Efficient approximate all-atom solvent accessible surface area method parameterized for folded and denatured protein conformations

Continuing advances in computer hardware and software are permitting atomic-resolution molecular simulations for longer time scales and on larger systems. Despite these advances, routinely performing atomistic simulations with explicit water for even small proteins, which reach the folding time of such proteins, remains intractable for the foreseeable future. An implicit approximation of the solvent environment using a solvent accessible surface area (SASA) term in a molecular mechanics potential function allows exclusion of the explicit water molecules in protein simulations. This reduces the number of particles by approximately an order of magnitude. We present a fast and acceptably accurate approximate all-atom SASA method parameterized using a set of folded and heat-denatured conformations of globular proteins. The parameters are shown to be transferable to folded and heat-denatured conformations for another set of proteins. Calculation of the approximate SASA and the associated derivatives with respect to atomic positions for a 4644 atom protein requires only 1/11th the CPU time required for calculation of the nonbonded interactions for this system. On a per atom basis, this algorithm is three times faster than the fastest previously published approximate SASA method and achieves the same level of accuracy.     

Rapid approximation to molecular surface area via the use of Boolean logic and look-up tables

We report the development of a new approximate method of calculating molecular surface areas. Our technique is based upon the method of Sharake and Rupley but incorporates several major advances. First, we represent the state of surface points as bits in a bit string so we can utilize Boolean operations to simultaneously turn off multiple test points in one Boolean AND operation. Second, we use a series of Boolean mask look-up tables to reduce the time complexity of the calculation of molecular surface area down to the same magnitude as doing a potential energy evaluation. When we use a 256 surface point sphere for all of the atoms in BPTI, a 454 nonhydrogen atom protein, and a 1.4-Å solvent probe, we in general underestimate the total solvent-accessible surface area (SASA) by approximately 1.25% with a correlation coefficient of 0.9990 over a wide range of conformations. The average CPU time required to calculate the SASA of a BPTI conformer is 0.58 s on an SGI 4D/220 workstation. We also describe a method by which we can calculate an approximate finite difference SASA gradient for BPTI in 0.79 of CPU time. © 1993 John Wiley & Sons, Inc.     

Application of the frozen atom approximation to the GB/SA continuum model for solvation free energy

The generalized Born/surface area (GB/SA) continuum model for solvation free energy is a fast and accurate alternative to using discrete water molecules in molecular simulations of solvated systems. However, computational studies of large solvated molecular systems such as enzyme-ligand complexes can still be computationally expensive even with continuum solvation methods simply because of the large number of atoms in the solute molecules. Because in such systems often only a relatively small portion of the system such as the ligand binding site is under study, it becomes less attractive to calculate energies and derivatives for all atoms in the system. To curtail computation while still maintaining high energetic accuracy, atoms distant from the site of interest are often frozen; that is, their coordinates are made invariant. Such frozen atoms do not require energetic and derivative updates during the course of a simulation. Herein we describe methodology and results for applying the frozen atom approach to both the generalized Born (GB) and the solvent accessible surface area (SASA) parts of the GB/SA continuum model for solvation free energy. For strictly pairwise energetic terms, such as the Coulombic and van-der-Waals energies, contributions from pairs of frozen atoms can be ignored. This leaves energetic differences unaffected for conformations that vary only in the positions of nonfrozen atoms. Due to the nonlocal nature of the GB analytical form, however, excluding such pairs from a GB calculation leads to unacceptable inaccuracies. To apply a frozen-atom scheme to GB calculations, a buffer region within the frozen-atom zone is generated based on a user-definable cutoff distance from the nonfrozen atoms. Certain pairwise interactions between frozen atoms in the buffer region are retained in the GB computation. This allows high accuracy in conformational GB comparisons to be maintained while achieving significant savings in computational time compared to the full (nonfrozen) calculation. A similar approach for using a buffer region of frozen atoms is taken for the SASA calculation. The SASA calculation is local in nature, and thus exact SASA energies are maintained. With a buffer region of 8 A for the frozen-atom cases, excellent agreement in differences in energies for three different conformations of cytochrome P450 with a bound camphor ligand are obtained with respect to the nonfrozen cases. For various minimization protocols, simulations run 2 to 10.5 times faster and memory usage is reduced by a factor of 1.5 to 5. Application of the frozen atom method for GB/SA calculations thus can render computationally tractable biologically and medically important simulations such as those used to study ligand-receptor binding conformations and energies in a solvated environment.     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

Joint neighbors approximation of macromolecular solvent accessible surface area

A new method for approximate analytical calculations of solvent accessible surface area (SASA) for arbitrary molecules and their gradients with respect to their atomic coordinates was developed. This method is based on the recursive procedure of pairwise joining of neighboring atoms. Unlike other available methods of approximate SASA calculations, the method has no empirical parameters, and therefore can be used with comparable accuracy in calculations of SASA in folded and unfolded conformations of macromolecules of any chemical nature. As shown by tests with globular proteins in folded conformations, average errors in absolute atomic surface area is around 1 A2, while for unfolded protein conformations it varies from 1.65 to 1.87 A2. Computational times of the method are comparable with those by GETAREA, one of the fastest exact analytical methods available today.     

Exact rotamer optimization for protein design

Computational methods play a central role in the rational design of novel proteins. The present work describes a new hybrid exact rotamer optimization (HERO) method that builds on previous dead-end elimination algorithms to yield dramatic performance enhancements. Measured on experimentally validated physical models, these improvements make it possible to perform previously intractable designs of entire protein core, surface, or boundary regions. Computational demonstrations include a full core design of the variable domains of the light and heavy chains of catalytic antibody 48G7 FAB with 74 residues and 10(128) conformations, a full core/boundary design of the beta1 domain of protein G with 25 residues and 10(53) conformations, and a full surface design of the beta1 domain of protein G with 27 residues and 10(60) conformations. In addition, a full sequence design of the beta1 domain of protein G is used to demonstrate the strong dependence of algorithm performance on the exact form of the potential function and the fidelity of the rotamer library. These results emphasize that search algorithm performance for protein design can only be meaningfully evaluated on physical models that have been subjected to experimental scrutiny. The new algorithm greatly facilitates ongoing efforts to engineer increasingly complex protein features.     

Numerical calculation of molecular surface area. I. Assessment of errors

Several points distributions have been used to calculate van der Waals surface areas of a set of molecules. It is shown that there is no strict correlation between the global statistical characteristics of the points distribution, such as deviation and standard deviation, and the accuracy of the calculation of molecular surface. Information about details of the points distribution is needed for predicting the precision of the results. The results show that points distributions produced by optimization of the U function of Le Grand and Merz [J. Comput. Chem., 14 , 349 (1993)] give the most accurate estimation of the molecular surface in numerical calculations. The precision of the numerical evaluation of the van der Waals surface areas has been assessed for 256, 512, 1024, and 2048 points on a single sphere. © 1996 by John Wiley & Sons, Inc.     

Preprocessing of rotamers for protein design calculations

We have developed a process that significantly reduces the number of rotamers in computational protein design calculations. This process, which we call Vegas, results in dramatic computational performance increases when used with algorithms based on the dead-end elimination (DEE) theorem. Vegas estimates the energy of each rotamer at each position by fixing each rotamer in turn and utilizing various search algorithms to optimize the remaining positions. Algorithms used for this context specific optimization can include Monte Carlo, self-consistent mean field, and the evaluation of an expression that generates a lower bound energy for the fixed rotamer. Rotamers with energies above a user-defined cutoff value are eliminated. We found that using Vegas to preprocess rotamers significantly reduced the calculation time of subsequent DEE-based algorithms while retaining the global minimum energy conformation. For a full boundary design of a 51 amino acid fragment of engrailed homeodomain, the total calculation time was reduced by 12-fold.     

vmdICE: a plug-in for rapid evaluation of molecular dynamics simulations using VMD

Molecular dynamics (MD) is a powerful in silico method to investigate the interactions between biomolecules. It solves Newton's equations of motion for atoms over a specified period of time and yields a trajectory file, containing the different spatial arrangements of atoms during the simulation. The movements and energies of each single atom are recorded. For evaluating of these simulation trajectories with regard to biomedical implications, several methods are available. Three well-known ones are the root mean square deviation (RMSD), the root mean square fluctuation (RMSF) and solvent accessible surface area (SASA). Herein, we present a novel plug-in for the software "visual molecular dynamics" (VMD) that allows an interactive 3D representation of RMSD, RMSF, and SASA, directly on the molecule. On the one hand, our plug-in is easy to handle for inexperienced users, and on the other hand, it provides a fast and flexible graphical impression of the spatial dynamics of a system for experts in the field.     

Probing Protein Surface with a Solvent Mimetic Carbene Coupled to Detection by Mass Spectrometry

Much knowledge into protein folding, ligand binding, and complex formation can be derived from the examination of the nature and size of the accessible surface area (SASA) of the polypeptide chain, a key parameter in protein science not directly measurable in an experimental fashion. To this end, an ideal chemical approach should aim at exerting solvent mimicry and achieving minimal selectivity to probe the protein surface regardless of its chemical nature. The choice of the photoreagent diazirine to fulfill these goals arises from its size comparable to water and from being a convenient source of the extremely reactive methylene carbene (:CH₂). The ensuing methylation depends primarily on the solvent accessibility of the polypeptide chain, turning it into a valuable signal to address experimentally the measurement of SASA in proteins. The superb sensitivity and high resolution of modern mass spectrometry techniques allows us to derive a quantitative signal proportional to the extent of modification (EM) of the sample. Thus, diazirine labeling coupled to electrospray mass spectrometry (ESI-MS) detection can shed light on conformational features of the native as well as non-native states, not easily addressable by other methods. Enzymatic fragmentation of the polypeptide chain at the level of small peptides allows us to locate the covalent tag along the amino acid sequence, therefore enabling the construction of a map of solvent accessibility. Moreover, by subsequent MS/MS analysis of peptides, we demonstrate here the feasibility of attaining amino acid resolution in defining the target sites.     

ADME evaluation in drug discovery. 2. Prediction of partition coefficient by atom-additive approach based on atom-weighted solvent accessible surface areas

A novel method for the calculations of 1-octanol/water partition coefficient (log P) of organic molecules has been presented here. The method, SLOGP v1.0, estimates the log P values by summing the contribution of atom-weighted solvent accessible surface areas (SASA) and correction factors. Altogether 100 atom/group types were used to classify atoms with different chemical environments, and two correlation factors were used to consider the intermolecular hydrophobic interactions and intramolecular hydrogen bonds. Coefficient values for 100 atom/group and two correction factors have been derived from a training set of 1850 compounds. The parametrization procedure for different kinds of atoms was performed as follows: first, the atoms in a molecule were defined to different atom/group types based on SMARTS language, and the correction factors were determined by substructure searching; then, SASA for each atom/group type was calculated and added; finally, multivariate linear regression analysis was applied to optimize the hydrophobic parameters for different atom/group types and correction factors in order to reproduce the experimental log P. The correlation based on the training set gives a model with the correlation coefficient (r) of 0.988, the standard deviation (SD) of 0.368 log units, and the absolute unsigned mean error of 0.261. Comparison of various procedures of log P calculations for the external test set of 138 organic compounds demonstrates that our method bears very good accuracy and is comparable or even better than the fragment-based approaches. Moreover, the atom-additive approach based on SASA was compared with the simple atom-additive approach based on the number of atoms. The calculated results show that the atom-additive approach based on SASA gives better predictions than the simple atom-additive one. Due to the connection between the molecular conformation and the molecular surface areas, the atom-additive model based on SASA may be a more universal model for log P estimation especially for large molecules.     

Extending the applicability of the O-ring theory to protein–DNA complexes

Many biological processes depend on protein-based interactions, which are governed by central regions with higher binding affinities, the hot-spots. The O-ring theory or the “Water Exclusion” hypothesis states that the more deeply buried central regions are surrounded by areas, the null-spots, whose role would be to shelter the hot-spots from the bulk solvent. Although this theory is well-established for protein–protein interfaces, its applicability to other protein interfaces remains unclear. Our goal was to verify its applicability to protein–DNA interfaces. We performed Molecular Dynamics simulations in explicit solvent of several protein–DNA complexes and measured a variety of solvent accessible surface area (SASA) features, as well as, radial distribution functions of hot-spots and null-spots. Our aim was to test the influence of water in their coordination sphere. Our results show that hot-spots tend to have fewer water molecules in their neighborhood when compared to null-spots, and higher values of ΔSASA, which confirms their occlusion from solvent. This study provides evidence in support of the O-ring theory with its applicability to a new type of protein-based interface: protein–DNA.     

A rapid method for calculating derivatives of solvent accessible surface areas of molecules

A novel method to calculate the derivatives of solvent accessible surface areas is presented. Unlike earlier analytic methods, which require the molecular topology and the use of global Gauss-Bonnet theorem, this method requires only the fractional accessibilities of surface arcs. We developed an efficient numerical algorithm to calculate the surface arcs by creating a uniform set of points on the circles of intersection between surface atoms. A hierarchical point density doubling scheme led to a logarithmic dependence of Central Processing Unit (CPU) time on the number of points used. This algorithm calculated area derivatives for a 1000-atom protein in 1.5 s on an SGI INDIGO² which were within 2% of the analytic area derivatives calculated with the program ANAREA. This algorithm scales linearly with the number of atoms for large molecules and is easily parallelizable. © 1995 by John Wiley & Sons, Inc.     

A generalized Langevin dynamics approach to model solvent dynamics effects on proteins via a solvent-accessible surface. The carboxypeptidase A inhibitor protein as a model

A generalized Langevin dynamics (GLD) scheme is derived for (bio)macromolecules having internal structure, arbitrary shapes and a size larger than solvent molecules (i.e. proteins). The concept of solvent-accessible surface area (SASA) is used to incorporate solvent effects via external forces thereby avoiding its explicit molecular representation. A simulation algorithm is implemented in the GROMOS molecular dynamics (MD) program including random forces and memory effects, while solvation effects enter via derivatives of the surface area. The potato carboxypeptidase inhibitor (PCI), a small protein, is used to numerically test the approach. This molecule has N- and C-terminal tails whose structure and fluctuations are solvent dependent. A 1-ns MD trajectory was analyzed in depth. X-ray and NMR structures are used in conjunction with MD simulations with and without explicit solvent to gauge the quality of the results. All the analyses showed that the GLD simulation approached the results obtained for the MD simulation with explicit simple-point-charge-model water molecules. The SASAs of the polar atoms show a natural exposure towards the solvent direction. A FLS solvent simulation was completed in order to sense memory effects. The approach and results presented here could be of great value for developing alternatives to the use of explicit solvent molecules in the MD simulation of proteins, expanding its use and the time-scale explored. Received: 2 February 2000 / Revised: 12 March 2000 / Accepted: 26 May 2000 / Published online: 2 November 2000     

Solvation thermodynamics of neutral and charged solutes using the solvation-layer interface condition continuum dielectric model

We demonstrate that the solvation-layer interface condition (SLIC) continuum dielectric model for molecular electrostatics, combined with a simple solvent-accessible-surface-area (SASA)-proportional model for nonpolar solvent effects, accurately predicts solvation entropies of neutral and charged small molecules. The SLIC/SASA model has only seven fitting parameters in total and achieves this accuracy using a training set with only 20 compounds. Despite this simplicity, solvation free energies and entropies are nearly as accurate as those predicted by the more sophisticated Langevin dipoles solvation model. Surprisingly, the model automatically reproduces the negligible contribution of electrostatics to the solvation of hydrophobic compounds. Opportunities for improvement include nonpolar solvation, anion solvation entropies, and heat capacities. More molecular realism may be needed for these quantities. To enable a future, explicit-solvent-based assessment of the SLIC/SASA implicit-solvent model, we predict solvation entropies for the Mobley test set, which are available as Supporting Information.     

Algorithm for rapid calculation of excluded volume of large molecules

An algorithm is described for rapid calculation of excluded volume of large molecules. The excluded volume is defined based on coordinates of constituent atoms as the volume of overlapping spheres, each standing for a space around an atom inaccessible for a solvent molecule. A computer program based on the algorithm has been tested on a protein, ovomucoid. The accuracy of the numerical calculation is discussed.     

CPSA与疏水性参数的遗传算法及神经网络法研究

用分子力学计算出“净”原子表面积,并利用量子化学方法计算出化合物的电荷加权部分表面积(CP-SA).在用遗传算法和神经网络法对改进的CPSA与有机醇类化合物的疏水性参数作相关分析时发现,改进的CPSA可有效地用于构效关系研究,且算法简洁易行,两种多元统计方法均得到了满意的结果.     

Accurate Backbone 13C and 15N Chemical Shift Tensors in Galectin-3 Determined by MAS NMR and QM/MM: Details of Structure and Environment Matter

Chemical shift tensors obtained from solid-state NMR spectroscopy are very sensitive reporters of structure and dynamics in proteins. While accurate ¹³C and ¹⁵N chemical shift tensors are accessible by magic angle spinning (MAS) NMR, their quantum mechanical calculations remain challenging, particularly for ¹⁵N atoms. Here we compare experimentally determined backbone ¹³C^α and ¹⁵N^H chemical shift tensors by MAS NMR with hybrid quantum mechanics/molecular mechanics/molecular dynamics (MD-QM/MM) calculations for the carbohydrate-binding domain of galectin-3. Excellent agreement between experimental and computed ¹⁵N^H chemical shift anisotropy values was obtained using the Amber ff15ipq force field when solvent dynamics was taken into account in the calculation. Our results establish important benchmark conditions for improving the accuracy of chemical shift calculations in proteins and may aid in the validation of protein structure models derived by MAS NMR.     

Molecular dynamics study of salt effects on micellization of N-dodecyl-N,N-dimethyl-3-ammonio-1-propane-sulfonate

In this paper, molecular dynamics simulation methods were used to investigate salt effects on micellization of N-Dodecyl-N,N-Dimethyl-3-Ammonio-1-Propane-sulfonate (SB12-3) in aqueous solution. It is proved that micelle shapes transform from spherical to prolate spherical shape after 30.0?ns simulation with different NaCl and CaCl₂ concentration. By comparison with the eccentricity value without salt addition, SB12-3 shows salt tolerance behaviors due to its unique “inner salt” structure of amphiphilic surfactant. Radial distribution function (RDF), hydrophobic groups solvent accessible surface area (SASA), hydrogen bond, and the deuterium order parameter (S_CD) are to elucidate salt effects on SB12-3 micelle formation. The radius of micelle is achieved by the related RDF value and in accordance with other researches. The addition of NaCl and CaCl₂ didn’t change the structure of micelle significantly and have little effects on the interactions between SB12-3 and water molecule. By comparison with the results without salt system, SASA of hydrophobic groups is almost the same, and SASA of hydrophilic groups and total molecule fluctuates only slightly. This further indicates that the surface of micelles is more hydrophilic due to the strong interactions between SB12-3 and water molecules. The existence of NaCl and CaCl₂ will enhance the hydrophilic interactions.