The weighted-volume derivative of a space-filling diagram

Exotic self-assembly of hard spheres in a morphometric solvent

The self-assembly of spheres into geometric structures, under various theoretical conditions, offers valuable insights into complex self-assembly processes in soft systems. Previous studies have utilized pair potentials between spheres to assemble maximum contact clusters in simulations and experiments. The morphometric approach to solvation free energy that we utilize here goes beyond pair potentials; it is a geometry-based theory that incorporates a weighted combination of geometric measures over the solvent accessible surface for solute configurations in a solvent. In this paper, we demonstrate that employing the morphometric model of solvation free energy in simulating the self-assembly of sphere clusters results, under most conditions, in the previously observed maximum contact clusters. Under other conditions, it unveils an assortment of extraordinary sphere configurations, such as double helices and rhombohedra. These exotic structures arise specifically under conditions where the interactions take multibody potentials into account. This investigation establishes a foundation for comprehending the diverse range of geometric forms in self-assembled structures, emphasizing the significance of the morphometric approach in this context.

Analyzing the Geometry and Dynamics of Viral Structures: A Review of Computational Approaches Based on Alpha Shape Theory, Normal Mode Analysis, and Poisson-Boltzmann Theories

The current SARS-CoV-2 pandemic highlights our fragility when we are exposed to emergent viruses either directly or through zoonotic diseases. Fortunately, our knowledge of the biology of those viruses is improving. In particular, we have more and more structural information on virions, i.e., the infective form of a virus that includes its genomic material and surrounding protective capsid, and on their gene products. It is important to have methods that enable the analyses of structural information on such large macromolecular systems. We review some of those methods in this paper. We focus on understanding the geometry of virions and viral structural proteins, their dynamics, and their energetics, with the ambition that this understanding can help design antiviral agents. We discuss those methods in light of the specificities of those structures, mainly that they are huge. We focus on three of our own methods based on the alpha shape theory for computing geometry, normal mode analyses to study dynamics, and modified Poisson-Boltzmann theories to study the organization of ions and co-solvent and solvent molecules around biomacromolecules. The corresponding software has computing times that are compatible with the use of regular desktop computers. We show examples of their applications on some outer shells and structural proteins of the West Nile Virus.

Computing the Volume, Surface Area, Mean, and Gaussian Curvatures of Molecules and Their Derivatives

Geometry is crucial in our efforts to comprehend the structures and dynamics of biomolecules. For example, volume, surface area, and integrated mean and Gaussian curvature of the union of balls representing a molecule are used to quantify its interactions with the water surrounding it in the morphometric implicit solvent models. The Alpha Shape theory provides an accurate and reliable method for computing these geometric measures. In this paper, we derive homogeneous formulas for the expressions of these measures and their derivatives with respect to the atomic coordinates, and we provide algorithms that implement them into a new software package, AlphaMol. The only variables in these formulas are the interatomic distances, making them insensitive to translations and rotations. AlphaMol includes a sequential algorithm and a parallel algorithm. In the parallel version, we partition the atoms of the molecule of interest into 3D rectangular blocks, using a kd-tree algorithm. We then apply the sequential algorithm of AlphaMol to each block, augmented by a buffer zone to account for atoms whose ball representations may partially cover the block. The current parallel version of AlphaMol leads to a 20-fold speed-up compared to an independent serial implementation when using 32 processors. For instance, it takes 31 s to compute the geometric measures and derivatives of each atom in a viral capsid with more than 26 million atoms on 32 Intel processors running at 2.7 GHz. The presence of the buffer zones, however, leads to redundant computations, which ultimately limit the impact of using multiple processors. AlphaMol is available as an OpenSource software.

Dynamic Coupling of Tyrosine 185 with the Bacteriorhodopsin Photocycle, as Revealed by Chemical Shifts, Assisted AF-QM/MM Calculations and Molecular Dynamic Simulations

Aromatic residues are highly conserved in microbial photoreceptors and play crucial roles in the dynamic regulation of receptor functions. However, little is known about the dynamic mechanism of the functional role of those highly conserved aromatic residues during the receptor photocycle. Tyrosine 185 (Y185) is one of the highly conserved aromatic residues within the retinal binding pocket of bacteriorhodopsin (bR). In this study, we explored the molecular mechanism of its dynamic coupling with the bR photocycle by automated fragmentation quantum mechanics/molecular mechanics (AF-QM/MM) calculations and molecular dynamic (MD) simulations based on chemical shifts obtained by 2D solid-state NMR correlation experiments. We observed that Y185 plays a significant role in regulating the retinal cis–trans thermal equilibrium, stabilizing the pentagonal H-bond network, participating in the orientation switch of Schiff Base (SB) nitrogen, and opening the F42 gate by interacting with the retinal and several key residues along the proton translocation channel. Our findings provide a detailed molecular mechanism of the dynamic couplings of Y185 and the bR photocycle from a structural perspective. The method used in this paper may be applied to the study of other microbial photoreceptors.

The Weighted Gaussian Curvature Derivative of a Space-Filling Diagram

The morphometric approach [11, 14] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [4], and the weighted mean curvature in [1], this yields the derivative of the morphometric expression of solvation free energy.

The Weighted Mean Curvature Derivative of a Space-Filling Diagram

Representing an atom by a solid sphere in 3-dimensional Euclidean space, we get the space-filling diagram of a molecule by taking the union. Molecular dynamics simulates its motion subject to bonds and other forces, including the solvation free energy. The morphometric approach [12, 17] writes the latter as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted mean curvature. Together with the derivatives of the weighted volume in [7], the weighted area in [3], and the weighted Gaussian curvature [1], this yields the derivative of the morphometric expression of the solvation free energy.

Completion of the Vimentin Rod Domain Structure Using Experimental Restraints: A New Tool for Exploring Intermediate Filament Assembly and Mutations

Electron paramagnetic resonance (EPR) spectroscopy of full-length vimentin and X-ray crystallography of vimentin peptides has provided concordant structural data for nearly the entire central rod domain of the protein. In this report, we use a combination of EPR spectroscopy and molecular modeling to determine the structure and dynamics of the missing region and unite the separate elements into a single structure. Validation of the linker 1-2 (L1-2) modeling approach is demonstrated by the close correlation between EPR and X-ray data in the previously solved regions. Importantly, molecular dynamic (MD) simulation of the constructed model agrees with spin label motion as determined by EPR. Furthermore, MD simulation shows L1-2 heterogeneity, with a concerted switching of states among the dimer chains. These data provide the first ever experimentally driven model of a complete intermediate filament rod domain, providing research tools for further modeling and assembly studies.

Morphometric Approach to Many-Body Correlations in Hard Spheres

We model the thermodynamics of local structures within the hard sphere liquid at arbitrary volume fractions through the morphometric calculation of n-body correlations. We calculate absolute free energies of local geometric motifs in excellent quantitative agreement with molecular dynamics simulations across the liquid and supercooled liquid regimes. We find a bimodality in the density library of states where fivefold symmetric structures appear lower in free energy than fourfold symmetric structures and from a single reaction path predict a dynamical barrier which scales linearly in the compressibility factor. The method provides a new route to assess changes in the free energy landscape at volume fractions dynamically inaccessible to conventional techniques.

Peptide Solubility Limits: Backbone and Side-Chain Interactions

We calculate the solubility limit of pentapeptides in water by simulating the phase separation in an oversaturated aqueous solution. The solubility limit order followed by our model peptides (GGRGG > GGDGG > GGGGG > GGVGG > GGQGG > GGNGG > GGFGG) is found to be the same as that reported for amino acid monomers from experiment (R > D > G > V > Q > N > F). Investigation of dynamical properties of peptides shows that the higher the solubility of a peptide is, the lower the time spent by the peptide in the aggregated cluster is. We also demonstrate that fluctuations in conformation and hydration number of peptide in monomeric form are correlated with the solubility of the peptide. We considered energetic mechanisms and dynamical properties of interbackbone CO-CO and CO···HN interactions. Our results confirm that CO-CO interactions more than the interbackbone H-bonds are important in peptide self-assembly and association. Further, we find that the stability of H-bonded peptide pairs arises mainly from coexisting CO-CO and CO···HN interactions.

Simple models for nonpolar solvation: Parameterization and testing

Implicit solvent models are important for many biomolecular simulations. The polarity of aqueous solvent is essential and qualitatively captured by continuum electrostatics methods like Generalized Born (GB). However, GB does not account for the solvent-induced interactions between exposed hydrophobic sidechains or solute-solvent dispersion interactions. These "nonpolar" effects are often modeled through surface area (SA) energy terms, which lack realism, create mathematical singularities, and have a many-body character. We have explored an alternate, Lazaridis-Karplus (LK) gaussian energy density for nonpolar effects and a dispersion (DI) energy term proposed earlier, associated with GB electrostatics. We parameterized several combinations of GB, SA, LK, and DI energy terms, to reproduce 62 small molecule solvation free energies, 387 protein stability changes due to point mutations, and the structures of 8 protein loops. With optimized parameters, the models all gave similar results, with GBLK and GBDILK giving no performance loss compared to GBSA, and mean errors of 1.7 kcal/mol for the stability changes and 2 Å deviations for the loop conformations. The optimized GBLK model gave poor results in MD of the Trpcage mini-protein, but parameters optimized specifically for MD performed well for Trpcage and three other small proteins. Overall, the LK and DI nonpolar terms are valid alternatives to SA treatments for a range of applications. © 2017 Wiley Periodicals, Inc.

Probik: Protein Backbone Motion by Inverse Kinematics

To investigate the parameters of the protein design problem that we are exploring in collaboration with biochemists, we have developed a tool that uses inverse kinematics to support moving small fragments of protein backbone, while respecting biochemists' desires to “remain in favorable regions of the Ramachandran plot” and “preserve ideal geometry”. By presenting estimates of derivatives in response to motion, we are able to refine these qualitative desires as we work with our collaborators. We then explore low-dimensional bases to parametrize the space of backbone motions.

Examining the assumptions underlying continuum-solvent models

Continuum-solvent models (CSMs) have successfully predicted many quantities, including the solvation-free energies (ΔG) of small molecules, but they have not consistently succeeded at reproducing experimental binding free energies (ΔΔG), especially for protein-protein complexes. Several CSMs break ΔG into the free energy (ΔGvdw) of inserting an uncharged molecule into solution and the free energy (ΔGel) gained from charging. Some further divide ΔGvdw into the free energy (ΔGrep) of inserting a nearly hard cavity into solution and the free energy (ΔGatt) gained from turning on dispersive interactions between the solute and solvent. We show that for 9 protein-protein complexes neither ΔGrep nor ΔGvdw was linear in the solvent-accessible area A, as assumed in many CSMs, and the corresponding components of ΔΔG were not linear in changes in A. We show that linear response theory (LRT) yielded good estimates of ΔGatt and ΔΔGatt, but estimates of ΔΔGatt obtained from either the initial or final configurations of the solvent were not consistent with those from LRT. The LRT estimates of ΔGel differed by more than 100 kcal/mol from the explicit solvent model's (ESM's) predictions, and its estimates of the corresponding component (ΔΔGel) of ΔΔG differed by more than 10 kcal/mol. Finally, the Poisson-Boltzmann equation produced estimates of ΔGel that were correlated with those from the ESM, but its estimates of ΔΔGel were much less so. These findings may help explain why many CSMs have not been consistently successful at predicting ΔΔG for many complexes, including protein-protein complexes.

Protein collapse driven against solvation free energy without H-bonds

Proteins collapse and fold because intramolecular interactions and solvent entropy, which favor collapse, outweigh solute-solvent interactions that favor expansion. Since the protein backbone actively participates in protein folding and some intrinsically disordered proteins are glycine rich, oligoglycines are good models to study the protein backbone as it collapses, both during conformational changes in disordered proteins and during folding. The solvation free energies of short glycine oligomers become increasingly favorable as chain length increases. In contrast, the solubility limits of glycine oligomers decrease with increasing chain length, indicating that peptide-peptide, and potentially solvent-solvent interactions, overcome peptide-solvent interactions to favor aggregation at finite concentrations of glycine oligomers. We have recently shown that hydrogen- (H-) bonds do not contribute significantly to the concentration-based aggregation of pentaglycines but that dipole-dipole (CO) interactions between the amide groups on the backbone do. Here we demonstrate for the collapse of oligoglycines ranging in length from 15 to 25 residues similarly that H-bonds do not contribute significantly to collapse but that CO dipole interactions do. These results illustrate that some intrapeptide interactions that determine the solubility limit of short glycine oligomers are similar to those that drive the collapse of longer glycine peptides.

Multibody correlations in the hydrophobic solvation of glycine peptides

Protein collapse during folding is often assumed to be driven by a hydrophobic solvation energy (ΔGvdw) that scales linearly with solvent-accessible surface area (A). In a previous study, we argued that ΔGvdw, as well as its attractive (ΔGatt) and repulsive (ΔGrep) components, was not simply a linear function of A. We found that the surface tensions, γrep, γatt, and γvdw, gotten from ΔGrep, ΔGatt, and ΔGvdw against A for four configurations of deca-alanine differed from those obtained for a set of alkanes. In the present study, we extend our analysis to fifty decaglycine structures and atomic decompositions. We find that different configurations of decaglycine generate different estimates of γrep. Additionally, we considered the reconstruction of the solvation free energy from scaling the free energy of solvation of each atom type, free in solution. The free energy of the isolated atoms, scaled by the inverse surface area the atom would expose in the molecule does not reproduce the γrep for the intact decaglycines. Finally, γatt for the decaglycine conformations is much larger in magnitude than those for deca-alanine or the alkanes, leading to large negative values of γvdw (-74 and -56 cal/mol/Å(2) for CHARMM27 and AMBER ff12sb force fields, respectively). These findings imply that ΔGvdw favors extended rather than compact structures for decaglycine. We find that ΔGrep and ΔGvdw have complicated dependencies on multibody correlations between solute atoms, on the geometry of the molecular surface, and on the chemical identities of the atoms.

ProteinVolume: calculating molecular van der Waals and void volumes in proteins

Background

Voids and cavities in the native protein structure determine the pressure unfolding of proteins. In addition, the volume changes due to the interaction of newly exposed atoms with solvent upon protein unfolding also contribute to the pressure unfolding of proteins. Quantitative understanding of these effects is important for predicting and designing proteins with predefined response to changes in hydrostatic pressure using computational approaches. The molecular surface volume is a useful metric that describes contribution of geometrical volume, which includes van der Waals volume and volume of the voids, to the total volume of a protein in solution, thus isolating the effects of hydration for separate calculations.

Results

We developed ProteinVolume, a highly robust and easy-to-use tool to compute geometric volumes of proteins. ProteinVolume generates the molecular surface of a protein and uses an innovative flood-fill algorithm to calculate the individual components of the molecular surface volume, van der Waals and intramolecular void volumes. ProteinVolume is user friendly and is available as a web-server or a platform-independent command-line version.

Conclusions

ProteinVolume is a highly accurate and fast application to interrogate geometric volumes of proteins. ProteinVolume is a free web server available on http://gmlab.bio.rpi.edu. Free-standing platform-independent Java-based ProteinVolume executable is also freely available at this web site.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-015-0531-2) contains supplementary material, which is available to authorized users.

Effects of geometry and chemistry on hydrophobic solvation

Inserting an uncharged van der Waals (vdw) cavity into water disrupts the distribution of water and creates attractive dispersion interactions between the solvent and solute. This free-energy change is the hydrophobic solvation energy (ΔG(vdw)). Frequently, it is assumed to be linear in the solvent-accessible surface area, with a positive surface tension (γ) that is independent of the properties of the molecule. However, we found that γ for a set of alkanes differed from that for four configurations of decaalanine, and γ = -5 was negative for the decaalanines. These findings conflict with the notion that ΔG(vdw) favors smaller A. We broke ΔG(vdw) into the free energy required to exclude water from the vdw cavity (ΔG(rep)) and the free energy of forming the attractive interactions between the solute and solvent (ΔG(att)) and found that γ < 0 for the decaalanines because -γ(att) > γ(rep) and γ(att) < 0. Additionally, γ(att) and γ(rep) for the alkanes differed from those for the decaalanines, implying that none of ΔG(att), ΔG(rep), and ΔG(vdw) can be computed with a constant surface tension. We also showed that ΔG(att) could not be computed from either the initial or final water distributions, implying that this quantity is more difficult to compute than is sometimes assumed. Finally, we showed that each atom's contribution to γ(rep) depended on multibody interactions with its surrounding atoms, implying that these contributions are not additive. These findings call into question some hydrophobic models.

Solubility and aggregation of Gly(5) in water

Experimentally, the solubility of oligoglycines in water decreases as its length increases. Computationally, the free energy of solvation becomes more favorable with chain length for short (n = 1–5) oligoglycines. We present results of large scale simulations with over 600 pentaglycines at varying concentrations in explicit solvent to consider the mechanism of aggregation. The solubility limit of Gly₅ for the force field used was calculated and compared with experimental values. We find that intermolecular interactions between pentaglycines are favored over interactions between glycine and water, leading to their aggregation. However, the interaction driving peptide associations, liquid–liquid phase separation, are not predominantly hydrogen bonding. Instead, non-hydrogen bonding interactions between partially charged atoms on the peptide backbone allow the formation of dipole–dipole and charge layering correlations that mechanistically stabilize the formation of large, stable peptide clusters.

Measuring the shapes of macromolecules - and why it matters

The molecular basis of life rests on the activity of biological macromolecules, mostly nucleic acids and proteins. A perhaps surprising finding that crystallized over the last handful of decades is that geometric reasoning plays a major role in our attempt to understand these activities. In this paper, we address this connection between geometry and biology, focusing on methods for measuring and characterizing the shapes of macromolecules. We briefly review existing numerical and analytical approaches that solve these problems. We cover in more details our own work in this field, focusing on the alpha shape theory as it provides a unifying mathematical framework that enable the analytical calculations of the surface area and volume of a macromolecule represented as a union of balls, the detection of pockets and cavities in the molecule, and the quantification of contacts between the atomic balls. We have shown that each of these quantities can be related to physical properties of the molecule under study and ultimately provides insight on its activity. We conclude with a brief description of new challenges for the alpha shape theory in modern structural biology.

Protein engineering and the use of molecular modeling and simulation: the case of heterodimeric Fc engineering

Computational and structure guided methods can make significant contributions to the development of solutions for difficult protein engineering problems, including the optimization of next generation of engineered antibodies. In this paper, we describe a contemporary industrial antibody engineering program, based on hypothesis-driven in silico protein optimization method. The foundational concepts and methods of computational protein engineering are discussed, and an example of a computational modeling and structure-guided protein engineering workflow is provided for the design of best-in-class heterodimeric Fc with high purity and favorable biophysical properties. We present the engineering rationale as well as structural and functional characterization data on these engineered designs.

Computational study on the different ligands induced conformation change of β2 adrenergic receptor-Gs protein complex

β₂ adrenergic receptor (β₂AR) regulated many key physiological processes by activation of a heterotrimeric GTP binding protein (Gs protein). This process could be modulated by different types of ligands. But the details about this modulation process were still not depicted. Here, we performed molecular dynamics (MD) simulations on the structures of β₂AR-Gs protein in complex with different types of ligands. The simulation results demonstrated that the agonist BI-167107 could form hydrogen bonds with Ser203^5.42, Ser207^5.46 and Asn293^6.55 more than the inverse agonist ICI 118,551. The different binding modes of ligands further affected the conformation of β₂AR. The energy landscape profiled the energy contour map of the stable and dissociated conformation of Gαs and Gβγ when different types of ligands bound to β₂AR. It also showed the minimum energy pathway about the conformational change of Gαs and Gβγ along the reaction coordinates. By using interactive essential dynamics analysis, we found that Gαs and Gβγ domain of Gs protein had the tendency to separate when the inverse agonist ICI 118,551 bound to β₂AR. The α5-helix had a relatively quick movement with respect to transmembrane segments of β₂AR when the inverse agonist ICI 118,551 bound to β₂AR. Besides, the analysis of the centroid distance of Gαs and Gβγ showed that the Gαs was separated from Gβγ during the MD simulations. Our results not only could provide details about the different types of ligands that induced conformational change of β₂AR and Gs protein, but also supplied more information for different efficacies of drug design of β₂AR.

Designing a ligand for pharmaceutical purposes

BACKGROUND

Drug approval applications to the FDA have shown a remarkably small increment compared with what was expected. In the last few years several efforts have been made to improve the results of rational drug design approaches and in particular to predict inhibitor-target structure and to evaluate the free energy of binding. Virtual database screening, combined with other computational methods, is one of the most promising methods to overcome this key issue.

OBJECTIVE

It is possible to understand how computational medicinal chemistry is changing, improving from its errors and moving towards becoming a more important tool for drug development.

METHODS

Some of the most recent modeling techniques have been presented and in particular the benefits of combining these techniques are highlighted.

RESULTS/CONCLUSION

At present computational chemists can understand the peculiar problems associated with the study of biological systems and on this basis they can choose the right collection of complementary in silico approaches to solve the medicinal chemistry problem in a better manner.

Geometric measures of large biomolecules: surface, volume, and pockets

Geometry plays a major role in our attempts to understand the activity of large molecules. For example, surface area and volume are used to quantify the interactions between these molecules and the water surrounding them in implicit solvent models. In addition, the detection of pockets serves as a starting point for predictive studies of biomolecule-ligand interactions. The alpha shape theory provides an exact and robust method for computing these geometric measures. Several implementations of this theory are currently available. We show however that these implementations fail on very large macromolecular systems. We show that these difficulties are not theoretical; rather, they are related to the architecture of current computers that rely on the use of cache memory to speed up calculation. By rewriting the algorithms that implement the different steps of the alpha shape theory such that we enforce locality, we show that we can remediate these cache problems; the corresponding code, UnionBall has an apparent O(n) behavior over a large range of values of n (up to tens of millions), where n is the number of atoms. As an example, it takes 136 sec with UnionBall to compute the contribution of each atom to the surface area and volume of a viral capsid with more than five million atoms on a commodity PC. UnionBall includes functions for computing analytically the surface area and volume of the intersection of two, three and four spheres that are fully detailed in an appendix. UnionBall is available as an OpenSource software.

Underexposed polar residues and protein stabilization

Increasing protein stability is interesting for practical reasons and because it tests our understanding of protein energetics. We explore here the feasibility of stabilizing proteins by replacing underexposed polar residues by apolar ones of similar size and shape. We have compared the stability of wild-type apoflavodoxin with that of a few carefully selected mutants carrying Y → F, Q → L, T → V or K → M replacements. Although a clear inverse correlation between native solvent exposures of replaced polar residues and stability of mutants is observed, most mutations fail to stabilize the protein. The promising exceptions are the two Q → L mutations tested, which characteristically combine the greatest reduction in polar burial with the greatest increase in apolar burial relative to wild type. Analysis of published stability data corresponding to a variety of mutant proteins confirms that, unlike Y → F or T → V replacements, Q → L mutations tend to be stabilizing, and it suggests that N → L mutations might be stabilizing as well. On the other hand, we show that the stability changes associated to the apoflavodoxin mutations can be rationalized in terms of differential polar and apolar burials upon folding plus a generic destabilizing penalty term. Simple equations combining these contributions predict stability changes in a large data set of 113 mutants (Y → F, Q → L or T → V) similarly well as more complex algorithms available on the Internet.

FAST MOLECULAR SOLVATION ENERGETICS AND FORCE COMPUTATION

The total free energy of a molecule includes the classical molecular mechanical energy (which is understood as the free energy in vacuum) and the solvation energy which is caused by the change of the environment of the molecule (solute) from vacuum to solvent. The solvation energy is important to the study of the inter-molecular interactions. In this paper we develop a fast surface-based generalized Born method to compute the electrostatic solvation energy along with the energy derivatives for the solvation forces. The most time-consuming computation is the evaluation of the surface integrals over an algebraic spline molecular surface (ASMS) and the fast computation is achieved by the use of the nonequispaced fast Fourier transform (NFFT) algorithm. The main results of this paper involve (a) an efficient sampling of quadrature points over the molecular surface by using nonlinear patches, (b) fast linear time estimation of energy and inter-molecular forces, (c) error analysis, and (d) efficient implementation combining fast pairwise summation and the continuum integration using nonlinear patches.

Structural determinants of protein evolution are context-sensitive at the residue level

Structural properties of a protein residue's microenvironment have long been implicated as agents of selective constraint. Although these properties are inherently quantitative, structure-based studies of protein evolution tend to rely upon coarse distinctions between "surface" and "buried" residues and between "interfacial" and "noninterfacial" residues. Using homology-mapped yeast protein structures, we explore the relationships between residue evolution and continuous structural properties of the residue microenvironment, including solvent accessibility, density and distribution of residue-residue contacts, and burial depth. We confirm the role of solvent exposure as a major structural determinant of residue evolution and also identify a weak secondary effect arising from packing density. The relationship between solvent exposure and evolutionary rate (d(N)/d(S)) is found to be strong, positive, and linear. This reinforces the notion that residue burial is a continuous property with quantitative fitness implications. Next, we demonstrate systematic variation in residue-level structure-evolution relationships resulting from changes in global physical and biological contexts. We find that increasing protein-core size yields a more rapid relaxation of selective constraint as solvent exposure increases, although solvent-excluded residues remain similarly constrained. Finally, we analyze the selective constraint in protein-protein interfaces, revealing two fundamentally different yet separable components: continuous structural constraint that scales with total residue burial and a more surprising fixed functional constraint that accompanies any degree of interface involvement. These discoveries serve to elucidate and unite structure-evolution relationships at the residue and whole-protein levels.

ProtSA: a web application for calculating sequence specific protein solvent accessibilities in the unfolded ensemble

Background

The stability of proteins is governed by the heat capacity, enthalpy and entropy changes of folding, which are strongly correlated to the change in solvent accessible surface area experienced by the polypeptide. While the surface exposed in the folded state can be easily determined, accessibilities for the unfolded state at the atomic level cannot be obtained experimentally and are typically estimated using simplistic models of the unfolded ensemble. A web application providing realistic accessibilities of the unfolded ensemble of a given protein at the atomic level will prove useful.

Results

ProtSA, a web application that calculates sequence-specific solvent accessibilities of the unfolded state ensembles of proteins has been developed and made freely available to the scientific community. The input is the amino acid sequence of the protein of interest. ProtSA follows a previously published calculation protocol which uses the Flexible-Meccano algorithm to generate unfolded conformations representative of the unfolded ensemble of the protein, and uses the exact analytical software ALPHASURF to calculate atom solvent accessibilities, which are averaged on the ensemble.

Conclusion

ProtSA is a novel tool for the researcher investigating protein folding energetics. The sequence specific atom accessibilities provided by ProtSA will allow obtaining better estimates of the contribution of the hydrophobic effect to the free energy of folding, will help to refine existing parameterizations of protein folding energetics, and will be useful to understand the influence of point mutations on protein stability.

Dopamine transporter comparative molecular modeling and binding site prediction using the LeuT(Aa) leucine transporter as a template

Pharmacological and behavioral studies indicate that binding of cocaine and the amphetamines by the dopamine transporter (DAT) protein is principally responsible for initiating the euphoria and addiction associated with these drugs. The lack of an X-ray crystal structure for the DAT or any other member of the neurotransmitter:sodium symporter (NSS) family has hindered understanding of psychostimulant recognition at the atomic level; structural information has been obtained largely from mutagenesis and biophysical studies. The recent publication of a crystal structure for the bacterial leucine transporter LeuT(Aa), a distantly related NSS family homolog, provides for the first time a template for three-dimensional comparative modeling of NSS proteins. A novel computational modeling approach using the capabilities of the Molecular Operating Environment program MOE 2005.06 in conjunction with other comparative modeling servers generated the LeuT(Aa)-directed DAT model. Probable dopamine and amphetamine binding sites were identified within the DAT model using multiple docking approaches. Binding sites for the substrate ligands (dopamine and amphetamine) overlapped substantially with the analogous region of the LeuT(Aa) crystal structure for the substrate leucine. The docking predictions implicated DAT side chains known to be critical for high affinity ligand binding and suggest novel mutagenesis targets in elucidating discrete substrate and inhibitor binding sites. The DAT model may guide DAT ligand QSAR studies, and rational design of novel DAT-binding therapeutics.

Structural motifs of biomolecules

Biomolecular structures are assemblies of emergent anisotropic building modules such as uniaxial helices or biaxial strands. We provide an approach to understanding a marginally compact phase of matter that is occupied by proteins and DNA. This phase, which is in some respects analogous to the liquid crystal phase for chain molecules, stabilizes a range of shapes that can be obtained by sequence-independent interactions occurring intra- and intermolecularly between polymeric molecules. We present a singularity-free self-interaction for a tube in the continuum limit and show that this results in the tube being positioned in the marginally compact phase. Our work provides a unified framework for understanding the building blocks of biomolecules.

Implicit nonpolar solvent models

We have systematically analyzed a new nonpolar solvent model that separates nonpolar solvation free energy into repulsive and attractive components. Our analysis shows that either molecular surfaces or volumes can be used to correlate with repulsive free energies of tested molecules in explicit solvent with correlation coefficients higher than 0.99. In addition, the attractive free energies in explicit solvent can also be reproduced with the new model with a correlation coefficient higher than 0.999. Given each component optimized, the new nonpolar solvent model is found to reproduce monomer nonpolar solvation free energies in explicit solvent very well. However, the overall accuracy of the nonpolar solvation free energies is lower than that of each component. In the more challenging dimer test cases, the agreement of the new model with explicit solvent is less impressive. Nevertheless, it is found that the new model works reasonably well for reproducing the relative nonpolar free energy landscapes near the global minimum of the dimer complexes.

Identification of Nonpeptide CCR5 Receptor Agonists by Structure-based Virtual Screening

A three-dimensional model of the chemokine receptor CCR5 has been built to fulfill structural peculiarities of its alpha-helix bundle and to distinguish known CCR5 antagonists from randomly chosen drug-like decoys. In silico screening of a library of 1.6 million commercially available compounds against the CCR5 model by sequential filters (drug-likeness, 2-D pharmacophore, 3-D docking, scaffold clustering) yielded a hit list of 59 compounds, out of which 10 exhibited a detectable binding affinity to the CCR5 receptor. Unexpectedly, most binders tested in a functional assay were shown to be agonists of the CCR5 receptor. A follow-up database query based on similarity to the most potent binders identified three new CCR5 agonists. Despite a moderate affinity of all nonpeptide ligands for the CCR5 receptor, one of the agonists was shown to promote efficient receptor internalization, which is a process therapeutically favorable for protection against HIV-1 infection.

Structure-Based Identification of Small Molecule Binding Sites Using a Free Energy Model

We separately have shown that the maximal druglike affinity of a given binding site on a protein can be calculated on the basis of the binding-site structure alone by using a desolvation-based free energy model along with the notion that druglike ligands fall into certain physiochemical property ranges. Here, we present an approach where we reformulate the calculated druggability affinity as an additive free energy to facilitate the searching of whole protein surfaces for druglike binding sites. The highest-scoring patches in many cases represent known ligand-binding sites for druggable targets, but not for difficult targets. This approach differs from other approaches in that it does not simply identify pockets with the greatest volume but instead identifies pockets that are likely to be amenable to druglike small-molecule binding. Combining the method with a functional residue prediction method called SCA (statistical coupling analysis) results in the prediction of potentially druggable allosteric binding sites on p38alpha kinase.

Assessing implicit models for nonpolar mean solvation forces: the importance of dispersion and volume terms

Continuum solvation models provide appealing alternatives to explicit solvent methods because of their ability to reproduce solvation effects while alleviating the need for expensive sampling. Our previous work has demonstrated that Poisson-Boltzmann methods are capable of faithfully reproducing polar explicit solvent forces for dilute protein systems; however, the popular solvent-accessible surface area model was shown to be incapable of accurately describing nonpolar solvation forces at atomic-length scales. Therefore, alternate continuum methods are needed to reproduce nonpolar interactions at the atomic scale. In the present work, we address this issue by supplementing the solvent-accessible surface area model with additional volume and dispersion integral terms suggested by scaled particle models and Weeks-Chandler-Andersen theory, respectively. This more complete nonpolar implicit solvent model shows very good agreement with explicit solvent results and suggests that, although often overlooked, the inclusion of appropriate dispersion and volume terms are essential for an accurate implicit solvent description of atomic-scale nonpolar forces.

Accurate detection of protein:ligand binding sites using molecular dynamics simulations

Accurate prediction of location of cavities and surface grooves in proteins is important, as these are potential sites for ligand binding. Several currently available programs for cavity detection are unable to detect cavities near the surface or surface grooves. In the present study, an optimized molecular dynamics based procedure is described for detection and quantification of interior cavities as well as surface pockets. This is based on the observation that the mobility of water in such pockets is significantly lower than that of bulk water. The algorithm efficiently detects surface grooves that are sites of protein-ligand and protein-protein interaction. The algorithm was also used to substantially improve the performance of an automated docking procedure for docking monomers of nonobligate protein-protein complexes. In addition, it was applied to predict key residues involved in the binding of the E. coli toxin CcdB with its inhibitor. Predictions were subsequently validated by mutagenesis experiments.

Accuracy of structure-derived properties in simple comparative models of protein structures

The accuracy of comparative models of proteins is addressed here. A set of 12 732 single-template models of sequences of known high-resolution structures was built by an automated procedure. Accuracy of several structure-derived properties, such as surface area, residue accessibility, presence of pockets, electrostatic potential and others, was determined as a function of template:target sequence identity by comparing models with their corresponding experimental structures. As expected, the average accuracy of structure-derived properties always increases with higher template:target sequence identity, but the exact shape of this relationship can differ from one property to another. A comparison of structure-derived properties measured from NMR and X-ray structures of the same protein shows that for most properties, the NMR/X-ray difference is of the same order as the error in models based on ∼40% template:target sequence identity. The exact sequence identity at which properties reach that accuracy varies between 25 and 50%, depending on the property being analyzed. A general characteristic of simple comparative models is that their surface has increased area as a consequence of being more rugged than that of experimental structures. This suggests that including solvent effects during model building or refinement could significantly improve the accuracy of surface properties in comparative models.