scholarly journals Three-dimensional stochastic model of actin–myosin binding in the sarcomere lattice

2016 ◽  
Vol 148 (6) ◽  
pp. 459-488 ◽  
Author(s):  
Srboljub M. Mijailovich ◽  
Oliver Kayser-Herold ◽  
Boban Stojanovic ◽  
Djordje Nedic ◽  
Thomas C. Irving ◽  
...  
Keyword(s):  
Kinetic Models ◽  
Striated Muscle ◽  
Three Dimensional ◽  
Limited Range ◽  
Mass Action ◽  
Myosin Filament ◽  
Mass Action Kinetic ◽  
Cross Bridge ◽  
Myosin Binding ◽  
Cross Bridges

The effect of molecule tethering in three-dimensional (3-D) space on bimolecular binding kinetics is rarely addressed and only occasionally incorporated into models of cell motility. The simplest system that can quantitatively determine this effect is the 3-D sarcomere lattice of the striated muscle, where tethered myosin in thick filaments can only bind to a relatively small number of available sites on the actin filament, positioned within a limited range of thermal movement of the myosin head. Here we implement spatially explicit actomyosin interactions into the multiscale Monte Carlo platform MUSICO, specifically defining how geometrical constraints on tethered myosins can modulate state transition rates in the actomyosin cycle. The simulations provide the distribution of myosin bound to sites on actin, ensure conservation of the number of interacting myosins and actin monomers, and most importantly, the departure in behavior of tethered myosin molecules from unconstrained myosin interactions with actin. In addition, MUSICO determines the number of cross-bridges in each actomyosin cycle state, the force and number of attached cross-bridges per myosin filament, the range of cross-bridge forces and accounts for energy consumption. At the macroscopic scale, MUSICO simulations show large differences in predicted force-velocity curves and in the response during early force recovery phase after a step change in length comparing to the two simplest mass action kinetic models. The origin of these differences is rooted in the different fluxes of myosin binding and corresponding instantaneous cross-bridge distributions and quantitatively reflects a major flaw of the mathematical description in all mass action kinetic models. Consequently, this new approach shows that accurate recapitulation of experimental data requires significantly different binding rates, number of actomyosin states, and cross-bridge elasticity than typically used in mass action kinetic models to correctly describe the biochemical reactions of tethered molecules and their interaction energetics.

Regulation of Contraction in Striated Muscle

2000 ◽  
Vol 80 (2) ◽  
pp. 853-924 ◽  
Author(s):  
A. M. Gordon ◽  
E. Homsher ◽  
M. Regnier
Keyword(s):  
Binding Sites ◽  
Thin Filament ◽  
Striated Muscle ◽  
Force Development ◽  
Cross Bridge ◽  
Hydrolysis Products ◽  
Strong Binding ◽  
Regulation Of Contraction ◽  
Myosin Binding ◽  
Cross Bridges

Ca2+ regulation of contraction in vertebrate striated muscle is exerted primarily through effects on the thin filament, which regulate strong cross-bridge binding to actin. Structural and biochemical studies suggest that the position of tropomyosin (Tm) and troponin (Tn) on the thin filament determines the interaction of myosin with the binding sites on actin. These binding sites can be characterized as blocked (unable to bind to cross bridges), closed (able to weakly bind cross bridges), or open (able to bind cross bridges so that they subsequently isomerize to become strongly bound and release ATP hydrolysis products). Flexibility of the Tm may allow variability in actin (A) affinity for myosin along the thin filament other than through a single 7 actin:1 tropomyosin:1 troponin (A7TmTn) regulatory unit. Tm position on the actin filament is regulated by the occupancy of NH-terminal Ca2+binding sites on TnC, conformational changes resulting from Ca2+ binding, and changes in the interactions among Tn, Tm, and actin and as well as by strong S1 binding to actin. Ca2+ binding to TnC enhances TnC-TnI interaction, weakens TnI attachment to its binding sites on 1–2 actins of the regulatory unit, increases Tm movement over the actin surface, and exposes myosin-binding sites on actin previously blocked by Tm. Adjacent Tm are coupled in their overlap regions where Tm movement is also controlled by interactions with TnT. TnT also interacts with TnC-TnI in a Ca2+-dependent manner. All these interactions may vary with the different protein isoforms. The movement of Tm over the actin surface increases the “open” probability of myosin binding sites on actins so that some are in the open configuration available for myosin binding and cross-bridge isomerization to strong binding, force-producing states. In skeletal muscle, strong binding of cycling cross bridges promotes additional Tm movement. This movement effectively stabilizes Tm in the open position and allows cooperative activation of additional actins in that and possibly neighboring A7TmTn regulatory units. The structural and biochemical findings support the physiological observations of steady-state and transient mechanical behavior. Physiological studies suggest the following. 1) Ca2+ binding to Tn/Tm exposes sites on actin to which myosin can bind. 2) Ca2+ regulates the strong binding of M·ADP·Pi to actin, which precedes the production of force (and/or shortening) and release of hydrolysis products. 3) The initial rate of force development depends mostly on the extent of Ca2+ activation of the thin filament and myosin kinetic properties but depends little on the initial force level. 4) A small number of strongly attached cross bridges within an A7TmTn regulatory unit can activate the actins in one unit and perhaps those in neighboring units. This results in additional myosin binding and isomerization to strongly bound states and force production. 5) The rates of the product release steps per se (as indicated by the unloaded shortening velocity) early in shortening are largely independent of the extent of thin filament activation ([Ca2+]) beyond a given baseline level. However, with a greater extent of shortening, the rates depend on the activation level. 6) The cooperativity between neighboring regulatory units contributes to the activation by strong cross bridges of steady-state force but does not affect the rate of force development. 7) Strongly attached, cycling cross bridges can delay relaxation in skeletal muscle in a cooperative manner. 8) Strongly attached and cycling cross bridges can enhance Ca2+ binding to cardiac TnC, but influence skeletal TnC to a lesser extent. 9) Different Tn subunit isoforms can modulate the cross-bridge detachment rate as shown by studies with mutant regulatory proteins in myotubes and in in vitro motility assays. These results and conclusions suggest possible explanations for differences between skeletal and cardiac muscle regulation and delineate the paths future research may take toward a better understanding of striated muscle regulation.

Abstract P338: Myopeptide Improves Contractile Mechanics In A Mouse Model Of Heart Failure Expressing Phosphoablated Cardiac Myosin Binding Protein-C

2021 ◽  
Vol 129 (Suppl_1) ◽  
Author(s):  
Rohit Singh ◽  
Sakthivel Sadayappan
Keyword(s):  
Heart Failure ◽  
Mouse Model ◽  
Protein C ◽  
Cardiac Myosin ◽  
Bridge Formation ◽  
Cross Bridge ◽  
Myosin Binding Protein ◽  
Myosin Binding Protein C ◽  
Myosin Binding ◽  
Cross Bridges

Rationale: Normal heart function depends on cardiac myosin binding protein-C (cMyBP-C) phosphorylation. Its decrease is associated with heart failure (HF) by inhibiting actomyosin interactions. In absence of cMyBP-C phosphorylation, the protein is bound to myosin S2, but released when phosphorylated, allowing myosin to form cross-bridges with actin. Challenging cMyBP-C/myosin S2 interaction by myopeptide (the first 126 amino acids of myosin S2) could promote actomyosin interaction in vitro , but its ability to improve contractility in HF remains untested. Objective: To test contractile function in skinned papillary fibers of a cMyBP-C dephosphorylated mouse model using myopeptide. Methods and Results: To mimic constitutive phosphoablation, a knock-in mouse model was established to express cMyBP-C in which serines 273, 282 and 302 were mutated to alanine (cMyBP-C AAA ). Western blotting revealed 50% and 100% of cMyBP-C AAA in het and homo mouse hearts, respectively. Echocardiography showed a decreased percentage of ejection fraction (28%, p<0.01) and fractional shortening (30%, p< 0.05) in both het and homo cMyBP-C AAA mice at 3 months of age, compared to knock-in negative controls. These mice also developed diastolic dysfunction with elevated ratio of E/A and E/e’ waves. Next, pCa-force measurements using skinned papillary fibers determined that maximal force (F max ) and rate of cross-bridge formation ( k tr ) were decreased in the cMyBP-C AAA groups, compared to the control. However, administration of dose-dependent myopeptide increased F max and k tr in wild-type and cMyBP-C AAA permeabilized skinned papillary fibers without affecting myofilament Ca 2+ sensitivity. Conclusions: Myopeptide can increase contractile force and rate of cross-bridge formation by releasing cMyBP-C/myosin S2 and promoting actomyosin formation of cross-bridges, thus validating its therapeutic potential.

scholarly journals Three-dimensional image reconstruction of insect flight muscle. I. The rigor myac layer.

1989 ◽  
Vol 109 (3) ◽  
pp. 1085-1102 ◽  
Author(s):  
K A Taylor ◽  
M C Reedy ◽  
L Córdova ◽  
M K Reedy
Keyword(s):  
Thin Filament ◽  
Flight Muscle ◽  
Insect Flight ◽  
Three Dimensional ◽  
Bridge Structure ◽  
Insect Flight Muscle ◽  
Single Filament ◽  
Cross Bridge ◽  
Cross Bridges

We have obtained detailed three-dimensional images of in situ cross-bridge structure in insect flight muscle by electron microscopy of multiple tilt views of single filament layers in ultrathin sections, supplemented with data from thick sections. In this report, we describe the images obtained of the myac layer, a 25-nm longitudinal section containing a single layer of alternating myosin and actin filaments. The reconstruction reveals averaged rigor cross-bridges that clearly separate into two classes constituting lead and rear chevrons within each 38.7-nm axial repeat. These two classes differ in tilt angle, size and shape, density, and slew. This new reconstruction confirms our earlier interpretation of the lead bridge as a two-headed cross-bridge and the rear bridge as a single-headed cross-bridge. The importance of complementing tilt series with additional projections outside the goniometer tilt range is demonstrated by comparison with our earlier myac layer reconstruction. Incorporation of this additional data reveals new details of rigor cross-bridge structure in situ which include clear delineation of (a) a triangular shape for the lead bridge, (b) a smaller size for the rear bridge, and (c) density continuity across the thin filament in the lead bridge. Within actin's regular 38.7-nm helical repeat, local twist variations in the thin filament that correlate with the two cross-bridge classes persist in this new reconstruction. These observations show that in situ rigor cross-bridges are not uniform, and suggest three different myosin head conformations in rigor.

scholarly journals Myosin Cross-bridge Behaviour in Contracting Muscle – The T1 Curve of Huxley & Simmons (1971) Revisited

2019 ◽  
Author(s):  
Carlo Knupp ◽  
John M. Squire
Keyword(s):  
Actin Filaments ◽  
Striated Muscle ◽  
X Ray Diffraction ◽  
Step Size ◽  
Weakly Bound ◽  
X Ray ◽  
Cross Bridge ◽  
Key Factor ◽  
Length Changes ◽  
Cross Bridges

The stiffness of the myosin cross-bridges is a key factor in analysing possible scenarios to explain myosin head changes during force generation in active muscles.&nbsp; The seminal study of Huxley and Simmons (1971: Nature 233: 533) suggested that most of the observed half-sarcomere instantaneous compliance (=1/stiffness) resides in the myosin heads.&nbsp;&nbsp;&nbsp; They showed with a so-called T1 plot that, after a very fast release, the half-sarcomere tension reduced to zero after a step size of about 60&Aring; (later with improved experiments reduced to 40&Aring;).&nbsp;&nbsp; However, later X-ray diffraction studies showed that myosin and actin filaments themselves stretch slightly under tension, which means that most (at least two-thirds) of the half sarcomere compliance comes from the filaments and not from cross-bridges.&nbsp;&nbsp;&nbsp; Here we have used a different approach, namely to model the compliances in a virtual half sarcomere structure in silico.&nbsp;&nbsp; We confirm that the T1 curve comes almost entirely from length changes in the myosin and actin filaments, because the calculated cross-bridge stiffness (probably greater than 0.4 pN/&Aring;) is higher than previous studies have suggested.&nbsp;&nbsp;&nbsp; In the light of this, we present a plausible modified scenario to describe aspects of the myosin cross-bridge cycle in active muscle.&nbsp;&nbsp; In particular, we suggest that, apart from the filament compliances, most of the cross-bridge contribution to the instantaneous T1 response comes from weakly-bound myosin heads, not myosin heads in strongly attached states.&nbsp;&nbsp; The strongly attached heads would still contribute to the T1 curve, but only in a very minor way, with a stiffness that we postulate could be around 0.1 pN/&Aring;, a value which would generate a working stroke close to 100 &Aring; from the hydrolysis of one ATP molecule.&nbsp; The new program can serve as a tool to calculate sarcomere elastic properties for any vertebrate striated muscle once various parameters have been determined (e.g. tension, T1 intercept, temperature, X-ray diffraction spacing results).

Cross bridge-dependent activation of contraction in cardiac myofibrils at low pH

1999 ◽  
Vol 276 (5) ◽  
pp. H1460-H1467 ◽  
Author(s):  
D. R. Swartz ◽  
D. Zhang ◽  
K. W. Yancey
Keyword(s):  
Atpase Activity ◽  
Calcium Binding ◽  
Striated Muscle ◽  
Contractile Activity ◽  
Low Ph ◽  
Myofibrillar Atpase ◽  
Peak Activity ◽  
Cross Bridge ◽  
Myofibrillar Atpase Activity ◽  
Cross Bridges

Striated muscle contracts in the absence of calcium at low concentrations of MgATP ([MgATP]), and this has been termed rigor activation because rigor cross bridges attach and activate adjacent actin sites. This process is well characterized in skeletal muscle but not in cardiac muscle. Rigor cross bridges are also thought to increase calcium binding to troponin C and play a synergistic role in activation. We tested the hypothesis that cross bridge-dependent activation results in an increase in contractile activity at normal and low pH values. Myofibrillar ATPase activity was measured as a function of pCa and [MgATP] at pH 7.0, and the data showed that, at pCa values of ≥5.5, there was a biphasic relationship between activity and [MgATP]. Peak activity occurred at 10–50 μM MgATP, and [MgATP] for peak activity was lower with increased pCa. The ATPase activity of rat cardiac myofibrils as a function of [MgATP] at a pCa of 9.0 was measured at several pH levels (pH 5.4–7.0). The ATPase activity as a function of [MgATP] was biphasic with a maximum at 8–10 μM MgATP. Lower pH did not result in a substantial decrease in myofibrillar ATPase activity even at pH 5.4. The extent of shortening, as measured by Z-line spacing, was greatest at 8 μM MgATP and less at both lower and higher [MgATP], and this response was observed at all pH levels. These studies suggest that the peak ATPase activity associated with low [MgATP] was coupled to sarcomere shortening. These results support the hypothesis that cross bridge-dependent activation of contraction may be responsible for contracture in the ischemic heart.

scholarly journals Myosin Cross-Bridge Behaviour in Contracting Muscle—The T1 Curve of Huxley and Simmons (1971) Revisited

2019 ◽  
Vol 20 (19) ◽  
pp. 4892 ◽  
Author(s):  
Knupp ◽  
Squire
Keyword(s):  
Actin Filaments ◽  
Striated Muscle ◽  
Reliable Estimate ◽  
X Ray Diffraction ◽  
Step Size ◽  
X Ray ◽  
Cross Bridge ◽  
Length Changes ◽  
The Cross ◽  
Cross Bridges

The stiffness of the myosin cross-bridges is a key factor in analysing possible scenarios to explain myosin head changes during force generation in active muscles. The seminal study of Huxley and Simmons (1971: Nature 233: 533) suggested that most of the observed half-sarcomere instantaneous compliance (=1/stiffness) resides in the myosin heads. They showed with a so-called T1 plot that, after a very fast release, the half-sarcomere tension reduced to zero after a step size of about 60Å (later with improved experiments reduced to 40Å). However, later X-ray diffraction studies showed that myosin and actin filaments themselves stretch slightly under tension, which means that most (at least two-thirds) of the half sarcomere compliance comes from the filaments and not from cross-bridges. Here we have used a different approach, namely to model the compliances in a virtual half sarcomere structure in silico. We confirm that the T1 curve comes almost entirely from length changes in the myosin and actin filaments, because the calculated cross-bridge stiffness (probably greater than 0.4 pN/Å) is higher than previous studies have suggested. Our model demonstrates that the formulations produced by previous authors give very similar results to our model if the same starting parameters are used. However, we find that it is necessary to model the X-ray diffraction data as well as mechanics data to get a reliable estimate of the cross-bridge stiffness. In the light of the high cross-bridge stiffness found in the present study, we present a plausible modified scenario to describe aspects of the myosin cross-bridge cycle in active muscle. In particular, we suggest that, apart from the filament compliances, most of the cross-bridge contribution to the instantaneous T1 response may come from weakly-bound myosin heads, not myosin heads in strongly attached states. The strongly attached heads would still contribute to the T1 curve, but only in a very minor way, with a stiffness that we postulate could be around 0.1 pN/Å, a value which would generate a working stroke close to 100 Å from the hydrolysis of one ATP molecule. The new model can serve as a tool to calculate sarcomere elastic properties for any vertebrate striated muscle once various parameters have been determined (e.g., tension, T1 intercept, temperature, X-ray diffraction spacing results).

scholarly journals Measuring myosin cross-bridge attachment time in activated muscle fibers using stochastic vs. sinusoidal length perturbation analysis

2011 ◽  
Vol 110 (4) ◽  
pp. 1101-1108 ◽  
Author(s):  
Bertrand C. W. Tanner ◽  
Yuan Wang ◽  
David W. Maughan ◽  
Bradley M. Palmer
Keyword(s):  
White Noise ◽  
Striated Muscle ◽  
Flight Muscle ◽  
Noise Analysis ◽  
Muscle Fibers ◽  
White Noise Analysis ◽  
Sinusoidal Analysis ◽  
Cross Bridge ◽  
Cross Bridges ◽  
Time Required

The average time myosin cross bridges remain bound to actin ( ton) can be measured by sinusoidal length perturbations (sinusoidal analysis) of striated muscle fibers using recently developed analytic methods. This approach allows measurements of ton in preparations possessing a physiologically relevant myofilament lattice. In this study, we developed an approach to measure ton in 5–10% of the time required for sinusoidal analysis by using stochastic length perturbations (white noise analysis). To compare these methods, we measured the influence of MgATP concentration ([MgATP]) on ton in demembranated myocardial strips from mice, sampling muscle behavior from 0.125 to 200 Hz with a 20-s burst of white noise vs. a 300-s series of sinusoids. Both methods detected a similar >300% increase in ton as [MgATP] decreased from 5 to 0.25 mM, differing by only 3–14% at any [MgATP]. Additional experiments with Drosophila indirect flight muscle fibers demonstrated that faster cross-bridge cycling kinetics permit further reducing of the perturbation time required to measure ton. This reduced sampling time allowed strain-dependent measurements of ton in flight muscle fibers by combining 10-s bursts of white noise during periods of linear shortening and lengthening. Analyses revealed longer ton values during shortening and shorter ton values during lengthening. This asymmetry may provide a mechanism that contributes to oscillatory energy transfer between the flight muscles and thoracic cuticle to power flight. This study demonstrates that white noise analysis can detect underlying molecular processes associated with dynamic muscle contraction comparable to sinusoidal analysis, but in a fraction of the time.

Oxytocin-mediated recruitment of slowly cycling cross bridges and isometric force in rat myometrium

1996 ◽  
Vol 270 (2) ◽  
pp. E203-E208
Author(s):  
A. L. Ruzycky ◽  
B. T. Ameredes
Keyword(s):  
Isometric Force ◽  
Additional Stress ◽  
Shortening Velocity ◽  
Cycling Rate ◽  
Quick Release ◽  
Cross Bridge ◽  
Cross Bridges ◽  
Unit Stress ◽  
Release Method ◽  
The Relationship

The relationship between cross-bridge cycling rate and isometric stress was investigated in rat myometrium. Stress production by myometrial strips was measured under resting, K+ depolarization, and oxytocin-stimulated conditions. Cross-bridge cycling rates were determined from measurements of maximal unloaded shortening velocity, using the quick-release method. Force redevelopment after the quick release was used as an index of cross-bridge attachment. With maximal K+ stimulation, stress increased with increased cross-bridge cycling (+76%; P < 0.05) and attached cross bridges (+112%; P < 0.05). Addition of oxytocin during K+ stimulation further increased stress (+30%; P < 0.05). With this force component, the cross-bridge cycling rate decreased (-60%; P < 0.05) similar to that under resting conditions. Attached cross-bridges did not increase with this additional stress. The results suggest two distinct mechanisms mediating myometrial contractions. One requires elevated intracellular calcium and rapidly cycling cross bridges. The other mechanism may be independent of calcium and appears to be mediated by slowly cycling cross bridges, supporting greater unit stress.

Cross-bridge blocker BTS permits direct measurement of SR Ca2+ pump ATP utilization in toadfish swimbladder muscle fibers

2003 ◽  
Vol 285 (4) ◽  
pp. C781-C787 ◽  
Author(s):  
Iain S. Young ◽  
Claire L. Harwood ◽  
Lawrence C. Rome
Keyword(s):  
Sarcoplasmic Reticulum ◽  
Direct Measurement ◽  
Motor Behavior ◽  
Force Generation ◽  
Skinned Fibers ◽  
Control Value ◽  
Cross Bridge ◽  
Direct Measurements ◽  
Hill Coefficients ◽  
Cross Bridges

Because the major processes involved in muscle contraction require rapid utilization of ATP, measurement of ATP utilization can provide important insights into the mechanisms of contraction. It is necessary, however, to differentiate between the contribution made by cross-bridges and that of the sarcoplasmic reticulum (SR) Ca2+ pumps. Specific and potent SR Ca2+ pump blockers have been used in skinned fibers to permit direct measurement of cross-bridge ATP utilization. Up to now, there was no analogous cross-bridge blocker. Recently, N-benzyl- p-toluene sulfonamide (BTS) was found to suppress force generation at micromolar concentrations. We tested whether BTS could be used to block cross-bridge ATP utilization, thereby permitting direct measurement of SR Ca2+ pump ATP utilization in saponin-skinned fibers. At 25 μM, BTS virtually eliminates force and cross-bridge ATP utilization (both <4% of control value). By taking advantage of the toadfish swimbladder muscle's unique right shift in its force-Ca2+ concentration ([Ca2+]) relationship, we measured SR Ca2+ pump ATP utilization in the presence and absence of BTS. At 25 μM, BTS had no effect on SR pump ATP utilization. Hence, we used BTS to make some of the first direct measurements of ATP utilization of intact SR over a physiological range of [Ca2+]at 15°C. Curve fits to SR Ca2+ pump ATP utilization vs. pCa indicate that they have much lower Hill coefficients (1.49) than that describing cross-bridge force generation vs. pCa (∼5). Furthermore, we found that BTS also effectively eliminates force generation in bundles of intact swimbladder muscle, suggesting that it will be an important tool for studying integrated SR function during normal motor behavior.

Heat production of rat anococcygeus muscle during isometric contraction

1988 ◽  
Vol 255 (4) ◽  
pp. C536-C542 ◽  
Author(s):  
J. S. Walker ◽  
I. R. Wendt ◽  
C. L. Gibbs
Keyword(s):  
Energy Expenditure ◽  
Heat Production ◽  
Progressive Increase ◽  
Isometric Contractions ◽  
Shortening Velocity ◽  
Anococcygeus Muscle ◽  
Cross Bridge ◽  
Time Integral ◽  
Rat Anococcygeus Muscle ◽  
Cross Bridges

Heat production, unloaded shortening velocity (Vus), and load-bearing capacity (LBC) were studied in the isolated rat anococcygeus muscle during isometric contractions at 27 degrees C. The relation between the total suprabasal heat produced and the stress-time integral for isometric contractions of various durations was curvilinear, demonstrating a decreasing slope as contractile duration increased. The rate of heat production at 600 s was approximately 68% of the peak value of 6.55 mW/g that occurred at 10 s. At the same time, force rose from a mean of 92 mN/mm2 at 10 s to a value of 140 mN/mm2 at 600 s. This produced a nearly threefold increase in the economy of force maintenance. The decline in the rate of heat production was accompanied by a decline in Vus from 0.56 Lo/s at 10 s to 0.28 Lo/s at 600 s, where Lo is the length for optimal force development. This suggests the fall in the rate of heat production was caused, at least in part, by a slowing of cross-bridge kinetics. The ratio of LBC to developed tension at 10 s was not significantly different from the ratio at 600 s, suggesting that the increase in tension was due to an increased number of attached cross bridges. The decline in heat production, therefore, appears contradictory, since an increased number of attached cross bridges would predict an increased rate of energy expenditure. The observations can be reconciled if either 1) the increase in force is caused by a progressive increase in the attachment time of a constant number of cross bridges that cycle at a lower frequency or 2) the decline in energy expenditure caused by the slowing of cross-bridge cycling is sufficient to mask the increase caused by the recruitment of additional cross bridges.

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