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.     

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.     

Two-step ligand binding and cooperativity. A model to describe the cooperative binding of myosin subfragment 1 to regulated actin.

The binding of actin to myosin subfragment 1 (S1) has been shown to occur as a two-step reaction. In the first step actin is weakly bound and then the complex isomerizes to the "rigor type" acto-S1 complex (Coates, J. H., A. H. Criddle, and M. A. Geeves, 1985 Biochem. J., 232:351-356). We propose here a model in which troponin/tropomyosin (Tn/Tm) controls the actin-S1 interaction by inhibiting the isomerization step. In this model the (actin)7 Tn/Tm unit is assumed to exist in two states: open and closed. S1 can bind to either of the two states but only the open form allows the isomerization reaction to take place. We demonstrate that this model can account for the cooperative binding of S1 and S1 nucleotide complexes to actin. The model provides a way of integrating both the effects of calcium and nucleotide on actin-S1 interactions.     

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.     

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)     

Proteolysis and binding of myosin subfragment 1 to actin

Rates of proteolytic cleavage of myosin subfragment 1 were measured in the absence and presence of different amounts of actin. The rates of tryptic digestion at the 50K/20K junction and papain digestion at the 25K/50K junction of the myosin head were progressively inhibited with increasing substoichiometric molar ratios of actin to myosin subfragment 1. The percentage inhibitions of digestion reactions corresponded precisely to the molar compositions of actin-subfragment 1 solutions and demonstrated that equimolar complexes of these proteins were responsible for the observed changes in the proteolysis of myosin heads.     

Differential binding of rabbit fast muscle myosin light chain isoenzymes to regulated actin

The direct binding of S1(A1) and S1(A2) to regulated actin has been investigated by centrifugation. Binding was measured in the presence of either Mg·AdoPP[NH]P or Mg·ADP at 24°C at various ionic strengths. At low ionic strength, in either the presence or absence of Ca²⁺, the binding of S1(A1) to regulated actin was always stronger than for S1(A2). As the ionic strength was increased the differential binding between S1(A1) and S1(A2) was still maintained in the presence of Ca²⁺ but not in its absence. These data are discussed in terms of a modifying role for the N-terminal region of the A1 light chain in regulation of the contractile process.     

The binding of heat-treated myosin subfragment 1 to actin and substructure considerations

Heat treatment of myosin subfragment 1 at 35 degrees C caused about 95% inactivation of the catalytic function but did not block its binding to actin. Heat-treated subfragment 1 showed specific, strong, and close to stoichiometric binding to actin. MgATP but not MgADP dissociated these complexes. However, in contrast to intact subfragment 1, the heat-treated protein did not polymerize G-actin and was not protected from trypsin by the binding to actin. Tryptic degradation of the 50K fragment abolished, or reduced greatly, the binding of heat-treated subfragment 1 to actin in solution but not on nitrocellulose overlays. These results are discussed in the context of subfragment 1 substructure.     

The binding of actin to phosphorylated and dephosphorylated myosin

The binding of actin to myosin containing phosphorylated and dephosphorylated light chains (LC2) was investigated by studying the influence of actin on Mg2+- and K+-stimulated ATPase of phosphorylated and dephosphorylated myosin and by comparing the influence of PPi on actomyosin formed from pure actin and phosphorylated or dephosphorylated myosin. The concentration of actin producing inhibition of one half of myosin K+-ATPase activity was 4.1 micro M and 7.7 micro M for phosphorylated and dephosphorylated myosin, respectively. Actomyosin formed from dephosphorylated myosin dissociated at lower PPi concentration than did that from the phosphorylated form. The extrapolated values of Km obtained from studies of the influence of actin on Mg2+-ATPase activity of dephosphorylated myosin were about twice as high as for the phosphorylated form. Thus, the affinity of phosphorylated myosin for actin was significantly higher under conditions studied.     

Myosin S2 is not required for effects of myosin binding protein-C on motility

The unique myosin binding protein-c "motif" near the N-terminus of myosin binding protein-C (MyBP-C) binds myosin S2. Previous studies demonstrated that recombinant proteins containing the motif and flanking regions (e.g., C1C2) affect thin filament movement in motility assays using heavy meromyosin (S1 plus S2) as the molecular motor. To determine if S2 is required for these effects we investigated whether C1C2 affects motility in assays using only myosin S1 as the motor protein. Results demonstrate that effects of C1C2 are comparable in both systems and suggest that the MyBP-C motif affects motility through direct interactions with actin and/or myosin S1.     

The binding constant of ATP to myosin S1 fragment.

The extent of ATP synthesis from ADP and Pi at the active centre of myosin subfragment 1 has been reinvestigated. The results have been interpreted using a treatment which is not dependent on the number or nature of the intermediates in the ATPase mechanism. An average value for the binding constant of ATP of (3.25 +/- 0.96) X 10(11) M-1 at pH 8.0 23 degrees C and ionic strength 0.12 M was obtained. Additional evidence is given to confirm that synthesis at the active site has been investigated.     

The regulation of myosin binding to actin filaments by Lethocerus troponin

Lethocerus indirect flight muscle has two isoforms of troponin C, TnC-F1 and F2, which are unusual in having only a single C-terminal calcium binding site (site IV, isoform F1) or one C-terminal and one N-terminal site (sites IV and II, isoform F2). We show here that thin filaments assembled from rabbit actin and Lethocerus tropomyosin (Tm) and troponin (Tn) regulate the binding of rabbit myosin to rabbit actin in much the same way as the mammalian regulatory proteins. The removal of calcium reduces the rate constant for S1 binding to regulated actin about threefold, independent of which TmTn is used. This is consistent with calcium removal causing the TmTn to occupy the B or blocked state to about 70% of the total. The mid point pCa for the switch differed for TnC-F1 and F2 (pCa 6.9 and 6.0, respectively) consistent with the reported calcium affinities for the two TnCs. Equilibrium titration of S1 binding to regulated actin filaments confirms calcium regulated binding of S1 to actin and shows that in the absence of calcium the three actin filaments (TnC-F1, TnC-F2 and mammalian control) are almost indistinguishable in terms of occupancy of the B and C states of the filament. In the presence of calcium TnC-F2 is very similar to the control with approximately 80% of the filament in the C-state and 10-15% in the fully on M-State while TnC-F1 has almost 50% in each of the C and M states. This higher occupancy of the M-state for TnC-F1, which occurs above pCa 6.9, is consistent with this isoform being involved in the calcium activation of stretch activation. However, it leaves unanswered how a C-terminal calcium binding site of TnC can activate the thin filament.     

Theoretical models for cooperative steady-state ATPase activity of myosin subfragment-1 on regulated actin

Recent theoretical work on the cooperative equilibrium binding of myosin subfragment-1-ADP to regulated actin, as influenced by Ca2+, is extended here to the cooperative steady-state ATPase activity of myosin subfragment-1 on regulated actin. Exact solution of the general steady-state problem will require Monte Carlo calculations. Three interrelated special cases are discussed in some detail and sample computer (not Monte Carlo) solutions are given. The eventual objective is to apply these considerations to in vitro experimental data and to in vivo muscle models.     

The binding of myosin subfragment 1 to actin can be measured by proteolytic rates method

The initial rates of tryptic digestion at the 50/20-kDa junction in myosin subfragment 1 (S-1) were determined for free S-1, acto-S-1, and acto-S-1 in the presence of magnesium adenyl-5'-yl imidodiphosphate (Mg AMP-PNP) and MgATP under ionic strength conditions ranging from 30 to 124 mM. The percentage of S-1 bound to actin in the presence of Mg AMP-PNP and MgATP was calculated from these rates for each set of digestion experiments. Parallel experiments carried out in an Airfuge centrifuge on identical acto-S-1 solutions yielded independent information on the binding of S-1 to actin. The results of binding measurements by these two methods were in excellent agreement in all cases tested, covering the range from 15 to 95% binding of S-1 to actin. Tryptic digestions of synthetic mixtures of S-1 and p-phenylenedimaleimide S-1 in the presence of actin demonstrated that a two-component system of myosin heads with different affinities for actin can be resolved into its constituents by the proteolytic rates method. The results of this work justify applications of the proteolytic rates method to actomyosin binding studies in more complex systems.     

Caldesmon binding to actin is regulated by calmodulin and phosphorylation via different mechanisms

Smooth muscle caldesmon (CaD) binds F-actin and inhibits actomyosin ATPase activity. The inhibition is reversed by Ca2+/calmodulin (CaM). CaD is also phosphorylated upon stimulation at sites specific for mitogen-activated protein kinases (MAPKs). Because of these properties, CaD is thought to be involved in the regulation of smooth muscle contraction. The molecular mechanism of the reversal of inhibition is not well understood. We have expressed His6-tagged fragments containing the sequence of the C-terminal region of human (from M563 to V793) and chicken (from M563 to P771) CaD as well as a variant of the chicken isoform with a Q766C point mutation. By cleavages with proteases, followed by high-speed cosedimentation with F-actin and mass spectrometry, we found that within the C-terminal region of CaD there are multiple actin contact points forming two clusters. Intramolecular fluorescence resonance energy transfer between probes attached to cysteine residues (the endogenous C595 and the engineered C766) located in these two clusters revealed that the C-terminal region of CaD is elongated, but it becomes more compact when bound to actin. Binding of CaM restores the elongated conformation and facilitates dissociation of the C-terminal CaD fragment from F-actin. When the CaD fragment was phosphorylated with a MAPK, only one of the two actin-binding clusters dissociated from F-actin, whereas the other remained bound. Taken together, these results demonstrate that while both Ca2+/CaM and MAPK phosphorylation govern CaD's function via a conformational change, the regulatory mechanisms are different.     

The C0C1 fragment of human cardiac myosin binding protein C has common binding determinants for both actin and myosin

The N-terminal domains of cardiac myosin binding protein C (MyBP-C) play a regulatory role in modulating interactions between myosin and actin during heart muscle contraction. Using NMR spectroscopy and small-angle neutron scattering, we have determined specific details of the interaction between the two-module human C0C1 cMyBP-C fragment and F-actin. The small-angle neutron scattering data show that C0C1 spontaneously polymerizes monomeric actin (G-actin) to form regular assemblies composed of filamentous actin (F-actin) cores decorated by C0C1, similar to what was reported in our earlier four-module mouse cMyBP-C actin study. In addition, NMR titration analyses show large intensity changes for a subset of C0C1 peaks upon addition of G-actin, indicating that human C0C1 interacts specifically with actin and promotes its assembly into filaments. During the NMR titration, peaks corresponding to cardiac-specific C0 domain are the first to be affected, followed by those from the C1 domain. No peak intensity or position changes were detected for peaks arising from the disordered proline/alanine-rich (P/A) linker connecting C0 with C1, despite previous suggestions of its involvement in binding actin. Of considerable interest is the observation that the actin-interaction “hot-spots” within the C0 and C1 domains, revealed in our NMR study, overlap with regions previously identified as binding to the regulatory light chain of myosin and to myosin ΔS2. Our results suggest that C0 and C1 interact with myosin and actin using a common set of binding determinants and therefore support a cMyBP-C switching mechanism between myosin and actin.     

Ventricular myosin light chain 1 is developmentally regulated and does not change in hypertension.

Cardiac myosin heavy chain (MHC) isoform distribution has been shown to undergo changes during development, in response to hormonal stimuli, and during pathologic states like hypertension. We initiated a study of myosin light chain 1 (MLC1) expression in cardiac tissue to determine whether MLC1 undergoes changes similar to those seen for MHC. We isolated a full length cDNA for the predominant MLC1 sequence in rat hearts. This gene is expressed in ventricular tissue at much higher levels than in atrial tissue. Based on its expression pattern and sequence homology, this cDNA encodes the rat ventricular MLC1 and has been named RVMLC1. RVMLC1 is expressed at very low levels in cardiac tissue during early development and is expressed abundantly after birth and in adult hearts. The expression of RVMLC1 was found not to change in the hearts of rats with renovascular hypertension.     

The tail domain of myosin Va modulates actin binding to one head

Calcium activates full-length myosin Va steady-state enzymatic activity and favors the transition from a compact, folded "off" state to an extended "on" state. However, little is known of how a head-tail interaction alters the individual actin and nucleotide binding rate and equilibrium constants of the ATPase cycle. We measured the effect of calcium on nucleotide and actin filament binding to full-length myosin Va purified from chick brains. Both heads of nucleotide-free myosin Va bind actin strongly, independent of calcium. In the absence of calcium, bound ADP weakens the affinity of one head for actin filaments at equilibrium and upon initial encounter. The addition of calcium allows both heads of myosin Va.ADP to bind actin strongly. Calcium accelerates ADP binding to actomyosin independent of the tail but minimally affects ATP binding. Although 18O exchange and product release measurements favor a mechanism in which actin-activated Pi release from myosin Va is very rapid, independent of calcium and the tail domain, both heads do not bind actin strongly during steady-state cycling, as assayed by pyrene actin fluorescence. In the absence of calcium, inclusion of ADP favors formation of a long lived myosin Va.ADP state that releases ADP slowly, even after mixing with actin. Our results suggest that calcium activates myosin Va by allowing both heads to interact with actin and exchange bound nucleotide and indicate that regulation of actin binding by the tail is a nucleotide-dependent process favored by linked conformational changes of the motor domain.