Long-term molecular dynamics simulations are used to compare the single particle dipole reorientation time, the diffusion constant, the viscosity, and the frequency-dependent dielectric constant of ...the coarse-grained big multipole water (BMW) model to two common atomistic three-point water models, SPC/E and TIP3P. In particular, the agreement between the calculated viscosity of BMW and the experimental viscosity of water is satisfactory. We also discuss contradictory values for the static dielectric properties reported in the literature. Employing molecular hydrodynamics, we show that the viscosity can be computed from single particle dynamics, circumventing the slow convergence of the standard approaches. Furthermore, our data indicate that the Kivelson relation connecting single particle and collective reorientation time holds true for all systems investigated. Since simulations with coarse-grained force fields often employ extremely large time steps, we also investigate the influence of time step on dynamical properties. We observe a systematic acceleration of system dynamics when increasing the time step. Carefully monitoring energy/temperature conservation is found to be a sufficient criterion for the reliable calculation of dynamical properties. By contrast, recommended criteria based on the ratio of fluctuations of total vs. kinetic energy are not sensitive enough.
Most proteins perform their function in aqueous solution. The interactions with water determine the stability of proteins and the desolvation costs of ligand binding or membrane insertion. However, ...because of experimental restrictions, absolute solvation free energies of proteins or amino acids are not available. Instead, solvation free energies are estimated based on side chain analog data. This approach implies that the contributions to free energy differences are additive, and it has often been employed for estimating folding or binding free energies. However, it is not clear how much the additivity assumption affects the reliability of the resulting data. Here, we use molecular dynamics–based free energy simulations to calculate absolute hydration free energies for 15 N-acetyl-methylamide amino acids with neutral side chains. By comparing our results with solvation free energies for side chain analogs, we demonstrate that estimates of solvation free energies of full amino acids based on group-additive methods are systematically too negative and completely overestimate the hydrophobicity of glycine. The largest deviation of additive protocols using side chain analog data was 6.7 kcal/mol; on average, the deviation was 4 kcal/mol. We briefly discuss a simple way to alleviate the errors incurred by using side chain analog data and point out the implications of our findings for the field of biophysics and implicit solvent models. To support our results and conclusions, we calculate relative protein stabilities for selected point mutations, yielding a root-mean-square deviation from experimental results of 0.8 kcal/mol.
Double decoupling absolute binding free energy simulations require an intermediate state at which the ligand is held solely by restraints in a position and orientation resembling the bound state. One ...possible choice consists of one distance, two angle, and three dihedral angle restraints. Here, I demonstrate that in practically all cases the analytical correction derived under the rigid rotator harmonic oscillator approximation is sufficient to account for the free energy of the restraints.
The use of the most accurate (i.e., QM or QM/MM) levels of theory for free energy simulations (FES) is typically not possible. Primarily, this is because the computational cost associated with the ...extensive configurational sampling needed for converging FES is prohibitive. To ensure the feasibility of QM-based FES, the “indirect” approach is generally taken, necessitating a free energy calculation between the MM and QM/MM potential energy surfaces. Ideally, this step is performed with standard free energy perturbation (Zwanzig’s equation) as it only requires simulations be carried out at the low level of theory; however, work from several groups over the past few years has conclusively shown that Zwanzig’s equation is ill-suited to this task. As such, many approximations have arisen to mitigate difficulties with Zwanzig’s equation. One particularly popular notion is that the convergence of Zwanzig’s equation can be improved by using interaction energy differences instead of total energy differences. Although problematic numerical fluctuations (a major problem when using Zwanzig’s equation) are indeed reduced, our results and analysis demonstrate that this “interaction energy approximation” (IEA) is theoretically incorrect, and the implicit approximation invoked is spurious at best. Herein, we demonstrate this via solvation free energy calculations using IEA from two different low levels of theory to the same target high level. Results from this proof-of-concept consistently yield the wrong results, deviating by ∼1.5 kcal/mol from the rigorously obtained value.
Non-equilibrium work switching simulations and Jarzynski's equation are a reliable method for computing free energy differences, ΔAlow→high, between two levels of theory, such as a pure molecular ...mechanical (MM) and a quantum mechanical/molecular mechanical (QM/MM) description of a system of interest. Despite the inherent parallelism, the computational cost of this approach can quickly become very high. This is particularly true for systems where the core region, the part of the system to be described at different levels of theory, is embedded in an environment such as explicit solvent water. We find that even for relatively simple solute-water systems, switching lengths of at least 5 ps are necessary to compute ΔAlow→high reliably. In this study, we investigate two approaches towards an affordable protocol, with an emphasis on keeping the switching length well below 5 ps. Inserting a hybrid charge intermediate state with modified partial charges, which resembles the charge distribution of the desired high level, makes it possible to obtain reliable calculations with 2 ps switches. Attempts using step-wise linear switching paths, on the other hand, did not lead to improvement, i.e., a faster convergence for all systems. To understand these findings, we analyzed the solutes' properties as a function of the partial charges used and the number of water molecules in direct contact with the solute, and studied the time needed for water molecules to reorient themselves upon a change in the solute's charge distribution.
The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force ...fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.
We present a new approach that incorporates flexibility based on extensive MD simulations of protein–ligand complexes into structure-based pharmacophore modeling and virtual screening. The approach ...uses the multiple coordinate sets saved during the MD simulations and generates for each frame a pharmacophore model. Pharmacophore models with the same pharmacophore features are pooled. In this way the high number of pharmacophore models that results from the MD simulation is reduced to only a few hundred representative pharmacophore models. Virtual screening runs are performed with every representative pharmacophore model; the screening results are combined and rescored to generate a single hit-list. The score for a particular molecule is calculated based on the number of representative pharmacophore models which classified it as active. Hence, the method is called common hits approach (CHA). The steps between the MD simulation and the final hit-list are performed automatically and without user interaction. We test the performance of CHA for virtual screening using screening databases with active and inactive compounds for 40 protein–ligand systems. The results of the CHA are compared to the (i) median screening performance of all representative pharmacophore models of protein–ligand systems, as well as to the virtual screening performance of (ii) a random classifier, (iii) the pharmacophore model derived from the experimental structure in the PDB, and (iv) the representative pharmacophore model appearing most frequently during the MD simulation. For the 34 (out of 40) protein–ligand complexes, for which at least one of the approaches was able to perform better than a random classifier, the highest enrichment was achieved using CHA in 68% of the cases, compared to 12% for the PDB pharmacophore model and 20% for the representative pharmacophore model appearing most frequently. The availabilithy of diverse sets of different pharmacophore models is utilized to analyze some additional questions of interest in 3D pharmacophore-based virtual screening.
Molecular dynamics simulations of twelve protein—ligand systems were used to derive a single, structure based pharmacophore model for each system. These merged models combine the information from the ...initial experimental structure and from all snapshots saved during the simulation. We compared the merged pharmacophore models with the corresponding PDB pharmacophore models, i.e., the static models generated from an experimental structure in the usual manner. The frequency of individual features, of feature types and the occurrence of features not present in the static model derived from the experimental structure were analyzed. We observed both pharmacophore features not visible in the traditional approach, as well as features which disappeared rapidly during the molecular dynamics simulations and which may well be artifacts of the initial PDB structure-derived pharmacophore model. Our approach helps mitigate the sensitivity of structure based pharmacophore models to the single set of coordinates present in the experimental structure. Further, the frequency with which specific features occur during the MD simulation may aid in ranking the importance of individual features.
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•Pharmacophore feature types display varying stability in MD simulations.•Features obtained from the crystal structure are on average stable.•Some features obtained from the crystal structure appear less than 10%.•Frequency information from MD simulations can be used to add/remove features.
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