Kinetics of actin-myosin binding. Myosin cooperativity and mixed single-headed and two-headed binding

A model is proposed for the kinetics of actin-myosin interaction that allows for the presence of both one- and two-headed myosin fragments, cooperativity between myosin sites, and the molecular weight distribution of actin filaments. The approach employed makes use of the notion of effectivity factors. In the most general case, the system is described by six coupled first-order differential equations. When only single-headed myosin (S1) is present, the model reduces to simpler versions introduced previously.     

The Hill model for binding myosin S1 to regulated actin is not equivalent to the McKillop-Geeves model

The Hill two-state cooperativity model and the McKillop-Geeves (McK-G) three-state model predict very similar binding traces of myosin subfragment 1 (S1) binding to regulated actin filaments in the presence and absence of calcium, and both fit the experimental data reasonably well [Chen et al., Biophys. J., 80, 2338-2349]. Here, we compared the Hill model and the McK-G model for binding myosin S1 to regulated actin against three sets of experimental data: the titration of regulated actin with S1 and the kinetics of S1 binding of regulated actin with either excess S1 to actin or excess actin to S1. Each data set was collected for a wide range of specified calcium concentrations. Both models were able to generate reasonable fits to the time course data and to titration data. The McK-G model can fit all three data sets with the same calcium-concentration-sensitive parameters. Only K(B) and K(T) show significant calcium dependence, and the parameters have a classic pCa curve. A unique set of the Hill model parameters was extremely difficult to estimate from the best fits of multiple sets of data. In summary, the McK-G cooperativity model more uniquely resolves parameters estimated from kinetic and titration data than the Hill model, predicts a sigmoidal dependence of key parameters with calcium concentration, and is simpler and more suitable for practical use.     

Relationship between regulated actomyosin ATPase activity and cooperative binding of myosin to regulated actin

The protein complex, troponin-tropomyosin, which is bound to the thin actin filament, regulates muscle contraction and relaxation. In the absence of Ca²⁺ the troponin-tropomyosin complex causes muscle to relax, whereas in the presence of Ca²⁺, contraction occurs. Biochemical studies have shown that the troponin-tropomyosin complex has a dual effect on the interaction of the myosin cross-bridge with actin. In the presence of ATP, troponin-tropomyosin strongly inhibits the actomyosin ATPase activity, whereas in the absence of ATP, troponin-tropomyosin confers positive cooperativity on the binding of myosin to actin. We have proposed a simple model [Hill, T. L., Greene, L. E., and Eisenberg, E. (1980)Proc. Natl. Acad. Sci. USA 77, 3186–3190] that accounts for these biochemical observations by postulating that the troponin-tropomyosin-actin complex (regulated actin) can occur in two forms, a turned-on form and a turned-off form. This model defines several cooperativity parameters that describe the behavior of regulated actin. In previous studies we have determined the values of these parameters by studying the cooperative binding of myosin to regulated actin in the absence of ATP. In the present study we also used ATPase and fluorescence measurements to determine these cooperativity parameters. Assuming that the fluorescence change occurs only when two adjacent tropomyosin units shift into the turned-on form, our results show that all three methods give the same values for the cooperativity parameters. These results confirm the prediction of our model that a regulated actin unit that is turned off not only binds S-1 weakly but is also unable to activate the actomyosin ATPase activity.     

Kinetics of actin-myosin binding. ATP-ase activity and sol-gel dissipative structures

The simple kinetic model of actin-myosin binding-dissociation process including ATP-ase activity is considered. We demonstrated how one may easily include cooperativity in such a model by using effectivity factors introduced in our previous papers. A possibility of further simplifying the model through quasi-stationary approximation for some variables is considered. Sol-gel dissipative structures and possible biological implications of such structures are discussed.     

Effect of ethylene glycol on the interaction of different myosin subfragment 1.nucleotide complexes with actin

To elucidate the structure of the cross-bridge intermediates in the actomyosin ATPase cycle, several laboratories have added both ethylene glycol and AMP-PNP to muscle fibers. These studies suggested that ethylene glycol shifts the structure of myosin.AMP-PNP toward the weak-binding conformation, i.e., toward the structure of myosin.ATP. Since only the weak-binding conformation of myosin subfragment 1 (S-1) binds with no apparent cooperativity to the troponin-tropomyosin-actin complex (regulated actin), we used this as a probe to examine the conformation of various S-1.nucleotide complexes in ethylene glycol. Our results show that ethylene glycol markedly weakens the binding strength of S-1, S-1.ADP, and S-1.AMP-PNP to actin but has almost no effect on the binding strength of S-1.ATP. As in muscle fibers, at 40% ethylene glycol, the binding strength of S-1.AMP-PNP to actin becomes very similar to the binding strength of S-1.ATP. In the presence of troponin-tropomyosin, the binding of S-1.AMP-PNP to actin shows no apparent cooperativity in 40% ethylene glycol. Therefore, our results confirm that ethylene glycol shifts the structure of the myosin.AMP-PNP toward the weak-binding conformation. However, our results also suggest that ethylene glycol has a direct effect on the regulated actin complex. This is shown by the fact that ethylene glycol markedly increases the cooperative binding of S-1.ADP to regulated actin both in the presence and in the absence of Ca2+.(ABSTRACT TRUNCATED AT 250 WORDS)     

A Mechanistic Model of Ca Regulation of Thin Filaments in Cardiac Muscle

We present a model of Ca-regulated thin filaments in cardiac muscle where tropomyosin is treated as a continuous elastic chain confined in the closed position on the actin helix by electrostatic forces. The main distinction from previous works is that the intrinsic stress-free helical shape of the tropomyosin chain was taken into account explicitly. This results in the appearance of a new, to our knowledge, tension-like term in the energy functional and the equilibrium equation. The competitive binding of calcium and the mobile segment of troponin-I to troponin-C were described by a simple kinetic scheme. The values of dimensionless model parameters were estimated from published data. A stochastic Monte Carlo simulation of calcium curves has been performed and its results were compared to published data. The model explains the high cooperativity of calcium response of the regulated thin filaments even in the absence of myosin heads. The binding of myosin heads to actin increases the calcium sensitivity while not affecting its cooperativity significantly. When the presence of calcium-insensitive troponin-C was simulated in the model, both calcium sensitivity and cooperativity decreased. All these features were previously observed experimentally.     

A Mechanistic Model of Ca Regulation of Thin Filaments in Cardiac Muscle

We present a model of Ca-regulated thin filaments in cardiac muscle where tropomyosin is treated as a continuous elastic chain confined in the closed position on the actin helix by electrostatic forces. The main distinction from previous works is that the intrinsic stress-free helical shape of the tropomyosin chain was taken into account explicitly. This results in the appearance of a new, to our knowledge, tension-like term in the energy functional and the equilibrium equation. The competitive binding of calcium and the mobile segment of troponin-I to troponin-C were described by a simple kinetic scheme. The values of dimensionless model parameters were estimated from published data. A stochastic Monte Carlo simulation of calcium curves has been performed and its results were compared to published data. The model explains the high cooperativity of calcium response of the regulated thin filaments even in the absence of myosin heads. The binding of myosin heads to actin increases the calcium sensitivity while not affecting its cooperativity significantly. When the presence of calcium-insensitive troponin-C was simulated in the model, both calcium sensitivity and cooperativity decreased. All these features were previously observed experimentally.     

Analysis of troponin-tropomyosin binding to actin. Troponin does not promote interactions between tropomyosin molecules.

The binding of tropomyosin to actin and troponin-tropomyosin to actin was analyzed according to a linear lattice model which quantifies two parameters: Ko, the affinity of the ligand for an isolated site on the actin filament, and gamma, the fold increase in affinity when binding is contiguous to an occupied site (cooperativity). Tropomyosin-actin binding is very cooperative (gamma = 90-137). Troponin strengthens tropomyosin-actin binding greatly but, surprisingly, does so solely by an 80-130-fold increase in Ko, while cooperativity actually decreases. Additionally, troponin complexes containing TnT subunits with deletions of either amino acids 1-69 (troponin70-259) or 1-158 (troponin159-259) were examined. Deletion of amino acids 1-69 had only small effects on Ko and y, despite this peptide's location spanning the joint between adjacent tropomyosins. Ca2+ reduced Ko by half for both troponin and troponin70-159 and had no detectable effect on cooperativity. Troponin159-259 had much weaker effects on tropomyosin-actin binding than did troponin70-259 and had no effect at all in the presence of Ca2+. This suggests the importance of Ca(2+)-insensitive interactions between tropomyosin and troponin T residues 70-159. Cooperativity was slightly lower for troponin159-259 than tropomyosin alone, suggesting that the globular head region of troponin affects tropomyosin-tropomyosin interactions along the thin filament.     

A new model of cooperative myosin-thin filament binding

Cooperative myosin binding to the thin filament is critical to regulation of cardiac and skeletal muscle contraction. This report delineates and fits to experimental data a new model of this process, in which specific tropomyosin-actin interactions are important, the tropomyosin-tropomyosin polymer is continuous rather than disjointed, and tropomyosin affects myosin-actin binding by shifting among three positions as in recent structural studies. A myosin- and tropomyosin-induced conformational change in actin is proposed, rationalizing the approximately 10,000-fold strengthening effect of myosin on tropomyosin-actin binding. Also, myosin S1 binding to regulated filaments containing mutant tropomyosins with internal deletions exhibited exaggerated cooperativity, implying an allosteric effect of tropomyosin on actin and allowing the effect's measurement. Comparisons among the mutants suggest the change in actin is promoted much more strongly by the middle of tropomyosin than by its ends. Regardless of calcium binding to troponin, this change in actin facilitates the shift in tropomyosin position to the actin inner domain, which is required for tight myosin-actin association. It also increases myosin-actin affinity 7-fold compared with the absence of troponin-tropomyosin. Finally, initiation of a shift in tropomyosin position is 100-fold more difficult than is its extension from one actin to the next, producing the myosin binding cooperativity that underlies cooperative activation of muscle contraction.     

Kinetic model for the interaction of myosin subfragment 1 with regulated actin

A one-dimensional kinetic Ising model is developed to describe the binding of myosin subfragment 1 (SF-1) to regulated actin. The model allows for cooperative interactions between individual actin sites with bound SF-1 ligands rather than assuming that groups of actin monomer sites change their state in a cooperative fashion. With the triplet closure approximation, the model yields a set of 16 independent differential (master) equations which may be solved numerically to yield the extent of binding as a function of time. The predictions of the model are compared with experiments on the transient binding of SF-1 to regulated actin in the presence of Ca2+ and in the absence of Ca2+ with varying amounts of SF-1 prebound to the actin filament and on the equilibrium binding of SF-1 X ADP to regulated actin in the absence of Ca2+. In all cases, the calculations fit the data to within the experimental errors. In the case of SF-1 X ADP, the results suggest that a repulsive interaction exists between adjacently bound SF-1 at the ends of two neighboring seven-site actin units.     

Cooperative regulation of myosin-S1 binding to actin filaments by a continuous flexible Tm–Tn chain

The regulation of striated muscle contraction involves cooperative interactions between actin filaments, myosin-S1 (S1), tropomyosin (Tm), troponin (Tn), and calcium. These interactions are modeled by treating overlapping tropomyosins as a continuous flexible chain (CFC), weakly confined by electrostatic interactions with actin. The CFC is displaced locally in opposite directions on the actin surface by the binding of either S1 or Troponin I (TnI) to actin. The apparent rate constants for myosin and TnI binding to and detachment from actin are then intrinsically coupled via the CFC model to the presence of neighboring bound S1s and TnIs. Monte Carlo simulations at prescribed values of the CFC stiffness, the CFC??s degree of azimuthal confinement, and the angular displacements caused by the bound proteins were able to predict the stopped-flow transients of S1 binding to regulated F-actin. The transients collected over a large range of calcium concentrations could be well described by adjusting a single calcium-dependent parameter, the rate constant of TnI detachment from actin, k _?I. The resulting equilibrium constant $ K_{\text{B}} \equiv 1/K_{\text{I}} $ varied sigmoidally with the free calcium, increasing from 0.12 at low calcium (pCa >7) to 12 at high calcium (pCa <5.5) with a Hill coefficient of ~2.15. The similarity of the curves for excess-actin and excess-myosin data confirms their allosteric relationship. The spatially explicit calculations confirmed variable sizes for the cooperative units and clustering of bound myosins at low calcium concentrations. Moreover, inclusion of negative cooperativity between myosin units predicted the observed slowing of myosin binding at excess-myosin concentrations.     

Theoretical kinetic studies of models for binding myosin subfragment-1 to regulated actin: Hill model versus Geeves model

It was previously shown that a one-dimensional Ising model could successfully simulate the equilibrium binding of myosin S1 to regulated actin filaments (T. L. Hill, E. Eisenberg and L. Greene, Proc. Natl. Acad. Sci. U.S.A. 77:3186-3190, 1980). However, the time course of myosin S1 binding to regulated actin was thought to be incompatible with this model, and a three-state model was subsequently developed (D. F. McKillop and M. A. Geeves, Biophys. J. 65:693-701, 1993). A quantitative analysis of the predicted time course of myosin S1 binding to regulated actin, however, was never done for either model. Here we present the procedure for the theoretical evaluation of the time course of myosin S1 binding for both models and then show that 1) the Hill model can predict the "lag" in the binding of myosin S1 to regulated actin that is observed in the absence of Ca++ when S1 is in excess of actin, and 2) both models generate very similar families of binding curves when [S1]/[actin] is varied. This result shows that, just based on the equilibrium and pre-steady-state kinetic binding data alone, it is not possible to differentiate between the two models. Thus, the model of Hill et al. cannot be ruled out on the basis of existing pre-steady-state and equilibrium binding data. Physical mechanisms underlying the generation of the lag in the Hill model are discussed.     

Theoretical studies on competitive binding of caldesmon and myosin S1 to actin: prediction of apparent cooperativity in equilibrium and slow-down in kinetics of S1 binding by caldesmon

Several laboratories have reported cooperative binding of S1 to actin in the presence of caldesmon. This cooperative binding has been interpreted with a model similar to that proposed for the binding of S1 to regulated actins in which the binding affinity of S1 is controlled by the position of the tropomyosin filaments. In a recent paper [Sen, A., Chen, Y., Yan, B., and Chalovich, J. M. (2001) Biochemistry 40, 5757-64], we showed qualitatively that S1 binding resulted in rapid dissociation of caldesmon from actin or actin-tropomyosin. This suggests that the cooperativity observed in the case of caldesmon is not due to a conformational change in actin-caldesmon but to the displacement of caldesmon. We show in this paper that the pure competitive binding model, in which both S1 and caldesmon are competing for the same binding sites on actin, can simulate quantitatively the effect of caldesmon on both the equilibrium and the kinetics of S1 binding to actin. This model successfully predicts an apparent cooperativity for the binding of S1 to actin-caldesmon without the need to assume multiple actin-caldesmon structures and produces a decreased rate of S1 binding to actin in the presence of caldesmon. This suggests that the inhibitory action of caldesmon on the actin-activated ATPase activity of myosin in solution and on the generation of active force in a contracting muscle may be simply due to the blocking of myosin binding sites on actin by caldesmon.     

A mosaic multiple-binding model for the binding of caldesmon and myosin subfragment-1 to actin.

Binding of caldesmon to actin causes a decrease in the quantity of bound myosin and results in a reduction in the rate of actin-activated adenosine triphosphate hydrolysis. It is generally assumed that the binding of caldesmon and myosin to actin is a pure competitive interaction. However, recent binding studies of enzyme digested caldesmon subfragments directed at mapping the actin binding site of caldesmon have shown that a small 8-kD fragment around the COOH-terminal can compete directly with the myosin subfragment 1 (S-1) binding to actin; at least one other fragment that binds to actin does not inhibit the actin-activated adenosine triphosphate activity of myosin. That is, only a part of the caldesmon sequence may be responsible for directly blocking the binding of S-1 to actin. This prompts us to question the actual mode of binding of intact caldesmon and myosin S-1 to actin: whether the entire intact caldesmon molecule is competing with S-1 binding (pure competitive model) or just a small part of it (mosaic multiple-binding model). To answer this question, we measured the amount of myosin S-1 and caldesmon bound per actin monomer as a function of the total concentration of S-1 added to the system at constant concentrations of actin and caldesmon. A formalism for calculating the titration data based on the pure competitive model and a mosaic multiple-binding model was then developed. When compared with theoretical calculations, it is found that the binding of caldesmon and S-1 to actin cannot be pure competitive if no cooperativity exists between S-1 and caldesmon.(ABSTRACT TRUNCATED AT 250 WORDS)     

Kinetics of actin-myosin binding. II. Two-variable model and actin gelation

We consider a model of actin-myosin interaction in which the sites belonging to each seven-site regulated actin unit are subdivided into two classes, "internal" and "external." The time evolution of each class of sites is considered separately, leading to a pair of coupled differential equations that may be integrated numerically. We also consider the critical sol-gel transition point for actin filaments crosslinked by two-headed heavy meromyosin (HMM). The possibility of new types of chemical oscillation and pattern formation arising from periodic sol-gel transitions is discussed.     

A Peek into Tropomyosin Binding and Unfolding on the Actin Filament

Background

Tropomyosin is a prototypical coiled coil along its length with subtle variations in structure that allow interactions with actin and other proteins. Actin binding globally stabilizes tropomyosin. Tropomyosin-actin interaction occurs periodically along the length of tropomyosin. However, it is not well understood how tropomyosin binds actin.

Principal Findings

Tropomyosin''s periodic binding sites make differential contributions to two components of actin binding, cooperativity and affinity, and can be classified as primary or secondary sites. We show through mutagenesis and analysis of recombinant striated muscle α-tropomyosins that primary actin binding sites have a destabilizing coiled-coil interface, typically alanine-rich, embedded within a non-interface recognition sequence. Introduction of an Ala cluster in place of the native, more stable interface in period 2 and/or period 3 sites (of seven) increased the affinity or cooperativity of actin binding, analysed by cosedimentation and differential scanning calorimetry. Replacement of period 3 with period 5 sequence, an unstable region of known importance for cooperative actin binding, increased the cooperativity of binding. Introduction of the fluorescent probe, pyrene, near the mutation sites in periods 2 and 3 reported local instability, stabilization by actin binding, and local unfolding before or coincident with dissociation from actin (measured using light scattering), and chain dissociation (analyzed using circular dichroism).

Conclusions

This, and previous work, suggests that regions of tropomyosin involved in binding actin have non-interface residues specific for interaction with actin and an unstable interface that is locally stabilized upon binding. The destabilized interface allows residues on the coiled-coil surface to obtain an optimal conformation for interaction with actin by increasing the number of local substates that the side chains can sample. We suggest that local disorder is a property typical of coiled coil binding sites and proteins that have multiple binding partners, of which tropomyosin is one type.     

Characterization of three regulatory states of the striated muscle thin filament

The troponin-tropomyosin-linked regulation of striated muscle contraction occurs through allosteric control by both Ca(2+) and myosin. The thin filament fluctuates between two extreme states: the inactive "off" state and the active "on" state. Intermediate states have been proposed from structural studies and transient kinetic measurements. However, in contrast to the well-characterised, on and off states, the mechanochemical properties of the intermediate states are much less well understood because of the instability of those states. In the present study, we have characterized a myosin-induced intermediate that is stabilized by cross-linking myosin motor domains (S1) to actin filaments (with a maximum of one S1 molecule for 50 actin monomers). A single S1 molecule is known to interact with two adjacent actin monomers. A detailed analysis revealed that thin filaments containing S1 molecules cross-linked to just one actin monomer (actin(1)-S1 complexes) are regulated with a 79% inhibition of the ATPase in the absence of Ca(2+). In contrast, filaments containing S1 molecules cross-linked at two positions, to two adjacent actin monomers (actin(2)-S1 complexes) totally lose their regulation in a highly cooperative manner. This loss of regulation was due both to an enhancement of the ATPase activity without calcium and an inhibition of the ATPase with calcium. Filaments containing actin(2)-S1 complexes, with significant ATPase activity in the absence of calcium (about 50%), did not move on a myosin-coated surface unless calcium was present. This partial uncoupling between the ATPase activity and in vitro motility in the absence of calcium demonstrates that the mechanical steps require actin-myosin contacts, which take place only in the on state and not in the off or intermediate states. These data provide new insights concerning the difference in cooperativity of Ca(2+) regulation that exists between the biochemical and mechanical cycles of the actin-myosin motor.     

Inhibition of actin polymerization decreases osteogeneic differentiation of mesenchymal stem cells through p38 MAPK pathway

Background

Mesenchymal Stem Cells (MSC) are important candidates for therapeutic applications due to their ex vivo proliferation and differentiation capacity. MSC differentiation is controlled by both intrinsic and extrinsic factors and actin cytoskeleton plays a major role in the event. In the current study, we tried to understand the initial molecular mechanisms and pathways that regulate the differentiation of MSC into osteocytes or adipocytes.

Results

We observed that actin modification was important during differentiation and differentially regulated during adipogenesis and osteogenesis. Initial disruption of actin polymerization reduced further differentiation of MSC into osteocytes and osteogenic differentiation was accompanied by increase in ERK1/2 and p38 MAPK phosphorylation. However, only p38 MAPK phosphorylation was down regulated upon inhibition of actin polymerization which as accompanied by decreased CD49E expression.

Conclusion

Taken together, our results show that actin modification is a pre-requisite for MSC differentiation into osteocytes and adipocytes and osteogenic differentiation is regulated through p38 MAPK phosphorylation. Thus by modifying their cytoskeleton the differentiation potential of MSC could be controlled which might have important implications for tissue repair and regeneration.     

Allosteric regulation of purine nucleoside phosphorylase.

Purine nucleoside phosphorylase (EC 2.4.2.1) from bovine spleen is allosterically regulated. With the substrate inosine the enzyme displayed complex kinetics: positive cooperativity vs inosine when this substrate was close to physiological concentrations, negative cooperativity at inosine concentrations greater than 60 microM, and substrate inhibition at inosine greater than 1 mM. No cooperativity was observed with the alternative substrate, guanosine. The activity of purine nucleoside phosphorylase toward the substrate inosine was sensitive to the presence of reducing thiols; oxidation caused a loss of cooperativity toward inosine, as well as a 10-fold decreased affinity for inosine. The enzyme also displayed negative cooperativity toward phosphate at physiological concentrations of Pi, but oxidation had no effect on either the affinity or cooperativity toward phosphate. The importance of reduced cysteines on the enzyme is thus specific for binding of the nucleoside substrate. The enzyme was modestly inhibited by the pyrimidine nucleotides CTP (Ki = 118 microM) and UTP (Ki = 164 microM), but showed greater sensitivity to 5-phosphoribosyl-1-pyrophosphate (Ki = 5.2 microM).     

Cooperative binding of tropomyosin to muscle and Acanthamoeba actin.

Analyses of the binding of tropomyosin to muscle and Acanthamoeba actin by the use of Scatchard plots indicate that the binding exhibits strong positive cooperativity in the presence of Mg2+. The cooperative nature of the binding is not affected by the presence of 80 mm KCl, but appears to decrease somewhat in the presence of heavy meromyosin or subfragment-1. Heavy meromyosin, subfragment-1, and KCl each increase the binding affinity of actin for tropomyosin; depending on the experimental condition and the type of actin involved, the apparent binding constant, Kapp, is in the range of 1 to 4 x 10(6) M-1. Muscle actin cross-linked with glutaraldehyde failed to bind tropomyosin even when heavy meromyosin, subfragment-1, or KCl were added as inducers, although the cross-linked actin still markedly activated the heavy meromyosin ATPase.