Comparison between self-guided Langevin dynamics and molecular dynamics simulations for structure refinement of protein loop conformations

This article presents a comparative analysis of two replica‐exchange simulation methods for the structure refinement of protein loop conformations, starting from low‐resolution predictions. The methods are self‐guided Langevin dynamics (SGLD) and molecular dynamics (MD) with a Nosé–Hoover thermostat. We investigated a small dataset of 8‐ and 12‐residue loops, with the shorter loops placed initially from a coarse‐grained lattice model and the longer loops from an enumeration assembly method (the Loopy program). The CHARMM22 + CMAP force field with a generalized Born implicit solvent model (molecular‐surface parameterized GBSW2) was used to explore conformational space. We also assessed two empirical scoring methods to detect nativelike conformations from decoys: the all‐atom distance‐scaled ideal‐gas reference state (DFIRE‐AA) statistical potential and the Rosetta energy function. Among the eight‐residue loop targets, SGLD out performed MD in all cases, with a median of 0.48 Å reduction in global root‐mean‐square deviation (RMSD) of the loop backbone coordinates from the native structure. Among the more challenging 12‐residue loop targets, SGLD improved the prediction accuracy over MD by a median of 1.31 Å, representing a substantial improvement. The overall median RMSD for SGLD simulations of 12‐residue loops was 0.91 Å, yielding refinement of a median 2.70 Å from initial loop placement. Results from DFIRE‐AA and the Rosetta model applied to rescoring conformations failed to improve the overall detection calculated from the CHARMM force field. We illustrate the advantage of SGLD over the MD simulation model by presenting potential‐energy landscapes for several loop predictions. Our results demonstrate that SGLD significantly outperforms traditional MD in the generation and populating of nativelike loop conformations and that the CHARMM force field performs comparably to other empirical force fields in identifying these conformations from the resulting ensembles. Published 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Assessing the quality of absolute hydration free energies among CHARMM‐compatible ligand parameterization schemes

Multipurpose atom‐typer for CHARMM (MATCH), an atom‐typing toolset for molecular mechanics force fields, was recently developed in our laboratory. Here, we assess the ability of MATCH‐generated parameters and partial atomic charges to reproduce experimental absolute hydration free energies for a series of 457 small neutral molecules in GBMV2, Generalized Born with a smooth SWitching (GBSW), and fast analytical continuum treatment of solvation (FACTS) implicit solvent models. The quality of hydration free energies associated with small molecule parameters obtained from ParamChem, SwissParam, and Antechamber are compared. Given optimized surface tension coefficients for scaling the surface area term in the nonpolar contribution, these automated parameterization schemes with GBMV2 and GBSW demonstrate reasonable agreement with experimental hydration free energies (average unsigned errors of 0.9–1.5 kcal/mol and R² of 0.63–0.87). GBMV2 and GBSW consistently provide slightly more accurate estimates than FACTS, whereas Antechamber parameters yield marginally more accurate estimates than the current generation of MATCH, ParamChem, and SwissParam parameterization strategies. Modeling with MATCH libraries that are derived from different CHARMM topology and parameter files highlights the importance of having sufficient coverage of chemical space within the underlying databases of these automated schemes and the benefit of targeting specific functional groups for parameterization efforts to maximize both the breadth and the depth of the parameterized space. © 2013 Wiley Periodicals, Inc.     

The use of a generalized born model for the analysis of protein conformational transitions: a comparative study with explicit solvent simulations for chemotaxis Y protein (CheY)

To investigate whether implicit solvent models are appropriate for mechanistic studies of conformational transition in proteins, a recently developed generalized Born model (GBSW) was applied to a small signaling protein, chemotaxis protein Y (CheY), with different combinations of the phosphorylation state and conformation of the system; the results were compared to explicit solvent simulations using a stochastic boundary condition. The subtle but distinct conformational transitions involved in CheY activation makes the system ideally suited for comparing implicit and explicit solvent models because these conformational transitions are potentially accessible in both types of simulations. The structural and dynamical properties analyzed include not only those localized to the active site region but also throughout the protein, such as sidechain methyl group order parameters, backbone hydrogen bonding lifetime and occupancy as well as principal components of the trajectories. Overall, many properties were well reproduced by the GBSW simulations when compared with the explicit solvent calculations, although a number of observations consistently point to the suggestion that the current parameterization of the GBSW model tends to overestimate hydrogen-bonding interactions involving both charged groups and (charge-neutral) backbone atoms. This deficiency led to overstabilization of certain secondary structural motifs and more importantly, qualitatively different behaviors for the active site groups (Thr 87, Ala 88, the beta4-alpha4 loop) in response to phosphorylation, when compared with explicit solvent simulations. The current study highlights the value of carrying out both explicit and implicit solvent simulations for complementary mechanistic insights in the analysis of conformational transition in biomolecules.     

Surveying implicit solvent models for estimating small molecule absolute hydration free energies

Implicit solvent models are powerful tools in accounting for the aqueous environment at a fraction of the computational expense of explicit solvent representations. Here, we compare the ability of common implicit solvent models (TC, OBC, OBC2, GBMV, GBMV2, GBSW, GBSW/MS, GBSW/MS2 and FACTS) to reproduce experimental absolute hydration free energies for a series of 499 small neutral molecules that are modeled using AMBER/GAFF parameters and AM1-BCC charges. Given optimized surface tension coefficients for scaling the surface area term in the nonpolar contribution, most implicit solvent models demonstrate reasonable agreement with extensive explicit solvent simulations (average difference 1.0-1.7 kcal/mol and R(2)=0.81-0.91) and with experimental hydration free energies (average unsigned errors=1.1-1.4 kcal/mol and R(2)=0.66-0.81). Chemical classes of compounds are identified that need further optimization of their ligand force field parameters and others that require improvement in the physical parameters of the implicit solvent models themselves. More sophisticated nonpolar models are also likely necessary to more effectively represent the underlying physics of solvation and take the quality of hydration free energies estimated from implicit solvent models to the next level.     

Evaluation of a knowledge‐based potential of mean force for scoring docked protein–ligand complexes

The Biomolecular Ligand Energy Evaluation Protocol (BLEEP) is a knowledge‐based potential derived from high‐resolution X‐ray structures of protein–ligand complexes. The performance of this potential in ranking the hypothetical structures resulting from a docking study has been evaluated using fifteen protein–ligand complexes from the Protein Data Bank. In the majority of complexes BLEEP was successful in identifying the native (experimental) binding mode or an alternative of low rms deviation (from the native) as the lowest in energy. Overall BLEEP is slightly better than the DOCK energy function in discriminating native‐like modes. Even when alternative binding modes rank lower than the native structure, a reasonable energy is assigned to the latter. Breaking down the BLEEP scores into the atom–atom contributions reveals that this type of potential is grossly dominated by longer range interactions (>5 Å), which makes it relatively insensitive to small local variations in the binding site. However, despite this limitation, the lack, at present, of accurate protein–ligand potentials means that BLEEP is a promising approach to improve the filtering of structures resulting from docking programs. Moreover, BLEEP should improve with the continuously increasing number of complexes available in the PDB. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 673–688, 2001     

Parallelization and improvements of the generalized born model with a simple sWitching function for modern graphics processors

Two fundamental challenges of simulating biologically relevant systems are the rapid calculation of the energy of solvation and the trajectory length of a given simulation. The Generalized Born model with a Simple sWitching function (GBSW) addresses these issues by using an efficient approximation of Poisson–Boltzmann (PB) theory to calculate each solute atom's free energy of solvation, the gradient of this potential, and the subsequent forces of solvation without the need for explicit solvent molecules. This study presents a parallel refactoring of the original GBSW algorithm and its implementation on newly available, low cost graphics chips with thousands of processing cores. Depending on the system size and nonbonded force cutoffs, the new GBSW algorithm offers speed increases of between one and two orders of magnitude over previous implementations while maintaining similar levels of accuracy. We find that much of the algorithm scales linearly with an increase of system size, which makes this water model cost effective for solvating large systems. Additionally, we utilize our GPU‐accelerated GBSW model to fold the model system chignolin, and in doing so we demonstrate that these speed enhancements now make accessible folding studies of peptides and potentially small proteins. © 2016 Wiley Periodicals, Inc.     

Molecular dynamics simulations of large integral membrane proteins with an implicit membrane model

The heterogeneous dielectric generalized Born (HDGB) methodology is an the extension of the GBMV model for the simulation of integral membrane proteins with an implicit membrane environment. Three large integral membrane proteins, the bacteriorhodopsin monomer and trimer and the BtuCD protein, were simulated with the HDGB model in order to evaluate how well thermodynamic and dynamic properties are reproduced. Effects of the truncation of electrostatic interactions were examined. For all proteins, the HDGB model was able to generate stable trajectories that remained close to the starting experimental structures, in excellent agreement with explicit membrane simulations. Dynamic properties evaluated through a comparison of B-factors are also in good agreement with experiment and explicit membrane simulations. However, overall flexibility was slightly underestimated with the HDGB model unless a very large electrostatic cutoff is employed. Results with the HDGB model are further compared with equivalent simulations in implicit aqueous solvent, demonstrating that the membrane environment leads to more realistic simulations.     

Efficient implementation of constant pH molecular dynamics on modern graphics processors

The treatment of pH sensitive ionization states for titratable residues in proteins is often omitted from molecular dynamics (MD) simulations. While static charge models can answer many questions regarding protein conformational equilibrium and protein–ligand interactions, pH‐sensitive phenomena such as acid‐activated chaperones and amyloidogenic protein aggregation are inaccessible to such models. Constant pH molecular dynamics (CPHMD) coupled with the Generalized Born with a Simple sWitching function (GBSW) implicit solvent model provide an accurate framework for simulating pH sensitive processes in biological systems. Although this combination has demonstrated success in predicting pK_a values of protein structures, and in exploring dynamics of ionizable side‐chains, its speed has been an impediment to routine application. The recent availability of low‐cost graphics processing unit (GPU) chipsets with thousands of processing cores, together with the implementation of the accurate GBSW implicit solvent model on those chipsets (Arthur and Brooks, J. Comput. Chem. 2016, 37, 927), provide an opportunity to improve the speed of CPHMD and ionization modeling greatly. Here, we present a first implementation of GPU‐enabled CPHMD within the CHARMM‐OpenMM simulation package interface. Depending on the system size and nonbonded force cutoff parameters, we find speed increases of between one and three orders of magnitude. Additionally, the algorithm scales better with system size than the CPU‐based algorithm, thus allowing for larger systems to be modeled in a cost effective manner. We anticipate that the improved performance of this methodology will open the door for broad‐spread application of CPHMD in its modeling pH‐mediated biological processes. © 2016 Wiley Periodicals, Inc.     

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.     

Protegrin‐1 orientation and physicochemical properties in membrane bilayers studied by potential of mean force calculations

Protegrin‐1 (PG‐1) belongs to the family of antimicrobial peptides. It interacts specifically with the membrane of a pathogen and kills the pathogen by releasing its cellular contents. To fully understand the energetics governing the orientation of PG‐1 in different membrane environments and its effects on the physicochemical properties of the peptide and membrane bilayers, we have performed the potential of mean force (PMF) calculations as a function of its tilt angle at four distinct rotation angles in explicit membranes composed of either DLPC (1,2‐dilauroylphosphatidylcholine) or POPC (1‐palmitoyl‐2‐oleoylphosphatidylcholine) lipid molecules. The resulting PMFs in explicit lipid bilayers were then used to search for the optimal hydrophobic thickness of the EEF1/IMM1 implicit membrane model in which a two‐dimensional PMF in the tilt and rotation space was calculated. The PMFs in explicit membrane systems clearly reveal that the energetically favorable tilt angle is affected by both the membrane hydrophobic thickness and the PG‐1 rotation angle. Local thinning of the membrane around PG‐1 is observed upon PG‐1 tilting. The thinning is caused by both hydrophobic mismatch and arginine‐lipid head group interactions. The two‐dimensional PMF in the implicit membrane is in good accordance with those from the explicit membrane simulations. The ensemble‐averaged Val16 ¹⁵N and ¹³CO chemical shifts weighted by the two‐dimensional PMF agree fairly well with the experimental values, suggesting the importance of peptide dynamics in calculating such ensemble properties for direct comparison with experimental observables. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Comparing pairwise‐additive and many‐body generalized Born models for acid/base calculations and protein design

Generalized Born (GB) solvent models are common in acid/base calculations and protein design. With GB, the interaction between a pair of solute atoms depends on the shape of the protein/solvent boundary and, therefore, the positions of all solute atoms, so that GB is a many‐body potential. For compute‐intensive applications, the model is often simplified further, by introducing a mean, native‐like protein/solvent boundary, which removes the many‐body property. We investigate a method for both acid/base calculations and protein design that uses Monte Carlo simulations in which side chains can explore rotamers, bind/release protons, or mutate. The fluctuating protein/solvent dielectric boundary is treated in a way that is numerically exact (within the GB framework), in contrast to a mean boundary. Its originality is that it captures the many‐body character while retaining the residue‐pairwise complexity given by a fixed boundary. The method is implemented in the Proteus protein design software. It yields a slight but systematic improvement for acid/base constants in nine proteins and a significant improvement for the computational design of three PDZ domains. It eliminates a source of model uncertainty, which will facilitate the analysis of other model limitations. © 2017 Wiley Periodicals, Inc.     

Ranking protein–protein docking results using steered molecular dynamics and potential of mean force calculations

Crystallization of protein–protein complexes can often be problematic and therefore computational structural models are often relied on. Such models are often generated using protein–protein docking algorithms, where one of the main challenges is selecting which of several thousand potential predictions represents the most near‐native complex. We have developed a novel technique that involves the use of steered molecular dynamics (sMD) and umbrella sampling to identify near‐native complexes among protein–protein docking predictions. Using this technique, we have found a strong correlation between our predictions and the interface RMSD (iRMSD) in ten diverse test systems. On two of the systems, we investigated if the prediction results could be further improved using potential of mean force calculations. We demonstrated that a near‐native (<2.0 Å iRMSD) structure could be identified in the top‐1 ranked position for both systems. © 2016 Wiley Periodicals, Inc.     

LEAP: Highly accurate prediction of protein loop conformations by integrating coarse‐grained sampling and optimized energy scores with all‐atom refinement of backbone and side chains

Prediction of protein loop conformations without any prior knowledge (ab initio prediction) is an unsolved problem. Its solution will significantly impact protein homology and template‐based modeling as well as ab initio protein‐structure prediction. Here, we developed a coarse‐grained, optimized scoring function for initial sampling and ranking of loop decoys. The resulting decoys are then further optimized in backbone and side‐chain conformations and ranked by all‐atom energy scoring functions. The final integrated technique called loop prediction by energy‐assisted protocol achieved a median value of 2.1 Å root mean square deviation (RMSD) for 325 12‐residue test loops and 2.0 Å RMSD for 45 12‐residue loops from critical assessment of structure‐prediction techniques (CASP) 10 target proteins with native core structures (backbone and side chains). If all side‐chain conformations in protein cores were predicted in the absence of the target loop, loop‐prediction accuracy only reduces slightly (0.2 Å difference in RMSD for 12‐residue loops in the CASP target proteins). The accuracy obtained is about 1 Å RMSD or more improvement over other methods we tested. The executable file for a Linux system is freely available for academic users at http://sparks‐lab.org . © 2013 Wiley Periodicals, Inc.     

Modeling peptide binding to anionic membrane pores

Peptide‐induced pore formation in membranes can be dissected into two steps: pore formation and peptide binding to the pore. A computational method is proposed to study the second step in anionic membranes. The electrostatic potential is obtained from numerical solutions to the Poisson–Boltzmann equation and is then used in conjunction with IMM1 (implicit membrane model 1). A double charge layer model is used to incorporate the effects of the membrane dipole potential. Inhomogeneity of the charge density in the pore, characterized by explicit membrane simulations of toroidal pores, is included in the model. This approach was applied to two extensively studied peptides, magainin and melittin. In agreement with previous work, binding to toroidal pores is more favorable than binding to the flat membrane. The dependence of binding energy on anionic content exhibits different patterns for the two peptides, in correlation with the different lipid selectivity that has been observed experimentally. © 2013 Wiley Periodicals, Inc.     

GRID: A high‐resolution protein structure refinement algorithm

The energy‐based refinement of protein structures generated by fold prediction algorithms to atomic‐level accuracy remains a major challenge in structural biology. Energy‐based refinement is mainly dependent on two components: (1) sufficiently accurate force fields, and (2) efficient conformational space search algorithms. Focusing on the latter, we developed a high‐resolution refinement algorithm called GRID. It takes a three‐dimensional protein structure as input and, using an all‐atom force field, attempts to improve the energy of the structure by systematically perturbing backbone dihedrals and side‐chain rotamer conformations. We compare GRID to Backrub, a stochastic algorithm that has been shown to predict a significant fraction of the conformational changes that occur with point mutations. We applied GRID and Backrub to 10 high‐resolution (≤ 2.8 Å) crystal structures from the Protein Data Bank and measured the energy improvements obtained and the computation times required to achieve them. GRID resulted in energy improvements that were significantly better than those attained by Backrub while expending about the same amount of computational resources. GRID resulted in relaxed structures that had slightly higher backbone RMSDs compared to Backrub relative to the starting crystal structures. The average RMSD was 0.25 ± 0.02 Å for GRID versus 0.14 ± 0.04 Å for Backrub. These relatively minor deviations indicate that both algorithms generate structures that retain their original topologies, as expected given the nature of the algorithms. © 2012 Wiley Periodicals, Inc.     

Comparison of generalized born and poisson models: Energetics and dynamics of HIV protease

This study characterizes the accuracy of energies and forces computed with a generalized Born (GB) model and the distance‐dependent dielectric (DDD) model with respect to detailed finite solutions of the Poisson equation (FDPE). Tests are done for a small molecule in solution and for HIV‐1 protease with inhibitor, KNI‐272. GB agrees well with FDPE for the small molecule, but less well for the protein system. The correlation between GB and FDPE energies is poorest in calculations of changes upon binding. Also, forces computed with the GB model are less accurate than energies. The DDD model is far less accurate than GB. Nanosecond stochastic dynamics simulations of HIV‐1 protease with an empty active site are used to examine the consequence of the models for the conformational preferences of the active site. Interestingly, the active site flaps remain near their starting conformations in the FDPE and GB simulations but collapse into the active site in the DDD simulation. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 295–309, 2000     

Struktur und magnetische Eigenschaften von Bis{3‐amino‐1,2,4‐triazolium(1+)}pentafluoromanganat(III): (3‐atriazH)2[MnF5]

Structure and Magnetic Properties of Bis{3‐amino‐1,2,4‐triazolium(1+)}pentafluoromanganate(III): (3‐atriazH)₂[MnF₅] The crystal structure of (3‐atriazH)₂[MnF₅], space group P1, Z = 4, a = 8.007(1) Å, b = 11.390(1) Å, c = 12.788(1) Å, α = 85.19(1)°, β = 71.81(1)°, γ = 73.87(1)°, R = 0.034, is built by octahedral trans‐chain anions [MnF₅]^2–_∞ separated by the mono‐protonated organic amine cations. The [MnF₆] octahedra are strongly elongated along the chain axis (<Mn–F_ax> 2.135 Å, <Mn–F_eq> 1.842 Å), mainly due to the Jahn‐Teller effect, the chains are kinked with an average bridge angle Mn–F–Mn = 139.3°. Below 66 K the compound shows 1D‐antiferromagnetism with an exchange energy of J/k = –10.8 K. 3D ordering is observed at T_N = 9.0 K. In spite of the large inter‐chain separation of 8.2 Å a remarkable inter‐chain interaction with |J′/J| = 1.3 · 10^–5 is observed, mediated probably by H‐bonds. That as well as the less favourable D/J ratio of 0.25 excludes the existence of a Haldene phase possible for Mn³⁺ (S = 2).     

Synthesis and Crystal Structure of [(1‐(Phenyltriazenido)‐2‐(phenyltriazeno)benzene)(nitrato)mercury(II)], {Hg[PhN3C6H4N3(H)Ph](NO3)}, a Complex with Weak Metal‐Arene π‐Interactions

The reaction of PhN₃(H)C₆H₄N₃(H)Ph with Hg(NO₃)₂ in THF in the presence of triethylamine yields {Hg[PhN₃C₆H₄N₃(H)Ph](NO₃)} as a yellow powder that can be recrystallized from THF/acetone. The crystals belong to the monoclinic system, space group P2₁ with the cell dimensions a = 9.639(2), b = 5.412(1), c = 19.675(4) Å, β= 97.47(3)°, V = 1017.7 (4) ų, Z = 2. The crystal structure determination (2668 unique reflections with [I>2σ(I)], 262 parameters, R₁ = 0.0393) shows that the structure consists of mononuclear complexes. Hg atoms are linearly coordinated by one N_α atom of the triazenide unit of the planar ligand [Hg‐N(1) = 2.101(8) Å] and an O atom of the NO₃^— ion [Hg‐O(1) = 2.11(1) Å]. Additional weak Hg‐N contacts [Hg‐N(4) = 2.662(9) and Hg‐N(3) = 2.851(9) Å] and an intramolecular hydrogen bond between the triazenide hydrogen and an O atom of the nitrate group are observed [N(6)‐H(6)···O(2) = 2.92(2) Å]. The complexes are stacked to infinite chains by metal‐arene π‐interactions. Each Hg atom is coordinated by the terminal phenyl rings of two neighboring complexes [Hg‐C from 3.40(1) to 4.10(1) Å] in a η² fashion.