Analytical approximation to the accessible surface area of proteins

Monte Carlo-Simulated Annealing and Machine Learning-Based Funneled Approach for Finding the Global Minimum Structure of Molecular Clusters

Understanding the physical underpinnings and geometry of molecular clusters is of great importance in many fields, ranging from studying the beginning of the universe to the formation of atmospheric particles. To this end, several approaches have been suggested, yet identifying the most stable cluster geometry (i.e., global potential energy minimum) remains a challenge, especially for highly symmetric clusters. Here, we suggest a new funneled Monte Carlo-based simulated annealing (SA) approach, which includes two key steps: generation of symmetrical clusters and classification of the clusters according to their geometry using machine learning (MCSA-ML). We demonstrate the merits of the MCSA-ML method in comparison to other approaches on several Lennard-Jones (LJ) clusters and four molecular clusters-Ser8(Cl-)2, H+(H2O)6, Ag+(CO2)8, and Bet4Cl-. For the latter of these clusters, the correct structure is unknown, and hence, we compare the experimental and simulated fragmentation patterns, and the fragmentation of the proposed global minimum matches experiments closely. Additionally, based on the fragmentation of the predicted betaine cluster, we were able to identify hitherto unknown neutral fragmentation channels. In comparison to results obtained with other methods, we demonstrated a superior ability of MCSA-ML to predict clusters with high symmetry and similar abilities to predict clusters with asymmetrical structures.

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.

Spiropyran/Merocyanine Amphiphile in Various Solvents: A Joint Experimental–Theoretical Approach to Photophysical Properties and Self-Assembly

This joint experimental-theoretical work focuses on molecular and photophysical properties of the spiropyran-containing amphiphilic molecule in organic and aqueous solutions. Being dissolved in tested organic solvents, the system demonstrates positive photochromism, i.e., upon UV stimulus the colorless spiropyran form is transformed into colorful merocyanine isomer. However, the aqueous solution of the amphiphile possesses a negative photochromism: the orange-red merocyanine form becomes thermodynamically more stable in water, and both UV and vis stimuli lead to the partial or complete photobleaching of the solution. The explanation of this phenomenon is given on the basis of density functional theory calculations and classical modeling including thermodynamic integration. The simulations reveal that stabilization of merocyanine in water proceeds with the energy of ca. 70 kJ mol−1, and that the Helmholtz free energy of hydration of merocyanine form is 100 kJ mol−1 lower as compared to the behavior of SP isomer in water. The explanation of such a difference lies in the molecular properties of the merocyanine: after ring-opening reaction this molecule transforms into a zwitterionic form, as evidenced by the electrostatic potential plotted around the opened form. The presence of three charged groups on the periphery of a flat conjugated backbone stimulates the self-assembly of merocyanine molecules in water, ending up with the formation of elongated associates with stack-like building blocks, as shown in molecular dynamics simulations of the aqueous solution with the concentration above critical micelle concentration. Our quantitative evaluation of the hydrophilicity switching in spiropyran/merocyanine containing surfactants may prompt the search for new systems, including colloidal and polymeric ones, aiming at remote tuning of their morphology, which could give new promising shapes and patterns for the needs of modern nanotechnology.

Salt-Induced Transitions in the Conformational Ensembles of Intrinsically Disordered Proteins

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid-liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the salt-specific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.

Resolution and characterization of confinement- and temperature-dependent dynamics in solvent phases that surround proteins in frozen aqueous solution by using spin-probe EPR spectroscopy

Spin probe electron paramagnetic resonance spectroscopy is applied to characterize the dynamics of concentric hydration and mesophase solvent domains that surround proteins within the ice boundary in frozen aqueous solutions. The solvent dynamics are tuned by variation of temperature (190-265K) and by the degree of ice boundary confinement, which is modulated by the volume of added cryosolvent (0-~50Å separation distance from protein surface). Goals are to: (1) characterize the protein-coupled solvent dynamics on correlation time scales of ~10^-10<τ<10^-7s, and spatial scales from protein surface to periphery of the surrounding solution, from the perspective of a free, small-molecule (~7Å diameter) probe, and (2) reveal properties of the solvent-protein coupling that can be correlated with protein functions, that are measureable under the same conditions. Rotational mobility of the nitroxide spin probe, TEMPOL, resolves and tracks two solvent components, the protein-associated domain (PAD; akin to hydration layer) and surrounding mesodomain, through their distinct temperature- and confinement-dependent values of τ and normalized weight. Detailed protocols are described for simulation of two-component nitroxide EPR spectra, which are categorized by line shape regime and guided by a library of template spectra and simulation parameters derived from two model soluble globular proteins. The order-disorder transition in the PAD, which is a universal feature of protein-coupled solvent dynamics, provides a well-defined, tunable property for elucidating mechanism in solvent-protein-function dynamical coupling. The low-temperature mesodomain system and EPR spin probe method are generally applicable to reveal solvent contributions to a broad range of macromolecule-mediated biological processes.

Energy Landscapes for Base-Flipping in a Model DNA Duplex

We explore the process of base-flipping for four central bases, adenine, guanine, cytosine, and thymine, in a deoxyribonucleic acid (DNA) duplex using the energy landscape perspective. NMR imino-proton exchange and fluorescence correlation spectroscopy studies have been used in previous experiments to obtain lifetimes for bases in paired and extrahelical states. However, the difference of almost 4 orders of magnitude in the base-flipping rates obtained by the two methods implies that they are exploring different pathways and possibly different open states. Our results support the previous suggestion that minor groove opening may be favored by distortions in the DNA backbone and reveal links between sequence effects and the direction of opening, i.e., whether the base flips toward the major or the minor groove side. In particular, base flipping along the minor groove pathway was found to align toward the 5′ side of the backbone. We find that bases align toward the 3′ side of the backbone when flipping along the major groove pathway. However, in some cases for cytosine and thymine, the base flipping along the major groove pathway also aligns toward the 5′ side. The sequence effect may be caused by the polar interactions between the flipping-base and its neighboring bases on either of the strands. For guanine flipping toward the minor groove side, we find that the equilibrium constant for opening is large compared to flipping via the major groove. We find that the estimated rates of base opening, and hence the lifetimes of the closed state, obtained for thymine flipping through small and large angles along the major groove differ by 6 orders of magnitude, whereas for thymine flipping through small angles along the minor groove and large angles along the major groove, the rates differ by 3 orders of magnitude.

Molecular dynamics simulation or structure refinement of proteins: are solvent molecules required? A case study using hen lysozyme

In protein simulation or structure refinement based on values of observable quantities measured in (aqueous) solution, solvent (water) molecules may be explicitly treated, omitted, or represented by a potential of mean-solvation-force term, depending on protein coordinates only, in the force field used. These three approaches are compared for hen egg white lysozyme (HEWL). This 129-residue non-spherical protein contains a variety of secondary-structure elements, and ample experimental data are available: 1630 atom–atom Nuclear Overhauser Enhancement (NOE) upper distance bounds, 213 ³ J-couplings and 200 S² order parameters. These data are used to compare the performance of the three approaches. It is found that a molecular dynamics (MD) simulation in explicit water approximates the experimental data much better than stochastic dynamics (SD) simulation in vacuo without or with a solvent-accessible-surface-area (SASA) implicit-solvation term added to the force field. This is due to the missing energetic and entropic contributions and hydrogen-bonding capacities of the water molecules and the missing dielectric screening effect of this high-permittivity solvent. Omission of explicit water molecules leads to compaction of the protein, an increased internal strain, distortion of exposed loop and turn regions and excessive intra-protein hydrogen bonding. As a consequence, the conformation and dynamics of groups on the surface of the protein, which may play a key role in protein–protein interactions or ligand or substrate binding, may be incorrectly modelled. It is thus recommended to include water molecules explicitly in structure refinement of proteins in aqueous solution based on nuclear magnetic resonance (NMR) or other experimentally measured data.

Enhancing the binding of the β-sheet breaker peptide LPFFD to the amyloid-β fibrils by aromatic modifications: A molecular dynamics simulation study

Alzheimer's is a fatal neurodegenerative disease for which there is no cure at present. The disease is characterized by the presence of plaques in the brains of a patient, which are composed mainly of aggregates of the amyloid-β peptide in the form of β-sheet fibrils. Here, we investigated the possibility of exploiting the superior binding ability of aromatic amino acids to a particular model of the amyloid-β fibrils. which is a difficult target for drug design. The β-sheet breaker peptide LPFFD was modified with aromatic amino acids and its binding to these fibrils was studied. We found that the orientation and the electrostatic complementarity of the modified peptide with respect to the fibrils played a crucial role in determining whether its binding was improved by the aromatic amino acids. The modified LPFFD peptides were able to bind to those fibril residues. which are important in the aggregation of amyloid-β peptides and thus can potentially inhibit the further aggregation of the amyloid-beta peptides by blocking their interactions. We found that the tryptophan modified LPFFD peptides had the best binding affinities. In most cases, the aromatic amino acids in the N-terminus of the modified peptides made more contacts with the fibrils than those in the C-terminus. We also found that increasing the aromatic content did not significantly improve the binding of the LPFFD peptide to the fibrils. Our study can serve as a basis for the design of novel peptide-based drugs for Alzheimer's disease in which aromatic interactions play an important role.

PupStruct: Prediction of Pupylated Lysine Residues Using Structural Properties of Amino Acids

Post-translational modification (PTM) is a critical biological reaction which adds to the diversification of the proteome. With numerous known modifications being studied, pupylation has gained focus in the scientific community due to its significant role in regulating biological processes. The traditional experimental practice to detect pupylation sites proved to be expensive and requires a lot of time and resources. Thus, there have been many computational predictors developed to challenge this issue. However, performance is still limited. In this study, we propose another computational method, named PupStruct, which uses the structural information of amino acids with a radial basis kernel function Support Vector Machine (SVM) to predict pupylated lysine residues. We compared PupStruct with three state-of-the-art predictors from the literature where PupStruct has validated a significant improvement in performance over them with statistical metrics such as sensitivity (0.9234), specificity (0.9359), accuracy (0.9296), precision (0.9349), and Mathew’s correlation coefficient (0.8616) on a benchmark dataset.

Fast Rescoring Protocols to Improve the Performance of Structure-Based Virtual Screening Performed on Protein-Protein Interfaces

Protein-protein interactions (PPIs) are attractive targets for drug design because of their essential role in numerous cellular processes and disease pathways. However, in general, PPIs display exposed binding pockets at the interface, and as such, have been largely unexploited for therapeutic interventions with low-molecular weight compounds. Here, we used docking and various rescoring strategies in an attempt to recover PPI inhibitors from a set of active and inactive molecules for 11 targets collected in ChEMBL and PubChem. Our focus is on the screening power of the various developed protocols and on using fast approaches so as to be able to apply such a strategy to the screening of ultralarge libraries in the future. First, we docked compounds into each target using the fast "pscreen" mode of the structure-based virtual screening (VS) package Surflex. Subsequently, the docking poses were postprocessed to derive a set of 3D topological descriptors: (i) shape similarity and (ii) interaction fingerprint similarity with a co-crystallized inhibitor, (iii) solvent-accessible surface area, and (iv) extent of deviation from the geometric center of a reference inhibitor. The derivatized descriptors, together with descriptor-scaled scoring functions, were utilized to investigate possible impacts on VS performance metrics. Moreover, four standalone scoring functions, RF-Score-VS (machine-learning), DLIGAND2 (knowledge-based), Vinardo (empirical), and X-SCORE (empirical), were employed to rescore the PPI compounds. Collectively, the results indicate that the topological scoring algorithms could be valuable both at a global level, with up to 79% increase in areas under the receiver operating characteristic curve for some targets, and in early stages, with up to a 4-fold increase in enrichment factors at 1% of the screened collections. Outstandingly, DLIGAND2 emerged as the best scoring function on this data set, outperforming all rescoring techniques in terms of VS metrics. The described methodology could help in the rational design of small-molecule PPI inhibitors and has direct applications in many therapeutic areas, including cancer, CNS, and infectious diseases such as COVID-19.

Analytical calculation of the solvent-accessible surface area and its nuclear gradients by stereographic projection: A general approach for molecules, polymers, nanotubes, helices, and surfaces

In this article, we explore an alternative to the analytical Gauss-Bonnet approach for computing the solvent-accessible surface area (SASA) and its nuclear gradients. These two key quantities are required to evaluate the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models. We extend a previously proposed analytical approach for finite systems based on the stereographic projection technique to infinite periodic systems such as polymers, nanotubes, helices, or surfaces and detail its implementation in the Crystal code. We provide the full derivation of the SASA nuclear gradients, and introduce an iterative perturbation scheme of the atomic coordinates to stabilize the gradients calculation for certain difficult symmetric systems. An excellent agreement of computed SASA with reference analytical values is found for finite systems, while the SASA size-extensivity is verified for infinite periodic systems. In addition, correctness of the analytical gradients is confirmed by the excellent agreement obtained with numerical gradients and by the translational invariance achieved, both for finite and infinite periodic systems. Overall therefore, the stereographic projection approach appears as a general, simple, and efficient technique to compute the key quantities required for the calculation of the nonelectrostatic contribution to the solvation energy and its nuclear gradients in implicit solvation models applicable to both finite and infinite periodic systems.

The four-helix bundle in cholinesterase dimers: Structural and energetic determinants of stability

The crystal structures of truncated forms of cholinesterases provide good models for assessing the role of non-covalent interactions in dimer assembly in the absence of cross-linking disulfide bonds. These structures identify the four-helix bundle that serves as the interface for formation of acetylcholinesterase and butyrylcholinesterase dimers. Here we performed a theoretical comparison of the structural and energetic factors governing dimerization. This included identification of inter-subunit and intra-subunit hydrogen bonds and hydrophobic interactions, evaluation of solvent-accessible surfaces, and estimation of electrostatic contributions to dimerization. To reveal the contribution to dimerization of individual amino acids within the contact area, free energy perturbation alanine screening was performed. Markov state modelling shows that the loop between the α13 and α14 helices in BChE is unstable, and occupies 4 macro-states. The order of magnitude of mean first passage times between these macrostates is ~10^-8 s. Replica exchange molecular dynamics umbrella sampling calculations revealed that the free energy of human BChE dimerization is -15.5 kcal/mol, while that for human AChE is -26.4 kcal/mol. Thus, the C-terminally truncated human butyrylcholinesterase dimer is substantially less stable than that of human acetylcholinesterase. An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:CHEMBIOINT:1.

Indolylarylsulfones, a fascinating story of highly potent human immunodeficiency virus type 1 non-nucleoside reverse transcriptase inhibitors

Indolylarylsulfones are a potent class of human immunodeficiency virus type 1 non-nucleoside reverse transcriptase inhibitors. In this review, the structure activity relationship (SAR) studies to improve the profile of sulfone L-737,126 discovered by Merck AG have been analysed with focus on introduction of the 3′,5′-dimethyl groups at the 3-phenylsulfonyl moiety, the 2-hydroxyethyl tail at the indole-2-carboxamide nitrogen, coupling of the carboxamide nitrogen with one or two glycinamide and alaninamide units, a fluorine atom at position 4 of the indole ring and correlation between configuration of the asymmetric centre and linker length. IAS derivatives look like promising drug candidates for the treatment of AIDS and related infections in combination with other antiretroviral agents.

Impact of branching on the conformational heterogeneity of the lipopolysaccharide from Klebsiella pneumoniae: Implications for vaccine design

Resistance of Klebsiella pneumoniae (KP) to antibiotics has motivated the development of an efficacious KP human vaccine that would not be subject to antibiotic resistance. Klebsiella lipopolysaccharide (LPS) associated O polysaccharide (OPS) types have provoked broad interest as a vaccine antigen as there are only 4 that predominate worldwide (O1, O2a, O3, O5). Klebsiella O1 and O2 OPS are polygalactans that share a common D-Gal-I structure, for which a variant D-Gal-III was recently discovered. To understand the potential impact of this variability on antigenicity, a detailed molecular picture of the conformational differences associated with the addition of the D-Gal-III (1 → 4)-α-Galp branch is presented using enhanced-sampling molecular dynamics simulations. In D-Gal-I two major conformational states are observed while the presence of the 1 → 4 branch in D-Gal-III resulted in only a single dominant extended state. Stabilization of the more folded states in D-Gal-I is due to a O4-H⋯O2 hydrogen bond in the linear backbone that cannot occur in D-Gal-III as the O4 is in the Galp(1 → 4)Galp glycosidic linkage. The impact of branching in D-Gal-III also significantly decreases the accessibility of the monosaccharides in the linear backbone region of D-Gal-I, while the accessibility of the terminal D-Gal-II region of the OPS is not substantially altered. The present results suggest that a vaccine that targets both the D-Gal-I and D-Gal-III LPS can be developed by using D-Gal-III as the antigen combined with cross-reactivity experiments using the Gal-II polysaccharide to assure that this region of the LPS is the primary epitope of the antigen.

Peptide and Protein Structure Prediction with a Simplified Continuum Solvent Model

A continuum solvent model based on screened Coulomb potentials has been simplified and parametrized to sample native-like structures in replica-exchange simulations of each of six different peptides and miniproteins. Low-energy, native, and non-native structures were used to iteratively refine 11 parameter values. The centroid of the largest cluster of structures sampled in simulations initiated from an extended conformation represents the predicted structure. The main-chain rms deviation of this prediction from the experimental structure was 0.47 Å for the 12-residue Trp-zip2, 0.86 Å for the 14-residue MBH12, 2.53 Å for the 17-residue U(1-17)T9D, 2.03 Å for the 20-residue BS1, 1.08 Å for the 20-residue Trp-cage, and 3.64 Å for the 35-residue villin headpiece subdomain HP35. The centroid of the sixth largest cluster sampled for HP35 deviated by 0.91 Å. The CHARMM22/CMAP force field was used, with an additional ψ torsion term for residues other than glycine and proline. Six parameters govern the dielectric response of the continuum solvent, and four values of surface tension approximate nonpolar effects. An atom's self-energy and interaction energies are screened independently, each depending on whether the atom is part of a charged group, a neutral hydrogen-bonding main-chain group, or any other neutral group. The parameters inferred result in strong main-chain hydrogen bonds, consistent with the view that protein folding is dominated by the formation of these bonds. (1,2) Conformations of MBH12 and BS1 were excluded from the energy-function refinement, suggesting the parameters, referred to as SCP18, are transferable. An efficient estimate of solvent-accessible surface area is also described.

Fast Pairwise Approximation of Solvent Accessible Surface Area for Implicit Solvent Simulations of Proteins on CPUs and GPUs

We propose a pairwise and readily parallelizable SASA-based nonpolar solvation approach for protein simulations, inspired by our previous pairwise GB polar solvation model development. In this work, we developed a novel function to estimate the atomic and molecular SASAs of proteins, which results in comparable accuracy as the LCPO algorithm in reproducing numerical icosahedral-based SASA values. Implemented in Amber software and tested on consumer GPUs, our pwSASA method reasonably reproduces LCPO simulation results, but accelerates MD simulations up to 30 times compared to the LCPO implementation, which is greatly desirable for protein simulations facing sampling challenges. The value of incorporating the nonpolar term in implicit solvent simulations is explored on a peptide fragment containing the hydrophobic core of HP36 and evaluating thermal stability profiles of four small proteins.

Binding Direction-Based Two-Dimensional Flattened Contact Area Computing Algorithm for Protein–Protein Interactions

Interactions between protein molecules are essential for the assembly, function, and regulation of proteins. The contact region between two protein molecules in a protein complex is usually complementary in shape for both molecules and the area of the contact region can be used to estimate the binding strength between two molecules. Although the area is a value calculated from the three-dimensional surface, it cannot represent the three-dimensional shape of the surface. Therefore, we propose an original concept of two-dimensional contact area which provides further information such as the ruggedness of the contact region. We present a novel algorithm for calculating the binding direction between two molecules in a protein complex, and then suggest a method to compute the two-dimensional flattened area of the contact region between two molecules based on the binding direction.

Photoisomers of Azobenzene Star with a Flat Core: Theoretical Insights into Multiple States from DFT and MD Perspective

This study focuses on comparing physical properties of photoisomers of an azobenzene star with benzene-1,3,5-tricarboxamide core. Three azobenzene arms of the molecule undergo a reversible trans-cis isomerization upon UV-vis light illumination giving rise to multiple states from the planar all-trans one, via two mixed states to the kinked all-cis isomer. Employing density functional theory, we characterize the structural and photophysical properties of each state indicating a role the planar core plays in the coupling between azobenzene chromophores. To characterize the light-triggered switching of solvophilicity/solvophobicity of the star, the difference in solvation free energy is calculated for the transfer of an azobenzene star from its gas phase to implicit or explicit solvents. For the latter case, classical all-atom molecular dynamics simulations of aqueous solutions of azobenzene star are performed employing the polymer consistent force field to shed light on the thermodynamics of explicit hydration as a function of the isomerization state and on the structuring of water around the star. From the analysis of two contributions to the free energy of hydration, the nonpolar van der Waals and the electrostatic terms, it is concluded that isomerization specificity largely determines the polarity of the molecule and the solute-solvent electrostatic interactions. This convertible hydrophilicity/hydrophobicity together with readjustable occupied volume and the surface area accessible to water, affects the self-assembly/disassembly of the azobenzene star with a flat core triggered by light.

Efficient gaussian density formulation of volume and surface areas of macromolecules on graphical processing units

We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. © 2017 Wiley Periodicals, Inc.

Geometric Potentials for Computational Protein Sequence Design

Computational protein sequence design is the rational design based on computer simulation of new protein molecules to fold to target three-dimensional structures, with the ultimate goal of designing novel functions. It requires a good understanding of the thermodynamic equilibrium properties of the protein of interest. Here, we consider the contribution of the solvent to the stability of the protein. We describe implicit solvent models, focusing on approximations of their nonpolar components using geometric potentials. We consider the surface area (SA) model in which the nonpolar solvation free energy is expressed as a sum of the contributions of all atoms, assumed to be proportional to their accessible surface areas (ASAs). We briefly review existing numerical and analytical approaches that compute the ASA. We describe in more detail the alpha shape theory as it provides a unifying mathematical framework that enables the analytical calculations of the surface area of a macromolecule represented as a union of balls.

Acknowledging Errors: Advanced Molecular Replacement with Phaser

Molecular replacement is a method for solving the crystallographic phase problem using an atomic model for the target structure. State-of-the-art methods have moved the field significantly from when it was first envisaged as a method for solving cases of high homology and completeness between a model and target structure. Improvements brought about by application of maximum likelihood statistics mean that various errors in the model and pathologies in the data can be accounted for, so that cases hitherto thought to be intractable are standardly solvable. As a result, molecular replacement phasing now accounts for the lion's share of structures deposited in the Protein Data Bank. However, there will always be cases at the fringes of solvability. I discuss here the approaches that will help tackle challenging molecular replacement cases.

Nested Monte Carlo study of random packing on the sphere

We consider two random sequential packing processes in which spheres of unit radius are randomly attached to the surface of a fixed unit sphere. Independent random spheres are generated and added successively, provided there is no overlap with previous spheres. In model 1, the process stops when a trial sphere intersects one of the previously-accepted spheres. In model 2, random sequential packing, any such overlapping trial sphere is discarded and the next random sphere is tried, until it is impossible to add any further spheres.

Previous workers have conjectured convincingly that no exact analytical solution is possible for this type of problem. We use Monte Carlo simulation methods to estimate transition probabilities for the two models. Because some probabilities are extremely small, a simulation using independent repetitions of the model would be inefficient. We designed a branching process of conditionally binomial trials, and performed over 108 trials on a supercomputer.

Protofold II: Enhanced Model and Implementation for Kinetostatic Protein Folding1

A reliable prediction of three-dimensional (3D) protein structures from sequence data remains a big challenge due to both theoretical and computational difficulties. We have previously shown that our kinetostatic compliance method (KCM) implemented into the Protofold package can overcome some of the key difficulties faced by other de novo structure prediction methods, such as the very small time steps required by the molecular dynamics (MD) approaches or the very large number of samples needed by the Monte Carlo (MC) sampling techniques. In this paper, we improve the free energy formulation used in Protofold by including the typically underrated entropic effects, imparted due to differences in hydrophobicity of the chemical groups, which dominate the folding of most water-soluble proteins. In addition to the model enhancement, we revisit the numerical implementation by redesigning the algorithms and introducing efficient data structures that reduce the expected complexity from quadratic to linear. Moreover, we develop and optimize parallel implementations of the algorithms on both central and graphics processing units (CPU/GPU) achieving speed-ups up to two orders of magnitude on the GPU. Our simulations are consistent with the general behavior observed in the folding process in aqueous solvent, confirming the effectiveness of model improvements. We report on the folding process at multiple levels, namely, the formation of secondary structural elements and tertiary interactions between secondary elements or across larger domains. We also observe significant enhancements in running times that make the folding simulation tractable for large molecules.

Focus on Chirality of HIV-1 Non-Nucleoside Reverse Transcriptase Inhibitors

Chiral HIV-1 non-nucleoside reverse transcriptase inhibitors (NNRTIs) are of great interest since one enantiomer is often more potent than the corresponding counterpart against the HIV-1 wild type (WT) and the HIV-1 drug resistant mutant strains. This review exemplifies the various studies made to investigate the effect of chirality on the antiretroviral activity of top HIV-1 NNRTI compounds, such as nevirapine (NVP), efavirenz (EFV), alkynyl- and alkenylquinazolinone DuPont compounds (DPC), diarylpyrimidine (DAPY), dihydroalkyloxybenzyloxopyrimidine (DABO), phenethylthiazolylthiourea (PETT), indolylarylsulfone (IAS), arylphosphoindole (API) and trifluoromethylated indole (TFMI) The chiral separation, the enantiosynthesis, along with the biological properties of these HIV-1 NNRTIs, are discussed.

A continuum solvent model of ion-ion interactions in water

The calculation of ion-ion interactions in water is a problem of long standing importance. Modelling these interactions is a prerequisite to explaining Hofmeister (specific ion) effects. We here generalize our solvation model of ions to calculate the free energy of two ions in water as a function of separation. The same procedure has previously been applied to calculate ion interactions with the air-water interface successfully. The Conductor like Screening Model (COSMO) is used. This treats the ions on a quantum mechanical level and calculates numerically the electrostatic response of the surrounding solvent. Estimates of the change in the cavity formation energy and the change in the ion-water dispersion energy as the ions approach are included separately. The calculated interaction potentials are too attractive and this is a significant issue. However, they do reproduce the affinity of similarly sized ions for each other, which is a crucial property of these potentials. They are also oscillatory, another important property. We normalize the potentials to reduce the over-attraction, and good correlation with experimental values is achieved. We identify the driving contributions to this like-prefers-like behaviour. We then put forward a plausible hypothesis for the over-attraction of the potentials. An agreeable feature of our approach is that it does not rely on salt specific parameters deliberately adjusted to reproduce experimental values.

Sulfation and cation effects on the conformational properties of the glycan backbone of chondroitin sulfate disaccharides

Chondroitin sulfate (CS) is one of several glycosaminoglycans that are major components of proteoglycans. A linear polymer consisting of repeats of the disaccharide -4GlcAβ1-3GalNAcβ1-, CS undergoes differential sulfation resulting in five unique sulfation patterns. Because of the dimer repeat, the CS glycosidic "backbone" has two distinct sets of conformational degrees of freedom defined by pairs of dihedral angles: (ϕ1, ψ1) about the β1-3 glycosidic linkage and (ϕ2, ψ2) about the β1-4 glycosidic linkage. Differential sulfation and the possibility of cation binding, combined with the conformational flexibility and biological diversity of CS, complicate experimental efforts to understand CS three-dimensional structures at atomic resolution. Therefore, all-atom explicit-solvent molecular dynamics simulations with Adaptive Biasing Force sampling of the CS backbone were applied to obtain high-resolution, high-precision free energies of CS disaccharides as a function of all possible backbone geometries. All 10 disaccharides (β1-3 vs β1-4 linkage × five different sulfation patterns) were studied; additionally, ion effects were investigated by considering each disaccharide in the presence of either neutralizing sodium or calcium cations. GlcAβ1-3GalNAc disaccharides have a single, broad, thermodynamically important free-energy minimum, whereas GalNAcβ1-4GlcA disaccharides have two such minima. Calcium cations but not sodium cations bind to the disaccharides, and binding is primarily to the GlcA -COO(-) moiety as opposed to sulfate groups. This binding alters the glycan backbone thermodynamics in instances where a calcium cation bound to -COO(-) can act to bridge and stabilize an interaction with an adjacent sulfate group, whereas, in the absence of this cation, the proximity of a sulfate group to -COO(-) results in two like charges being both desolvated and placed adjacent to each other and is found to be destabilizing. In addition to providing information on sulfation and cation effects, the present results can be applied to building models of CS polymers and as a point of comparison in studies of CS polymer backbone dynamics and thermodynamics.

On the energy components governing molecular recognition in the framework of continuum approaches

Molecular recognition is a process that brings together several biological macromolecules to form a complex and one of the most important characteristics of the process is the binding free energy. Various approaches exist to model the binding free energy, provided the knowledge of the 3D structures of bound and unbound molecules. Among them, continuum approaches are quite appealing due to their computational efficiency while at the same time providing predictions with reasonable accuracy. Here we review recent developments in the field emphasizing on the importance of adopting adequate description of physical processes taking place upon the binding. In particular, we focus on the efforts aiming at capturing some of the atomistic details of the binding phenomena into the continuum framework. When possible, the energy components are reviewed independently of each other. However, it is pointed out that rigorous approaches should consider all energy contributions on the same footage. The two major schemes for utilizing the individual energy components to predict binding affinity are outlined as well.

Atomistic level molecular dynamics simulation on the solubilization mechanism of aromatic molecules in anionic micelles

Benzene is solubilized in the palisade layer, toluene in the core (or central region), phenol at the surface and pyridine in micelle–water interface. During micellar enhanced ultrafiltration, phenol will have least rejection while benzene is maximum.

Indolylarylsulfones carrying a heterocyclic tail as very potent and broad spectrum HIV-1 non-nucleoside reverse transcriptase inhibitors

We synthesized new indolylarylsulfone (IAS) derivatives carrying a heterocyclic tail at the indole-2-carboxamide nitrogen as potential anti-HIV/AIDS agents. Several new IASs yielded EC50 values <1.0 nM against HIV-1 WT and mutant strains in MT-4 cells. The (R)-11 enantiomer proved to be exceptionally potent against the whole viral panel; in the reverse transcriptase (RT) screening assay, it was remarkably superior to NVP and EFV and comparable to ETV. The binding poses were consistent with the one previously described for the IAS non-nucleoside reverse transcriptase inhibitors. Docking studies showed that the methyl group of (R)-11 points toward the cleft created by the K103N mutation, different from the corresponding group of (S)-11. By calculating the solvent-accessible surface, we observed that the exposed area of RT in complex with (S)-11 was larger than the area of the (R)-11 complex. Compounds 6 and 16 and enantiomer (R)-11 represent novel robust lead compounds of the IAS class.

TRIFORCE: Tessellated Semianalytical Solvent Exposed Surface Areas and Derivatives

We present a new approach to the calculation of solvent-accessible surface areas of molecules with potential application to surface area based methods for determination of solvation free energies. As in traditional analytical and statistical approaches, this new algorithm, called TRIFORCE, reports both component areas and derivatives as a function of the atomic coordinates and radii. Unique to TRIFORCE are the rapid and scalable approaches for the determination of sphere intersection points and numerical estimation of the surface areas, derivatives, and other properties that can be associated with the surface area facets. The algorithm performs a special tessellation and semianalytical integration that uses a precomputed look-up table. This provides a simple way to balance numerical accuracy and memory usage. TRIFORCE calculates derivatives in the same manner, enabling application in force-dependent activities such as molecular geometry minimization. TRIFORCE is available free of charge for academic purposes as both a C++ library, which can be directly interfaced to existing molecular simulation packages, and a web-accessible application.

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.

SCEDS: protein fragments for molecular replacement in Phaser

A method is described for generating protein fragments suitable for use as molecular-replacement (MR) template models. The template model for a protein suspected to undergo a conformational change is perturbed along combinations of low-frequency normal modes of the elastic network model. The unperturbed structure is then compared with each perturbed structure in turn and the structurally invariant regions are identified by analysing the difference distance matrix. These fragments are scored with SCEDS, which is a combined measure of the sphericity of the fragments, the continuity of the fragments with respect to the polypeptide chain, the equality in number of atoms in the fragments and the density of C(α) atoms in the triaxial ellipsoid of the fragment extents. The fragment divisions with the highest SCEDS are then used as separate template models for MR. Test cases show that where the protein contains fragments that undergo a change in juxtaposition between template model and target, SCEDS can identify fragments that lead to a lower R factor after ten cycles of all-atom refinement with REFMAC5 than the original template structure. The method has been implemented in the software Phaser.

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.

New functionalities in the GROMOS biomolecular simulation software

Since the most recent description of the functionalities of the GROMOS software for biomolecular simulation in 2005 many new functions have been implemented. In this article, the new functionalities that involve modified forces in a molecular dynamics (MD) simulation are described: the treatment of electronic polarizability, an implicit surface area and internal volume solvation term to calculate interatomic forces, functions for the GROMOS coarse-grained supramolecular force field, a multiplicative switching function for nonbonded interactions, adiabatic decoupling of a number of degrees of freedom with temperature or force scaling to enhance sampling, and nonequilibrium MD to calculate the dielectric permittivity or viscosity. Examples that illustrate the use of these functionalities are given.

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Accessibility and partner number of protein residues, their relationship and a webserver, ContPlot for their display

Background

Depending on chemical features residues have preferred locations – interior or exterior – in protein structures, which also determine how many other residues are found around them. The close packing of residues is the hallmark of protein interior and protein-protein interaction sites.

Results

The average values of accessible surface area (ASA) and partner number (PN, the number of other residues within a distance of 4.5 Å from any atom of a given residue) of different residues have been determined and a webserver, ContPlot has been designed to display these values (relative to the average values) along the protein sequence. This would be useful to visually identify residues that are densely packed, or those involved in protein-protein interactions. The skewness observed in the distribution of PNs is indicative of the hydrophobic or hydrophilic nature of the residue. The variation of ASA with PN can be analytically expressed in terms of a cubic equation. These equations (one for each residue) can be used to estimate the ASA of a polypeptide chain using the PNs of the individual residues in the structure.

Conclusion

The atom-based PNs (obtained by counting surrounding atoms) are highly correlated to the residue-based PN, indicating that the latter can adequately capture the atomic details of packing. The average values of ASA and PN associated with each residue should be useful in protein structure prediction or fold-recognition algorithm. ContPlot would provide a handy tool to assess the importance of a residue in the protein structure or interaction site.

Progress and challenges in predicting protein-protein interaction sites

The identification of protein-protein interaction sites is an essential intermediate step for mutant design and the prediction of protein networks. In recent years a significant number of methods have been developed to predict these interface residues and here we review the current status of the field. Progress in this area requires a clear view of the methodology applied, the data sets used for training and testing the systems, and the evaluation procedures. We have analysed the impact of a representative set of features and algorithms and highlighted the problems inherent in generating reliable protein data sets and in the posterior analysis of the results. Although it is clear that there have been some improvements in methods for predicting interacting sites, several major bottlenecks remain. Proteins in complexes are still under-represented in the structural databases and in particular many proteins involved in transient complexes are still to be crystallized. We provide suggestions for effective feature selection, and make it clear that community standards for testing, training and performance measures are necessary for progress in the field.

Solvent accessible surface area approximations for rapid and accurate protein structure prediction

The burial of hydrophobic amino acids in the protein core is a driving force in protein folding. The extent to which an amino acid interacts with the solvent and the protein core is naturally proportional to the surface area exposed to these environments. However, an accurate calculation of the solvent-accessible surface area (SASA), a geometric measure of this exposure, is numerically demanding as it is not pair-wise decomposable. Furthermore, it depends on a full-atom representation of the molecule. This manuscript introduces a series of four SASA approximations of increasing computational complexity and accuracy as well as knowledge-based environment free energy potentials based on these SASA approximations. Their ability to distinguish correctly from incorrectly folded protein models is assessed to balance speed and accuracy for protein structure prediction. We find the newly developed “Neighbor Vector” algorithm provides the most optimal balance of accurate yet rapid exposure measures.

A simple Calpha-SC potential with higher accuracy for protein fold recognition

In this paper, an improved C(alpha)-SC energy potential designed for protein fold recognition was reported. It consists of three extremely simple interaction terms which are supposed to be the dominant interactions in protein folding: residue-residue contact, hydrophobicity and pseudodihedral potentials. The potential function only contains 210 contacts, one hydrophobic and one torsion parameters, which have been optimized using an interior point algorithm of linear programming. Tests of the derived potential function on commonly used decoy sets illustrate that it outperforms most of the existing coarse-grained potentials in terms of its capabilities in recognizing native structures and consistency in achieving high Z-scores across decoy sets, and it has almost equivalent performance to the potentials which considered complex intra-molecular interactions. The results show that our scoring function is a generally prospective potential for protein structure prediction and modeling with regard to its recognition and computation efficacy.