Intrinsic conformational properties of deoxyribonucleosides: implicated role for cytosine in the equilibrium among the A, B, and Z forms of DNA.

Structural properties of biomolecules are dictated by their intrinsic conformational energetics in combination with environmental contributions. Calculations using high-level ab initio methods on the deoxyribonucleosides have been performed to investigate the influence of base on the intrinsic conformational energetics of nucleosides. Energy minima in the north and south ranges of the deoxyribose pseudorotation surfaces have been located, allowing characterization of the influence of base on the structures and energy differences between those minima. With all bases, chi values associated with the south energy minimum are lower than in canonical B-DNA, while chi values associated with the north energy minimum are close to those in canonical A-DNA. In deoxycytidine, chi adopts an A-DNA conformation in both the north and south energy minima. Energy differences between the A and B conformations of the nucleosides are <0.5 kcal/mol in the present calculations, except with deoxycytidine, where the A form is favored by 2.3 kcal/mol, leading the intrinsic conformational energetics of GC basepairs to favor the A form of DNA by 1.5 kcal/mol as compared with AT pairs. This indicates that the intrinsic conformational properties of cytosine at the nucleoside level contribute to the A form of DNA containing predominately GC-rich sequences. In the context of a B versus Z DNA equilibrium, deoxycytidine favors the Z form over the B form by 1.6 kcal/mol as compared with deoxythymidine, suggesting that the intrinsic conformational properties of cytosine also contribute to GC-rich sequences occurring in Z DNA with a higher frequency than AT-rich sequences. Results show that the east pseudorotation energy barrier involves a decrease in the furanose amplitude and is systematically lower than the inversion barrier, with the energy differences influenced by the base. Energy barriers going from the south (B form) sugar pucker to the east pseudorotation barrier are lower in pyrimidines as compared with purines, indicating that the intrinsic conformational properties associated with base may also influence the sugar pseudorotational population distribution seen in DNA crystal structures and the kinetics of B to A transitions. The present work provides evidence that base composition, in addition to base sequence, can influence DNA conformation.     

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.     

Cooperative transition between two helical conformations in a linear system: Poly-L-proline I ⇌ II. I. Equilibrium studies

The solvent-induced conformational transition between the two helical forms of poly-L -proline is studied as a model for cooperative order ? order transitions. The chain length dependent equilibrium data in two solvent systems are described by Schwarz's theory, which is based upon the most general formulation of the linear Ising model with nearest neighbor interactions. The parameter σ which describes the difficulty of nucleation of a I (II) residue in an uninterrupted II (I)-helix is 10^?5 in both solvent systems. The ratios of the nucleation difficulties of states I and II at the ends of the chains β′ and β″ are very different in the two systems. Nucleation difficulty within the chain is interpreted as being due to unfavorable excess interaction energies at the I–II and II–I junctions, which add up to 7 kcal/mole of nuclei as calculated from the σ value. A similar value is computed from the atomic interactions at the junctions. In contrast to this intrinsic properly of poly-L -proline, the energies of I and II residues at the ends are heavily influenced by interactions of the endgroups with the solvent. The above values of the nucleation parameters are determined by a new least-square fitting procedure which does not necessitate the assumption of the dependence of the equilibrium constant s for propagation upon the external parameters, but yields this function from the experimental transition data. A quantitative explanation of this experimental s function through the binding of solvent is attempted. In the transition region a very small free energy change (about 0.1 kcal/mole), arising from a preferential binding of solvent molecules to one of the conformational states, is sufficient for a complete conversion from one helical form to the other.     

Allosteric conversion of Z DNA to an intercalated right-handed conformation by daunomycin

Absorbance and fluorescence methods were used to measure the binding of the anticancer drug daunomycin to poly (dGdC) under ionic conditions that initially favor the left-handed Z conformation of the polymer. Drug binding was cooperative under these conditions and may be fully accounted for by an allosteric model in which the drug binds preferentially (but not exclusively) to the right-handed B conformation and shifts the polymer from the Z to an intercalated right-handed conformation. Quantitative analysis of binding isotherms in terms of the allosteric model allowed for estimation of the equilibrium constants for the conversion of a base pair at a B-Z interface from the Z to the B conformation and for the formation of a base pair in the B conformation within a stretch of helix in the Z conformation. The free energy of the Z to B conversion of a base pair was calculated from this data and ranges from +0.03 to +0.3 kcal/mol over the NaCl range of 2.4-3.5 M. The free energy for the formation of a B-Z junction was nearly constant at +4.0 kcal/mol over the same range of NaCl concentrations. The salt dependence of the free energy of the Z to B transition indicates preferential Na+ binding to the Z form and that there is a net release of Na+ upon conversion of a base pair from the Z to the B conformation. The energetically unfavorable Z to B transition was found by this analysis to be driven by coupling to the energetically favorable interaction of daunomycin with B form DNA. In 3.5 M NaCl, for example, the free energy change for the overall reaction (Z DNA base pairs) + (daunomycin) in equilibrium with (right-handed complex) is -7.0 kcal/mol, nearly all of which is contributed by the binding of drug to B DNA. Analysis using the allosteric model also shows that the number of base pairs converted from the Z to the B conformation per bound drug molecule is salt dependent and provides evidence that drug molecules partition into regions of the polymer in the right-handed conformation.     

Empirical solvation models in the context of conformational energy searches: application to bovine pancreatic trypsin inhibitor.

Continuum solvation models that estimate free energies of solvation as a function of solvent accessible surface area are computationally simple enough to be useful for predicting protein conformation. The behavior of three such solvation models has been examined by applying them to the minimization of the conformational energy of bovine pancreatic trypsin inhibitor. The models differ only with regard to how the constants of proportionality between free energy and surface area were derived. Each model was derived by fitting to experimentally measured equilibrium solution properties. For two models, the solution property was free energy of hydration. For the third, the property was NMR coupling constants. The purpose of this study is to determine the effect of applying these solvation models to the nonequilibrium conformations of a protein arising in the course of global searches for conformational energy minima. Two approaches were used: (1) local energy minimization of an ensemble of conformations similar to the equilibrium conformation and (2) global search trajectories using Monte Carlo plus minimization starting from a single conformation similar to the equilibrium conformation. For the two models derived from free energy measurements, it was found that both the global searches and local minimizations yielded conformations more similar to the X-ray crystallographic structures than did searches or local minimizations carried out in the absence of a solvation component of the conformational energy. The model derived from NMR coupling constants behaved similarly to the other models in the context of a global search trajectory. For one of the models derived from measured free energies of hydration, it was found that minimization of an ensemble of near-equilibrium conformations yielded a new ensemble in which the conformation most similar to the X-ray determined structure PTI4 had the lowest total free energy. Despite the simplicity of the continuum solvation models, the final conformation generated in the trajectories for each of the models exhibited some of the characteristics that have been reported for conformations obtained from molecular dynamics simulations in the presence of a bath of explicit water molecules. They have smaller root mean square (rms) deviations from the experimentally determined conformation, fewer incorrect hydrogen bonds, and slightly larger radii of gyration than do conformations derived from search trajectories carried out in the absence of solvent.     

The role of methylation in the intrinsic dynamics of B- and Z-DNA

Methylation of cytosine at the 5-carbon position (5 mC) is observed in both prokaryotes and eukaryotes. In humans, DNA methylation at CpG sites plays an important role in gene regulation and has been implicated in development, gene silencing, and cancer. In addition, the CpG dinucleotide is a known hot spot for pathologic mutations genome-wide. CpG tracts may adopt left-handed Z-DNA conformations, which have also been implicated in gene regulation and genomic instability. Methylation facilitates this B-Z transition but the underlying mechanism remains unclear. Herein, four structural models of the dinucleotide d(GC)(5) repeat sequence in B-, methylated B-, Z-, and methylated Z-DNA forms were constructed and an aggregate 100 nanoseconds of molecular dynamics simulations in explicit solvent under physiological conditions was performed for each model. Both unmethylated and methylated B-DNA were found to be more flexible than Z-DNA. However, methylation significantly destabilized the BII, relative to the BI, state through the Gp5mC steps. In addition, methylation decreased the free energy difference between B- and Z-DNA. Comparisons of α/γ backbone torsional angles showed that torsional states changed marginally upon methylation for B-DNA, and Z-DNA. Methylation-induced conformational changes and lower energy differences may contribute to the transition to Z-DNA by methylated, over unmethylated, B-DNA and may be a contributing factor to biological function.     

Thermodynamics and mechanism of alpha helix initiation in alanine and valine peptides

We used molecular dynamics simulations to study the folding/unfolding of one of turn of an alpha helix in Ac-(Ala)3-NHMe and Ac-(Val)3-NHMe. Using specialized sampling techniques, we computed free energy surfaces as functions of a conformational coordinate that corresponds to alpha helices at small values and to extended conformations at large values. Analysis of the peptide conformations populated during the simulations showed that alpha helices, reverse turns, and extended conformations correspond to minima on the free energy surfaces of both peptides. The free energy difference between alpha helix and extended conformations, determined from the equilibrium constants for helix unfolding, is approximately -1 kcal/mol for Ac-(Ala)3-NHMe and -5 kcal/mol for Ac-(Val)3-NHMe. The mechanism observed in our simulations, which includes reverse turns as important intermediates along the helix folding/unfolding pathway, is consistent with a mechanism proposed previously. Our results predict that both peptides (but especially the Ala peptide) have a much larger equilibrium constant for helix initiation than is predicted by the helix-coil transition theory with the host-guest parameters. We also predict a much greater difference in the equilibrium constants than the theory predicts. Insofar as helix initiation is concerned, our results suggest that the large difference between the helical propensities of Ala and Val cannot be explained by simple concepts such as side-chain rotamer restriction or unfavorable steric interactions. Rather, the origin of the difference appears to be quite complicated because it involves subtle differences in the solvation of the two peptides. The two peptides have similar turn-extended equilibria but very different helix-turn equilibria, and the difference in helical propensities reflects the fact that the helix-turn equilibrium strongly favors the turns in Ac-(Val)3-NHMe, while it favors the helices in Ac-(Ala)3-NHMe. We also computed thermodynamic decompositions of the free energy surfaces, and these revealed that the helix-turn equilibria are vastly different primarily because the changes in peptide-water interactions that accompany helix-to-turn conformational changes are qualitatively different for the two peptides.     

Amino acid conformational preferences and solvation of polar backbone atoms in peptides and proteins

Amino acids in peptides and proteins display distinct preferences for alpha-helical, beta-strand, and other conformational states. Various physicochemical reasons for these preferences have been suggested: conformational entropy, steric factors, hydrophobic effect, and backbone electrostatics; however, the issue remains controversial. It has been proposed recently that the side-chain-dependent solvent screening of the local and non-local backbone electrostatic interactions primarily determines the preferences not only for the alpha-helical but also for all other main-chain conformational states. Side-chains modulate the electrostatic screening of backbone interactions by excluding the solvent from the vicinity of main-chain polar atoms. The deficiency of this electrostatic screening model of amino acid preferences is that the relationships between the main-chain electrostatics and the amino acid preferences have been demonstrated for a limited set of six non-polar amino acid types in proteins only. Here, these relationships are determined for all amino acid types in tripeptides, dekapeptides, and proteins. The solvation free energies of polar backbone atoms are approximated by the electrostatic contributions calculated by the finite difference Poisson-Boltzmann and the Langevin dipoles methods. The results show that the average solvation free energy of main-chain polar atoms depends strongly on backbone conformation, shape of side-chains, and exposure to solvent. The equilibrium between the low-energy beta-strand conformation of an amino acid (anti-parallel alignment of backbone dipole moments) and the high-energy alpha conformation (parallel alignment of backbone dipole moments) is strongly influenced by the solvation of backbone polar atoms. The free energy cost of reaching the alpha conformation is by approximately 1.5 kcal/mol smaller for residues with short side-chains than it is for the large beta-branched amino acid residues. This free energy difference is comparable to those obtained experimentally by mutation studies and is thus large enough to account for the distinct preferences of amino acid residues. The screening coefficients gamma(local)(r) and gamma(non-local)(r) correlate with the solvation effects for 19 amino acid types with the coefficients between 0.698 to 0.851, depending on the type of calculation and on the set of point atomic charges used. The screening coefficients gamma(local)(r) increase with the level of burial of amino acids in proteins, converging to 1.0 for the completely buried amino acid residues. The backbone solvation free energies of amino acid residues involved in strong hydrogen bonding (for example: in the middle of an alpha-helix) are small. The hydrogen bonded backbone is thus more hydrophobic than the peptide groups in random coil. The alpha-helix forming preference of alanine is attributed to the relatively small free energy cost of reaching the high-energy alpha-helix conformation. These results confirm that the side-chain-dependent solvent screening of the backbone electrostatic interactions is the dominant factor in determining amino acid conformational preferences.     

Hydration and conformational equilibria of simple hydrophobic and amphiphilic solutes.

We consider whether the continuum model of hydration optimized to reproduce vacuum-to-water transfer free energies simultaneously describes the hydration free energy contributions to conformational equilibria of the same solutes in water. To this end, transfer and conformational free energies of idealized hydrophobic and amphiphilic solutes in water are calculated from explicit water simulations and compared to continuum model predictions. As benchmark hydrophobic solutes, we examine the hydration of linear alkanes from methane through hexane. Amphiphilic solutes were created by adding a charge of +/-1e to a terminal methyl group of butane. We find that phenomenological continuum parameters fit to transfer free energies are significantly different from those fit to conformational free energies of our model solutes. This difference is attributed to continuum model parameters that depend on solute conformation in water, and leads to effective values for the free energy/surface area coefficient and Born radii that best describe conformational equilibrium. In light of these results, we believe that continuum models of hydration optimized to fit transfer free energies do not accurately capture the balance between hydrophobic and electrostatic contributions that determines the solute conformational state in aqueous solution.     

Electron transfer between horse heart and Candida krusei cytochromes c in the free and bound states

Electron transfer between horse heart and Candida krusei cytochromes c in the free and phosvitin-bound states was examined by difference spectrum and stopped-flow methods. The difference spectra in the wavelength range of 540-560 nm demonstrated that electrons are exchangeable between the cytochromes c of the two species. The equilibrium constants of the electron transfer reaction for the free and phosvitin-bound forms, estimated from these difference spectra, were close to unity at 20 degrees C in 20 mM Tris-HCl buffer (pH 7.4). The electron transfer rate for free cytochrome c was (2-3).10(4) M-1.s-1 under the same conditions. The transfer rate for the bound form increased with increase in the binding ratio at ratios below half the maximum, and was almost constant at higher ratios up to the maximum. The maximum electron exchange rate was about 2.10(6) M-1.s-1, which is 60-70 times that for the free form at a given concentration of cytochrome c. The activation energy of the reaction for the bound cytochrome c was equal to that for the free form, being about 10 kcal/mol. The dependence of the exchange rate on temperature, cytochrome c concentration and solvent viscosity suggests that enhancement of the electron transfer rate between cytochromes c on binding to phosvitin is due to increase in the collision frequency between cytochromes c concentrated on the phosvitin molecule.     

A conformational analysis of the (+) anti BPDE adduct to the guanine amino group of dCpdG

The (+) anti isomer of benz[a]pyrene diol epoxide (BPDE), 7 beta, 8 alpha-dihydroxy-9 alpha, 10 alpha-epoxy-7,8,9,10-tetrahydrobenz [a] pyrene has been identified as the probable tumorigenic lesion in mammalian systems. It forms a predominant adduct with DNA at N2 of guanine. In order to elucidate its conformation in atomic resolution detail, minimized conformational potential energy calculations were performed for the adduct with dCpdG. A global conformation search involving about 1000 trials was made. The lowest energy conformation had stacking between the hydrocarbon and the adjacent cytidine, in agreement with CD studies on modified GpU and UpG. This conformer differed from the B form most notably in the guanine glycosidic torsion, which is high anti. The next lowest energy form had torsion angles like the B form, with guanine-cytidine stacking. These two conformers differ in energy by only 2.1 kcal./mole, suggesting that their relative stability could easily be reversed in larger polymers, or under specific environmental conditions. Other conformations, with base-hydrocarbon or base-base stacking are also found, at somewhat higher energies. The Z form is at 7.8 kcal./mole. Thus, this adduct stabilizes the B form, in contrast with the N2 linked AAF adduct, which stabilizes the Z conformation.     

Effects of 5 cytosine methylation on the B-Z transition in DNA restriction fragments and recombinant plasmids

Alternating (dC-dG)n regions in DNA restriction fragments and recombinant plasmids were methylated at the 5 position of the cytosine residues by the HhaI methylase. Methylation lowers the concentration of NaCl or MgCl2 necessary to cause the B-Z conformational transition in these sequences. Ionic strengths higher than physiological conditions are required to form the Z conformation when the methylated (dC-dG)n tract is contiguous with regions that do not form Z structures, in contrast to the results with the DNA polymer poly(m5dC-dG) . poly(m5dC-dG). In supercoiled plasmids containing (dC-dG)n sequences, methylation reduces the number of negative supercoils necessary to stabilize the Z conformation. Calculations of the observed free energy contributions of the B-Z junction and cytosine methylation suggest that two junctions offset the favorable effect of methylation on the Z conformation in (dC-dG)n sequences (about 29 base-pairs in length). Studies with individual methylated topoisomers demonstrate that increasing Na+ concentration up to approximately 0.2 M inhibits the formation of the Z conformation in the (m5dC-dG)n region of supercoiled plasmids. The results suggest that methylation may serve as a triggering mechanism for Z DNA formation in supercoiled DNAs.     

1H NMR and circular dichroism studies of the B and Z conformations of the self-complementary deoxyhexanucleotide d(m5C-G-C-G-m5-C-G): mechanism of the Z-B-coil transitions

The double-helical conformations of d(m5-C-G-C-G-m5-C-G) in aqueous solution were studied by circular dichroism and 1H NMR spectroscopy. In 0.1 M NaCl, only the B form is detected whereas the Z form is strongly predominant in 3 M NaCl. In the presence of 2 M NaCl, two resonance signals corresponding to the B and Z duplexes were observed for each proton below 50 degrees C, indicating a slow exchange between B and Z. However, the B-Z exchange becomes intermediate or fast in the 55-80 degrees C temperature interval. By contrast the exchange between B helix and single-stranded (or coil) forms is much faster for the same temperature conditions. The Z form is only detectable when the coil form is practically absent. With decreasing temperature the B form decreases in favor of the Z form. From proton line-width measurements under various experimental conditions, it was also shown that Z exchanges only with B, while the latter also exchanges with the single-stranded form (S): Z in equilibrium B in equilibrium S. The enthalpy value is about 8 +/- 1 kcal/mol for the B-Z transition and about 40 +/- 2 kcal/mol for the B-S dissociation (2 M NaCl solution). The activation energy is about 47 +/- 2 kcal/mol for the Z----B and 39 +/- 2 kcal/mol for the B----Z reaction. Very good agreement between the experimental results and computed data (based on the above kinetic reaction model) was found for the B, Z, and coil proportions. The B-Z transition of methylated d(C-G)n oligomers is only possible when the Watson-Crick hydrogen bonds between the CG base pairs are firmly maintained; otherwise, the transformation from B to Z would not occur, and B-S dissociation would take place instead.     

Membrane protein conformational change dependent on the hydrophobic environment

Two conformational states of the coat protein of the filamentous bacteriophage M13 have been detected in detergent solution by using magnetic resonance techniques. When 3-fluorotyrosine is incorporated in place of the two tyrosine residues in the protein, four 19F nuclear magnetic resonance signals are observed, two for each conformer of the protein. The equilibrium between the two forms can be modulated by pH, temperature, and detergent structure. The rate of interconversion of the isomers is rapid on the minutes time scale but is slow relative to the T1 relaxation time of the fluorine resonances of approximately 50 ms. The conformational change between the conformers results in the perturbation of a basic residue in the protein such that this group has a pKa of approximately 9.5 in one state which shifts to 10.5 or more in the other conformational state. The temperature dependence of the equilibrium suggests an enthalpy difference of about 10 kcal/mol which is offset by entropy to give nearly zero free energy difference between the states at pH 8.3 in deoxycholate solution at room temperature. This suggests a substantial reorganization of the noncovalent interactions defining the two conformational states. The conformational equilibrium is strongly dependent on detergent structure and the presence of phospholipid in the detergent micelle. The results are not consistent with a strong, specific lipid binding to the protein but appear to be consistent with a more general effect of the overall micelle structure on the conformational state of the protein.     

Method of determining the relative stability of different conformational states of biological macromolecules

A general approach to the determination of relative stability of any pair of con-formational states of biological macromolecules or their complexes (in particular, to the determination of relative stability of native and disordered states of the macromolecule) has been suggested. For determining the free energy difference of the two states under the conditions when one of them is considerably more advantageous than the other, it is necessary for the macromolecule to be influenced by the transforming agent which levels free energies of both the conformational states, and to determine the external parameter derivative of the free energy difference in the region of the conformational transition induced by the change in this parameter. If the character of the dependence of this derivative on the external parameter (temperature, solvent composition, etc.) is known, then this allows the determination of the free energy difference of the two states under the conditions considered, even including conditions far from the transition region. The value of the derivative of the free energy difference in the transition region in many cases can be measured directly (in particular, when using calorimetry), while in cases when a direct measurement of the derivative is impossible, it can often he estimated experimentally from the steepness of the conformational transition. The methods of this estimation and also a possible character of the change of the considered derivative during variation of the external parameter are considered for the case when the transforming agent is one of the components of the solvent and, consequently, the derivative of the free energy difference is equal to the difference of number of molecules of this component hound with the macromolecule in two conformational states.     

Modeling loop reorganization free energies of acetylcholinesterase: a comparison of explicit and implicit solvent models

The treatment of hydration effects in protein dynamics simulations varies in model complexity and spans the range from the computationally intensive microscopic evaluation to simple dielectric screening of charge-charge interactions. This paper compares different solvent models applied to the problem of estimating the free-energy difference between two loop conformations in acetylcholinesterase. Molecular dynamics (MD) simulations were used to sample potential energy surfaces of the two basins with solvent treated by means of explicit and implicit methods. Implicit solvent methods studied include the generalized Born (GB) model, atomic solvation potential (ASP), and the distance-dependent dieletric constant. By using the linear response approximation (LRA), the explicit solvent calculations determined a free-energy difference that is in excellent agreement with the experimental estimate, while rescoring the protein conformations with GB or the Poisson equation showed inconsistent and inferior results. While the approach of rescoring conformations from explicit water simulations with implicit solvent models is popular among many applications, it perturbs the energy landscape by changing the solvent contribution to microstates without conformational relaxation, thus leading to non-optimal solvation free energies. Calculations applying MD with a GB solvent model produced results of comparable accuracy as observed with LRA, yet the electrostatic free-energy terms were significantly different due to optimization on a potential energy surface favored by an implicit solvent reaction field. The simpler methods of ASP and the distance-dependent scaling of the dielectric constant both produced considerable distortions in the protein internal free-energy terms and are consequently unreliable.     

Downhill binding energy surface of the barnase–barstar complex

We have employed biased molecular dynamics simulations in explicit solvent to characterize the one‐dimensional potential of mean force for the dissociation process of the barnase–barstar protein–protein complex. Unbinding of barstar from wild‐type barnase was compared with dissociation from four charge‐deletion mutants of barnase. Interestingly, we find in all cases that unbinding of barnase and barstar is an uphill process on a smooth, tilted energy landscape. The total free energy difference between the dissociated and bound state was similar for wild‐type barnase–barstar and for the R87A mutant of barnase. The values for the three other mutant barnase mutants K27A, R59A, and R83Q were only about half as much. Besides, we have analyzed the conformational dynamics of important residues at the barnase–barstar interface. In the bound state, their conformational fluctuations are reduced relatively to the free state because of the formation of intermolecular contacts. Interestingly, we find that some residues also show decreased mobility at intermediate stages of the unbinding process suggesting that these residues may be involved in the first contacts being formed on binding. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 977–985, 2010.     

Free energies of protein decoys provide insight into determinants of protein stability

We have calculated the stability of decoy structures of several proteins (from the CASP3 models and the Park and Levitt decoy set) relative to the native structures. The calculations were performed with the force field-consistent ES/IS method, in which an implicit solvent (IS) model is used to calculate the average solvation free energy for snapshots from explicit simulations (ESs). The conformational free energy is obtained by adding the internal energy of the solute from the ESs and an entropic term estimated from the covariance positional fluctuation matrix. The set of atomic Born radii and the cavity-surface free energy coefficient used in the implicit model has been optimized to be consistent with the all-atom force field used in the ESs (cedar/gromos with simple point charge (SPC) water model). The decoys are found to have a consistently higher free energy than that of the native structure; the gap between the native structure and the best decoy varies between 10 and 15 kcal/mole, on the order of the free energy difference that typically separates the native state of a protein from the unfolded state. The correlation between the free energy and the extent to which the decoy structures differ from the native (as root mean square deviation) is very weak; hence, the free energy is not an accurate measure for ranking the structurally most native-like structures from among a set of models. Analysis of the energy components shows that stability is attained as a result of three major driving forces: (1) minimum size of the protein-water surface interface; (2) minimum total electrostatic energy, which includes solvent polarization; and (3) minimum protein packing energy. The detailed fit required to optimize the last term may underlie difficulties encountered in recovering the native fold from an approximate decoy or model structure.     

Weak protein-protein interactions are sufficient to drive assembly of hepatitis B virus capsids

Hepatitis B virus (HBV) is an enveloped DNA virus with a spherical capsid (or core). The capsid is constructed from 120 copies of the homodimeric capsid protein arranged with T = 4 icosahedral symmetry. We examined in vitro assembly of purified E. coli expressed HBV capsid protein. After equilibration, concentrations of capsid and dimer were evaluated by size exclusion chromatography. The extent of assembly increased as temperature and ionic strength increased. The concentration dependence of capsid assembly conformed to the equilibrium expression: K(capsid) = [capsid]/[dimer](120). Given the known geometry for HBV capsids and dimers, the per capsid assembly energy was partitioned into energy per subunit-subunit contact. We were able to make three major conclusions. (i) Weak interactions (from -2.9 kcal/mol at 21 degrees C in low salt to -4.4 kcal/mol at 37 degrees C in high salt) at each intersubunit contact result in a globally stable capsid; weak intersubunit interactions may be the basis for the phenomenon of capsid breathing. (ii) HBV assembly is characterized by positive enthalpy and entropy. The reaction is entropy-driven, consistent with the largely hydrophobic contacts found in the crystal structure. (iii) Increasing NaCl concentration increases the magnitude of free energy, enthalpy, and entropy, as if ionic strength were increasing the amount of hydrophobic surface buried by assembly. This last point leads us to suggest that salt acts by inducing a conformational change in the dimer from an assembly-inactive form to an assembly-active form. This model of conformational change linked to assembly is consistent with immunological differences between dimer and capsid.