Accurate prediction of protonation state as a prerequisite for reliable MM-PB(GB)SA binding free energy calculations of HIV-1 protease inhibitors

Binding free energies were calculated for the inhibitors lopinavir, ritonavir, saquinavir, indinavir, amprenavir, and nelfinavir bound to HIV-1 protease. An MMPB/SA-type analysis was applied to conformational samples from 3 ns explicit solvent molecular dynamics simulations of the enzyme-inhibitor complexes. Binding affinities and the sampled conformations of the inhibitor and enzyme were compared between different HIV-1 protease protonation states to find the most likely protonation state of the enzyme in the complex with each of the inhibitors. The resulting set of protonation states leads to good agreement between calculated and experimental binding affinities. Results from the MMPB/SA analysis are compared with an explicit/implicit hybrid scheme and with MMGB/SA methods. It is found that the inclusion of explicit water molecules may offer a slight advantage in reproducing absolute binding free energies while the use of the Generalized Born approximation significantly affects the accuracy of the calculated binding affinities.     

Analysis of biomolecular chaos in aqueous solution

 The tropoelastin peptide CH₃CO-Gly-Leu-Gly-Gly-NHCH₃ has been modeled in aqueous solution by means of force-field molecular dynamics simulations and its motion characterized using nonlinear dynamics theory. The trajectory R(t) of the representative system point in configurational space has been considered. Fractional Brownian motion with anomalous diffusion is observed resulting from chaotic dynamics of molecules on fractal media. The chaos of the peptide is a consequence of nonlinear effects such as hydrodynamic interactions of the chain due to the poor solvent role of water. The viscous drag is pointed out and should be due to the percolation network of hydrogen-bonded water molecules. The method of reconstruction of the phase space using the embedding theorem is applied to the trajectory D _ee(t) of the peptide end-to-end distance. The existence of a low-dimensional chaotic attractor for dissipative systems has been demonstrated. The dynamical high-entropy state of the peptide in solution strengthens the transition-to-chaos mechanism for the elastin elasticity. Received: 14 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

An atomistic model of passive membrane permeability: application to a series of FDA approved drugs

We apply an atomistic model of passive membrane permeability to a series of weakly basic drugs. The computational model uses conformational sampling in combination with an all-atom force field and implicit solvent model to estimate relative passive membrane permeabilities. The model does not require the use of training data for rank-ordering compounds, and as such represents a different approach from the more commonly employed QSPR models. We compare the computational results to previously published experimental PAMPA and Caco-2 permeabilities.     

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     

Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth-permittivity finite difference Poisson-Boltzmann method

A fast stable finite difference Poisson-Boltzmann (FDPB) model for implicit solvation in molecular dynamics simulations was developed using the smooth permittivity FDPB method implemented in the OpenEye ZAP libraries. This was interfaced with two widely used molecular dynamics packages, AMBER and CHARMM. Using the CHARMM-ZAP software combination, the implicit solvent model was tested on eight proteins differing in size, structure, and cofactors: calmodulin, horseradish peroxidase (with and without substrate analogue bound), lipid carrier protein, flavodoxin, ubiquitin, cytochrome c, and a de novo designed 3-helix bundle. The stability and accuracy of the implicit solvent simulations was assessed by examining root-mean-squared deviations from crystal structure. This measure was compared with that of a standard explicit water solvent model. In addition we compared experimental and calculated NMR order parameters to obtain a residue level assessment of the accuracy of MD-ZAP for simulating dynamic quantities. Overall, the agreement of the implicit solvent model with experiment was as good as that of explicit water simulations. The implicit solvent method was up to eight times faster than the explicit water simulations, and approximately four times slower than a vacuum simulation (i.e., with no solvent treatment).     

Recent advances in molecular dynamics simulation towards the realistic representation of biomolecules in solution

Coupled advances in empirical force fields and classical molecular dynamics simulation methodologies, combined with the availability of faster computers, has lead to significant progress towards accurately representing the structure and dynamics of biomolecular systems, such as proteins, nucleic acids, and lipids in their native environments. Thanks to these advances, simulation results are moving beyond merely evaluating force fields, displaying expected structural fluctuations, or demonstrating low root-mean-squared deviations from experimental structures and now provide believable structural insight into a variety of processes such as the stabilization of A-DNA in mixed water and ethanol solution or reversible β-peptide folding in methanol. The purpose of this overview is to take stock of these recent advances in biomolecular simulation and point out some common deficiencies exposed in longer simulations. The most significant methodological advances relate to the development of fast methods to properly treat long-range electrostatic interactions, and in this regard the fast Ewald methods are becoming the de facto standard. Received: 9 April 1998 / Accepted: 21 May 1998 / Published online: 13 August 1998     

An approximate but efficient method to calculate free energy trends by computer simulation: Application to dihydrofolate reductase-inhibitor complexes

Summary Derivatives of free energy differences have been calculated by molecular dynamics techniques. The systems under study were ternary complexes of Trimethoprim (TMP) with dihydrofolate reductases of E. coli and chicken liver, containing the cofactor NADPH. Derivatives are taken with respect to modification of TMP, with emphasis on altering the 3-, 4- and 5-substituents of the phenyl ring. A linear approximation allows the encompassing of a whole set of modifications in a single simulation, as opposed to a full perturbation calculation, which requires a separate simulation for each modification. In the case considered here, the proposed technique requires a factor of 1000 less computing effort than a full free energy perturbation calculation. For the linear approximation to yield a significant result, one has to find ways of choosing the perturbation evolution, such that the initial trend mirrors the full calculation. The generation of new atoms requires a careful treatment of the singular terms in the non-bonded interaction. The result can be represented by maps of the changed molecule, which indicate whether complex formation is favoured under movement of partial charges and change in atom polarizabilities. Comparison with experimental measurements of inhibition constants reveals fair agreement in the range of values covered. However, detailed comparison fails to show a significant correlation. Possible reasons for the most pronounced deviations are given.     

用分子动力学模拟方法研究磺酰脲化合物在溶液中构象的变化

农药化合物通常在溶液中起作用 ,由于溶剂的作用 ,其结构与在固体状态下有很大不同 ,因此研究农药化合物分子在溶液中结构的变化 ,对于了解农药作用机理以及与受体的相互作用是非常有意义的 .磺酰脲是一种超高效低毒 ,有着重要用途的除草剂 ,因而得到了广泛的应用与研究 .我们曾对其结构与性能的关系进行了系统的研究 ,并在此基础上建立了一个能解释若干实验规律的初级作用模型 [1] .但是以往有关结构的研究都是针对晶体和真空中的自由构象进行的 .由于在实际溶液中的结构情况会有所不同 ,因此 ,研究分子在不同溶液中的行为具有十分重要的意…     

Application of the thin-shell formulation to the numerical modeling of Stern layer in biomolecular electrostatics

In this article, the thin-shell formulation is applied to efficiently modeling the Stern layer within computational algorithms oriented toward the boundary element solution of the linearized Poisson-Boltzmann equation. The attention is focused on the calculation of the electrostatic potential in proximity to a biomolecule immersed in an electrolyte medium. Following the proposed approach, the Stern layer is made to collapse to a zero-thickness region (two-dimensional surface) with interface conditions linking the electrostatic potential over the molecular and the bulk ion accessible surfaces. Advantages lie in the limitation of divergent integral problems and in the halving of the unknown number, with a significant impact on computational time and memory requirements when modeling large biomolecules.     

The separation of enantiomers on modified cyclodextrin columns: Measurements and molecular modeling

The enantiomers of 2-chloropropionic acid methyl ester, cis-pinane, 2-bromoethylbenzene, 2-bromobutane, 2-hydroxybutane trifluoroacetyl ester, and styrene oxide have been resolved on an octakis-(3-O-butyryl-2,6-di-O-pentyl)-γ-cyclo-dextrin capillary column, and the separation of the styrene oxide enantiomers has also been studied on columns coated with octakis-(3-O-trifluoroacetyl-2,6-di-O-pentyl)-cyclodextrin, octakis-(2,3,6-tri-O-pentyl)-γ-cyclodextrin, heptakis-(3-O-trifluoroacetyl-2,6-di-O-pentyl)-β -cyclodextrin, and heptakis-(2,3,6-tri-O-methyl)-β-cyclodextrin. Thermodynamic parameters (ΔG, ΔH, and ΔS) were determined from variable temperature measurements. The inclusion complexes containing styrene oxide were also studied by molecular modeling techniques. It has been found that a combined molecular mechanics–molecular dynamics approach may be a valuable tool for rationalizing the qualitative trends observed in the experimental separation factors. For the inclusion complexes considered here it is shown that the orientation of the guest relative to the cyclodextrin host is determined by the size and polarity of the cyclodextrin.     

Force field evaluation for biomolecular simulation: free enthalpies of solvation of polar and apolar compounds in various solvents.

Recently, the GROMOS biomolecular force field parameter set 53A6--which has been parametrized to reproduce experimentally determined free enthalpies of hydration and solvation in cyclohexane of amino acid side-chain analogs--was presented. To investigate the transferability of the new parameter set, we calculated free enthalpies of solvation of a range of polar and apolar compounds in different solvents (methanol, dimethyl sulfoxide (DMSO), acetonitrile, and acetone) from molecular dynamics simulations using the GROMOS 53A6 force field. For methanol and DMSO, parameters were used that are available in the 53A6 parameter set. For acetonitrile, a recently developed model was taken and for acetone, two models available in literature were used. We found that trends in and values for the solvation free enthalpies are in satisfactory agreement with experiment, except for the solvation in acetone for which deviations from experiment can be explained in terms of the properties of the models used.     

Effective Born radii in the generalized Born approximation: the importance of being perfect

Generalized Born (GB) models provide, for many applications, an accurate and computationally facile estimate of the electrostatic contribution to aqueous solvation. The GB models involve two main types of approximations relative to the Poisson equation (PE) theory on which they are based. First, the self-energy contributions of individual atoms are estimated and expressed as "effective Born radii." Next, the atom-pair contributions are estimated by an analytical function f(GB) that depends upon the effective Born radii and interatomic distance of the atom pairs. Here, the relative impacts of these approximations are investigated by calculating "perfect" effective Born radii from PE theory, and enquiring as to how well the atom-pairwise energy terms from a GB model using these perfect radii in the standard f(GB) function duplicate the equivalent terms from PE theory. In tests on several biological macromolecules, the use of these perfect radii greatly increases the accuracy of the atom-pair terms; that is, the standard form of f(GB) performs quite well. The remaining small error has a systematic and a random component. The latter cannot be removed without significantly increasing the complexity of the GB model, but an alternative choice of f(GB) can reduce the systematic part. A molecular dynamics simulation using a perfect-radii GB model compares favorably with simulations using conventional GB, even though the radii remain fixed in the former. These results quantify, for the GB field, the importance of getting the effective Born radii right; indeed, with perfect radii, the GB model gives a very good approximation to the underlying PE theory for a variety of biomacromolecular types and conformations.     

Variation of atomic charges on proton transfer in strong hydrogen bonds: the case of anionic and neutral imidazole-acetate complexes

The variation of atomic charges upon proton transfer in hydrogen bonding complexes of 4-methylimidazole, in both neutral and protonated cationic forms, and acetate anion, is investigated. These complexes model the histidine (neutral and protonated)-aspartate pair present in active sites of proteases where strong N--H...O hydrogen bonds are formed. Three procedures (Merz-Kollman scheme, Natural Population Analysis, and Atoms in Molecules Method) are used to compute atomic charges and explore their variation upon H-transfer in the gas phase and in the presence of two continuum media with dielectric constants 5 (protein interiors) and 78.39 (water). The effect of electron correlation was also studied by comparing Hartree-Fock and MP2 results for both complexes in the gas phase. Greater net charge interchanged upon H-transfer is observed in the anionic complex with respect to the neutral complex. Raising the polarity of the medium increases the amount of net charge transfer in both complexes, although the neutral system exhibits a larger sensitivity to the presence of solvent. Charge transfer associated to N--H...O and N...H--O bonds reveal the ionic contribution to the interaction depending on the number of charged subunits but the presence of solvent affects little this quantity. The lack of electron correlation overestimates all the charges as well as their variations and so uncorrelated calculations should be avoided.     

Identification of novel Plasmodium falciparum PI4KB inhibitors as potential anti-malarial drugs: Homology modeling,molecular docking and molecular dynamics simulations

The current study was set to discover selective Plasmodium falciparum phosphatidylinositol-4-OH kinase type III beta (pfPI4KB) inhibitors as potential antimalarial agents using combined structure-based and ligand-based drug discovery approach. A comparative model of pfPI4KB was first constructed and validated using molecular docking techniques. Performance of Autodock4.2 and Vina4 software in predicting the inhibitor-PI4KB binding mode and energy was assessed based on two Test Sets: Test Set I contained five ligands with resolved crystal structures with PI4KB, while Test Set II considered eleven compounds with known IC50 value towards PI4KB. The outperformance of Autodock as compared to Vina was reported, giving a correlation coefficient (R²) value of 0.87 and 0.90 for Test Set I and Test Set II, respectively. Pharmacophore-based screening was then conducted to identify drug-like molecules from ZINC database with physicochemical similarity to two potent pfPI4KB inhibitors –namely cpa and cpb. For each query inhibitor, the best 1000 hits in terms of TanimotoCombo scores were selected and subjected to molecular docking and molecular dynamics (MD) calculations. Binding energy was then estimated using molecular mechanics–generalized Born surface area (MM-GBSA) approach over 50 ns MD simulations of the inhibitor-pfPI4KB complexes. According to the calculated MM-GBSA binding energies, ZINC78988474 and ZINC20564116 were identified as potent pfPI4KB inhibitors with binding energies better than those of cpa and cpb, with ΔG_binding ≥ −34.56 kcal/mol. The inhibitor-pfPI4KB interaction and stability were examined over 50 ns MD simulation; as well the selectivity of the identified inhibitors towards pfPI4KB over PI4KB was reported.     

Molecular dynamics simulation of acetamide solvation using interaction energy components: Application to structural and energy properties

Molecular dynamics simulation of an aqueous solution of acetamide was performed using Lennard–Jones 12-6-1 potentials to describe the solute–solvent interactions, and TIP3P to describe the water–water interactions. The Morokuma decomposition scheme and the ESIE solute atomic charges were used to reproduce the molecular parameters of the solute–water interaction potential. The results showed that the functions that use the EX-PL-DIS-ES interaction model lead to good values of the structural and energy properties (in particular, the hydration shell and the solvation energies) when they are compared with those from using AMBER-derived parameters, and with the available theoretical and experimental data.     

Numerical interpretation of molecular surface field in dielectric modeling of solvation

Continuum solvent models, particularly those based on the Poisson‐Boltzmann equation (PBE), are widely used in the studies of biomolecular structures and functions. Existing PBE developments have been mainly focused on how to obtain more accurate and/or more efficient numerical potentials and energies. However to adopt the PBE models for molecular dynamics simulations, a difficulty is how to interpret dielectric boundary forces accurately and efficiently for robust dynamics simulations. This study documents the implementation and analysis of a range of standard fitting schemes, including both one‐sided and two‐sided methods with both first‐order and second‐order Taylor expansions, to calculate molecular surface electric fields to facilitate the numerical calculation of dielectric boundary forces. These efforts prompted us to develop an efficient approximated one‐dimensional method, which is to fit the surface field one dimension at a time, for biomolecular applications without much compromise in accuracy. We also developed a surface‐to‐atom force partition scheme given a level set representation of analytical molecular surfaces to facilitate their applications to molecular simulations. Testing of these fitting methods in the dielectric boundary force calculations shows that the second‐order methods, including the one‐dimensional method, consistently perform among the best in the molecular test cases. Finally, the timing analysis shows the approximated one‐dimensional method is far more efficient than standard second‐order methods in the PBE force calculations. © 2017 Wiley Periodicals, Inc.