Adiabatic compressibility of myosin subfragment-1 and heavy meromyosin with or without nucleotide

A model of muscle contraction based on the Langevin equation with actomyosin potentials

We propose a muscle contraction model that is essentially a model of the motion of myosin motors as described by a Langevin equation. This model involves one-dimensional numerical calculations wherein the total force is the sum of a viscous force proportional to the myosin head velocity, a white Gaussian noise produced by random forces and other potential forces originating from the actomyosin structure and intra-molecular charges. We calculate the velocity of a single myosin on an actin filament to be 4.9-49 μm/s, depending on the viscosity between the actomyosin molecules. A myosin filament with a hundred myosin heads is used to simulate the contractions of a half-sarcomere within the skeletal muscle. The force response due to a quick release in the isometric contraction is simulated using a process wherein crossbridges are changed forcibly from one state to another. In contrast, the force response to a quick stretch is simulated using purely mechanical characteristics. We simulate the force-velocity relation and energy efficiency in the isotonic contraction and adenosine triphosphate consumption. The simulation results are in good agreement with the experimental results. We show that the Langevin equation for the actomyosin potentials can be modified statistically to become an existing muscle model that uses Maxwell elements.

Comparison of left ventricular diastolic filling with myocyte bulk modulus using Doppler echocardiography and acoustic microscopy in pressure-overload left ventricular hypertrophy and cardiac amyloidosis

BACKGROUND

The myocardial bulk modulus has been described as the constitutive properties of the left ventricular (LV) wall and is measured as rho V2 (rho = density, V = sound speed) using acoustic microscopy.

HYPOTHESIS

The study was undertaken to assess the relationship between the myocyte bulk modulus and transmitral inflow patterns in patients with pressure-overload LV hypertrophy (LVH) and cardiac amyloidosis (AMD).

METHODS

In 8 patients with LVH, 8 with AMD, and 10 controls without heart disease, the transmitral inflow pattern was recorded by Doppler echocardiography before death, and myocardial tissue specimens were obtained at autopsy. The tissue density and sound speed in the myocytes were measured by microgravimetry and acoustic microscopy, respectively. The diameters of the myocytes were measured on histopathologic specimens stained by the elastica Van Gieson method.

RESULTS

In the subendocardium, the myocyte bulk modulus was larger in LVH (2.98 x 10(9) N/m2, p < 0.001) and smaller in AMD (2.61 x 10(9) N/m2, p < 0.001) than in the controls (2.87 x 10(9) N/m2). The myocyte diameter in LVH (26 +/- 1 microns) was larger than that in the control (21 +/- 1 microns, p < 0.001) and AMD (20 +/- 1 microns, p < 0.001). The bulk modulus in the subendocardial myocyte significantly correlated with the deceleration time (DT) of the early transmitral inflow (r = 0.689, p = 0.028 in control, r = 0.774, p = 0.024 in LVH, and r = 0.786, p = 0.021 in AMD).

CONCLUSION

The changes in the myocyte elasticity as represented by the bulk modulus were limited to the subendocardial layers and may be related to relaxation abnormalities in LVH and a reduction in LV compliance in AMD.

Nanomechanical properties of globular proteins: lactate oxidase

We report on the study of the nanomechanical properties of a lactate oxidase (LOx) monolayer immobilized on gold substrates by atomic force microscopy techniques operating under buffer conditions. Topographical contact mode imaging evidenced the protein deformation under the applied tip load. We performed approaching force curves with both stiff and soft cantilevers by imposing maximum loads of 1.6 nN and 400 pN, respectively. We found that the experimental data were well fitted by the Hertz model for a conical indenter. The use of two types of cantilevers allowed us to check further the consistency of the applicability of the Hertz model to the experimental data. After analyzing 180 curves, we obtained an average value of Young's modulus for the LOx layer in the 0.5-0.8 GPa range. These results agreed with those obtained for LOx submonolayer deposits on mica substrates, which allows discarding any important contribution from the underlying substrate on the measured properties. This range of values is closer to those obtained by other techniques on other globular proteins in comparison with those reported in previous AFM studies on similar systems. We found that for our experimental conditions the force curves can be, in principle, well fitted by the Hertz model for both conical and spherical indenter geometries. However, as the Young's modulus obtained for both geometries can differ appreciably, it becomes necessary to assess which indenter geometry is more adequate to explain the experimental data. For such purpose a systematic study of the indentation versus applied force curves obtained from both fittings for all the experimental curves was done.

Exploring the electronic and mechanical properties of protein using conducting atomic force microscopy

In interfacing man-made electronic components with specifically folded biomacromolecules, the perturbative effects of junction structure on any signal generated should be considered. We report herein on the electron-transfer characteristics of the blue copper metalloprotein, azurin, as characterized at a refined level by conducting atomic force microscopy (C-AFM). Specifically, the modulation of current-voltage (I-V) behavior with compressional force has been examined. In the absence of assignable resonant electron tunneling within the confined bias region, from -1 to 1 V, the I-V behavior was analyzed with a modified Simmons formula. To interpret the variation of tunneling barrier height and barrier length obtained by fitting with the modified Simmons formula, an atom packing density model associated with protein mechanical deformation was proposed and simulated by molecular dynamics. The barrier heights determined at the minimum forces necessary for stable electrical contact correlate reasonably well with those estimated from bulk biophysical (electroanalytical and photochemical) experiments previously reported. At higher forces, the tunnel barrier decreases to fall within the range observed with saturated organic systems. Molecular dynamics simulations revealed changes in secondary structure and atomic density of the protein with respect to compression. At low compression, where transport measurements are made, secondary structure is retained, and atomic packing density is observed to increase linearly with force. These predictions, and those made at higher compression, are consistent with both experimentally observed modulations of tunneling barrier height with applied force and the applicability of the atom packing density model of electron tunneling in proteins to molecular-level analyses.

A linear correlation between the energetics of allosteric communication and protein flexibility in the Escherichia coli cyclic AMP receptor protein revealed by mutation-induced changes in compressibility and amide hydrogen-deuterium exchange

Amino acid substitutions at distant sites in the Escherichia coli cyclic AMP receptor protein (CRP) have been shown to affect both the nature and magnitude of the energetics of cooperativity of cAMP binding, ranging from negative to positive. In addition, the binding to DNA is concomitantly affected. To correlate the effects of amino acid substitutions on the functional energetics and global structural properties in CRP, the partial specific volume (v(o)), the coefficient of adiabatic compressibility (beta(s)(o)), and the rate of amide proton exchange were determined for the wild-type and eight mutant CRPs (K52N, D53H, S62F, T127L, G141Q, L148R, H159L, and K52N/H159L) by using sound velocity, density measurements, and hydrogen-deuterium exchange as monitored by Fourier transform infrared spectroscopy at 25 degrees C. These mutations induced large changes in v(o) (0.747-0.756 mL/g) and beta(s)(o) (6.89-9.68 Mbar(-1)) compared to the corresponding values for wild-type CRP (v(o)= 0.750 mL/g and beta(s)(o)= 7.98 Mbar(-1)). These changes in global structural properties correlated with the rate of amide proton exchange. A linear correlation was established between beta(s)(o) and the energetics of cooperativity of binding of cAMP to the high-affinity sites, regardless of the nature of cooperativity, be it negative or positive. This linear correlation indicates that the nature and magnitude of cooperativity are a continuum. A similar linear correlation was established between compressibility and DNA binding affinity. In addition, linear correlations were also found among the dynamics of CRP and functional energetics. Double mutation (K52N/H159L) at positions 52 and 159, whose alpha-carbons are separated by 34.6 A, showed nonadditive effects on v(o) and beta(s)(o). These results demonstrate that a small alteration in the local structure due to amino acid substitution is dramatically magnified in the overall protein dynamics which plays an important role in modulating the allosteric behavior of CRP.

Volumetric properties of proteins

Structural and thermodynamic characterizations of a variety of intra- and intermolecular interactions stabilizing/destabilizing protein systems represent a major part of multidisciplinary efforts aimed at solving the problems of protein folding and binding. To this end, volumetric techniques have been successfully used to gain insights into protein hydration and intraglobular packing. Despite the fact that the use of volumetric measurements in protein-related studies dates back to the 1950s, such measurements still represent a relatively untapped yet potentially informative means for tackling the problems of protein folding and binding. This notion has been further emphasized by recent advances in the development of highly sensitive volumetric instrumentation that has led to intensifying volumetric investigations of protein systems. This paper reviews the volumetric properties of proteins and their low-molecular-weight analogs, in particular, discussing the recent progress in the use of volumetric data for studying conformational transitions of proteins as well as protein-ligand, protein-protein, and protein-nucleic acid interactions.

Plastic deformation of protein monolayers

Globular proteins are peculiar solids that display both local stability of their conformation and the ability to undergo large cooperative changes of shape (conformational changes). If one forces a large deformation of the molecule, such that the structure is necessarily changed, it is not obvious whether the deformed globule can still remain a solid or whether it will melt. Is it possible to plastically deform a protein? Here we investigate this question with a micro-mechanical experiment on a small region (approximately 10 molecules) of a protein monolayer adsorbed on a rigid surface. For the two proteins studied, albumin and myoglobin, we observed that the molecules can be substantially deformed (approximately 1-2 nm deformation) by comparatively small stresses applied for sufficiently long times. The deformation is irreversible, and the protein remains in the solid state (i.e., displays a nonzero shear modulus). The dynamics of the deformation is approximately logarithmic in time, similar to creep in solids. These results show that globular proteins adsorbed on a surface can be plastically deformed.

Relationship between myocardial tissue density measured by microgravimetry and sound speed measured by acoustic microscopy

If myocardial tissue can be assumed to be fluid-like, myocardial tissue elasticity can be estimated by the sound speed of tissue based on the equation K = rho(c)2, where K is the elastic bulk modulus, rho is density, and c is the sound speed of tissue. However, little data exist regarding the relationship between the sound speed of tissue and tissue density. The purpose of the present study was to evaluate the relationship between the sound speed of tissue and tissue density of various diseased myocardia. Myocardial tissue specimens at autopsy were obtained from 10 control patients without cardiovascular disease, 8 patients with pressure overload left ventricular hypertrophy (POLVH), and 8 patients with cardiac amyloidosis (AMD). Myocardial tissue sound speed was measured using a scanning acoustic microscope operating in the frequency of 450 MHz, and tissue density was measured by microgravimetry. The sound speed in POLVH (1639 +/- 17 m/s) was higher and that in AMD (1565 +/- 11 m/s) was lower than that in control patients (1615 +/- 15 m/s) (p < 0.001) at the temperature of 20-22 degrees C. The density in POLVH (1.087 +/- 0.004 g/cm3) was higher and that in AMD (1.072 +/- 0.003 g/cm3) was lower than that in control patients (1.082 +/- 0.003 g/cm3) (p < 0.001). Tissue density correlated with sound speed in all three groups (r = 0.96, p < 0.001). Therefore, myocardial tissue sound speed data obtained by acoustic microscopy enabled us to evaluate tissue elasticity without measuring tissue density directly.

Evaluation of left atrial wall elasticity using acoustic microscopy

Left atrial wall elasticity is one of the important factors regulating left atrial stiffness and functions. The authors evaluated left atrial wall elasticity by measuring the sound speed through the left atrial wall, based on the hypothesis that high elasticity tissues will yield larger sound speed values through the tissue, and examined age-associated changes in left atrial wall elasticity. Left atrium specimens were obtained from 30 normal subjects (age, 15-95 years) at autopsy. An acoustic microscope, operating at 450 MHz, was used to measure the sound speed in the endocardium and the myocardium of the left atrium. The sound speeds in endocardium and myocardium demonstrated significant correlation with age (r = 0.74, p<0.0001 and r = 0.47, p<0.01, respectively). These findings indicate that left atrial wall elasticity increased with advancing age. These changes may lead to deterioration of left atrial compliance and eventual left atrial failure in older subjects.

Viscoelastic properties of f-actin, microtubules, f-actin/alpha-actinin, and f-actin/hexokinase determined in microliter volumes with a novel nondestructive method

A nondestructive method to determine viscoelastic properties of gels and fluids involves an oscillating glass fiber serving as a sensor for the viscosity of the surrounding fluid. Extremely small displacements (typically 1-100 nm) are caused by the glass rod oscillating at its resonance frequency. These displacements are analyzed using a phase-sensitive acoustic microscope. Alterations of the elastic modulus of a fluid or gel change the propagation speed of a longitudinal acoustic wave. The system allows to study quantities as small as 10 microliters with temporal resolution >1 Hz. For 2-100 microM f-actin gels a final viscosity of 1.3-9.4 mPa s and a final elastic modulus of 2.229-2.254 GPa (corresponding to 1493-1501 m/s sound velocity) have been determined. For 10- to 100-microM microtubule gels (native, without stabilization by taxol), a final viscosity of 1.5-124 mPa s and a final elastic modulus of 2.288-2. 547 GPa (approximately 1513-1596 m/s) have been determined. During polymerization the sound velocity in low-concentration actin solutions increased up to +1.3 m/s (approximately 1.69 kPa) and decreased up to -7 m/s (approximately 49 kPa) at high actin concentrations. On polymerization of tubulin a concentration-dependent decrease of sound velocity was observed, too (+48 to -12 m/s approximately 2.3-0.1 MPa, for 10- to 100-microM tubulin). This decrease was interpreted by a nematic phase transition of the actin filaments and microtubules with increasing concentration. 2 mM ATP (when compared to 0.2 mM ATP) increased polymerization rate, final viscosity and elastic modulus of f-actin (17 microM). The actin-binding glycolytic enzyme hexokinase also accelerated the polymerization rate and final viscosity but elastic modulus (2.26 GPa) was less than for f-actin polymerized in presence of 0.2 mM ATP (2.28 GPa).

Why does intermittent hydrostatic pressure enhance the mineralization process in fetal cartilage?

The purpose of this study was to determine which factor is the most likely one to have stimulated the mineralization process in the in vitro experiments of Klein-Nulend et al. (Arth. Rheum., 29, 1002-1009, 1986), in which fetal cartilaginous metatarsals were externally loaded with an intermittent hydrostatic pressure, by compressing the gas phase above the culture medium. Analytical calculations excluded the possibility that the tissue was stimulated by changes in dissolved gas concentration, pH or temperature of the culture medium through compression of the gas phase. The organ culture experiments were also mechanically analyzed using a poroelastic finite element (FE) model of a partly mineralized metatarsal with compressible solid and fluid constituents. The results showed that distortional strains occurred in the region where mineralization proceeded. The value of this strain was, however, very sensitive to the value of the intrinsic compressibility modulus of the solid matrix (Ks). For realistic values of Ks the distortional strain was probably too small (about 2 microstrain) to have stimulated the mineralization. If the distortional strain was not the factor to have enhanced the mineralization process, then the only candidate variable left is the hydrostatic pressure itself. We hypothesize that the pressure may have created the physical environment enhancing the mineralization process. When hydrostatic pressure is applied, the balance of the chemical potential of water across cell membranes may be disturbed, and restored again by diffusion of ions until equilibrium is reached again. The diffusion of ions may have contributed to the mineralization process.

Pressure denaturation of proteins: evaluation of compressibility effects

One of the key pieces of information from pressure denaturation experiments is the standard volume change for unfolding (Delta V(o)). The pressure dependence of the volume change, the standard compressibility change (Delta K(o)T), is typically assumed to be zero in the analysis of these experiments. We show here that this assumption can be incorrect and that the neglect of compressibility differences can skew the interpretation of experimental results. Analysis of experimental, variable-pressure NMR data for bovine pancreatic ribonuclease A in 2H2O at pH 2.0 and 295 K yielded the following statistically significant, non-zero values: Delta K(o) T = 0.015 +/- 0.002 mL mol-1 bar-1, Delta V(o) = -21 +/- 2 mL mol-1, and Delta G(o) = 2.8 +/- 0.3 kcal mol-1. The experimental protein stability is in good agreement with one (Delta G(o) = 2.5 kcal mol-1) determined independently for the same protein by calorimetry at atmospheric pressure under equivalent conditions [Makhatadze, G. I., Clore, G. M., and Gronenborn, A. M. (1995) Nat. Struct. Biol. 2, 852-855]. The positive value for Delta K(o)T indicates that the denatured form of ribonuclease A is more compressible than the native form; this is explained in terms of an interplay between the intrinsic compressibility of the protein and solvation effects. When the same data were fitted to a model that assumes a zero compressibility change, the Delta G(o) value of 4. 0 +/- 0.1 kcal mol-1 returned by the model no longer agreed with the independent measurement, and the Delta V(o) returned by the model was a very different -59 +/- 1 mL mol-1. By contrast, it was not possible to carry out a similar thermodynamic analysis of fluorescence spectroscopic data for the denaturation of staphylococcal nuclease to yield well-defined values of Delta G(o), Delta V(o), and Delta K(o)T. This limitation was shown by evaluation of synthetic data to be intrinsic to spectroscopic data whose analysis requires fitting of the plateaus at either side of the transition. Because NMR data do not have this requirement, they can be analyzed more rigorously.

Adiabatic compressibility of flagellin and flagellar filament of Salmonella typhimurium

The partial specific volume and adiabatic compressibility of flagellin, its F40 fragment deprived of the disordered terminal regions, from Ala-1 to Arg-65 and from Ser-451 to Arg-494, and the flagellar filament of Salmonella typhimurium were determined from the density and the sound velocity measurements at 15 degrees C. The partial specific volumes were 0.728 cm3/g, 0.745 cm3/g, and 0.734 cm3/g, and the partial specific adiabatic compressibilities were 4.0 x 10(-12) cm2/dyn, 6.7 x 10(-12) cm2/dyn, and 4.7 x 10(-12) cm2/dyn, for flagellin, F40, and the filament, respectively. The smaller values of flagellin than those of F40 are reasonably explained by the presence of disordered terminal regions, which are supposed to be highly hydrated by water molecules. The volume increase upon polymerization of flagellin into the filament is also confirmed by depolymerization under a high pressure. The smaller volume and compressibility of the filament compared with those of F40 suggest an extensive hydration of the filament on its complex surface structure, which surpasses the effect on the volume and compressibility by a possible increase in the cavity volume at intersubunit interfaces upon polymerization.

Coupling of protein surface hydrophobicity change to ATP hydrolysis by myosin motor domain

Dielectric spectroscopy with microwaves in the frequency range between 0.2 and 20 GHz was used to study the hydration of myosin subfragment 1 (S1). The data were analyzed by a method recently devised, which can resolve the total amount of water restrained by proteins into two components, one with a rotational relaxation frequency (fc) in the gigahertz region (weakly restrained water) and the other with lower fc (strongly restrained water). The weight ratio of total restrained water to S1 protein thus obtained (0.35), equivalent to 2100 water molecules per S1 molecule, is not much different from the values (0.3-0.4) for other proteins. The weakly restrained component accounts for about two-thirds of the total restrained water, which is in accord with the number of water molecules estimated from the solvent-accessible surface area of alkyl groups on the surface of the atomic model of S1. The number of strongly restrained water molecules coincides with the number of solvent-accessible charged or polar atoms. The dynamic behavior of the S1-restrained water during the ATP hydrolysis was also examined in a time-resolved mode. The result indicates that when S1 changes from the S1.ADP state into the S1.ADP.P1 state (ADP release followed by ATP binding and cleavage), about 9% of the weakly restrained waters are released, which are restrained again on slow P1 release. By contrast, there is no net mobilization of strongly restrained component. The observed changes in S1 hydration are quantitatively consistent with the accompanying large entropy and heat capacity changes estimated by calorimetry (Kodama, 1985), indicating that the protein surface hydrophobicity change plays a crucial role in the enthalpy-entropy compensation effects observed in the steps of S1 ATP hydrolysis.

Osmotic pressure probe of actin-myosin hydration changes during ATP hydrolysis

Osmotic stress in the 0.5-5 x 10(6) dyne/cm2 range was used to perturb the hydration of actin-myosin-ATP intermediates during steady-state hydrolysis. Polyethylene glycol (PEG) (1000 to 4000 Da), in the 1 to 10 wt% range, which does not cause protein precipitation, did not significantly affect the apparent KM or the Vmax for MgATP hydrolysis by myosin subfragment 1 (S1) alone, nor did it affect the value for the phosphate burst. Consistent with the kinetic data, osmotic stress did not affect nucleotide-induced changes in the fluorescence intensities of S1 tryptophans or of fluorescein attached to Cys-707. The accessibility of the fluorescent ATP analog, epsilon ADP, to acrylamide quenching was also unchanged. These data suggest that none of the steps in the ATP hydrolysis cycle involve substantial hydration changes, which might occur for the opening or closing of the ATP site or of other crevices in the S1 structure. In contrast, KM for the interaction of S1.MgADP.Pi with actin decreased tenfold in this range of osmotic pressure, suggesting that formation of actin.S1.MgADP.Pi involves net dehydration of the proteins. The dehydration volume increases as the size of the PEG is increased, as expected for a surface-excluded osmolyte. The measured dehydration volume for the formation of actin.S1.MgADP.Pi was used to estimate the surface area of the binding interface. This estimate was consistent with the area determined from the atomic structures of actin and myosin, indicating that osmotic stress is a reliable probe of actin.myosin.ATP interactions. The approach developed here should be useful for determining osmotic stress and excluded volume effects in situ, which are much larger than those of typical in vitro conditions.

A large compressibility change of protein induced by a single amino acid substitution

The adiabatic compressibility (beta s) was determined, by means of the precise sound velocity and density measurements, for a series of single amino acid substituted mutant enzymes of Escherichia coli dihydrofolate reductase (DHFR) and aspartate aminotransferase (AspAT). Interestingly, the beta s values of both DHFR and AspAT were influenced markedly by the mutations at glycine-121 and valine-39, respectively, in which the magnitude of the change was proportional to the enzyme activity. This result demonstrates that the local change of the primary structure plays an important role in atomic packing and protein dynamics, which leads to the modified stability and enzymatic function. This is the first report on the compressibility of mutant proteins.

Compressibility and specific volume of actin decrease upon G to F transformation

We measured the densities as well as the sound velocities in solutions of G-actin, F-actin and the reconstituted thin filament. Using the data obtained, we determined their partial specific volumes and partial specific adiabatic compressibilities. The objectives were to investigate the volume change of actin upon polymerization and to detect the conformational change associated with the ca2+-binding to the reconstituted thin filament. The partial specific volume and the partial specific adiabatic compressibility of G-actin were 0.749 cm3/g and 9.3 x 10(-12) cm2/dyne, respectively. The results suggest that G-actin is a rather soft protein compared with other globular proteins. The partial specific volumes of F-actin were in a range of 0.63 -0.66 cm3/g depending on the solvent conditions. The partial specific adiabatic compressibilities of F-actin were negative (-(7-13) x 10(-12) cm3/dyne). These data indicate that the amount of hydration may increase by several times upon polymerization assuming that the size of the cavity remains constant. We detected little difference between the partial specific adiabatic compressibility of the reconstituted thin filament in a Ca2+-bound state and that in a Ca2+-unbound state. This suggests that the Ca2+ binding affected not the subunit itself but the inter-subunit junction.