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• W3198186923 abstract "Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin–myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin–myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation. Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin–myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin–myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation. Molecular motors such as myosin and kinesin often work in groups to perform diverse biological functions such as vesicle transport, cell division, wound healing, and muscle contraction (1Bray D. Cell Movement from Molecules to Motility.1st Ed. Garland Publishing, New York, NY2001Google Scholar, 2Howard J. Mechanics of Motor Proteins and the Cytoskeleton.1st Ed. Sinauer Associates, Sunderland, MA2001Google Scholar, 3Phillips R. Kondev J. Theriot J. Physical Biology of the Cell.1st Ed. Garland Science, New York, NY2010Google Scholar). The mechanochemistry of individual motors is in many instances well characterized (4Baker J.E. Brosseau C. Joel P.B. Warshaw D.M. The biochemical kinetics underlying actin movement generated by one and many skeletal muscle myosin molecules.Biophys. J. 2002; 82: 2134-2147Abstract Full Text Full Text PDF PubMed Scopus (92) Google Scholar, 5Palmiter K. Tyska M.J. Dupuis D.E. Alpert N.R. Warshaw D.M. Kinetic differences at the single molecule level account for the functional diversity of rabbit cardiac myosin isoforms.J. Physiol. 1999; 519 Pt 3: 669-678Crossref PubMed Scopus (100) Google Scholar, 6Veigel C. Molloy J.E. Schmitz S. Kendrick-jones J. Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers.Nat. Cell Biol. 2003; 5: 980-986Crossref PubMed Scopus (262) Google Scholar, 7Svoboda K. Block S.M. Force and velocity measured for single kinesin molecules.Cell. 1994; 77: 773-784Abstract Full Text PDF PubMed Scopus (700) Google Scholar, 8Baker J.E. Krementsova E.B. Kennedy G.G. Armstrong A. Trybus K.M. Warshaw D.M. Myosin V processivity: Multiple kinetic pathways for head-to-head coordination.Proc. Natl. Acad. Sci. U. S. A. 2004; 101: 5542-5546Crossref PubMed Scopus (137) Google Scholar), and determining how molecular motor mechanics scale from single molecule to ensemble mechanochemistry is the next step in understanding the macroscopic mechanics of biological systems. Our understanding of the factors that influence macroscopic mechanics is currently underdeveloped. These factors include basic relationships between motor kinetics, energetics, force generation, force transmission, compliant linkages, and external loads. The goal of this study is to better define these relationships in order to more accurately describe the emergent mechanics of molecular motor ensembles. Optical traps and in vitro motility experiments have been used to study how force and motion generation change with increasing numbers, N, of motors (9Kad N.M. Kim S. Warshaw D.M. VanBuren P. Baker J.E. Single-myosin crossbridge interactions with actin filaments regulated by troponin-tropomyosin.Proc. Natl. Acad. Sci. U. S. A. 2005; 102: 16990-16995Crossref PubMed Scopus (60) Google Scholar, 10Brizendine R.K. Alcala D.B. Carter M.S. Haldeman B.D. Facemyer K.C. Baker J.E. Cremo C.R. Velocities of unloaded muscle filaments are not limited by drag forces imposed by myosin cross-bridges.Proc. Natl. Acad. Sci. U. S. A. 2015; 112: 11235-11240Crossref PubMed Scopus (28) Google Scholar, 11Walcott S. Warshaw D.M. Debold E.P. Mechanical coupling between myosin molecules causes differences between ensemble and single-molecule measurements.Biophys. J. 2012; 103: 501-510Abstract Full Text Full Text PDF PubMed Scopus (73) Google Scholar) and in general show that the mechanics of many motors working together is not a simple sum of the molecular mechanics of individual motors (4Baker J.E. Brosseau C. Joel P.B. Warshaw D.M. The biochemical kinetics underlying actin movement generated by one and many skeletal muscle myosin molecules.Biophys. J. 2002; 82: 2134-2147Abstract Full Text Full Text PDF PubMed Scopus (92) Google Scholar, 12Kaya M. Tani Y. Washio T. Hisada T. Higuchi H. Coordinated force generation of skeletal myosins in myofilaments through motor coupling.Nat. Commun. 2017; 8: 16036Crossref PubMed Scopus (33) Google Scholar, 13Pertici I. Bongini L. Melli L. Bianchi G. Salvi L. Falorsi G. Squarci C. Bozó T. Cojoc D. Kellermayer M.S.Z. Lombardi V. Bianco P. A myosin II nanomachine mimicking the striated muscle.Nat. Commun. 2018; 9: 3532Crossref PubMed Scopus (20) Google Scholar). Consistent with the chemical thermodynamic model that we first proposed over 20 years ago (14Baker J.E. Thomas D.D. A thermodynamic muscle model and a chemical basis for A. V. Hill’ s muscle equation.J. Muscle Res. Cell Motil. 2000; 21: 335-344Crossref PubMed Scopus (29) Google Scholar), many studies now indicate that force is collectively generated and thermally distributed within systems of motors (12Kaya M. Tani Y. Washio T. Hisada T. Higuchi H. Coordinated force generation of skeletal myosins in myofilaments through motor coupling.Nat. Commun. 2017; 8: 16036Crossref PubMed Scopus (33) Google Scholar, 13Pertici I. Bongini L. Melli L. Bianchi G. Salvi L. Falorsi G. Squarci C. Bozó T. Cojoc D. Kellermayer M.S.Z. Lombardi V. Bianco P. A myosin II nanomachine mimicking the striated muscle.Nat. Commun. 2018; 9: 3532Crossref PubMed Scopus (20) Google Scholar, 15Uçar M.C. Lipowsky R. Collective force generation by molecular motors is determined by strain-induced unbinding.Nano Lett. 2020; 20: 669-676Crossref PubMed Scopus (8) Google Scholar). This leads to emergent mechanochemical properties (12Kaya M. Tani Y. Washio T. Hisada T. Higuchi H. Coordinated force generation of skeletal myosins in myofilaments through motor coupling.Nat. Commun. 2017; 8: 16036Crossref PubMed Scopus (33) Google Scholar, 13Pertici I. Bongini L. Melli L. Bianchi G. Salvi L. Falorsi G. Squarci C. Bozó T. Cojoc D. Kellermayer M.S.Z. Lombardi V. Bianco P. A myosin II nanomachine mimicking the striated muscle.Nat. Commun. 2018; 9: 3532Crossref PubMed Scopus (20) Google Scholar, 16Hooft A.M. Maki E.J. Cox K.K. Baker J.E. An accelerated state of myosin-based actin motility.Biochemistry. 2007; 46: 3513-3520Crossref PubMed Scopus (46) Google Scholar) that are more accurately described by the thermodynamics of a motor ensemble than by molecular mechanics (14Baker J.E. Thomas D.D. A thermodynamic muscle model and a chemical basis for A. V. Hill’ s muscle equation.J. Muscle Res. Cell Motil. 2000; 21: 335-344Crossref PubMed Scopus (29) Google Scholar, 17Baker J.E. LaConte L.E.W. Brust-Mascher I. Thomas D.D. Mechanochemical coupling in spin-labeled, active, isometric muscle.Biophys. J. 1999; 77: 2657-2664Abstract Full Text Full Text PDF PubMed Scopus (35) Google Scholar, 18Baker J.E. Free energy transduction in a chemical motor model.J. Theor. Biol. 2004; 228: 467-476Crossref PubMed Scopus (19) Google Scholar). With thousands of myosin molecules working together to generate force and movement, muscle is an ideal system in which to study emergent motor behaviors. In the 1920s and 1930s, early pioneers in biophysics like A.V. Hill and W.O. Fenn made precise measurements of muscle power and heat output (19Hill A.V. The heat of shortening and the dynamic constants of muscle.Proc. R. Soc. Lond. B. 1938; 126: 136-195Crossref Google Scholar, 20Fenn W. A quantitative comparison between the energy liberated and the work performed by the isolated sartorius muscle of the frog.J. Physiol. 1923; 58: 175-203Crossref PubMed Scopus (255) Google Scholar, 21Fenn W.O. Brody H. Petrilli A. The tension developed by human muscles at different velocities of muscle shortening.Am. J. Physiol. 1931; 97: 1-14Crossref Google Scholar) that established macroscopic energetic constraints (like muscle force) on muscle mechanics and chemistry using classical chemical thermodynamics. Since then, researchers have focused more on reductionist approaches using electron microscopy, X-ray diffraction, spectroscopic techniques, stopped flow kinetics, crystal structures, and single molecule mechanics measurements (22Rayment I. Rypniewski W.R. Schmidt-Bäse K. Smith R. Tomchick D.R. Benning M.M. Winkelmann D.A. Wesenberg G. Holden H.M. Three-dimensional structure of myosin subfragment-1: A molecular motor.Science. 1993; 261: 50-58Crossref PubMed Scopus (1849) Google Scholar, 23Kabsch W. Mannherz H.G. Suck D. Pai E.F. Holmes K.C. Atomic structure of the actin:DNase I complex.Nature. 1990; 347: 37-44Crossref PubMed Scopus (1515) Google Scholar, 24Lymn R.W. Taylor E.W. Mechanism of adenosine triphosphate hydrolysis by actomyosin.Biochemistry. 1971; 10: 4617-4624Crossref PubMed Scopus (1011) Google Scholar, 25Sabido-David C. Hopkins S.C. Saraswat L.D. Lowey S. Goldman Y.E. Irving M. Orientation changes of fluorescent probes at five sites on the myosin regulatory light chain during contraction of single skeletal muscle fibres.J. Mol. Biol. 1998; 279: 387-402Crossref PubMed Scopus (45) Google Scholar, 26Goldman Y.E. Kinetics of the actomyosin ATPase in muscle fibers.Annu. Rev. Physiol. 1987; 49: 637-654Crossref PubMed Scopus (141) Google Scholar, 27Holmes K.C. Geeves M.A. The structural basis of muscle contraction.Philos. Trans. R. Soc. Lond. B Biol. Sci. 2000; 355: 419-431Crossref PubMed Scopus (121) Google Scholar, 28Baker J.E. Brust-Mascher I. Ramachandran S. LaConte L.E. Thomas D.D. A large and distinct rotation of the myosin light chain domain occurs upon muscle contraction.Proc. Natl. Acad. Sci. U. S. A. 1998; 95: 2944-2949Crossref PubMed Scopus (123) Google Scholar, 29Ross J.L. Ali M.Y. Warshaw D.M. Cargo transport: Molecular motors navigate a complex cytoskeleton.Curr. Opin. Cell Biol. 2008; 20: 41-47Crossref PubMed Scopus (237) Google Scholar) to provide detailed structural, biochemical, and mechanical descriptions of the molecules involved in muscle contraction. For example, from these studies we now know that the basic molecular mechanism for muscle contraction involves a discrete displacement of an actin filament generated by a myosin structural change induced by strong actin binding. However, despite these remarkable insights into basic molecular mechanisms, it is still unclear how these observable, simple, discrete molecular mechanisms scale up to the mechanics and chemistry of muscle in a way that is consistent with the macroscopic energetic constraints described by Hill and Fenn (19Hill A.V. The heat of shortening and the dynamic constants of muscle.Proc. R. Soc. Lond. B. 1938; 126: 136-195Crossref Google Scholar, 21Fenn W.O. Brody H. Petrilli A. The tension developed by human muscles at different velocities of muscle shortening.Am. J. Physiol. 1931; 97: 1-14Crossref Google Scholar) and more recently implied by our observation that the free energy for the discrete myosin working step is a function of muscle force (17Baker J.E. LaConte L.E.W. Brust-Mascher I. Thomas D.D. Mechanochemical coupling in spin-labeled, active, isometric muscle.Biophys. J. 1999; 77: 2657-2664Abstract Full Text Full Text PDF PubMed Scopus (35) Google Scholar). The conventional independent force model of muscle contraction assumes that actin sliding velocities, Vmax, are limited by detachment of individual myosin motors from actin (30Huxley A.F. Muscle structure and theories of contraction.Prog. Biophys. Biophys. Chem. 1957; 7: 255-318Crossref PubMed Google Scholar). However, this model does not account for the thermal equilibration of forces that exists in most chemical systems and is inconsistent with the observation that Vmax is influenced by both actin–myosin attachment (4Baker J.E. Brosseau C. Joel P.B. Warshaw D.M. The biochemical kinetics underlying actin movement generated by one and many skeletal muscle myosin molecules.Biophys. J. 2002; 82: 2134-2147Abstract Full Text Full Text PDF PubMed Scopus (92) Google Scholar, 10Brizendine R.K. Alcala D.B. Carter M.S. Haldeman B.D. Facemyer K.C. Baker J.E. Cremo C.R. Velocities of unloaded muscle filaments are not limited by drag forces imposed by myosin cross-bridges.Proc. Natl. Acad. Sci. U. S. A. 2015; 112: 11235-11240Crossref PubMed Scopus (28) Google Scholar, 16Hooft A.M. Maki E.J. Cox K.K. Baker J.E. An accelerated state of myosin-based actin motility.Biochemistry. 2007; 46: 3513-3520Crossref PubMed Scopus (46) Google Scholar, 18Baker J.E. Free energy transduction in a chemical motor model.J. Theor. Biol. 2004; 228: 467-476Crossref PubMed Scopus (19) Google Scholar, 31Bárány M. ATPase activity of myosin correlated with speed of muscle shortening.J. Gen. Physiol. 1967; 50: 197-218Crossref PubMed Scopus (1368) Google Scholar) and detachment kinetics (30Huxley A.F. Muscle structure and theories of contraction.Prog. Biophys. Biophys. Chem. 1957; 7: 255-318Crossref PubMed Google Scholar, 32Uyeda T.Q. Kron S.J. Spudich J.A. Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin.J. Mol. Biol. 1990; 214: 699-710Crossref PubMed Scopus (361) Google Scholar). Here we use mathematical modeling and an in vitro motility assay to better understand how both attachment and detachment kinetics contribute to Vmax. In an in vitro motility assay, the velocity, V(N), at which actin filaments slide over a bed of myosin molecules increases with increasing numbers, N, of myosin molecules, saturating at a maximum velocity, Vmax, through a mechanism that continues to be disputed. For decades, it has widely been assumed that—in accord with independent force models—Vmax is limited by what are effectively molecular mechanical barriers to force transmission between independent force generators (30Huxley A.F. Muscle structure and theories of contraction.Prog. Biophys. Biophys. Chem. 1957; 7: 255-318Crossref PubMed Google Scholar, 32Uyeda T.Q. Kron S.J. Spudich J.A. Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin.J. Mol. Biol. 1990; 214: 699-710Crossref PubMed Scopus (361) Google Scholar). Specifically, a single strongly bound myosin head is assumed to prevent the working step of other myosin heads from moving actin and transmitting forces between them, and thus movement is limited by detachment of the resistive myosin head. To describe this hypothetical mechanical limit to Vmax, we consider the probability, P(N), that N myosin heads stall actin movement by myosin working steps. According to the independent force model, P(N) is simply the probability that at least one myosin head is bound to actin (32Uyeda T.Q. Kron S.J. Spudich J.A. Myosin step size. Estimation from slow sliding movement of actin over low densities of heavy meromyosin.J. Mol. Biol. 1990; 214: 699-710Crossref PubMed Scopus (361) Google Scholar). According to a collective displacement model that we recently developed, P(N) is the probability that at least one myosin head is bound to actin and has reached the end of its mechanical tether (33Brizendine R.K. Sheehy G.G. Alcala D.B. Novenschi S.I. Baker J.E. Cremo C.R. A mixed-kinetic model describes unloaded velocities of smooth, skeletal, and cardiac muscle myosin filaments in vitro.Sci. Adv. 2017; 3eaao2267Crossref PubMed Scopus (16) Google Scholar). Here we develop a thermodynamic force model in which P(N) is the probability that an ensemble of myosin heads collectively reaches an internal stall force. Of importance, P(N) in the latter two models is clearly less than that in the independent force model. In all models, when P(N) = 1, actin movement can only occur with the detachment of the resistive head(s) (see Experimental procedures), at which point V(N) saturates at a Vmax that is limited by actin–myosin detachment kinetics. Although this solid-state, detachment limit is theoretically possible within any of the above models, here we show that experimentally it is never reached (P(N) is always less than one) by myosin ensembles under physiological conditions. We determine the chemical kinetics underlying V(N), P(N), and Vmax using an in vitro motility assay to directly measure and correlate, under nearly identical conditions, the N-dependence of actin sliding velocities, V(N); actin-activated ATPase activity, v(N); small molecule inhibition of ATPase activity; force generation against a mechanical load, F(N); and calcium sensitivity of thin filaments, pCa50(N). In all cases, we observe that these N-dependent measurements saturate at an N similar to that at which v(N) saturates, consistent with saturation of myosin-binding sites on actin. According to an independent force model this means that, at saturating N, there is an insufficient number of myosin heads for processive movement (P(N) < 1). Here we show that, according to a thermodynamic force model, a peak V is reached well before the detachment limit (P(N) < 1) with at least one myosin head strongly bound to actin. Our data and analysis support a classic chemical thermodynamic framework for describing motor ensemble mechanochemistry, demonstrating that force generation is thermally equilibrated within ensemble motor systems. Here, within this formal framework, we continue to develop the first molecularly explicit models for how myosin working steps, resistive myosin heads, and external loads influence V(N) and how their relative contributions change with changes in N, linker compliance, and actin–myosin kinetics and energetics. These chemical thermodynamic mechanisms are broadly applicable to any molecular motor ensemble and account for our observations that both V(N) and v(N) are influenced by the strain-dependent kinetics of the myosin working step and that V(N) saturates at a Vmax that is influenced 40% by attachment kinetics and 60% by detachment kinetics. Figure 1A is a kinetic scheme of the actin–myosin ATPase reaction showing that the working step of a myosin head displaces an actin filament a distance d, upon strong actin binding at a rate katt, and a myosin head detaches from actin at a rate kdet. In an independent force model (Fig. 1B, top) actin sliding velocities are described in terms of the kinetics and mechanics of an individual myosin head, Vmax = d·kdet. According to this model, Vmax is fully determined by the displacement, d, generated by a single myosin head and by a single rate constant, kdet (Fig. 1C), and thus Vmax is inherently detachment limited. The N-dependence of V is determined by the probability that at least one myosin head is strongly bound to actin (i.e., one strongly bound myosin head is sufficient to prevent the working step of other myosin heads from moving actin). In a chemical thermodynamic model (Fig. 1B, bottom) multiple myosin heads collectively move an actin filament at Vatt = d·v (Fig. 1D) where v is the bulk (N-dependent) ATPase rate. A myosin head strongly bound to an actin filament imposes a resistive but nonarresting load against actin movement, and with increasing N a detachment limited Vdet = L·kdet is approached when a stall force is reached at the bulk (N-dependent) average maximum displacement, L. Movement resumes when myosin heads detach from actin at a bulk (N-dependent) rate (Fig. 1D). Figure 1D shows that, according to a thermodynamic model, actin sliding velocities are influenced by both attachment and detachment kinetics. The N-dependent velocities, V(N), predicted by these two models are fundamentally different. Figure 2, A–C show the effects of attachment kinetics (katt of 55, 8, and 2 s−1) on V(N) predicted by three models (see Experimental procedures): independent force (equation), collective displacement (equation), and thermodynamic force (discrete state simulation). According to all three models, when N is increased without bound (no saturation of binding sites), V(N) eventually saturates at a Vdet that is independent of N and katt and decreasing katt increases the myosin KM (N at half Vdet) without affecting Vmax = Vdet. We use an in vitro motility assay to directly test whether decreasing katt increases KM without affecting Vmax = Vdet. Counter to predictions of all three models, Figure 2D shows that blebbistatin inhibition of katt (34Kovács M. Tóth J. Hetényi C. Málnási-Csizmadia A. Sellers J.R. Mechanism of blebbistatin inhibition of myosin II.J. Biol. Chem. 2004; 279: 35557-35563Abstract Full Text Full Text PDF PubMed Scopus (679) Google Scholar) inhibits Vmax without increasing KM. This is consistent with previous studies showing that, at saturating N, Vmax is influenced by katt (35Stewart T.J. Jackson D.R. Smith R.D. Shannon S.F. Cremo C.R. Baker J.E. Actin sliding velocities are influenced by the driving forces of actin-myosin binding.Cell. Mol. Bioeng. 2013; 6: 26-37Crossref PubMed Scopus (14) Google Scholar). These results suggest that Vmax in a motility assay is not detachment limited (i.e., is not equal to Vdet) and indicate that V(N) saturates before a detachment limit is reached (when P(N) < 1). Here we test an alternative hypothesis that V(N) saturates not at the detachment limit but with the saturation of myosin-binding sites on actin. According to this hypothesis, V(N) and the actin–myosin ATPase rate, v(N), should exhibit similar saturation kinetics (KM) and correlated maximal activities (Vmax and vmax) (Equation 2). To test this prediction, we directly measured the N-dependence of both V and v in motility assays to determine Vmax and vmax and the myosin KM for V and v at two different ionic strengths. Figure 3 shows the N-dependence of v in an in vitro motility assay both with and without actin filaments. Because both experiments were prepared identically with the exception of the addition of actin, the difference in these activities is the actin-activated activity. From the activities in Figure 3 and the myosin densities and flow cell geometry described (36Harris D.E. Warshaw D.M. Smooth and skeletal muscle myosin both exhibit low duty cycles at zero load in vitro.J. Biol. Chem. 1993; 268: 14764-14768Abstract Full Text PDF PubMed Google Scholar), we estimated the baseline Mg-ATPase activity of myosin on the motility surface to be approximately 2 s−1, which is more than 30-fold higher than that measured in solution studies (37Taylor E.W. Sleep J.A. Intermediate states of actomyosin adenosine triphosphatase.Biochemistry. 1976; 15: 5813-5817Crossref PubMed Scopus (35) Google Scholar). This suggests that binding of myosin to the surface partially activates Mg-ATPase and/or that some of the basal activity comes from myosin in solution (not bound to the surface) that was not completely removed with the washes. Previous studies (36Harris D.E. Warshaw D.M. Smooth and skeletal muscle myosin both exhibit low duty cycles at zero load in vitro.J. Biol. Chem. 1993; 268: 14764-14768Abstract Full Text PDF PubMed Google Scholar) have shown a linear increase in myosin ATPase activity (no actin) with increasing N similar to that shown in Figure 3, suggesting that saturation of the motility surface contributes to neither the saturation of V(N) nor v(N). To maximize the v signal, we used higher concentrations of actin in this assay than typically used in a motility assay, and we confirmed that the majority of actin filaments were still moving under these conditions. Assuming an actin-activated ATPase activity of 40 s−1 (20-fold over 2 s−1), the ∼4-fold actin activation of ATPase activity observed at low N in Figure 3 suggests that ∼20% of myosin on the surface are activated by actin in this assay. Figure 4 shows v(N) and V(N) measurements obtained in a motility assay at two different ionic strengths fit to hyperbolas. These data show that increasing KCl from 50 to 100 mM results in similar decreases in both Vmax and vmax (32 ± 20% and 51 ± 28%, respectively), consistent with Vatt influencing Vmax (Equation 2). The observed decrease in Vmax with increasing KCl at high ionic strength is consistent with previous studies (38Homsher E. Wang F. Sellers J.R. Factors affecting movement of F-actin filaments propelled by skeletal muscle heavy meromyosin.Am. J. Physiol. 1992; 262: C714-C723Crossref PubMed Google Scholar). Both V(N) and v(N) exhibit similar saturation kinetics with KM values of 16 ± 8 and 46 ± 32, respectively, at 50 mM KCl and 17 ± 9 and 23 ± 13, respectively, at 100 mM KCl. To further test the saturation kinetic hypothesis and its implications for the models in Figure 2C, we measured the N-dependence of V(N) against a mechanical load. Force generation by myosin molecules along an actin filament increases linearly with the number, N, of myosin available to bind that actin filament. Thus, according to our hypothesis, the KM for myosin force generation in a motility assay should resemble that of both V(N) and v(N) determined above. We tested this prediction by measuring the N-dependence of myosin force generation against a mechanical load imposed by α-actinin in a motility assay. Alpha-actinin binds to actin and when adhered to a motility surface imposes a mechanical load against actin movement by weakly linking actin to the surface. In effect, α-actinin acts as a frictional load (39Greenberg M.J. Moore J.R. The molecular basis of frictional loads in the in vitro motility assay with applications to the study of the loaded mechanochemistry of molecular motors.Cytoskeleton (Hoboken). 2010; 67: 273-285Crossref PubMed Scopus (56) Google Scholar) that slows V. Assuming that the force, F(N), collectively generated by myosin molecules against this load increases with N as F(N) = Funi·N⋅r (where r is the fraction of strongly bound, force-generating myosin heads) the N-dependence of V(N) is described by Equation 1.V(N)=(1/γ)⋅Funi⋅N⋅r(1) where Funi is the average force generated per myosin head and γ is a frictional coefficient that, according to a molecular model for friction (2Howard J. Mechanics of Motor Proteins and the Cytoskeleton.1st Ed. Sinauer Associates, Sunderland, MA2001Google Scholar), equals Nα⋅κα⋅tα where Nα, κα, tα are the bound number, stiffness, and bound lifetime of α-actinin molecules. According to a classical chemical thermodynamic formalism, Funi = ΔG/d, where ΔG is the free energy for the working step (14Baker J.E. Thomas D.D. A thermodynamic muscle model and a chemical basis for A. V. Hill’ s muscle equation.J. Muscle Res. Cell Motil. 2000; 21: 335-344Crossref PubMed Scopus (29) Google Scholar, 17Baker J.E. LaConte L.E.W. Brust-Mascher I. Thomas D.D. Mechanochemical coupling in spin-labeled, active, isometric muscle.Biophys. J. 1999; 77: 2657-2664Abstract Full Text Full Text PDF PubMed Scopus (35) Google Scholar). Equation 1 is analogous to the myosin detachment-limited model illustrated in Figure 1D; only here at sufficiently high α-actinin concentrations V is influenced by α-actinin detachment kinetics. Specifically, the distance α-actinin compliant linkages are collectively displaced at stall is Lα = Funi⋅N⋅r/Nα⋅κα and the detachment rate of α-actinin is kdetα = 1/tα. Thus, the α-actinin equivalent of the myosin detachment limited velocity illustrated in Figure 1D is V = Lα/(1/kdetα + Lα/Vatt), which at relatively high Vatt approaches the α-actinin equivalent of Equation 2. The collective force formalism provides a clear working-step influenced mechanism for V(N) against a mechanical load (Equation 1). This is in contrast to the independent force generator equivalent of Equation 3, which inverts the actual physical agency in this relationship. Because the independent force formalism requires that myosin heads generate force locally, myosin working steps can neither directly move actin filaments nor di" @default.
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• W3198186923 title "Velocity of myosin-based actin sliding depends on attachment and detachment kinetics and reaches a maximum when myosin-binding sites on actin saturate" @default.
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