Reversible Unfolding–Refolding of Rubredoxin: A Single‐Molecule Force Spectroscopy Study

In metalloproteins, metal centers serve as active sites for a range of functional purposes and as important structural elements to facilitate protein folding and assembly. It is challenging to observe the reversible unfolding and refolding of metalloproteins because of a loss or decomposition of the metal center. Here, the reversible unfolding–refolding of the iron–sulfur protein rubredoxin was observed directly using single‐molecule force spectroscopy. The results demonstrate that the iron can remain attached to the CXXC motif when rubredoxin is unfolded. Upon relaxation, the unfolded rubredoxin can refold into its native holo state with the reconstituted FeS₄ center. The possible loss of iron from the unfolded protein prevents rubredoxin from refolding into its native holo state. These results demonstrated that unfolding of rubredoxin is reversible, as long as the iron remains attached, and provide experimental evidence for the iron‐priming mechanism for the folding of rubredoxin.     

Reorganization free energies for long-range electron transfer in a porphyrin-binding four-helix bundle protein

To explore the possibility of electron transport in a recently designed four-helix bundle protein (Cochran, F. V.; et al. J. Am. Chem. Soc. 2005, 127, 1346), we have computed the reorganization free energy for (i) oxidation of a single Ru-porphyrin cofactor and (ii) electron self-exchange between two Ru-porphyrin cofactors binding to the solvated protein. Sampling the classical electrostatic energy gap for 20 ns, we find that the fluctuations are well described by Gaussian statistics and obtain reorganization free energies of 0.90 +/- 0.04 eV for oxidation and 1.36 +/- 0.08 eV for self-exchange. The latter is 0.1-0.2 eV higher than the experimental estimate for interprotein electron self-exchange in cytochrome b5. As in natural electron carriers, inner-sphere reorganization is very small, 88 meV for self-exchange between two model cofactors computed at the density functional level of theory. Decomposing the outer-sphere reorganization free energy, we find that the solvent (aqueous ionic solution) is the primary outer-sphere medium for oxidation, contributing 0.60 eV (69%). The protein contributes only 0.27 eV (31%). For self-exchange, the solvent contribution, 0.68 eV (54%), and the protein contribution, 0.59 eV (46%), are almost equally important. The large solvent contribution is due to the slow decay of dipole reorientation of the solvent as a function of distance to the cofactor, implying that the change in the electric field upon electron transfer is not as effectively screened by the four-helix bundle protein. However, ranking the residues according to their free energy contributions, it is suggested that the reorganization free energy can be decreased by about 0.2 eV if two glutamine residues in the vicinity of the cofactor are mutated into less polar amino acids.     

Solvent reorganization entropy of electron transfer in polar solvents

We report the results of molecular dynamics simulations of the solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile at varying temperatures. The simulations confirm the prediction of microscopic solvation theories of a positive reorganization entropy in polar solvents. The results of simulations are analyzed in terms of the splitting of the reorganization entropy into the contributions from the solute-solvent interaction and from the alteration of the solvent structure induced by the solute. These two contributions mutually cancel each other, resulting in the reorganization entropy amounting to only a fraction of each component.     

Understanding the mechanism of short-range electron transfer using an immobilized cupredoxin

The hydrophobic patch of azurin (AZ) from Pseudomonas aeruginosa is an important recognition surface for electron transfer (ET) reactions. The influence of changing the size of this region, by mutating the C-terminal copper-binding loop, on the ET reactivity of AZ adsorbed on gold electrodes modified with alkanethiol self-assembled monolayers (SAMs) has been studied. The distance-dependence of ET kinetics measured by cyclic voltammetry using SAMs of variable chain length, demonstrates that the activation barrier for short-range ET is dominated by the dynamics of molecular rearrangements accompanying ET at the AZ-SAM interface. These include internal electric field-dependent low-amplitude protein motions and the reorganization of interfacial water molecules, but not protein reorientation. Interfacial molecular dynamics also control the kinetics of short-range ET for electrostatically and covalently immobilized cytochrome c. This mechanism therefore may be utilized for short-distance ET irrespective of the type of metal center, the surface electrostatic potential, and the nature of the protein-SAM interaction.     

Solvation studies of a zinc finger protein in hydrated ionic liquids

The solvation of the zinc finger protein with the PDB-ID “5ZNF” in hydrated ionic liquids was studied at varying water content. 1-Ethyl-3-methylimidazolium and trifluoromethanesulfonate were the cation and anion, respectively. The protein stability as well as the solvation structure, the shell dynamics and the shell resolved dielectric properties were investigated by means of molecular dynamics simulations. The lengths of the respective trajectories extended up to 200 nanoseconds in order to cover the complete solvent dynamics. Considering the above mentioned properties as a function of the water content they all exhibit a maximum or minimum at the very same mole fraction. While the exact value x(H(2)O) = 0.927 depends on the underlying force field, its origin may be traced back to the competition between the van der Waals and the electrostatic energy of the protein as well as to the transition from aqueous dielectric screening to ionic charge screening with decreasing water content. The parameter-free Voronoi decomposition of space served as a basis for the analysis of most results. In particular, solvation shells were naturally inferred from this concept. In addition to the molecular analysis a mesoscopic view is given in terms of dielectric properties. Thereby, the net dielectric constant is decomposed into contributions from the protein, the first and second solvation shells as well as the bulk. Cross-terms between these components are given, too.     

Proton binding to proteins: pK(a) calculations with explicit and implicit solvent models

Ionizable residues play important roles in protein structure and activity, and proton binding is a valuable reporter of electrostatic interactions in these systems. We use molecular dynamics free energy simulations (MDFE) to compute proton pKa shifts, relative to a model compound in solution, for three aspartate side chains in two proteins. Simulations with explicit solvent and with an implicit, dielectric continuum solvent are reported. The implicit solvent simulations use the generalized Born (GB) model, which provides an approximate, analytical solution to Poisson's equation. With explicit solvent, the direction of the pKa shifts is correct in all three cases with one force field (AMBER) and in two out of three cases with another (CHARMM). For two aspartates, the dielectric response to ionization is found to be linear, even though the separate protein and solvent responses can be nonlinear. For thioredoxin Asp26, nonlinearity arises from the presence of two substates that correspond to the two possible orientations of the protonated carboxylate. For this side chain, which is partly buried and has a large pKa upshift, very long simulations are needed to correctly sample several slow degrees of freedom that reorganize in response to the ionization. Thus, nearby Lys57 rotates to form a salt bridge and becomes buried, while three waters intercalate along the opposite edge of Asp26. Such strong and anisotropic reorganization is very difficult to predict with Poisson-Boltzmann methods that only consider electrostatic interactions and employ a single protein structure. In contrast, MDFE with a GB dielectric continuum solvent, used for the first time for pKa calculations, can describe protein reorganization accurately and gives encouraging agreement with experiment and with the explicit solvent simulations.     

Brownian dynamics simulation of a model simple electrolyte in solvents of low dielectric constant

Brownian dynamics simulations are performed to investigate the ionic transport of model simple electrolytes, in which ions are interacting with each other through the repulsive core and Coulombic interactions. The equivalent conductivity and self-diffusion coefficient show minima as the function of the number density of ions when the dielectric constant of the solvent is low. Although the minimum of the former is in harmony with various experiments, no experiment has ever been reported on that of the latter. The analysis of time-dependent transport coefficients reveals that the presence of the minima is ascribed to the slow dynamics, rather than to static association models. The inclusion of a model function that resembles the short-range part of the potential of mean force induced by solvent affects the transport coefficients qualitatively, which suggests the importance of solvent-induced potential of mean force in the conduction mechanism of electrolytes in solvents of low dielectric constant.     

How the local geometry of the Cu-binding site determines the thermal stability of blue copper proteins

Identifying the factors that govern the thermal resistance of cupredoxins is essential for understanding their folding and stability, and for improving our ability to design highly stable enzymes with potential biotechnological applications. Here, we show that the thermal unfolding of plastocyanins from two cyanobacteria--the mesophilic Synechocystis and the thermophilic Phormidium--is closely related to the short-range structure around the copper center. Cu K-edge X-ray absorption spectroscopy shows that the bond length between Cu and the S atom from the cysteine ligand is a key structural factor that correlates with the thermal stability of the cupredoxins in both oxidized and reduced states. These findings were confirmed by an additional study of a site-directed mutant of Phormidium plastocyanin showing a reverse effect of the redox state on the thermal stability of the protein.     

Enthalpy-entropy contributions to the potential of mean force of nanoscopic hydrophobic solutes

Entropic and enthalpic contributions to the hydrophobic interaction between nanoscopic hydrophobic solutes, modeled as graphene plates in water, have been calculated using molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble with free energy perturbation methodology. We find the stabilizing contribution to the free energy of association (contact pair formation) to be the favorable entropic part, the enthalpic contribution being highly unfavorable. The desolvation barrier is dominated by the unfavorable enthalpic contribution, despite a fairly large favorable entropic compensation. The enthalpic contributions, incorporating the Lennard-Jones solute-solvent terms, largely determine the stability of the solvent separated configuration. We decompose the enthalpy into a direct solute-solute term, the solute-solvent interactions, and the remainder that contains pressure-volume work as well as contributions due to solvent reorganization. The enthalpic contribution due to changes in water-water interactions arising from solvent reorganization around the solute molecules is shown to have major contribution in the solvent induced enthalpy change.     

Contribution of charged groups to the enthalpic stabilization of the folded states of globular proteins

In this paper we use the results from all-atom molecular dynamics (MD) simulations of proteins and peptides to assess the individual contribution of charged atomic groups to the enthalpic stability of the native state of globular proteins and investigate how the distribution of charged atomic groups in terms of solvent accessibility relates to protein enthalpic stability. The contributions of charged groups is calculated using a comparison of nonbonded interaction energy terms from equilibrium simulations of charged amino acid dipeptides in water (the "unfolded state") and charged amino acids in globular proteins (the "folded state"). Contrary to expectation, the analysis shows that many buried, charged atomic groups contribute favorably to protein enthalpic stability. The strongest enthalpic contributions favoring the folded state come from the carboxylate (COO(-)) groups of either Glu or Asp. The contributions from Arg guanidinium groups are generally somewhat stabilizing, while N(+)(3) groups from Lys contribute little toward stabilizing the folded state. The average enthalpic gain due to the transfer of a methyl group in an apolar amino acid from solution to the protein interior is described for comparison. Notably, charged groups that are less exposed to solvent contribute more favorably to protein native-state enthalpic stability than charged groups that are solvent exposed. While solvent reorganization/release has favorable contributions to folding for all charged atomic groups, the variation in folded state stability among proteins comes mainly from the change in the nonbonded interaction energy of charged groups between the unfolded and folded states. A key outcome is that the calculated enthalpic stabilization is found to be inversely proportional to the excess charge density on the surface, in support of an hypothesis proposed previously.     

Iso-energy cutoff for the calculation of interionic potential of mean force in water

An iso-energy cutoff scheme is introduced for the calculation of the potential of mean force between two ions in water. The cutoff criterion is based on the optimal interaction of the water dipole with the ion pair, for which analytical expressions are derived. Formulas are also derived to characterize the solvent reorganization contribution to the potential of mean force. Treatment of the contributions from waters outside the cutoff is also discussed. © 1994 John Wiley & Sons, Inc.     

Influence of Nonlocal Effects on Kinetic Parameters of Heterogeneous Charge Transfer Reactions

The influence of the spatial dispersion of the solvent and of the effect of the electrical field penetration into a metal on the free energy of the solvent reorganization and the activation free energy for heterogeneous charge transfer reactions is studied. The calculations are based on the exactly solved model of a sharp metal/electrolyte interface, the model of a Born sphere for the ion, and the three-mode approximation for the dielectric function of the solvent. In the sharp-interface model, in the case of a mirror reflection, a relationship for the dielectric tensor of a heterogeneous system comprising two contacting media with a plane interface is obtained, along with an expression for the potential created by a point charge. This expression formally coincides with the expression derived earlier by Vorotyntsev and Kornyshev, but it contains true bulk dielectric functions of contacting media. In the model of the Born sphere for the ion and the three-mode approximation for the dielectric function of the solvent, an expression for the potential of image forces, which determines the dependence of the solvent reorganization energy on the distance from the reacting ion to the electrode, is obtained. It is shown that both the reorganization energy and the activation free energy decrease with decreasing distance from the ion to the electrode. The calculation results are compared with estimates of the reorganization energy obtained from experimental data for the reaction Fe³⁺/Fe²⁺ and the reaction of the hydronium ion discharge.     

New-generation amber united-atom force field

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.     

Detection of discriminative sequence motifs in proteins obtained from prokaryotes grown at various temperatures

Recent investigations on the stability of proteins have demonstrated various structural factors, but few have considered sequence factors such as protein motifs. These motifs represent highly conserved regions and describe critical regions that may only exist on proteins that remain functional at high temperatures. This investigation presents a method for identifying and comparing corresponding mesophilic and thermophilic sequence motifs between protein families. Discriminative motifs that are conserved only in the mesophilic or thermophilic subfamily are identified. Analysis of the results shows that, although the subfamilies of most protein families share similar motifs, some discriminative motifs are present in particular thermophilic/mesophilic subfamilies. The thermophilic discriminative motifs are conserved only in thermophilic organisms, revealing that physiochemical principles support thermostability.