Hydrational and intrinsic compressibilities of globular proteins

Partial compressibilities of globular proteins in water are reviewed. Contribution of hydrational and of intrinsic compressibilities to experimental partial quantity have been evaluated from ultrasonic data using two independent methods: (a) additive calculation of the hydrational contributions of the surface atomic groups and (b) an analysis of correlation between partial compressibility and molecular surface area. The value (14 ± 3) × 10^?6 bar ^?1 for the isothermal compressibility coefficient of the protein interior at 25°C was obtained as an average value for variety of globular proteins. This value is similar to that of solid organic polymers. Possible relaxation contribution to partial compressibility is roughly estimated from comparison of thermodynamic with x-ray data on protein compressibility. The average compressibility of water in the hydration shell of proteins was found to be 35 × 10^?6 bar ^?1, which is 20% less than that of pure water. © 1993 John Wiley & Sons, Inc.     

The influence of correlated protein-water volume fluctuations on the apparent compressibility of proteins determined by ultrasonic velocimetry

The elasticity of proteins, expressed by the compressibility, is potentially one of the most important properties of proteins because of the close relationship with its functionality. The compressibility of solutions can be determined by measurements of sound velocity and density. These quantities are related by the Newton-Laplace equation. In order to interpret the apparent compressibility of solutes in highly dilute solutions, it is required to consider the relation between compressibility and sound velocity of the solution using an appropriate reference system. The classical approach usually gives too small values for the apparent compressibility when compared with other methods. We show that the difference can partially be explained if the correlated volume fluctuations of the solvent are taken into consideration. A special attention is given to the compressibility of proteins. Finally, the present paper is not intended to replace established approaches, but it wants to create awareness that the classical mixing rules refer to ideal gasses assuming uncorrelated volume fluctuations and that a considerable part of the hydration effects could be explained by correlated volume fluctuations.     

Compressibility-structure relationship of globular proteins

The adiabatic compressibility, -beta s, of 11 globular proteins in water was determined by means of sound velocity measurements at 25 degrees C. All the proteins studied except for subtilisin showed positive -beta s values, indicating the large internal compressibility of the protein molecules. The intrinsic compressibility of proteins free from the hydration effect appeared to be comparable to that of normal ice. The compressibility data for 25 proteins, including 14 reported previously [Gekko, K., & Noguchi, H. (1979) J. Phys. Chem. 83, 2706-2714], were statistically analyzed to examine the correlation of the compressibility with some structural parameters and the amino acid compositions of proteins. It was found that -beta s increases with increasing partial specific volume and hydrophobicity of proteins. The helix element also seemed to be a dynamic domain to increase -beta s. Four amino acid residues (Leu, Glu, Phe, and His) greatly increased -beta s, and another four (Asn, Gly, Ser, and Thr) decreased it. Some empirical equations were derived for the estimation of the -beta s values of unknown proteins on the basis of their amino acid compositions. The volume fluctuations of proteins revealed by the compressibility data were in the range of 30-200 mL/mol, which corresponded to about 0.3% of the total protein volume. The conformational fluctuation seemed to enhance the thermal stability of proteins.     

Localized density pulses in lipid membranes on the piсosecond time scale

Physical mechanisms for the modulation of lipid nanodomain dynamics and transport of small molecules across the lipid bilayer of biological membranes can have considerable functional significance. The longitudinal propagating compression–expansion mode in a single-component lipid bilayer is considered on a spatial scale comparable to the bilayer thickness. The expression used for free energy per lipid molecule includes a term with the gradient of the area per lipid molecule. The finite character of the stress relaxation time in the lipid bilayer, which causes significant attenuation of viscous damping at sufficiently high frequencies, is taken into account. A hydrodynamic ad hoc model that describes soliton-like excitations in the bilayer is proposed. The possibility of formation and propagation of nanoscale pulses of lipid density with velocities determined by surface compressibility of the bilayer (similarly to the propagation of sound) is demonstrated for the picosecond time scale.     

Theory of acoustic mode vibrations of DNA fibers

A previous model for acoustic mode vibrations of a DNA molecule in water is extended to the case of an array of many DNA molecules, as occurs in the fibers studied in most experimental work on DNA. The acoustic modes of this system are found to consist of coupled modes of water sound vibrations and DNA acoustic modes. This model is used to study the electrostatic coupling of acoustic vibrations to the relaxational modes of the orientational degrees of freedom of the water molecules. It is found that the long-range or macroscopic electric field generated by the acoustic mode vibrations of the water-DNA system gives too small a damping and frequency shift of the acoustic modes to account for the observations on DNA fibers. Therefore, the observed damping and frequency shifts are most likely due to either friction between the surrounding water and the vibrating DNA, or coupling to the water orientation degrees of freedom resulting from the short range (i.e., screened) Coulomb interaction. The latter explanation (which is most likely the correct one) implies that the relaxation time of the hydration shell water is longer than the observed relaxation time by a factor of the static dielectric constant of the hydration water.     

Model-free analysis for large proteins at high magnetic field strengths

Protein backbone dynamics is often characterized using model-free analysis of three sets of ¹⁵N relaxation data: longitudinal relaxation rate (R ₁), transverse relaxation rate (R ₂), and ¹⁵N–{H} NOE values. Since the experimental data is limited, a simplified model-free spectral density function is often used that contains one Lorentzian describing overall rotational correlation but not one describing internal motion. The simplified spectral density function may be also used in estimating the overall rotational correlation time, by making the R ₂/R ₁ largely insensitive to internal motions, as well as used as one of the choices in the model selection protocol. However, such approximation may not be valid for analysis of relaxation data of large proteins recorded at high magnetic field strengths since the contribution to longitudinal relaxation from the Lorentzian describing the overall rotational diffusion of the molecule is comparably small relative to that describing internal motion. Here, we quantitatively estimate the errors introduced by the use of the simplified spectral density in model-free analysis for large proteins at high magnetic field strength.     

Volumetric effects of ionization of amino and carboxyl termini of alpha,omega-aminocarboxylic acids

We have determined the partial molar volumes and adiabatic compressibilities of a homologous series of six alpha,omega-aminocarboxylic acids over a broad pH range at 25 degrees C. We interpret the resulting data in terms of the changes in hydration associated with neutralization of amino and carboxyl termini. By combining our volumetric results with pH-dependent data on 1-anilinonaphthalene-8-sulfonic acid fluorescence we propose the following explanation to the long-standing observation that changes in volume and compressibility accompanying neutralization of a carboxyl group depend on the type of the solute in contrast to solute-independent changes in these parameters accompanying neutralization of an amino group. Unlike amino groups, neutralized carboxyl groups are capable of forming hydrogen-bonded structures stabilized by hydrogen bonds between the carbonyl oxygen of one solute molecule and the hydroxyl group of another molecule. Formation of such hydrogen-bonded structures causes an additional decrease in solute hydration with concomitant increases in volume and compressibility. Furthermore, solutes with large aliphatic moieties may form larger associates stabilized, in addition to intermolecular hydrogen bonds, by hydrophobic interactions which will result in further increases in volume and compressibility. In the aggregate, our results emphasize the need for further studies focused on developing an understanding of the role of electrostatic interactions in stabilizing/destabilizing proteins and protein complexes.     

Cholesterol-induced variations in the volume and enthalpy fluctuations of lipid bilayers.

The sound velocity and density of suspensions of large unilamellar liposomes from dimyristoylphosphatidylcholine with admixed cholesterol have been measured as a function of temperature around the chain melting temperature of the phospholipid. The cholesterol-to-phospholipid molar ratio xc has been varied over a wide range (0 </= xc </= 0.5). The temperature dependence of the sound velocity number, of the apparent specific partial volume of the phospholipid, and of the apparent specific adiabatic compressibility have been derived from the measured data. These data are particularly discussed with respect to the volume fluctuations within the samples. A theoretical relation between the compressibility and the excess heat capacity of the bilayer system has been derived. Comparison of the compressibilities (and sound velocity numbers) with heat capacity traces display the close correlation between these quantities for bilayer systems. This correlation appears to be very useful as it allows some of the mechanical properties of membrane systems to be calculated from the specific heat capacity data and vice versa.     

Intramolecular dielectric screening in proteins

This paper investigates the microscopic mechanisms of charge screening by proteins. For this purpose, we introduce the generalized susceptibility of a protein in response to a point charge, which is a scalar quantity dependent on position within the protein. The contribution to the susceptibility from atomic polarizabilities, associated with electronic degrees of freedom, is found to be highly uniform. By contrast, that from dynamic dipolar relaxation, associated with nuclear degrees of freedom, varies greatly between different regions of the protein. We investigate the possible r?le of this variation in the activity of proteins that interact functionally with charged species, and we formulate and test the hypothesis that this variation is correlated to functional activity. Model calculations give encouraging support to this hypothesis. The protein's dielectric properties are represented by a standard model in which electronic relaxation is described by a set of atomic polarizabilities, and dipolar relaxation is treated as a perturbation to normal mode dynamics. The model yields the desired susceptibility in closed form. Its obvious limitations are discussed. It is applied to several test systems, and is compared to various continuum models. Four model alpha-helices are considered, three of which play a r?le in vivo in the binding of charged ligands. We show that the intramolecular screening, and its spatial variation, can indeed play a part in this binding. The electron transfer between ferri- and ferrocytochrome c is considered. The dielectric relaxation of each molecule, associated respectively with its oxidation or its reduction, is known to be directly related to the activation free energy for the electron transfer reaction. Our analysis of the dielectric susceptibility will thus permit an estimate of this activation free energy. We show that the relaxation of the atomic positions ("dipolar relaxation") contributes 1 kcal/mol to this activation free energy, and that the molecule achieves this low value by providing a low dipolar susceptibility throughout its central part. In this case, the spatial variation of the susceptibility has a clear functional r?le.     

Implications of protein folding. Additivity schemes for volumes and compressibilities

Partial specific volume and compressibility properties of the extended state of proteins are estimated from additivity schemes using revised amino acid and peptide data. These calculated properties are compared with the experimental data of the native state in order to assess the contribution from folding. Results of this treatment show that, in the case of partial specific volumes, there is close agreement between the two data sets for a number of proteins. The implication is that subtle compensatory contributions in volume occur during the folding process. In the case of compressibilities, however, a substantial difference is observed which is believed to arise because of the hydrophobic interior created in the native protein as a result of the folding process. Using suitable measures of protein hydrophobicities and estimates of the fraction of buried apolar residues, a "micellar model of protein compressibility" is proposed and tested for several proteins. Results obtained from this model show good agreement with the experimental data for the native state of a number of proteins.     

Mechanical properties ofChlorella cell walls as determined by the suspension method

The so-called suspension method was employed to measure the mechanical properties ofChlorella cell walls. This method worked well for the present sample. The ratio of compressibility of the cell wall to that of water was 0.62 at room temperature at frequencies of 1.5 and 2.0 MH_z. Temperature dependence of compressibility was similar to that of many polymer samples. A difference of compressibility was observed at two different stages of the cell cycle ofChlorella, but any difference of volume viscosity was not as obvious. The more extensive the enlargement growth of the cell, the larger was the compressibility. The existence of a relaxation mechanism in the order of microseconds was postulated from measurements of the frequency dependence of the attenuation of sound waves.     

Picosecond relaxations in model substances for proteins: A millimeter-wave investigation on crystalline alkyl amides

The dielectric absorption at millimeter-wave (mm-wave) frequencies (50–150 GHz) of N-methylacetamide (NMA), N,N-dimethylacetamide (DiNMA), and N,N-dimethylacrylamide (DiNMAcry) is measured. Measurements are performed using the oversized-cavity technique in the temperature range from liquid helium to room temperature. Additionally, a mm-wave interferometeric measurement at room temperature is made. NMA and DiNMAcry exhibit monotonic increases of the absorption coefficient with temperature as well as with frequency. For DiNMA a monotonic increase of the absorption coefficient with frequency is also found, while the absorption coefficient as a function of temperature shows a pronounced maximum at approximately 30 K. At this maximum the absorption coefficient of DiNMA exceeds those of NMA and DiNMAcry by about two orders of magnitude. The dielectric behavior of the three substances can be described by relaxation processes in asymmetric double-well potentials. For the low-temperature relaxation in DiNMA the double well could be established by two possible positions of the molecule in the crystal that are separated by a rotational movement. Hydrogen bonds and long side chains may hinder these relaxational movements in NMA and DiNMAcry, respectively, and thereby account for their comparatively lower absorption. The results are compared with similar results recently obtained on proteins and synthetic biopolymers.     

Proton longitudinal relaxation investigation of histidyl residues in human normal adult hemoglobin.

The longitudinal relaxation of the C2 protons of surface histidyl residues as well as other aromatic protons of human normal adult deoxyhemoglobin investigated at 360 MHz is discussed in terms of the theory proposed by Kalk and Berendsen for the proton longitudinal relaxation in proteins (Kalk, A., and H.J.C. Berendsen. 1976. J. Magn. Reson. 24:343-366). The role of the four paramagnetic iron atoms of deoxyhemoglobin as fast-relaxing sinks for the overall proton longitudinal relaxation is evaluated according to the model proposed by Bloembergen for the relaxation of nuclei in crystals containing paramagnetic centers (Bloembergen, N. 1949. Physica. 15:386-426). The results suggest that the effectiveness of the paramagnetic iron atoms of deoxyhemoglobin for the overall proton longitudinal relaxation is reduced as a result of slower spin diffusion and wide distribution of methyl groups within the hemoglobin molecule. Thus, deoxyhemoglobin provides a good model for investigating the influence of cross relaxation on proton longitudinal relaxation in proteins at the slow motion limit and in the presence of paramagnetic centers. For the C2 protons of surface histidyl residues, we show that the cross relaxation resulting from the interresidue dipolar interaction makes an important contribution to their longitudinal relaxation.     

Water and Backbone Dynamics in a Hydrated Protein

Rotational immobilization of proteins permits characterization of the internal peptide and water molecule dynamics by magnetic relaxation dispersion spectroscopy. Using different experimental approaches, we have extended measurements of the magnetic field dependence of the proton-spin-lattice-relaxation rate by one decade from 0.01 to 300 MHz for ¹H and showed that the underlying dynamics driving the protein ¹H spin-lattice relaxation is preserved over 4.5 decades in frequency. This extension is critical to understanding the role of ¹H₂O in the total proton-spin-relaxation process. The fact that the protein-proton-relaxation-dispersion profile is a power law in frequency with constant coefficient and exponent over nearly 5 decades indicates that the characteristics of the native protein structural fluctuations that cause proton nuclear spin-lattice relaxation are remarkably constant over this wide frequency and length-scale interval. Comparison of protein-proton-spin-lattice-relaxation rate constants in protein gels equilibrated with ²H₂O rather than ¹H₂O shows that water protons make an important contribution to the total spin-lattice relaxation in the middle of this frequency range for hydrated proteins because of water molecule dynamics in the time range of tens of ns. This water contribution is with the motion of relatively rare, long-lived, and perhaps buried water molecules constrained by the confinement. The presence of water molecule reorientational dynamics in the tens of ns range that are sufficient to affect the spin-lattice relaxation driven by ¹H dipole-dipole fluctuations should make the local dielectric properties in the protein frequency dependent in a regime relevant to catalytically important kinetic barriers to conformational rearrangements.     

Undulation Contributions to the Area Compressibility in Lipid Bilayer Simulations

It is here shown that there is a considerable system size-dependence in the area compressibility calculated from area fluctuations in lipid bilayers. This is caused by the contributions to the area fluctuations from undulations. This is also the case in experiments. At present, such a contribution, in most cases, is subtracted from the experimental values to obtain a true area compressibility. This should also be done with the simulation values. Here, this is done by extrapolating area compressibility versus system size, down to very small (zero) system size, where undulations no longer exist. The area compressibility moduli obtained from such simulations do not agree with experimental true area compressibility moduli as well as the uncorrected ones from contemporary or earlier simulations, but tend, instead, to be ∼50% too large. As a byproduct, the bending modulus can be calculated from the slope of the compressibility modulus versus system-size. The values obtained in this way for the bending modulus are then in good agreement with experiment.     

Compressibility gives new insight into protein dynamics and enzyme function

The adiabatic compressibility of enzyme is largely influenced by binding of coenzyme and substrate, due to the changes in atomic packing. Amino acid substitution also induces large changes in compressibility parallel to enzyme activity. These results demonstrate that a small alteration of local structure by ligand binding and mutation is dramatically magnified in the flexibility of protein molecule to affect the function. Compressibility gives new insight into protein dynamics and enzyme function from the aspect of atomic packing or cavity which cannot be obtained by other techniques.     

The thermodynamics of protein-protein recognition as characterized by a combination of volumetric and calorimetric techniques: the binding of turkey ovomucoid third domain to alpha-chymotrypsin

We have used ultrasonic velocimetry, high-precision densimetry, and fluorescence spectroscopy, in conjunction with isothermal titration and differential scanning calorimetry, to characterize the binding of turkey ovomucoid third domain (OMTKY3) to alpha-chymotrypsin. We report the changes in volume and adiabatic compressibility that accompany the association of these proteins at 25 degrees C and pH 4.5. In addition, we report the changes in free energy, enthalpy, entropy, and heat capacity upon the binding of OMTKY3 to alpha-chymotrypsin over a temperature range of 20-40 degrees C. Our volume and compressibility data, in conjunction with X-ray crytsallographic data on the OMTKY3-alpha-chymotrypsin complex, suggest that 454(+/-22) water molecules are released to the bulk state upon the binding of OMTKY3 to alpha-chymotrypsin. Furthermore, these volumetric data suggest that the intrinsic compressibility of the two proteins decreases by 7%. At each temperature studied, OMTKY3 association with alpha-chymotrypsin is entropy driven with a large, unfavorable enthalpy contribution. The observed entropy of the binding reflects interplay between two very large favorable and unfavorable terms. The favorable term reflects an increase in the hydrational entropy resulting from release to the bulk of 454 water molecules. The unfavorable term is related to a decrease in the configurational entropy and, consequently, a decrease in the conformational dynamics of the two proteins. In general, we discuss the relationship between macroscopic and microscopic properties, in particular, identifying and quantifying the role of hydration in determining the thermodynamics of protein recognition as reflected in volumetric and calorimetric parameters.     

Kinetics of carboxymyoglobin and oxymyoglobin studied by picosecond spectroscopy.

Picosecond studies of carboxymyoglobin (MbCO) and oxymyoglobin (MbO2) reveal that excitation at 530 nm induces photodissociation at less than 8 ps. The kinetic and structural changes were monitored by following absorbance changes at selected wave-lengths in the Soret (B) band and in the Q band. Within the 10 ps-0.45 ns period of time over which our experiments were conducted, the absorbance changes in the Soret and Q bands for MbCO and MbO2 correspond to the conventional long-term, steady-state deoxymyoglobin difference spectra (Mb-MbCO and Mb-MbO2), as determined by comparison of isosbestic, maximum, and minimum points. In addition, MbCO exhibits a decay to a steady state in the Soret band (monitored at 440 nm). The onset of the decay immediately follows photodissociation and has a rate of (8 +/- 3) X 10(9) s-1 (tau = 125 +/- 50 ps). During the 10 ps-0.45 ns observation window, relaxation is not seen for MbO2 in the Soret band, nor is relaxation observed in the Q band for either MbCO or MbO2. We conclude from these results that the steady state that we observed for MbCO and MbO2 is most likely the stable form of deoxymyoglobin, and the relaxational differences between MbCO and MbO2 observed in the Soret band indicate that the electronic destabilization after ligand detachment is very different for these molecules. We believe that these relaxational differences may be related to differences in tertiary structural changes, or due to the fact that the MbCO (S = 0) molecule passes through an intermediate spin Mb (S = 1) state before relaxing the the Mb (S = 2) state.     

Proton nuclear magnetic resonance study of a selectively deuterated mouse monoclonal antibody: use of two-dimensional homonuclear Hartmann-Hahn spectroscopy

A 1H NMR study of a selectively deuterated mouse anti-dansyl monoclonal antibody is reported. Two-dimensional homonuclear Hartmann-Hahn (2D-HOHAHA) spectroscopy was found to be effective for establishing the connectivity between the C2-H and C4-H protons of His residues in the antibody molecule. It has been concluded that 1) even in the case of large proteins such as an antibody, HOHAHA peaks can be observed for amino acid residues that are located in a flexible environment, and 2) deuterium labeling is effective in reducing the efficiency of spin relaxation and makes it possible to increase the number of observed HOHAHA cross peaks. It was suggested that 2D-HOHAHA can also be used to obtain information concerning the flexible parts of antibody molecules.     

Structural-dynamic properties of the tryptophan residue environment in melittin

The structural dynamics of the environment of the single tryptophan residue in melittin was studied by site-selective red-edge-excitation fluorescence spectroscopy. The dependence of the spectral shift on transition from excitation in a maximum (at 280 nm) to long-wavelength edge (305 nm) was studied as a function of temperature. It was shown, that for melittin at high ionic strength (tetramer), the three regions of temperature dependence of the red-edge effect are observed: retarded relaxation (up to +30 degrees C), relaxational changes of spectra (from +30 to +50 degrees C) and thermal changes of structure (above +50 degrees C). The dipolar-re-orientational relaxation time and activation energy of orientation motions in the environment of indolic ring in the tetrameric melittin structure were estimated. Extrapolation from relaxational region to room temperature results in relaxation time 40 ns. In monomeric melittin (at low ionic strength) the red-edge shift of spectra is absent. The distinct differences in character of thermal quenching of fluorescence between monomeric and tetrameric forms of melittin are observed. It follows, that the short-wave-length fluorescence shift on monomer-tetramer transition is due to both the reduction of polarity, and the increase in rigidity of tryptophan environment, the absence of relaxation motions at nanosecond times.