On the elastic properties of tetramethylrhodamine F-actin.

(Iodoacetamido)tetramethylrhodamine disrupts F-actin. At the 1:1 fluorophore to actin (as monomer) ratio approximately 80% of the protein becomes non-sedimentable. The fluorescent, non-sedimentable actin copolymerizes with G-actin to yield fluorescent filaments. The tensile strength of these filaments changes with the ratio of the fluorescent non-sedimentable actin to the G-actin, being 1.6 pN, 2.9 pN and 3.6 pN at the 1/4, 2/3 and 1/1 ratios, respectively. These tensile strengths are approximately two orders of magnitude lower than those obtained by decoration of F-actin with phalloidin.

Thermodynamic features of myosin filament suspensions: implications for the modeling of muscle contraction.

The analysis of myosin filament suspensions shows that these solutions are characterized by highly nonideal behavior. From these data a model is constructed that allows us to predict that 1) when subjected to an increasing protein osmotic pressure, myosin filaments experience an elastic deformation, which is not linearly related to the acting force; and 2) at constant protein osmotic pressure, when the cross-bridges of the myosin filaments are subjected to an external, nonosmotic force parallel to the filament axis, they are deformed and the water activity coefficient is altered. As a consequence, in muscle, passive and active shortening of the sarcomere is expected to promote the change of the water-water and of the water-protein interactions. We thus propose to depict muscle contraction as a chemo-osmoelastic transduction, where the analysis of the energy partition during the power stroke requires consideration of the osmotic factor in addition to the chemoelastic ones.

A possible solvent effect of adenosine diphosphate influences the binding of 1,N6 ethenoadenosine diphosphate to myosin from skeletal muscle.

Skeletal muscle myosin displays two independent and equivalent binding sites for 1,N6 ethenoadenosine diphosphate, with a dissociation constant of 24.7 microM. MgADP, 10 to 40 microM, behaves as a pure competitive type inhibitor (K(SI)=8-9 microM) for the binding of 1,N6 ethenoadenosine diphosphate to skeletal muscle myosin. On the contrary, the inhibition by MgADP, 0.11-1.54 mM, is neither competitive nor non-competitive nor mixed, as is revealed by the analysis with the general kinetic equation (K.J. Laidler, P.S. Bunting, The Chemical Kinetics of Enzyme Action, 2nd ed., Clarendon, Oxford, 1973, p. 94). To explain our finding we propose that MgADP operates a complex type of inhibition, acting both directly as a competitor for myosin active sites, and indirectly by perturbing the regions of the solvent near to the protein.

Dissecting the free energy of formation of the 1:1 actomyosin complex.

The behaviour of solutions of pure myosin, of pure F-actin and of the equimolar mixture of myosin and of F-actin is studied. It is found that the chemical potential of the two proteins, in separate solutions, increases monotonically with the increase of protein osmotic pressure. A method is presented to determine the chemical potential of the 1:1 actin-myosin complex formed from equimolar solutions of myosin and of F-actin (as monomer). This is the first evaluation of the chemical potential of actomyosin under conditions similar to those of skeletal muscle. It is found that the filament suspensions of myosin and of the 1:1 actin-myosin complex display a high non-ideal behavior as well as distinctly different energy profiles as a function of protein osmotic pressure. This supports the hypothesis that, in muscle: (a) detached cross-bridge change significantly their free energy when sarcomere is shifting from the relaxed to the active or to the rigor state; and (b) the cross-bridge attachment-detachment process is accompanied by changes of muscle protein osmotic pressure.

Anomalous binding of MgADP to myosin of skeletal muscle.

Binding of adenosine diphosphate to skeletal muscle myosin was studied using a range of concentrations from 0 to 2 mM. Up to 0.2 mM adenosine diphosphate two equivalent and independent nucleotide binding sites were detected, characterized by the single association constant of 5 x 10(4)M(-1). At greater adenosine diphosphate concentrations a decreasing binding capacity was noticed, bound nucleotide being essentially approximately 0.1 mol/mol at a 1-2mM adenosine diphosphate concentration. We tentatively propose that nucleotides act indirectly on myosin by promoting the perturbation of the solvent, which is supported by the fact that polyphosphates are known powerful kosmotropes.

A highly non-ideal solution: the contractile system of skeletal muscle.

The contractile system is a highly non-ideal solution. The activities of its components must be determined in order to achieve a meaningful representation of cross-bridge kinetics and of chemio-mechanical transduction. Osmotic techniques may help in this respect. A few examples are presented. Protein osmotic pressure influences cross-bridges by determining (1) their free energy minimum, (2) their stiffness and (3) their contractile force.

Rhodamine phalloidin F-actin: critical concentration versus tensile strength.

The mechanic and elastic properties of rhodamine phalloidin F-actin were investigated as a function of the ionic strength and in the absence of Mg2+. By increasing ionic strength from 3 to 19 mM, critical concentration decreased from 146 to 36 nM and the yield strength increased from 5.6 pN to 28.6 pN. At the ionic strength of 12-13 mM, the elastic modulus by stretching increased by 330-430 kP. nm-1 up to the break point, where it was 38-44.2 MP. The work required to break the filament, 403-439 kJ.M-1 provides an estimate of the free energy of annealing of rhodamine phalloidin F-actin, the annealing constant being 2.8 x 1074 M-1.

Protein cross talking through osmotic work: the free energy of formation of the MgADP-myosin complexes at the muscle protein osmotic pressure.

A method is presented to determine the energy of formation of the myosin-ADP complexes at the muscle protein osmotic pressure. It is found that, at 18 kP, the putative protein osmotic pressure in skeletal muscle, the increase of MgADP from 0.05 to 2 mmolal, increases the free energy of myosin-ADP and of myosin-(ADP)2 by 0. 756 and by 9.85 kJ/mol, respectively, and decreases the free energy of myosin by 8.34 kJ erg/mol. It is pointed out that the local changes of water chemical potential, induced by the binding of MgADP to myosin, can be sensed by other structures of the contractile machinery, which per se may even be insensitive to MgADP. Cross talking between macromolecules can thus be achieved by changes of the water chemical potential.

Myofibrils of skeletal muscle: the activity coefficient of orthophosphate.

In the myofibrils of skeletal muscle, at 22 degrees C, pH 7.1 and at the physiological protein osmotic pressure of 1.8 x 10(5) dynes/cm2, orthophosphate behaves quite ideally, the activity coefficient being 0.85. Under the same conditions and at saturation, 2.67 mumoles of orthophosphate are bound per gram of dry myofibrils, with a dissociation constant of 7 x 10(-5) molal. Work is in progress to determine the activity coefficients of adenine nucleotide analogues. This work is needed to assess the actual value of the free energy of hydrolysis of ATP in muscle.

What is the diameter of the actin filament?

The limits of the most recent models of the actin filament are discussed. These model are generated without taking into account the effect of protein osmotic pressure and, in general, of the solvent conditions. As a result they do not provide a bona fide representation of the actin filament in vivo. A new 'fluttering wing' model is proposed which predicts that orientation of the monomers, intermonomer contacts and diameter of the actin filament are sensitive to protein osmotic pressure and to interaction with regulatory proteins.

Is nebulin truly a component of the thin filament?

Thin filaments were prepared from rabbit and beef skeletal muscle with three different procedures, both at high and low ionic strength. Nebulin was always found to be associated with the myosin fraction and was always absent from the thin filament fraction.

A model relating protein osmotic pressure to the stiffness of the cross-bridge components and the contractile force of skeletal muscle.

We have modeled the effect of protein osmotic pressure on the orientation of the monomer in F-actin, in tropomyosin-F-actin, in the myosin subfragment-1 decorated F-actin and in the myosin subfragment-1 decorated tropomyosin-F-actin. According to the model, at the physiological protein osmotic pressure (18 kPa), the elastic moduli by bending of the monomer in F-actin and in tropomyosin-F-actin are calculated to be 4.74 MPa and 5.8 MPa, respectively. The elastic moduli by bending of the monomer in the myosin subfragment-1 decorated F-actin and in the myosin subfragment-1 decorated tropomyosin-F-actin are calculated to be 22MPa and 22.3MPa, respectively. These latter values are in excellent agreement with the values of the elastic moduli by stretching found for the fibres of frog and rabbit muscle. We have also calculated that, at the physiological protein osmotic pressure, the myosin subfragment-1 decorated F-actin rigor complex can develop a force of 3.96 pN, a force correctly oriented to promote the sliding of the actin filament toward the center of the sarcomere. The magnitude of this force is comparable to that reported for intact skeletal muscle. In contrast, the myosin subfragment-1 decorated tropomyosin-F-actin rigor complex develops a much smaller driving force, that favours relaxation. Apparently tropomyosin uncouples the osmotic and the mechanical event. It is proposed that the elastic energy for muscle contraction is provided by protein osmotic pressure.

The osmotic properties and free energy of formation of the actomyosin rigor complexes from rabbit muscle.

We have studied the osmotic properties of the calcium-regulated actomyosin complexes from skeletal muscle at the protein osmotic pressure of 18 kPa and a different actin-to-myosin molar ratios. Essentially, protein solutions were equilibrated against a solution of poly(ethylene glycol) 40,000 of known macromolecular osmotic pressure. At the end of the equilibration the water and the protein masses of the protein solutions were determined gravimetrically and the protein molar concentration was calculated. In this reconstructed system we have found following, at the actin-to-molar ratio of 2.6 (the most likely stoichiometry of these two proteins in the dense region of the A band) the average distance between the myosin filaments is 34.2 nm, this equals the interfilament distance in the intact fibre of muscle in rigor, at the sarcomere length of 3.38 micrograms. The formation of the F-actin-myosin and of the tropomyosin-F-actin-myosin rigor complexes involves the largest free energy changes, -5.38 kJ/mol myosin and -5.67 kJ/mol myosin, respectively. The formation of the troponin-tropomyosin-F-actin-myosin(Ca) rigor complex from myosin and troponin-tropomyosin-F-actin(Ca) occurs with the free energy change of -3.43 kJ/mol myosin. Of these -3.43 kJ, -1.81 kJ are provided by the endergonic conversion of troponin-tropomyosin-F-actin(EGTA) into troponin-tropomyosin-F-actin (Ca). The transition of myosin and of troponin-tropomyosin-F-actin(EGTA) into the -F-actin-myosin(Ca) rigor complex is accompanied by a 5.8% increase of volume. The increase of volume is due to a large influx of water, which is essentially protein-hydration water.

The stiffness of the crossbridge is a function of the intrinsic protein osmotic pressure generated by the crossbridge itself.

A model is presented that makes it possible to determine the stiffness of the crossbridge from protein osmotic stress experiments. The model was elaborated while studying the osmotic properties of F-actin and of myosin subfragment-1 F-actin. These studies showed that the elastic modulus by bending of the monomer is directly related to the intrinsic protein osmotic pressure of the system. At a protein osmotic pressure of 1.8 x 10(5) dynes/cm2, the physiological protein osmotic pressure of frog skeletal muscle, it was found that the elastic moduli by bending of the monomer in F-actin and in the myosin subfragment-1 decorated F-actin are 6.5 X 10(7) and 3.3 X 10(8) dynes/cm2, respectively. The value of the elastic modulus by bending of the monomer in the myosin subfragment-1 decorated F-actin compares favorably with the values of the elastic modulus by stretching determined in skeletal muscle fibres.

F-actin levels but not actin polymerization are affected by triphenyltin in HL-60 cells.

The toxin triphenyl tin (TPT), Sn(C(6)H(5))(+)(3) caused a rapid decrease in the F-actin content of promyelocytic human leukemia cells (HL-60) chemically differentiated to neutrophils. Prior incubation (2 min) of the cells with 10 µM TPT did not modify the extent of actin polymerization inducible either by a receptor-mediated stimulus (chemotactic peptide fMLP) or by a direct activator of G proteins (AlF(-)(4)). The inorganic tin salts SnCl(2) and SnCl(4) did not affect F-actin content or production of HL-60 cells. Microfilament thiol groups were not reduced by exposure of cells to TPT, but even increased. When F-actin was exposed to 10 |GmM triphenyltin in a cell-free system, the depolymerizing effect was not detectable. Thus, TPT does not affect cytoskeletal protein directly but depends for its toxicity on some other induced change, probably ionic/osmotic in the intact cell.

Osmotic properties of myosin subfragment 1: implications of the mechanism of muscle contraction.

The osmotic behavior of myosin subfragment 1 was studied at 22 degrees C and pH 7.45 in 0.1 m KCl, 2 mm MgCl2, and 10 mm triethanolamine or in 25 mm phosphate, 2 mm MgCl2, and 2 mm MgADP. It was found that, in 0.1 m KCl, myosin subfragment 1 behaved as a spheroidal particle, with an average diameter of 8.09 nm, composed of two myosin subfragment 1 molecules. The lower limit of the thermodynamic dimerization constant was estimated to be 3.5 x 10(4) M-1. Above 5 mm as monomer, myosin subfragment 1 departed from the behavior expected of a dimeric spheroidal model because of the onset of a "hydration force." This force measured at the contact distance between particles equals 2.18 x 10(7) dynes/cm2 and falls off exponentially with a decay distance of 0.27 nm. In 25 mm orthophosphate, myosin subfragment 1, with an increase in the protein osmotic pressure, shifted from the behavior of a sphere to that of a cylinder. Between 1 x 10(5) and 4 x 10(5) dynes/cm2, the behavior of myosin subfragment 1 was different in the presence and in the absence of MgADP. In particular, at 1.8 x 10(5) dynes/cm2, the protein osmotic pressure in frog muscle, myosin subfragment 1 behaved as a sphere of 3.21-nm radius in the presence of MgADP and as a cylinder with a length to diameter ratio of 2.07 in the absence of MgADP. Under the solution conditions used in this work, S1 never behaved as a fully extended particle.

The "in vitro motility assay" and phalloidin-F-actin.

We have compared the osmotic properties of the hydrated, native actin filament and of hydrated phalloidin-F-actin. We have found that phalloidin-F-actin interacts much more strongly with water than native F-actin. It is therefore very likely that the interaction with myosin (that requires the expulsion of the protein solvation water) is more problematic for phalloidin-F-actin that for native F-actin. We conclude that phalloidin-F-actin is not a bona fide substitute for native F-actin in the "in vitro motility assay".

Osmotic properties of the calcium-regulated actin filament.

The diameter of the actin filament decreases with an increase of the protein osmotic pressure. This phenomenon is accompanied by a decrease of the angle (alpha) formed between the long axis of the actin monomer and the pointed end of the filament axis. At 1.8 x 10(5) dyn/cm2 (the protein osmotic pressure in frog muscle) the diameter is 8.34 nm and the angle (alpha) is 61.5 degrees. The interfilament distance of tropomyosin-decorated actin filaments, at a set of different osmotic pressures, is larger than that of F-actin filaments. This suggests that the two tropomyosin helices project out of the contour of the actin filament. The tropomyosin-decorated actin filament is more rigid than F-actin. At 1.8 x 10(5) dyn/cm2, the angle (alpha) is 76.4 degrees, as compared to the value of 61.5 degrees for F-actin. The interfilament distance of troponin-tropomyosin-decorated actin filaments is sensitive to Ca2+: in the physiological range of protein osmotic pressure it decreases from 13.3 nm, in the presence of 2 mM EGTA, to 12.2 nm in the presence of 0.2 mM CaCl2. Two alternative models are proposed to explain the decrease in interfilament distance. (a) Calcium shifts tropomyosin along the actin monomer, toward the filament axis (the classical model). (b) Calcium releases the rigidity of the tropomyosin-decorated filament and restores the original plasticity of F-actin. The consequent decrease of the angle (alpha) brings the tropomyosin helices nearer to the filament axis, without any real movement of tropomyosin along the actin monomer.

Actin may contribute to the power stroke in the binary actomyosin system.

At the physiological protein osmotic pressure, the angle formed between the long axis of the actin monomer and the pointed end of the filament axis is roughly 61 degrees in F-actin and about 90 degrees in the myosin subfragment 1--decorated F-actin. This implies that, in the course of the contractile cycle, actin itself contributes, by about 4 nm, to the displacement of the actin filament toward the center of the sarcomer.