffer (0.3 M KCl, 25 mM imidazole,
1 mM EGTA, 4 mM MgCl2, and 10 mM DTT, pH 7.4). The final laser trap buffer
contained 25 mM KCl, 25 mM imidazole, 1 mM EGTA, 4 mM MgCl2, 10 mM DTT, and
oxygen scavengers (0.1 mg.ml-1 glucose oxidase, 0.018 mg.ml-1 catalase, 2.3 mg.ml-1
glucose) and was adjusted to either pH 7.4 or 6.4 (with the addition of HCl). The final
motility buffer had the same composition as the final trapping buffer but also contained
methylcellulose to help keep the actin filaments in contact with the myosin coated
surface. The MgATP concentration in the trapping and motility buffers was varied from
0.5µM to 10mM.
To maintain a constant ionic strength and a 3-mM free Mg+2
concentration, the KCl and MgCl2 concentrations were adjusted according to the
constants contained within the MaxChelator (Version 2.50) software program (32).
In vitro motility and single molecule laser trap assays.
The in vitro motility assay was performed at 30oC and data analyzed as previously
described (43). The three-bead laser trap assay was performed as described by Guilford et
al. (12) using the instrumentation detailed in Kad et al. (17). Briefly, manipulating the
microscope stage, allowed two 1µm silica beads to be captured in separate laser traps, a
single actin filament was then attached to the NEM-myosin/NAV coated beads (the
combination of NEM-myosin/NAV coating allowed for a strong bead-actin-bead
assembly at mM ATP concentrations). Pre-tension was then imposed on the bead-actinbead assembly (~4 pN), and the stiffness (~0.02pN/nm) of the combined assembly was
5
determined using the equipartition method (12). The bead-actin-bead assembly was then
lowered onto a third microsphere (3µm diameter) sparsely coated with myosin. The laser
trap experiments were performed at room temperature (20oC).
Analysis of single molecule data records
The raw displacement of the actin-attached bead was obtained from the output of
a quadrant photodiode in the laser trap assay and was acquired and processed as
previously described (12). Each recording consisted of roughly two minutes of data,
containing hundreds of events. Myosin’s unitary step size (d) and duration of strong
actin binding (ton) were determined using mean variance analysis as previously described
(12). A Student’s t-test for independent samples was used to determine pH-induced
differences in d with significance set at p<0.05. An ANOVA was used to analyze ton
values as a function of [ATP] in the single molecule data with a Tukey’s HSD post-hoc
test used to locate significant differences (p<0.05).
Results
Effect of low pH on Vactin
Decreasing the pH from 7.4 to 6.4 in the motility assay severely depressed
myosin’s ability to translocate actin at all ATP concentrations between 0.001 and 10mM
(Figure 1). This depressive effect of low pH was readily reversible with Vactin fully
restored following the re-infusion of a pH 7.4 buffer (data not shown). When fit to a
Michaelis-Menten relationship, the extrapolated maximum Vactin at pH 6.4 (4.1µm.s-1)
was reduced 36% compared to that at pH 7.4 (6.4µm.s-1), as previously observed (13). In
6
addition, low pH induced a more than 10-fold increase in the Km, from 83µM at pH 7.4 to
850µM at pH 6.4 (Figure 1), indicating that the depressive effect of low pH on Vactin is
more pronounced at sub-saturating ATP concentrations.
Effect of low pH on myosin molecular mechanics
To determine the underlying molecular mechanisms of the depressive effects of
pH on Vactin, we characterized the mechanics (d) and kinetics (ton) of single skeletal
muscle myosin molecules in the laser trap assay. These experiments were initially
performed at low ATP concentrations (≤10µM) to enhance the detection of myosin
binding to actin by prolonging the attached lifetime following the powerstroke.
Step size, d: At pH 7.4 and low ATP(≤10µM), binding events (Figure 2) were
characterized by an average step size of 10nm (Table 1), as determined by mean variance
(MV) analysis, consistent with previous estimates from whole chicken skeletal muscle
myosin (12). In contrast, at pH 6.4 and low ATP, binding events were broadly distributed
and centered near 0nm, which drastically altered the profile of the MV histogram (Figure
2). The average step size, d, at pH 6.4 and 10 M ATP was reduced by 40% to 6 ± 5nm
and by 80% at 0.5 and 1 M ATP to 2 ± 1nm (Table 1).
To determine if the apparent reduction in the myosin step size at low pH was
ATP-dependent, experiments were also performed at 1mM ATP. At pH 6.4, binding
events were no longer broadly distributed with d being restored at 1mM ATP to 9 ± 3nm,
statistically equivalent to that at pH 7.4 at both 1 and 10 M ATP (Table 1). Although a
comparison to d at pH 7.4 and 1mM ATP would have been more appropriate, skeletal
muscle myosin binding events under these conditions are extremely short-lived (< 10ms;
Baker et al. 2002) and difficult to resolve in the laser trap assay (see Figure 2, left).
7
However, based on the two ATP concentrations (i.e. 1 and 10 M) used in this study and
other studies from our laboratory, using slower muscle myosin isoforms, there is no
apparent effect of ATP concentration on myosin’s inherent step size at pH 7.4 (3; 23; 29).
Therefore, the dependence of d on ATP concentration at low pH suggests that lowering
pH can affect processes that result in a productive powerstroke (see Discussion).
Attached lifetime, ton: Although the apparent reduction in d at ≤10µM ATP, pH
6.4 may contribute to the slowed Vactin at these ATP concentrations, the inability of Vactin
to recover at elevated ATP (see Figure 1) even though d was restored to normal at 1mM
ATP, suggests that one or more biochemical transitions in the actomyosin ATPase cycle
might be slowed by low pH. This is further emphasized by the large shift in Km (Figure
1). Therefore, we examined the effects of low pH on myosin’s attached lifetime (ton)
since ton is determined by the time waiting for ADP release (1/k-ADP) and subsequent ATP
binding (1/(k+ATP [ATP])) to the active site (i.e. ton=(1/k-ADP)+(1/(k+ATP[ATP])) (29),
where k-ADP is the rate of ADP release and k+ATP is the second-order ATP binding rate.
By measuring ton as a function of ATP concentration, we can determine if k-ADP and/or
k+ATP are altered by lowering pH.
As expected, ton was ATP-dependent at both high and low pH levels (Table 1). At
1µM ATP, low pH did not significantly affect ton but at 10µM ATP, ton was prolonged
three-fold at pH 6.4 (Table 1). Additionally at 1mM ATP, under acidic conditions the
observed ton value of 31 ± 9ms (Table 1) is once again three-fold longer than an
extrapolated estimate of ton at saturating ATP and pH 7.4, based on our previous work
(3). A comparison to an extrapolated estimate of ton was necessary since binding events
at 1mM ATP and pH 7.4 are typically below our detection limit (Figure 2, bottom left).
8
We fit the myosin detachment rate, 1/ton (see above), at pH 6.4 as a function of ATP
concentration (Figure 3) to the following equation to estimate k-ADP and k+ATP:
1/ton = (k-ADP * k+ATP [ATP])/( k+ATP [ATP] + k-ADP)
Based on the fit, k+ATP was estimated to be 5.2 ± 4.6, x 106M-1.s-1(Mean ± SE), whereas
k-ADP was 33 ± 7.s-1 (Mean ± SE).
Discussion
Mechanism for decreased Vactin at low pH
The pH dependence of Vactin observed in the present investigation using chicken
skeletal myosin confirms our previous experiments examining Vactin over a range of pH
values (13) with similar results observed for mammalian skeletal (22) and cardiac muscle
myosin (46). At the single molecule level, the observed decrease in Vactin with low pH
could be due either to a decrease in d and/or an increase in ton (i.e. Vactin~ d/ton) (15). In
addition, at the ensemble level we have shown that Vactin is also governed by the
mechanical interactions between myosin molecules that simultaneously interact with the
actin filament (43). Here we propose that lowering pH at physiological ATP does not
alter skeletal myosin’s inherent motion generating capacity, d, but rather the reduced
Vactin results from slowed kinetics associated with ton and that the emergence of a
population of non-productive actomyosin interactions may act as an internal load in the
motility assay.
Low pH increases non-productive actomyosin interactions: At limiting
concentrations of ATP (<10µM), the step size decreased as much as 80% at pH 6.4
(Table 1). Myosin’s step size is due to a rotation of the light chain binding domain, acting
9
as a lever arm to amplify small conformational changes in the myosin head (34; 44).
Therefore low pH could induce a structural alteration in myosin to reduce its lever arm
rotation (21) and/or stiffness (37) to account for the diminished step size. We do not favor
this explanation and propose that myosin’s inherent step size is unchanged by low pH and
that the presence of a broadly distributed population of binding events centered at 0nm
displacement biases the estimate of d to lower values. In support of this, at pH 7.4 and
1 M ATP, the step size for a given myosin molecule is clearly defined by a distinct 10nm
population (see Figure 2). In contrast at pH 6.4, the event population becomes broadly
distributed about a mean of 2nm. Based on a model simulation (see Figure 4 legend for
details), the apparently shorter step size at pH 6.4 could arise from myosin generating a
normal 10nm displacement but more often binds to actin without generating a
powerstroke. This non-productive interaction would randomly capture the actin filament
during its Brownian excursion in the laser trap, resulting in a broadly distributed event
population near 0nm (40). Additionally, these non-productive binding events are
seemingly ATP-dependent given that at pH 6.4 and 1mM ATP, step sizes are no longer
broadly distributed and are restored to the well-defined 10nm population.
What is the origin of these non-productive actomyosin interactions and why
should they be ATP-dependent? The cross-bridge cycle is illustrated in Figure 5 in which
myosin is either weakly- or strongly-bound to actin depending on the nucleotide present
in the active site. Following the powerstroke, myosin remains strongly-bound to actin
(i.e. ton) until ADP is released and subsequent binding of ATP to the rigor state. Upon
ATP-induced detachment, myosin-ATP may remain in a short-lived post-powerstroke
state (42) before transitioning to a myosin-ATP state that is in rapid equilibrium between
10
pre- and post-powerstroke states, as indicated by the position of the lever arm in
crystallographic data (35). Upon hydrolysis, the lever arm is re-primed, completing the
cross-bridge cycle (39). Given that low pH may slow hydrolysis, there is a finite
probability that the post-powerstroke M-ATP state might exist and that rebinding of this
state to actin would induce ATP release from myosin, which is supported by biochemical
data (38). This scenario would effectively return myosin to the strongly-bound,
nucleotide-free rigor state. In the laser trap, this process would be mechanically expressed
as a binding event that merely captures the actin filament during its Brownian motion and
thus give rise to the broad distribution of events as shown previously using slowlyhydrolyzable analogs of ATP (39).
The fact that a broad event population is seen at low ≤10 M ATP and not at 1mM
ATP offers additional support that these binding events involve rigor-like actomyosin
complexes that are sensitive to ATP. Based on a second order ATP-binding rate of 5 x
106 M-1.s-1, at 1mM ATP the non-productive events would be extremely short-lived
(<1ms) and therefore not detected in the laser trap. In fact, additional simulations (as
described above and presented in Figure 4), demonstrate that the contribution of the
broadly distributed non-productive events to the overall event population observed at
1 M ATP is reduced as the ATP concentration is increased to 1mM. As the duration of
non-productive events is decreased with increasing ATP concentrations, the productive
events once again predominate, restoring the step size to its normal 10nm value.
Therefore we propose that lowering pH does not directly affect myosin’s inherent motion
generation but rather its kinetics so that slowing of the transition out of the ATP-bound
11
post powerstroke state or hydrolysis itself (Figure 5) would thus favor myosin rebinding
to actin in a non-motion generating strongly-bound state.
The presence of non-productive actomyosin interactions could serve as an internal
load to slow Vactin at all ATP concentrations studied, even physiological ATP
concentrations. We have shown previously in the motility assay that chemically modified
myosins that trap myosin in a weak- (pPDM-modified) or strong-binding (NEMmodified) state impede the motion generated by normally cycling myosins (43). With the
duration of these putative non-productive binding events at pH 6.4 being sensitive to
ATP, the effective load presented by these events would be greater at lower ATP
concentrations. This internal load might explain the rightward shift in the Vactin/ [ATP]
relationship and therefore the apparent change in Km, supporting the hypothesis that
acidosis slows shortening velocity in muscle fibers by imposing an increased resistive
drag (36).
Low pH prolongs ton: At 1mM ATP, which is near physiological (18), Vactin at pH
6.4 was reduced 65% compared to that at pH 7.4 (Figure 1). Although the resistive load
created by non-productive binding events may contribute to this slowing, the prolonged
ton at 1mM ATP is the most likely determinant of Vactin. To demonstrate this directly, we
took advantage of the slower kinetics associated with smooth muscle myosin (23) so that
the effect of low pH on ton at 1mM ATP could be determined without relying on an
assumed value of ton for skeletal myosin at pH 7.4 (3). At 1mM ATP and pH 6.4, smooth
muscle binding events were characterized by a step size of 9nm, as at pH 7.4, but as
predicted for skeletal myosin, ton was ~3-fold longer than at pH 7.4 (Figure 6), providing
direct support that low pH does prolong ton at normal physiologic ATP concentrations.
12
Based on the ATP-dependence of ton at pH 6.4 (Figure 3), low pH has little or no
effect on the rate of ATP-binding to myosin since the estimated k+ATP is within the range
of values reported for solution (24) as well as laser trap studies (3). This is further
confirmed by the observation that ton in the laser trap assay is unaffected at low ATP
(1 M) where the lifetime is dominated by rigor. However, low pH does appear to slow
the rate of ADP release from myosin, since k-ADP is at least 3-fold slower than our
previous estimate at pH 7.4 (100.s-1, (3)) providing support for the hypothesis that proton
exchange occurs with the ADP-release step (19). In a detachment limited model of Vactin
this slowed ADP-release rate would significantly contribute to the low pH-induced
depression of Vactin in the motility assay (Figure 1). The increased ADP-lifetime would
increase ton and thus might be expected to increase maximal isometric force, in contrast to
evidence from single muscle fibers (5; 31). However, this could be reconciled if acidosis
also slows myosin’s overall ATPase rate (5) to a greater extent than the attached lifetime.
This scenario would effectively reduce myosin’s duty ratio resulting in a lower average
force per cross-bridge.
It is unclear how low pH affects the kinetics of the cross-bridge cycle at a
structural level. However, one or more amino acids within the active site that are crucial
to nucleotide-dependent transitions in the cross-bridge cycle may be protonated at low
pH. This might alter myosin’s ability to cleave the gamma phosphate of ATP and
increase its affinity for ADP both of which are suggested by the data presented. Histidine
residues could play a role in these effects because they have a pKa (6.0) closest to the
range of pH values used in the present investigation. Interestingly, the depressive effects
of low pH have been shown to be dependent on the isoform of myosin heavy chain
13
(MHC) expressed in a muscle fiber (26), thus a comparison of the sequences of the MHC
could provide information regarding the residues crucial to low pH-induced decreases in
Vactin.
Implications for Fatigue:
Intracellular acidosis has been a primary suspect in muscular fatigue and reduced
muscle force generation since the 19th century (10). Edman and Mattiazzi (6) were
among the first to attribute the decline in maximal shortening velocity to increased
myoplasmic H+ in isolated muscle preparations. While the depressive effect of acidosis
on maximal isometric force appears to be minimal near physiological temperatures (20;
31), the effect on unloaded shortening appears to be temperature independent over the
range between 15-30oC (20). The large acidosis-induced decrease in velocity, observed
in single fibers, was also evident under loaded shortening and suggests that acidosis can
reduce the peak power-generating capacity of muscle (9; 20).
The motility assay and single molecule experiments can provide insight into the
molecular mechanism underlying pH-dependent muscular fatigue. Even at or slightly
below normal physiologically ATP concentrations (18), the 10-fold increase in Km for
ATP caused by low pH (Figure 1) could lead to a significant reduction in shortening
velocity in fibers. The reduction in ATP may be even more important than previously
thought because there is evidence that reductions in intracellular ATP can be as great as
80% following short bouts of intense exercise (18). This effect is fiber type dependent
with a greater reduction in intracellular ATP in fast type II vs. slow type I fibers (18).
Thus combining this observation with an increased acid production and Km for ATP may
help explain the greater rate of fatigue of fast type II vs. slow type I muscle (8).
14
The present findings may not apply entirely to the situation in both skinned and
intact muscle for several reasons. For example, Metzger and Moss (25) suggests that
acidosis may decrease filament lattice spacing (1), which can slow unloaded shortening
velocity in muscle fibers (41). Such an effect would of course be dependent on the
highly ordered structure of muscle which is not present in the assays employed in the
present investigation. In addition, actin filaments used in the present experiments do not
include the regulatory proteins, tropomyosin and troponin, which are known to modulate
actomyosin kinetics (14) and also mediate the pH effect on the force-calcium relationship
in muscle fibers (27). Thus, future studies that incorporate fully regulated thin filaments
in the laser trap assay (16) could partition the effect of low pH between the direct effects
on actomyosin performance from the effects mediated through regulatory proteins.
Regardless, this study does provide direct evidence that low pH profoundly affects
myosin’s ability to translocate actin, whereby Vactin is slowed by both a reduced rate of
ADP release from myosin and the appearance of an increased proportion of nonproductive actomyosin interactions, both of which at the ensemble level would create an
effective internal load to movement.
15
Acknowledgements
Edward P. Debold is now affiliated with the Department of Kinesiology at the University
of Massachusetts. E.P.D would like to posthumously thank Devra Hendelman for
inspiring him to rigorously pursue the question of muscular fatigue. The authors also
thank members of the Warshaw Laboratory for their helpful comments and discussions
during the development of this project. In addition we thank Guy Kennedy of the
Instrumentation and Modeling Facility at the University of Vermont, for his expertise in
design and maintenance of the laser trap.
Grants: This work was supported by the National Institutes of Health (HL059408,
HL085489).
16
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21
Figure legends
Figure 1. Vactin vs ATP. Actin filament velocities (Vactin) from in vitro motility assays as
a function of [ATP]. Squares and circles represent data for pH 7.4 and pH 6.4
respectively. Values displayed are means ± SD at pH 6.4 from several myosin
preparations. At pH 7.4, each point represents the average of 20 filament velocities from
one myosin preparation. Each data set was fit to the Michaelis-Menten equation yielding
values for Vmax (6.4 and 4.1
m.s-1 at pH 7.4 and 6.4 respectively) and Km (83 and
850 M at pH 7.4 and 6.4 respectively). The goodness-of-fit for each data set exceeded an
R2 value of 0.85.
Figure 2. Sample single molecule data records. Short sections (~10sec) of 1-3min data
records that typically contained 100-200 events are displayed. Data were obtained using
a three bead laser-trap assay (12). The entire 1-3min data was used to construct the
adjacent 3-D MV histogram (see Methods). “B” indicates the estimated peak of the
baseline population and “e” indicates the peak of the event population.
Separate
experiments were performed at pH 7.4 and pH 6.4 at each ATP concentration indicated.
No significant event population was discernable at 1mM ATP and pH 7.4, likely due the
lifetime of strong attachment being more rapid than the resolution of the instrumentation
(see Discussion).
Figure 3. Detachment rate as a function of [ATP].
Detachment rates on the y-axis
were obtained by taking the reciprocal of the strongly bound lifetime (1/ton). Data points
are means ± SD. The data were fit to a two parameter hyperbola (Detachment rate =
(k-ADP * k+ATP * [ATP]) / ((k+ATP * [ATP]) + k-ADP) using SigmaPlot® 8.0 and had an R2
22
value of 0.75. The fit yielded estimates ± SEM for k-ADP (33 ± 7.s-1) and k+ATP 5.2 ± 4.6
*106 .M-1.s-1.
Figure 4. Simulated single molecule data. Single molecule data were simulated with
two kinds of binding events; one that binds actin productively and generates a full
displacement (10nm) and a second, rigor-like population, that binds actin but generates
no net displacement (0nm), having a very broad displacement distribution.
The
simulations were performed using custom software previously described (12) with the
ratio of non-productive to productive events set at 6 to 1. In the simulations the ADP
release rate was set to 33.s-1 (Figure 3) whereas the rigor state lifetime was varied to
simulate increasing ATP concentrations based on a second-order ATP-dependent
dissociation constant of 5 x 106 .M-1.s-1 (Figure 3). The lifetime of the productive binding
events was the sum of the ADP and rigor state lifetimes, whereas the non-productive
events were determined by only the rigor lifetime. At 1 M ATP, the event population is
broadly distributed (see MV-histogram) giving a value for d (2.5nm) equivalent to that
observed at pH 6.4 (and 1
M ATP) for real data (see Figure 2). However, with
increasing ATP concentrations, the lifetime of the non-productive events become shorter
and barely evident at 10 M ATP. The step size for the 10 M ATP condition is 6nm,
similar to the real data (see Table 1). At 1mM ATP, the non-productive events are below
the detection limits of the MV analysis so that only the productive, 10nm population
remain, and thus restore the step size back to its 10nm normal value.
Figure 5. A model of the cross-bridge cycle at low pH. In a normal cross-bridge cycle
ATP binding causes dissociation from actin after which myosin goes through a series of
transitions leading to the hydrolysis of ATP and re-priming of the lever arm. Upon
23
rebinding to actin myosin releases Pi and generates a lever arm rotation as it goes from a
pre- to post-powerstroke state. Myosin then releases ADP while attached to actin and
remains bound until ATP again induces the release from actin. At low pH, re-priming
may be slowed, thus favoring the M.ATP state (38). Myosin will then rebind to actin in
the M.ATP state, governed by the reverse rate constant, allowing actin to induce the
release of ATP from myosin reforming the rigor state. This non-productive binding will
lead to a broadly distributed event population around 0nm due to Brownian capture. This
is evident in the broadly distributed event population in the MV histogram at pH 6.4 and
1 M ATP (Figs. 2 and 4).
However, the duration of the strongly bound state is
dependent on the ATP concentration, therefore at 1mM ATP non-productive binding
events are below the limit of detection of the laser trap and only the productive events
remain visible. d is therefore restored at 1mM ATP and pH 6.4 determined by MV
analysis (Fig. 2).
Figure 6. Sample single molecule records for smooth muscle myosin. Displacement
records and MV histograms from smooth muscle myosin at 1mM ATP at pH 7.4 and 6.4.
Chicken gizzard whole smooth muscle myosin was used under conditions identical to
those for skeletal muscle myosin (see Methods). One 90sec trace was used to determine
d and ton at low pH while at pH 7.4 d and ton were determined based on five 90-120 sec
data records. The mean d was unaffected by low pH (9nm at pH 7.4 vs 9nm at pH 6.4)
while the mean ton was three-fold longer (27ms at pH 7.4 vs 100ms at pH 6.4), consistent
with the observations in skeletal myosin.
24
Tables
Table 1. Mean single molecule parameters.
d (nm)
ton (ms)
[ATP]
pH 7.4
pH 6.4
pH 7.4
pH 6.4
0.5 M
n/a
2±2
n/a
200 ± 114
1 M
10 ± 2
2 ± 1*
178 ± 67
119 ± 22
10 M
11 ± 2
6±5
21 ± 31
70 ± 31*
1mM
10#
9±3
10#
31 ± 9
The values displayed, obtained by MV analysis, are the mean ± SD from 4 to 10 single
molecule data records, each 1-3min in length, containing hundreds of events. # indicates
an extrapolated or estimated value from Baker et al. (3). * indicates significantly different
(p< 0.05) from the value at the corresponding [ATP] at pH 7.4. The data were analyzed
using a two-way ANOVA (pH x ATP) with a Tukey’s HSD post-hoc test to locate
specific differences. A subset of data using smooth muscle myosin at 1mM ATP showed
that d was unaffected by low pH (9nm at pH 7.4 vs 9nm at pH 6.4) while ton was threefold longer (27ms at pH 7.4 vs 100ms at pH 6.4), consistent with the observations in
skeletal myosin.
Velocity (μm.s-1)
6
pH 7.4
4
pH 6.4
2
0
0
2
4
6
ATP (mM)
Figure 1
8
10
12
e
10
300
100
B
10
e
Variance (nm2)
-20 0
20
Displacement (nm)
300
100
B
10
-20 0
20
Displacement (nm)
Figure 2
300
100
B
e
10
-30
0
30
Displacement (nm)
Variance (nm2)
10µM ATP
1mM ATP
B
300
100
B
e
10
-30
0
30
Displacement (nm)
Variance (nm2)
1sec
100
30
-30
0
Displacement (nm)
20nm
Variance (nm2)
1µM ATP
300
Variance (nm2)
pH 6.4
Variance (nm2)
pH 7.4
300
100
B
e
10
-20 0
20
Displacement (nm)
Detachment Rate (s-1)
40
30
20
10
0
1e-7
1e-6
1e-5
1e-4
[ATP] (M)
Figure 3
1e-3
1e-2
1 μM ATP
10 μM ATP
1 mM ATP
Figure 4
300
B
e
100
10
-20
Variance (nm2)
1sec
Variance (nm2)
25nm
Variance (nm2)
Simulated data
20
0
300
B
e
100
10
-30
30
0
300
100
B
e
10
30
-30
0
Displacement (nm)
Post-powerstroke
ADP
rigor
ATP
ADP
Pre-powerstroke
ADP
Pi
Pi
Post-powerstroke
t on
Pre-powerstroke
ATP
Re-priming
Slowed at low pH
Figure 5
ADP
Pi
pH 6.4
Variance (nm2)
300
100
e
10
20nm
0
20
-20
Displacement (nm)
1s
Variance (nm2)
pH 7.4
B
300
100
1mM ATP
B
e
10
-20
0
20
Displacement (nm)
Figure 6