Molecular modelling of the mass density of single proteins

Using molecular dynamics (MD) simulations, the density of single proteins and its temperature dependence was modelled starting from the experimentally determined protein structure and a generic, transferable force field, without the need of prior parameterization. Although all proteins consist of the same 20 amino acids, their density in aqueous solution varies up to 10% and the thermal expansion coefficient up to twofold. To model the protein density, systematic MD simulations were carried out for 10 proteins with a broad range of densities (1.32–1.43?g/cm³) and molecular weights (7–97?kDa). The simulated densities deviated by less than 1.4% from their experimental values that were available for four proteins. Further analyses of protein density showed that it can be essentially described as a consequence of amino acid composition. For five proteins, the density was simulated at different temperatures. The simulated thermal expansion coefficients ranged between 4.3 and 7.1?×?10^?4?K^?1 and were similar to the experimentally determined values of ribonuclease-A and lysozyme (deviations of 2.4 and 14.6%, respectively). Further analyses indicated that the thermal expansion coefficient is linked to the temperature dependence of atomic fluctuations: proteins with a high thermal expansion coefficient show a low increase in flexibility at increasing temperature. A low increase in atomic fluctuations with temperature has been previously described as a possible mechanism of thermostability. Thus, a high thermal expansion coefficient might contribute to protein thermostability.     

Anomalous temperature dependence of the thermal expansion of proteins

The temperature dependence of the apparent expansibility of lysozyme and ovalbumin in solution has been measured as a function of pH. This temperature dependence is explained in terms of suppressed fluctuations in bound water due to the protein. It is shown that the thermal expansion coefficient of bound water is different from bulk water. The pH dependence can be explained by increased hydration of side chains at lower pH. The amount in volume of hydration water in a typical protein-water system varies from 0.16 to 0.7. How the intrinsic thermal expansion coefficient of proteins can be derived from the apparent quantity is discussed. Intrinsic values of the thermal expansion coefficient for lysozyme at room temperature are between 1.7 and 4.4 x 10(-4) K-1 for a 10% solution.     

Computational studies on mutant protein stability: The correlation between surface thermal expansion and protein stability

Thermal stability of mutant proteins has been investigated using temperature dependent molecular dynamics (MD) simulations in vacuo. The numerical modeling was aimed at mimicking protein expansion upon heating. After the conditions for an expanding protein accessible surface area were established for T4 lysozyme and barnase wild-type proteins, MD simulations were carried out under the same conditions using the crystal structures of several mutant proteins. The computed thermal expansion of the accessible surface area of mutant proteins was found to be strongly correlated with their experimentally measured stabilities. A similar, albeit weaker, correlation was observed for model mutant proteins. This opens the possibility of obtaining stability information directly from protein structure.     

Physicochemical properties of blue fluorescent protein determined via molecular dynamics simulation

Blue fluorescent protein (BFP) is a mutant of green fluorescent protein (GFP), where the chromophore has been modified to shift the emitted fluorescence into the blue spectral region. In this study, MD calculations were performed with the GROMACS simulation package and AMBER force field to investigate the dependence of BFPs physicochemical properties on temperature and applied pressure. The MD approach enabled us to calculate the compressibility of protein itself, separately from the nontrivial contribution of the hydration shell, which is difficult to achieve experimentally. The computed compressibility of BFP (3.94 x10(-5) MPa(-1)) is in agreement with experimental values of globular proteins. The center-of-mass diffusion coefficient of BFP and its dependence on temperature and pressure, which plays an important role in its application as a probe for intracellular liquid viscosity measurement, was calculated and found to be in good agreement with photobleaching recovery experimental data. We have shown that decreased temperature as well as applied pressure increases the water viscosity, but the concomitant decrease of the BFP diffusion coefficient behaves differently from Stokes-Einstein formula. It is shown that the number of hydrogen bonds around the protein grows with pressure, which explains the aforementioned deviation. Pressure also reduces root mean square (RMS) fluctuations, especially those of the most flexible residues situated in the loops. The analysis of the RMS fluctuations of the backbone Calpha atoms also reveals that the most rigid part of BFP is the center of the beta-barrel, in accord with temperature B factors obtained from the Protein Data Bank.     

Anisotropic atomic motions in high-resolution protein crystallography molecular dynamics simulations

Molecular dynamics (MD) simulations using empirical force fields are popular for the study of proteins. In this work, we compare anisotropic atomic fluctuations in nanosecond-timescale MD simulations with those observed in an ultra-high-resolution crystal structure of crambin. In order to make our comparisons, we have developed a compact graphical technique for assessing agreement between spatial atomic distributions determined by MD simulations and observed anisotropic temperature factors.     

Configurational entropy elucidates the role of salt-bridge networks in protein thermostability

Detailed knowledge of how networks of surface salt bridges contribute to protein thermal stability is essential not only to understand protein structure and function but also to design thermostable proteins for industrial applications. Experimental studies investigating thermodynamic stability through measurements of free energy associated with mutational alterations in proteins provide only macroscopic evidence regarding the structure of salt-bridge networks and assessment of their contribution to protein stability. Using explicit-solvent molecular dynamics simulations to provide insight on the atomic scale, we investigate here the structural stability, defined in terms of root-mean-square fluctuations, of a short polypeptide designed to fold into a stable trimeric coiled coil with a well-packed hydrophobic core and an optimal number of intra- and interhelical surface salt bridges. We find that the increase of configurational entropy of the backbone and side-chain atoms and decreased pair correlations of these with increased temperature are consistent with nearly constant atom-positional root-mean-square fluctuations, increased salt-bridge occupancies, and stronger electrostatic interactions in the coiled coil. Thus, our study of the coiled coil suggests a mechanism in which well-designed salt-bridge networks could accommodate stochastically the disorder of increased thermal motion to produce thermostability.     

Thermostabilization of Bacillus circulans xylanase: computational optimization of unstable residues based on thermal fluctuation analysis

Low thermostability often hampers the applications of xylanases in industrial processes operated at high temperature, such as degradation of biomass or pulp bleaching. Thermostability of enzymes can be improved by the optimization of unstable residues via protein engineering. In this study, computational modeling instead of random mutagenesis was used to optimize unstable residues of Bacillus circulans xylanase (Bcx). The thermal fluctuations of unstable residues known as important to the thermal unfolding of Bcx were investigated by the molecular dynamics (MD) simulations at 300 K and 330 K to identify promising residues. The N52 site in unstable regions showed the highest thermal fluctuations. Subsequently, computational design was conducted to predict the optimal sequences of unstable residues. Five optimal single mutants were predicted by the computational design, and the N52Y mutation showed the thermostabilization effect. The N52 residue is conserved in Bacillus species xylanases and the structure analysis revealed that the N52Y mutation introduced more hydrophobic clusters for thermostability, as well as a more favorable aromatic stacking environment for substrate binding. We confirm that flexible residues at high temperature in unstable regions can be promising targets to improve thermostability of enzymes.     

Generalized correlation for biomolecular dynamics

Correlated motions in biomolecules are often essential for their function, e.g., allosteric signal transduction or mechanical/thermodynamic energy transport. Because correlated motions in biomolecules remain difficult to access experimentally, molecular dynamics (MD) simulations are particular useful for their analysis. The established method to quantify correlations from MD simulations via calculation of the covariance matrix, however, is restricted to linear correlations and therefore misses part of the correlations in the atomic fluctuations. Herein, we propose a general statistical mechanics approach to detect and quantify any correlated motion from MD trajectories. This generalized correlation measure is contrasted with correlations obtained from covariance matrices for the B1 domain of protein G and T4 lysozyme. The new method successfully quantifies correlations and provides a valuable global overview over the functionally relevant collective motions of lysozyme. In particular, correlated motions of helix 1 together with the two main lobes of lysozyme are detected, which are not seen by the conventional covariance matrix. Overall, the established method misses more than 50% of the correlation. This failure is attributed to both, an interfering and unnecessary dependence on mutual orientations of the atomic fluctuations and, to a lesser extent, attributed to nonlinear correlations. Our generalized correlation measure overcomes these problems and, moreover, allows for an improved understanding of the conformational dynamics by separating linear and nonlinear contributions of the correlation.     

Plasma decay in the afterglow of a high-voltage nanosecond discharge in air

The decay of air plasma produced by a high-voltage nanosecond discharge at room temperature and gas pressures in the range of 1–10 Torr was studied experimentally and theoretically. The time dependence of the electron density was measured with a microwave interferometer. The initial electron density was about 10¹² cm⁻³. The discharge homogeneity was monitored using optical methods. The dynamics of the charged particle densities in the discharge afterglow was simulated by numerically solving the balance equations for electron and ions and the equation for the electron temperature. It was shown that, under these experimental conditions, plasma electrons are mainly lost due to dissociative and three-body recombination with ions. Agreement between the measured and calculated electron densities was achieved only when the rate constant of the three-body electron-ion recombination was increased by one order of magnitude and the temperature dependence of this rate constant was modified. This indicates that the mechanism for three-body recombination of molecular ions differs from that of the well-studied mechanism of atomic ion recombination.     

Prediction and rationalization of the pH dependence of the activity and stability of family 11 xylanases

This paper presents a study of the pH dependence of the activity and stability of a set of family 11 xylanases for which X-ray structures are available, using the PROPKA approach. The xylanases are traditionally divided into basic and acidic xylanases, depending on whether the catalytic acid is hydrogen bonded to an Asn or Asp residue. Using X-ray structures, the predicted pH values of optimal activity of the basic xylanases are in the range of 5.2-6.9, which is in reasonable agreement with the available experimental values of 5-6.5. In the case of acidic xylanases, there are only four X-ray structures available, and using these structures, the predicted pHs of optimal activity are in the range of 4.2-5.0, compared to an observed range of 2-4.6. The influence of dynamical fluctuations of the protein structure is investigated for Bacillus agaradhaerens and Aspergillus kawachii xylanase using molecular dynamics (MD) simulations to provide snapshots from which average values can be computed. This decreases the respective predicted pH optima from 6.2-6.7 and 4.8 to 5.3 +/- 0.3 and 4.0 +/- 0.2, respectively, which are in better agreement with the observed values of 5.6 and 2, respectively. The change is primarily due to structural fluctuations of an Arg residue near the catalytic nucleophile, which lowers its pKa value compared to using the X-ray structure. The MD simulations and some X-ray structures indicate that this Arg residue can form a hydrogen bond to the catalytic base, and it is hypothesized that this hydrogen bond is stabilized by an additional hydrogen bond to another Glu residue present only in acidic xylanases. Formation of such a hydrogen bond is predicted to lower the pH optimum of A. kawachii xylanase to 2.9 +/- 0.3, which is in reasonable agreement with the observed value of 2. The predicted pH of optimal stability is in excellent agreement with the pH value at which the melting temperature (Tm) is greatest. Some correlation is observed between the pH-dependent free energy of unfolding and Tm, suggesting that the thermostability of the xylanases is partly due to a difference in residues with shifted pKa values. Thus, the thermostability of xylanases (and proteins in general) can perhaps be increased by mutations that introduce ionizable residues with pKa values significantly lower than standard values.     

Influence of Structural Symmetry on Protein Dynamics

Structural symmetry in homooligomeric proteins has intrigued many researchers over the past several decades. However, the implication of protein symmetry is still not well understood. In this study, we performed molecular dynamics (MD) simulations of two forms of trp RNA binding attenuation protein (TRAP), the wild-type 11-mer and an engineered 12-mer, having two different levels of circular symmetry. The results of the simulations showed that the inter-subunit fluctuations in the 11-mer TRAP were significantly smaller than the fluctuations in the 12-mer TRAP while the internal fluctuations were larger in the 11-mer than in the 12-mer. These differences in thermal fluctuations were interpreted by normal mode analysis and group theory. For the 12-mer TRAP, the wave nodes of the normal modes existed at the flexible interface between the subunits, while the 11-mer TRAP had its nodes within the subunits. The principal components derived from the MD simulations showed similar mode structures. These results demonstrated that the structural symmetry was an important determinant of protein dynamics in circularly symmetric homooligomeric proteins.     

Conformational flexibility, hydration and state parameter fluctuations of fibroblast growth factor-10: effects of ligand binding

Differential effects of ligand binding on local and global fibroblast growth factor-10 (FGF-10) flexibility and stability have been investigated utilizing a variety of experimental and computational techniques. Normal mode analysis was used to predict the low frequency motions and regional flexibility of FGF-10. Similarly, regional variations in local folding/unfolding equilibria were characterized with the COREX/BEST algorithm. Experimental adiabatic and isothermal compressibilities of FGF-10 alone and in the presence of polyanions are compared. Furthermore, the effect of polyanions on the coefficient of thermal expansion is compared. Measurements of density, heat capacity, compressibility, and expansibility were combined to calculate experimentally determined volume and enthalpy fluctuations. Global effects of polyanions on FGF-10 flexibility, thermodynamic fluctuations, and hydration vary depending on the size and charge density of the polyanion. Local effects of polyanions were investigated utilizing time-resolved fluorescence spectroscopy and red edge excitation spectroscopy (REES). Increased rigidity of the protein matrix or an increased solvent response surrounding the Trp residues is observed in the presence of polyanions. Similarly, time-resolved spectroscopy reveals increased ground state heterogeneity and increased dipole relaxation on the time scale of fluorescence for FGF-10 in the presence of polyanions. These polyanions increase heterogeneity, global flexibility, and fluctuations while increasing the melting temperature (Tm) of FGF-10.     

Conformational dynamics of cytochrome c: correlation to hydrogen exchange.

We study the dynamical fluctuations of horse heart cytochrome c by molecular dynamics (MD) simulations in aqueous solution, at four temperatures: 300 K, 360 K, 430 K, and 550 K. Each simulation covers a production time of at least 1.5 nanoseconds (ns). The conformational dynamics of the system is analyzed in terms of collective motions that involve the whole protein, and local motions that involve the formation and breaking of intramolecular hydrogen bonds. The character of the MD trajectories can be described within the framework of rugged energy landscape dynamics. The MD trajectories sample multiple conformational minima, with basins in protein conformational space being sampled for a few hundred picoseconds. The trajectories of the system in configurational space can be described in terms of diffusion of a particle in real space with a waiting time distribution due to partial trapping in shallow minima. As a consequence of the hierarchical nature of the dynamics, the mean square displacement autocorrelation function, <|x(t) - x(0)|2>, exhibits a power law dependence on time, with an exponent of around 0.5 for times shorter than 100 ps, and an exponent of 1.75 for longer times. This power law behavior indicates that the system exhibits suppressed diffusion (sub-diffusion) in sampling of configurational space at time scales shorter than 100 ps, and enhanced (super-diffusion) at longer time scales. The multi-basin feature of the trajectories is present at all temperatures simulated. Structural changes associated with inter-basin displacements correspond to collective motions of the Omega loops and coiled regions and relative motions of the alpha-helices as rigid bodies. Similar motions may be involved in experimentally observed amide hydrogen exchange. However, some groups showing large correlated motions do not expose the amino hydrogens to the solvent. We show that large fluctuations are not necessarily correlated to hydrogen exchange. For example, regions of the proteins forming alpha helices and turns show significant fluctuations, but as rigid bodies, and the hydrogen bonds involved in the formation of these structures do not break in proportion to these fluctuations. Proteins 1999;36:175-191. Published 1999 Wiley-Liss, Inc.     

Predicted melt curve and liquid-state transport properties of TATB from molecular dynamics simulations

The melt curve and the liquid-state transport properties shear viscosity, self-diffusion coefficient and thermal conductivity of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) were predicted using all-atom molecular dynamics simulations. The TATB melt curve was obtained using solid–liquid coexistence simulations and is in good accord with the Simon–Glatzel equation. The temperature dependencies of the shear viscosity and self-diffusion coefficient are predicted to obey Arrhenius behaviour for pressures up to P = 20 kbar. The thermal conductivity has a linear temperature dependence for P < 15 kbar and a linear density (ρ) dependence for ρ > 1200 kg m^?3. At similar densities the shear viscosity of liquid TATB is close to the predictions for liquid nitromethane [58] but lower than the predictions for liquid HMX [24] and RDX [59]. The self-diffusion coefficient for TATB is predicted to be higher than predictions for nitromethane, HMX and RDX at similar densities. The conductivity of TATB is ≈20% greater than the conductivity of liquid HMX at a given density.     

Simulations of a protein crystal: explicit treatment of crystallization conditions links theory and experiment in the streptavidin-biotin complex

A 250 ns molecular dynamics simulation of the biotin-liganded streptavidin crystal lattice, including cryoprotectant molecules and crystallization salts, is compared to a 250 ns simulation of the lattice solvated with pure water. The simulation using detailed crystallization conditions preserves the initial X-ray structure better than the simulation using pure water, even though the protein molecules display comparable mobility in either simulation. Atomic fluctuations computed from the simulation with crystallization conditions closely reproduce fluctuations derived from experimental temperature factors (correlation coefficient of 0.88, omitting two N-terminal residues with very high experimental B-factors). In contrast, fluctuations calculated from the simulation with pure water were less accurate, particularly for two of the streptavidin loops exposed to solvent in the crystal lattice. Finally, we obtain good agreement between the water and cryoprotectant densities obtained from the simulated crystallization conditions and the electron density due to solvent molecules in the X-ray structure. Our results suggest that detailed lattice simulations with realistic crystallization conditions can be used to assess potential function parameters, validate simulation protocols, and obtain valuable insights that solution-phase simulations do not easily provide. We anticipate that this will prove to be a powerful strategy for molecular dynamics simulations of biomolecules.     

Enhanced thermal stability achieved without increased conformational rigidity at physiological temperatures: spatial propagation of differential flexibility in rubredoxin hybrids

The extreme thermal stability of proteins from hyperthermophilic organisms is widely believed to arise from an increased conformational rigidity in the native state. In apparent contrast to this paradigm, both Pyrococcus furiosus (Pf) rubredoxin, the most thermostable protein characterized to date, and its Clostridium pasteurianum (Cp) mesophile homolog undergo a transient conformational opening of their multi-turn segments, which is more favorable in hyperthermophile proteins below room temperature. Substitution of the hyperthermophile multi-turn sequence into the mesophile protein sequence yields a hybrid, (14-33(Pf)) Cp, that exhibits a 12 degrees increase in its reversible thermal unfolding transition midpoint. Nuclear magnetic resonance (NMR) magnetization transfer-based hydrogen exchange was used to monitor backbone conformational dynamics in the subsecond time regime. Despite the substantially increased thermostability, flexibility throughout the entire main chain of the more thermostable hybrid is equal to or greater than that of the wild type mesophile rubredoxin near its normal growth temperature. In comparison to the identical core residues of the (14-33(Pf)) Cp rubredoxin hybrid, six spatially clustered residues in the parental mesophile protein exhibit a substantially larger temperature dependence of exchange. The exchange behavior of these six residues closely matches that observed in the multi-turn segment, consistent with a more extensive conformational process. These six core residues exhibit a much weaker temperature dependence of exchange in the (14-33(Pf)) Cp hybrid, similar to that observed for the multi-turn segment in its parental Pf rubredoxin. These results suggest that differential temperature dependence of flexibility can underlie variations in thermostability observed for mesophile versus hyperthermophile homologs.     

Quantification and visualization of molecular surface flexibility

Two new methods for the quantification and visualization of the flexibility of molecular surfaces are presented. Both methods rely on results of molecular dynamics (MD) simulations. Whereas method I is based on a simple but fast grid-counting algorithm, method II uses a mapping function that allows for a sharp and clear visualization of atomic RMS fluctuations on a molecular surface. To demonstrate the scope of the methods, MD simulations of two proteins, PTI and ubiquitin, were performed. The flexibility data are mapped onto the molecular surfaces of the proteins and visualized using texture mapping technology available on modern workstations.     

Thermal coefficients of the methyl groups within ubiquitin

Physiological processes such as protein folding and molecular recognition are intricately linked to their dynamic signature, which is reflected in their thermal coefficient. In addition, the local conformational entropy is directly related to the degrees of freedom, which each residue possesses within its conformational space. Therefore, the temperature dependence of the local conformational entropy may provide insight into understanding how local dynamics may affect the stability of proteins. Here, we analyze the temperature dependence of internal methyl group dynamics derived from the cross-correlated relaxation between dipolar couplings of two CH bonds within ubiquitin. Spanning a temperature range from 275 to 308 K, internal methyl group dynamics tend to increase with increasing temperature, which translates to a general increase in local conformational entropy. With this data measured over multiple temperatures, the thermal coefficient of the methyl group order parameter, the characteristic thermal coefficient, and the local heat capacity were obtained. By analyzing the distribution of methyl group thermal coefficients within ubiquitin, we found that the N-terminal region has relatively high thermostability. These results indicate that methyl groups contribute quite appreciably to the total heat capacity of ubiquitin through the regulation of local conformational entropy.     

Effect of anisotropy and anharmonicity on protein crystallographic refinement. An evaluation by molecular dynamics

Molecular dynamics simulations are employed to determine the errors introduced by anharmonicity and anisotropy in the structure and temperature factors obtained for proteins by refinement of X-ray diffraction data. Simulations (25 ps and 300 ps) of metmyoglobin are used to generate time-averaged diffraction data at 1.5 A resolution. The crystallographic restrained-parameter least-squares refinement program PROLSQ is used to refine models against these simulated data. The resulting atomic positions and isotropic temperature factors are compared with the average structure and fluctuations calculated directly from the simulations. It is found that significant errors in the atomic positions and fluctuations are introduced by the refinement, and that the errors increase with the magnitude of the atomic fluctuations. Of particular interest is the fact that the refinement generally underestimates the atomic motions. Moreover, while the actual fluctuations go up to a mean-square value of about 5 A2, the X-ray results never go above approximately 2 A2. This systematic deviation in the motional parameters appears to be due to the use of a single-site isotropic model for the atomic fluctuations. Many atoms have multiple peaks in their probability distribution functions. For some atoms, the multiple peaks are seen in difference electron density maps and it is possible to include these in the refinement as disordered residues. However, for most atoms the refinement fits only one peak and neglects the rest, leading to the observed errors in position and temperature factor. The use of strict stereochemical restraints is inconsistent with the average dynamical structure; nevertheless, refinement with tight restraints results in structures that are comparable to those obtained with loose restraints and better than those obtained with no restraints. The results support the use of tight stereochemical restraints, but indicate that restraints on the variation of temperature factors are too restrictive.