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.     

Conformational deformation in deoxymyoglobin by hydrostatic pressure

Pressure effect on the equilibrium conformation in sperm whale deoxymyoglobin and its volume fluctuation are studied by the normal mode analysis and strain tensor analysis. The pressure-induced deformation of interhelix regions are found to be remarkably more compressed than the other parts of the molecule. The intrahelix compressibility is shown to be relatively small. We also calculate the compressibility of the three hydrophobic clusters, located at the bottom, distal, and proximal side of the heme. Its value is found to decrease in the indicated order. The average compressibility of these hydrophobic clusters is less than the average interhelix compressibility, even though there are large cavities in these clusters. In order to study overall deformation, we define a linear compressibility and calculate it for all pairs of C^αatoms. The pressure-induced deformation is observed to be heterogeneous also in this analysis. The calculated root-mean-square displacement of the constituent atoms in the equilibrium conformation at 1,000 atm from those at 0 atm is 0.12 Å, which is much smaller in magnitude than the average value of the atomic fluctuations at room temperature. In the water solvent, the volume excluded by the protein molecule in the equilibrium conformation is reduced by 0.9%, when the pressure is raised from 0 to 1,000 atm. The calculated magnitude of the root-mean-square volume fluctuation is 0.3% of the excluded volume at room temperature. The square of the volume fluctuation is given as a sum of contributions from individual normal modes. Contributions from low frequency normal modes are found to dominate over those from higher frequency normal modes. The estimated value of the isothermal compressibility of deoxymyoglobin is 9.37 × 10^?12 cm²/dyn. © 1993 Wiley-Liss, Inc.     

Decomposition of protein experimental compressibility into intrinsic and hydration shell contributions

The experimental determination of protein compressibility reflects both the protein intrinsic compressibility and the difference between the compressibility of water in the protein hydration shell and bulk water. We use molecular dynamics simulations to explore the dependence of the isothermal compressibility of the hydration shell surrounding globular proteins on differential contributions from charged, polar, and apolar protein-water interfaces. The compressibility of water in the protein hydration shell is accounted for by a linear combination of contributions from charged, polar, and apolar solvent-accessible surfaces. The results provide a formula for the deconvolution of experimental data into intrinsic and hydration contributions when a protein of known structure is investigated. The physical basis for the model is the variation in water density shown by the surface-specific radial distribution functions of water molecules around globular proteins. The compressibility of water hydrating charged atoms is lower than bulk water compressibility, the compressibility of water hydrating apolar atoms is somewhat larger than bulk water compressibility, and the compressibility of water around polar atoms is about the same as the compressibility of bulk water. We also assess whether hydration water compressibility determined from small compound data can be used to estimate the compressibility of hydration water surrounding proteins. The results, based on an analysis from four dipeptide solutions, indicate that small compound data cannot be used directly to estimate the compressibility of hydration water surrounding proteins.     

Molecular dynamics simulations of human rhinovirus and an antiviral compound

The human rhinovirus 14 (HRV14) protomer, with or without the antiviral compound WIN 52084s, was simulated using molecular dynamics and rotational symmetry boundary conditions to model the effect of the entire icosahedral capsid. The protein asymmetrical unit, comprising four capsid proteins (VP1, VP2, VP3, and VP4) and two calcium ions, was solvated both on the exterior and the interior to fill the inside of the capsid. The stability of the simulations of this large system (~800 residues and 6,650 water molecules) is comparable to more conventional globular protein simulations. The influence of the antiviral compound on compressibility and positional fluctuations is reported. The compressibility, estimated from the density fluctuations in the region of the binding pocket, was found to be greater with WIN 52084s bound than without the drug, substantiating previous computations on reduced viral systems. An increase in compressibility correlates with an entropically more favorable system. In contrast to the increase in density fluctuations and compressibility, the positional fluctuations decreased dramatically for the external loops of VP1 and the N-terminus of VP3 when WIN 52084s is bound. Most of these VP1 and VP3 loops are found near the fivefold axis, a region whose mobility was not considered in reduced systems, but can be observed with this simulation of the full viral protomer. Altered loop flexibility is consistent with changes in proteolytic sensitivity observed experimentally. Moreover, decreased flexibility in these intraprotomeric loops is noteworthy since the externalization of VP4, part of VP1, and RNA during the uncoating process is thought to involve areas near the fivefold axis. Both the decrease in positional fluctuations at the fivefold axis and the increase in compressibility near the WIN pocket are discussed in relationship to the antiviral activity of stabilizing the virus against uncoating.     

Binding of bovine pancreatic trypsin inhibitor to trypsinogen: spectroscopic and volumetric studies

We have investigated the binding of bovine pancreatic trypsin inhibitor (BPTI) to bovine trypsinogen by combining ultrasonic velocimetry, high precision densimetry, and fluorescence spectroscopy. We report the changes in volume, adiabatic compressibility, van't Hoff enthalpy, entropy, and free energy that accompany the association of the two proteins at 25 degrees C and pH 8.0. We have used the measured changes in volume and compressibility in conjunction with available structural data to characterize the binding-induced changes in the hydration properties and intrinsic packing of the two proteins. Our estimate reveals that 110 +/- 40 water molecules become released to the bulk from the hydration shells of BPTI and trypsinogen. Furthermore, we find that the intrinsic coefficient of adiabatic compressibility of the two proteins decreases by 14 +/- 2%, which is suggestive of the binding-induced rigidification of the proteins' interior. BPTI-trypsinogen association is an entropy-driven event which proceeds with an unfavorable change in enthalpy. The favorable change in entropy results from partial compensation between two predominant terms. Namely, a large favorable change in hydrational entropy slightly prevails over a close in magnitude but opposite in sign change in configurational entropy. The reduction in configurational entropy and, consequently, protein dynamics is consistent with the observed decrease in intrinsic compressibility. In general, results of this work emphasize the vital role that water plays in modulating protein recognition events.     

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.     

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.     

Harmonic and anharmonic aspects in the dynamics of BPTI: a normal mode analysis and principal component analysis.

A comparison is made between a 200-ps molecular dynamics simulation in vacuum and a normal mode analysis on the protein bovine pancreatic trypsin inhibitor (BPTI) in order to elucidate the dual aspects of harmonicity and anharmonicity in the dynamics of proteins. The molecular dynamics trajectory is analyzed using principal component analysis, an effective harmonic analysis suited for comparison with the results from the normal mode analysis. The results suggest that the first principal component shows qualitatively different behavior from higher principal components and is associated with apparent barrier crossing events on an anharmonic conformational energy surface. The higher principal components appear to have probability distributions that are well approximated by Gaussians, indicating harmonicity. Eliminating the contribution from the first principal component reveals a great deal of correspondence between the 2 methods. This correspondence, however, involves a factor of 2, as the variances of the distribution of the higher principal components are, on average, roughly twice those found from the normal mode analysis. A model is proposed to reconcile these results with those from previous analyses.     

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.     

Harmonicity and anharmonicity in protein dynamics: A normal mode analysis and principal component analysis

A comparison of a normal mode analysis and principal component analysis of a 200-ps molecular dynamics trajectory of bovine pancreatic trypsin inhibitor in vacuum has been made in order to further elucidate the harmonic and anharmonic aspects in the dynamics of proteins. An anharmonicity factor is defined which measures the degree of anharmonicity in the modes, be they principal modes or normal modes, and it is shown that the principal mode system naturally divides into anharmonic modes with peak frequencies below 80 cm^?1, and harmonic modes with frequencies above this value. In general the larger the mean-square fluctuation of a principal mode, the greater the degree of anharmonicity in its motion. The anharmonic modes represent only 12% of the total number of variables, but account for 98% of the total mean-square fluctuation. The transitional nature of the anharmonic motion is demonstrated. The results strongly suggest that in a large subspace, the free energy surface, as probed by the simulation, is approximated by a multi-dimensional parabola which is just a resealed version of the parabola corresponding to the harmonic approximation to the conformational energy surface at a single minimum. After 200 ps, the resealing factor, termed the “normal mode resealing factor,” has apparently converged to a value whereby the mean-square fluctuation within the subspace is about twice that predicted by the normal mode analysis. © 1995 Wiley-Liss, Inc.     

Population dynamics of two small pelagic fish in the central-south area off Chile: delayed density-dependence and biological interaction

It is widely believed that environmental variability is the main cause for fluctuations in commercially exploited small pelagic fish populations around the world. Nevertheless, density-dependent factors also can drive population dynamics. In this paper, we analyzed thirteen years of a relative abundance index of two clupeoids fish populations coexisting in the central-south area off Chile, namely the common sardine, Strangomera bentincki, and anchovy, Engraulis ringens. We applied the classical diagnostic tools of time series analysis to the observed time-series. Also, the realized per capita population growth rate was studied with the aim of detecting the feedback structure that is characterizing the population dynamics of the two species. The analysis suggests that population fluctuations of the two species have an important density-dependent component, displaying first-order (direct density-dependent) and second-order (delayed density-dependent) simultaneously. The density-dependent component explained 70.5 and 55.6 % of the realized per capita population growth rate of common sardine and anchovy, respectively. The deterministic skeleton model showed an asymptotic convergence to equilibrium density. In presence of a stochastic environment, fluctuations were reproduced for the species showing a component of fluctuation with a period of 4 year. The intrinsic dynamics of each species is typical of interacting species resulting from trophic interactions. It is postulated that the second-order dynamics of S. bentincki and E. ringens in central-south Chile, may be the result from interactions with a specialist predator (the fishing fleet), interacting with exogenous environmental factors.     

Fluctuations and membrane heterogeneity

Biological membranes contain many specialized domains, ranging from tens of nanometers to several microns in size and characterized by different concentrations and compositions of protein. Because these domains influence membrane function, considerable attention has focused on understanding their origin. Here it is shown that number fluctuations and nonspecific interprotein interactions can lead to considerable heterogeneity in the distribution of membrane proteins, and to an associated submicron-scale domain structure. Number fluctuations were analyzed by modeling the membrane as a two-dimensional fluid containing interacting protein solutes. The characteristic size and lifetime of a domain in which one would expect to observe a fluctuation of specified magnitude was calculated; snapshots showing fluctuation-induced heterogeneity were generated by Monte Carlo simulation. Domain size was found to depend on the nature of the interprotein force (e.g., attractive or repulsive) and on the average protein concentration. Domain size was largest at low protein concentrations and in the presence of attractive interprotein forces, and was smallest at high protein concentrations and in the presence of repulsive interprotein forces. Domain lifetime was found to depend on domain size and on the diffusion coefficient of the proteins. In a 'typical' membrane containing 5-nm proteins with diffusion coefficient 10(-10) cm(2)/s at a density of 1000 proteins/microm(2), a 30% fluctuation will yield domains characterized by a 2-fold difference in local concentration; these domains persist over a distance of about 100 nm and have a lifetime of about 0.25 s. These results can be used to analyze the domain structure commonly observed in electron micrographs, and have implications for both number fluctuation and Monte Carlo studies of the distribution and dynamics of membrane proteins.     

Structural features that predict real-value fluctuations of globular proteins

It is crucial to consider dynamics for understanding the biological function of proteins. We used a large number of molecular dynamics (MD) trajectories of nonhomologous proteins as references and examined static structural features of proteins that are most relevant to fluctuations. We examined correlation of individual structural features with fluctuations and further investigated effective combinations of features for predicting the real value of residue fluctuations using the support vector regression (SVR). It was found that some structural features have higher correlation than crystallographic B‐factors with fluctuations observed in MD trajectories. Moreover, SVR that uses combinations of static structural features showed accurate prediction of fluctuations with an average Pearson's correlation coefficient of 0.669 and a root mean square error of 1.04 Å. This correlation coefficient is higher than the one observed in predictions by the Gaussian network model (GNM). An advantage of the developed method over the GNMs is that the former predicts the real value of fluctuation. The results help improve our understanding of relationships between protein structure and fluctuation. Furthermore, the developed method provides a convienient practial way to predict fluctuations of proteins using easily computed static structural features of proteins. Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Pressure-Dependent Structure Changes in Barnase on Ligand Binding Reveal Intermediate Rate Fluctuations

In this work we measured ¹H NMR chemical shifts for the ribonuclease barnase at pressures from 3 MPa to 200 MPa, both free and bound to d(CGAC). Shift changes with pressure were used as restraints to determine the change in structure with pressure. Free barnase is compressed by ∼0.7%. The largest changes are on the ligand-binding face close to Lys-27, which is the recognition site for the cleaved phosphate bond. This part of the protein also contains the buried water molecules. In the presence of d(CGAC), the compressibility is reduced by ∼70% and the region of structural change is altered: the ligand-binding face is now almost incompressible, whereas changes occur at the opposite face. Because compressibility is proportional to mean square volume fluctuation, we conclude that in free barnase, volume fluctuation is largest close to the active site, but when the inhibitor is bound, the fluctuations become much smaller and are located mainly on the opposite face. The timescale of the fluctuations is nanoseconds to microseconds, consistent with the degree of ordering required for the fluctuations, which are intermediate between rapid uncorrelated side-chain dynamics and slow conformational transitions. The high-pressure technique is therefore useful for characterizing motions on this relatively inaccessible timescale.     

Molecular dynamics simulations of human glutathione transferase P1-1: conformational fluctuations of the apo-structure.

We have investigated by molecular dynamics simulations the conformational fluctuations of the monomer of human apo-glutathione transferase P1-1. After attainment of steady-state dynamics, the structural fluctuations involve mainly the protein segments that participate also in the holo-apo transition discussed in the accompanying article (Stella et al., 1999:37:1-9.). The most mobile region is the C-terminal segment of helix 2. In contrast, helices 1, 6, 7, and 8 constitute a relatively rigid protein core. An "essential dynamics" analysis of the simulation shows that the largest fluctuations involve specific regions of glutathione transferases. In such regions, atomic motions are correlated. Motions of helix 2 are accounted for by the second most prominent principal component, which reveals a fluctuation between two distinct conformations. The residues that constitute the H-site undergo a breathing motion, possibly relevant during the binding of hydrophobic cosubstrates. Based on our simulation, several experimental findings can be rationalized, including the viscosity-dependent reactivity of Cys 47 and Cys 101 as well as the selective proteolysis of the peptide bond between Lys 44 and Ala 45. We have also modeled the structural changes that lead to the formation of an intrachain disulfide bridge between cysteines 47 and 101 and to the inactivation of the enzyme. The resulting structure maintains essentially the native fold except for helix 2, which closes the G-site. Proteins 1999;37:10-19.     

Dynamical allosterism in the mechanism of action of DNA mismatch repair protein MutS

The multidomain protein Thermus aquaticus MutS and its prokaryotic and eukaryotic homologs recognize DNA replication errors and initiate mismatch repair. MutS actions are fueled by ATP binding and hydrolysis, which modulate its interactions with DNA and other proteins in the mismatch-repair pathway. The DNA binding and ATPase activities are allosterically coupled over a distance of ∼70 Å, and the molecular mechanism of coupling has not been clarified. To address this problem, all-atom molecular dynamics simulations of ∼150 ns including explicit solvent were performed on two key complexes—ATP-bound and ATP-free MutS⋅DNA(+T bulge). We used principal component analysis in fluctuation space to assess ATP ligand-induced changes in MutS structure and dynamics. The molecular dynamics-calculated ensembles of thermally accessible structures showed markedly small differences between the two complexes. However, analysis of the covariance of dynamical fluctuations revealed a number of potentially significant interresidue and interdomain couplings. Moreover, principal component analysis revealed clusters of correlated atomic fluctuations linking the DNA and nucleotide binding sites, especially in the ATP-bound MutS⋅DNA(+T) complex. These results support the idea that allosterism between the nucleotide and DNA binding sites in MutS can occur via ligand-induced changes in motion, i.e., dynamical allosterism.     

Brownian dynamics simulation of helix-capping motifs

Helix-capping motifs are believed to play an important role in stabilizing alpha-helices and defining helix start and stop signals. We performed microsecond scale Brownian dynamics simulations to study ten XAAD sequences, with X = (A,E,I,L,N,Q,S,T,V,Y), to examine their propensity to form helix capping motifs and correlate these results with those obtained from analyzing a structural database of proteins. For the widely studied capping box motif S**D, where the asterisk can be any amino acid residue, the simulations suggested that one of the two hydrogen bonds proposed earlier as a stabilizing factor might not be as important. On the other hand, side-chain interactions between the capping residue and the third residue downstream on the polypeptide chain might also play a role in stabilizing this motif. These results are consistent with explicit-solvent molecular dynamics simulations of two capping box motifs found in the proteins BPTI and alpha-dendrotoxin. Principal component analysis of the SAAD trajectory showed that the first three principal components, after those corresponding to translational-rotational motion were removed, accounted for more than half of the conformational fluctuations. The first component separated the conformational space into two parts with the all-helical conformation and the capping box motif lying largely in one part. The second component, on the other hand, could be used to describe conformational transitions between the all-helical form and the capping box motif.     

中国兽类种群生态学研究进展与展望

兽类种群生态学是现代生态学的核心研究内容。Charles Sutherland Elton在20世纪20年代发现小哺乳动物种群波动现象,标志着现代种群生态学研究的开始。什么因素调节种群波动的问题一直是现代种群生态学领域的研究热点。我国兽类种群生态学研究始于20世纪50年代,迄今,已走过了70年的发展历程,并取得了重要成果。本综述基于20世纪50年代以来我国学者在主流中文期刊及科学引文索引（Science Citation Index,简称SCI）刊物发表的历史文献,分别从种群波动格局、种群统计参数变化、种群内部和外部调节等不同层面评述了我国在鼠类和大型兽类种群生态学的研究历程及现状,同时探讨了未来的研究方向。