SIMS: computation of a smooth invariant molecular surface

Structural basis for the attachment of a paramyxoviral polymerase to its template

The nucleocapsid of measles virus is the template for viral RNA synthesis and is generated through packaging of the genomic RNA by the nucleocapsid protein (N). The viral polymerase associates with the nucleocapsid through a small, trihelical binding domain at the carboxyl terminus of the phosphoprotein (P). Translocation of the polymerase along the nucleocapsid during RNA synthesis is thought to involve the repeated attachment and release of the binding domain. We have investigated the interaction between the binding domain from measles P (amino acids 457-507) and the sequence it recognizes within measles N (amino acids 477-505). By using both solution NMR spectroscopy and x-ray crystallography, we show that N(487-503) binds as a helix to the surface created by the second (alpha2) and third (alpha3) helices of P(457-507), in an orientation parallel to the helix alpha3, creating a four-helix bundle. The binding interface is tightly packed and dominated by hydrophobic amino acids. Binding and folding of N(487-503) are coupled. However, when not bound to P, N(487-503) does not resemble a statistical random coil but instead exists in a loosely structured state that mimics the bound conformation. We propose that before diffusional encounter, the ensemble of accessible conformations for N(487-503) is biased toward structures capable of binding P, facilitating rapid association of the two proteins. This study provides a structural analysis of polymerase-template interactions in a paramyxovirus and presents an example of a protein-protein interaction that must be only transiently maintained as part of its normal function.

Can Contact Potentials Reliably Predict Stability of Proteins?

The simplest approximation of interaction potential between amino acid residues in proteins is the contact potential, which defines the effective free energy of a protein conformation by a set of amino acid contacts formed in this conformation. Finding a contact potential capable of predicting free energies of protein states across a variety of protein families will aid protein folding and engineering in silico on a computationally tractable time-scale. We test the ability of contact potentials to accurately and transferably (across various protein families) predict stability changes of proteins upon mutations. We develop a new methodology to determine the contact potentials in proteins from experimental measurements of changes in protein's thermodynamic stabilities (DeltaDeltaG) upon mutations. We apply our methodology to derive sets of contact interaction parameters for a hierarchy of interaction models including solvation and multi-body contact parameters. We test how well our models reproduce experimental measurements by statistical tests. We evaluate the maximum accuracy of predictions obtained by using contact potentials and the correlation between parameters derived from different data-sets of experimental (DeltaDeltaG) values. We argue that it is impossible to reach experimental accuracy and derive fully transferable contact parameters using the contact models of potentials. However, contact parameters may yield reliable predictions of DeltaDeltaG for datasets of mutations confined to the same amino acid positions in the sequence of a single protein.

Modeling the hydration of proteins: prediction of structural and hydrodynamic parameters from X-ray diffraction and scattering data

The implications of protein-water interactions are of importance for understanding the solution behavior of proteins and for analyzing the fine structure of proteins in aqueous solution. Starting from the atomic coordinates, by bead modeling the scattering and hydrodynamic properties of proteins can be predicted reliably (Debye modeling, program HYDRO). By advanced modeling techniques the hydration can be taken into account appropriately: by some kind of rescaling procedures, by modeling a water shell, by iterative comparisons to experimental scattering curves (ab initio modeling) or by special hydration algorithms. In the latter case, the surface topography of proteins is visualized in terms of dot surface points, and the normal vectors to these points are used to construct starting points for placing water molecules in definite positions on the protein envelope. Bead modeling may then be used for shaping the individual atomic or amino acid residues and also for individual water molecules. Among the tuning parameters, the choice of the scaling factor for amino acid hydration and of the molecular volume of bound water turned out to be crucial. The number and position of bound water molecules created by our hydration modeling program HYDCRYST were compared with those derived from X-ray crystallography, and the capability to predict hydration, structural and hydrodynamic parameters (hydrated volume, radius of gyration, translational diffusion and sedimentation coefficients) was compared with the findings generated by the water-shell approach CRYSOL. If the atomic coordinates are unknown, ab initio modeling approaches based on experimental scattering curves can provide model structures for hydrodynamic predictions.

Directional shape complementarity at the protein-DNA interface

Nature utilizes various styles of architecture for DNA-binding proteins to recognize diverse DNA sequences, a process facilitated by a complementary surface between protein and DNA. However, the extent and ways this 'shape complementarity' occurs at the protein-DNA interface have yet to be characterized. Here, by analyzing a set of diverse protein-DNA complexes of known three-dimensional structures, we investigated whether the normal vectors of a protein surface at the interface exhibited any relationship with DNA conformation. Generally, the normal vectors of a DNA-contacting protein surface distinctly preferred certain angles, enabling them to align with certain axes characterizing the conformation of DNA. Thus, a new geometric property of DNA-binding protein is demonstrated, i.e. the "shape complementarity" of protein-DNA recognition clearly bears the property of "directionality".

On the transferability of hydration-parametrized continuum electrostatics models to solvated binding calculations

Using molecular mechanics force field partial atomic charges, we show the nonuniqueness of the parametrization of continuum electrostatics models with respect to solute atomic radii and interior dielectric constant based on hydration (vacuum-to-water transfer) free energy data available for small molecules. Moreover, parameter sets that are optimal and equivalent for hydration free energy calculations lead to large variations of calculated absolute and relative electrostatic binding free energies. Hence, parametrization of solvation effects based on hydration data, although a necessary condition, is not sufficient to guarantee its transferability to the calculation of binding free energies in solution.

Profiling charge complementarity and selectivity for binding at the protein surface

A novel analysis and representation of the protein surface in terms of electrostatic binding complementarity and selectivity is presented. The charge optimization methodology is applied in a probe-based approach that simulates the binding process to the target protein. The molecular surface is color coded according to calculated optimal charge or according to charge selectivity, i.e., the binding cost of deviating from the optimal charge. The optimal charge profile depends on both the protein shape and charge distribution whereas the charge selectivity profile depends only on protein shape. High selectivity is concentrated in well-shaped concave pockets, whereas solvent-exposed convex regions are not charge selective. This suggests the synergy of charge and shape selectivity hot spots toward molecular selection and recognition, as well as the asymmetry of charge selectivity at the binding interface of biomolecular systems. The charge complementarity and selectivity profiles map relevant electrostatic properties in a readily interpretable way and encode information that is quite different from that visualized in the standard electrostatic potential map of unbound proteins.

Determination of the effective dielectric constant from the accurate solution of the Poisson equation

Constant dielectric (CD) and distance-dependent dielectric (DDD) functions are the most popular and widespread in the Molecular Mechanics simulations of large molecular systems. In this article, we present a simple procedure to derive an effective dielectric constant, epsilon (out,eff), for these two methods based on numerical solutions of the Poisson equation. It was found that because of the very approximate nature of the CD and DDD models there is no universal epsilon (out,eff), which will work equally well for all molecular systems. For example, different MD trajectories of the same molecule can produce different optimal epsilon (out,eff)s. The DDD function was found to yield better agreement with the numerical solutions of the Poisson equation than a CD model does. The reason is that a DDD function gives a better description of the electrostatic interactions at short distances between the atoms. Another interesting finding of this study is that under certain conditions epsilon (out,eff) can take negative values for a system of two atoms at a limited distance range. However, in principle, there is nothing to prevent the epsilon (out,eff) from taking negative values for specific conformations of some molecules.

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.

Comparative investigations of biopolymer hydration by physicochemical and modeling techniques

The comparative investigation of biopolymer hydration by physicochemical techniques, particularly by small-angle X-ray scattering, has shown that the values obtained differ over a wide range, depending on the nature of the polymer and the environmental conditions. In the case of simple proteins, a large number of available data allow the derivation of a realistic average value for the hydration (0.35 g of water per gram of protein). As long as the average properties of proteins are considered, the use of such a default value is sufficient. Modeling approaches may be used advantageously, in order to differentiate between different assumptions and hydration contributions, and to correctly predict hydrodynamic properties of biopolymers on the basis of their three-dimensional structure. Problems of major concern are the positioning and the properties of the water molecules on the biopolymer surface. In this context, different approaches for calculating the molecular volume and surface of biopolymers have been applied, in addition to the development of appropriate hydration algorithms.

Cathepsins X and B can be differentiated through their respective mono- and dipeptidyl carboxypeptidase activities

Several new cysteine proteases of the papain family have been discovered in the past few years. To help in the assignment of physiological roles and in the design of specific inhibitors, a clear picture of the specificities of these enzymes is needed. One of these novel enzymes, cathepsin X, displays a unique specificity, cleaving single amino acid residues at the C-terminus of substrates very efficiently. In this study, the carboxypeptidase activities and substrate specificity of cathepsins X and B have been investigated in detail and compared. Using quenched fluorogenic substrates and HPLC measurements, it was shown that cathepsin X preferentially cleaves substrates through a monopeptidyl carboxypeptidase pathway, while cathepsin B displays a preference for the dipeptidyl pathway. The preference for one or the other pathway is about the same for both enzymes, i.e., approximately 2 orders of magnitude, a result supported by molecular modeling of enzyme-substrate complexes. Cleavage of a C-terminal dipeptide of a substrate by cathepsin X can become more important under conditions that preclude efficient monopeptidyl carboxypeptidase activity, e.g., nonoptimal interactions in subsites S(2)-S(1). These results confirm that cathepsin X is designed to function as a monopeptidyl carboxypeptidase. Contrary to a recent report [Klemencic, I., et al. (2000) Eur. J. Biochem. 267, 5404-5412], it is shown that cathepsins X and B do not share similar activity profiles, and that reagents are available to clearly distinguish the two enzymes. In particular, CA074 was found to inactivate cathepsin B at least 34000-fold more efficiently than cathepsin X. The insights obtained from this and previous studies have been used to produce an inhibitor designed to exploit the unique structural features responsible for the carboxypeptidase activity of cathepsin X. Although of moderate potency, this E-64 derivative is the first reported example of a cathepsin X-specific inhibitor.

ES/IS: estimation of conformational free energy by combining dynamics simulations with explicit solvent with an implicit solvent continuum model

This paper reviews a recently developed method for calculating the total conformational free energy of a solute macromolecule in water solvent. The method consists of a relatively short simulation by molecular dynamics with explicit solvent molecules (ES) to produce a set of microstates of the macroscopic conformation. Conformational internal solute energy and entropy are obtained from the simulation, the latter in the quasi-harmonic approximation by analysis of the covariance matrix. The implicit solvent (IS) surface energy-dielectric continuum model is used to calculate the average solvation free energy as the sum of the free energies of creating the solute-size hydrophobic cavity, of the van der Waals solute-solvent interactions and of the polarization of water solvent by the solute's charges. We have earlier applied this method to calculate the conformational free energy of native and intentionally misfolded globular conformations of proteins (the EMBL set of deliberately misfolded proteins), and have obtained good discrimination in favor of the native conformations in all instances. These results are summarized and further analyzed to show that, on average, three major component terms of the free energy all contribute in favor of discrimination. We discuss possible improvements of the ES/IS method. It is shown how the force field can be made self-consistent by adapting the parameters for calculation of surface and polarization free energies closely to the molecular mechanics force field used in the dynamics simulation, using established simulation methods to compute free energies for cavity formation and a charging process with the molecular mechanics force field to provide a set of (quasi-experimental) reference data that can be used to refine the parameters of the continuum models. The molecular surface area together with a microscopic surface free energy near 70 cal/(mol A2) is found to be a consistent descriptor of the cavity free energy. Preliminary results indicate that a linear-response approximation for the polarization of water solvent reaction near typical polar and charged protein groups is accurate to within approximately 90%.

Geometrical and sequence characteristics of alpha-helices in globular proteins

Understanding the sequence-structure relationships in globular proteins is important for reliable protein structure prediction and de novo design. Using a database of 1131 alpha-helices with nonidentical sequences from 205 nonhomologous globular protein chains, we have analyzed structural and sequence characteristics of alpha-helices. We find that geometries of more than 99% of all the alpha-helices can be simply characterised as being linear, curved, or kinked. Only a small number of alpha-helices ( approximately 4%) show sharp localized bends in their middle regions, and thus are classified as kinked. Approximately three-fourths (approximately 73%) of the alpha-helices in globular proteins show varying degrees of smooth curvature, with a mean radius of curvature of 65 +/- 33 A; longer helices are less curved. Computation of helix accessibility to the solvent indicates that nearly two-thirds of the helices ( approximately 66%) are largely buried in the protein core, and the length and geometry of the helices are not correlated with their location in the protein globule. However, the amino acid compositions and propensities of individual amino acids to occur in alpha-helices vary with their location in the protein globule, their geometries, and their lengths. In particular, Gln, Glu, Lys, and Arg are found more often in helices near the surface of globular proteins. Interestingly, kinks often seem to occur in regions where amino acids with low helix propensities (e.g., beta-branched and aromatic residues) cluster together, in addition to those associated with the occurrence of proline residues. Hence the propensities of individual amino acids to occur in a given secondary structure depend not only on conformation but also on its length, geometry, and location in the protein globule.