Calculation of ligand binding free energies from molecular dynamics simulations

A recently developed method for predicting binding affinities in ligand–receptor complexes, based on interaction energy averaging and conformational sampling by molecular dynamics simulation, is presented. Polar and nonpolar contributions to the binding free energy are approximated by a linear scaling of the corresponding terms in the average intermolecular interaction energy for the bound and free states of the ligand. While the method originally assumed the validity of electrostatic linear response, we show that incorporation of systematic deviations from linear response derived from free energy perturbation calculations enhances the accuracy of the approach. The method is applied to complexes of wild-type and mutant human dihydrofolate reductases with 2,4-diaminopteridine and 2,4-diaminoquinazoline inhibitors. It is shown that a binding energy accuracy of about 1 kcal/mol is attainable even for multiply ionized compounds, such as methotrexate, for which electrostatic interactions energies are very large. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 77–88, 1998     

Insight into herbicide resistance of W574L mutant Arabidopsis thaliana acetohydroxyacid synthase:molecular dynamics simulations and binding free energy calculations

Acetohydroxyacid synthase(AHAS) is the target enzyme of several classes of herbicides,such as sulfonylureas and imidazolinones.Now many mutant AHASs with herbicide resistance have emerged along with extensive use of herbicides,therefore it is imperative to understand the detailed interaction mechanism and resistance mechanism so as to develop new potent inhibitors for wild-type or resistant AHAS.With the aid of available crystal structures of the Arabidopsis thaliana(At) AHAS-inhibitor complex,molecular dyn...     

Insight into herbicide resistance of W574L mutant Arabidopsis thaliana acetohydroxyacid synthase: molecular dynamics simulations and binding free energy calculations

Acetohydroxyacid synthase (AHAS) is the target enzyme of several classes of herbicides, such as sulfonylureas and imidazolinones. Now many mutant AHASs with herbicide resistance have emerged along with extensive use of herbicides, therefore it is imperative to understand the detailed interaction mechanism and resistance mechanism so as to develop new potent inhibitors for wild-type or resistant AHAS. With the aid of available crystal structures of the Arabidopsis thaliana (At) AHAS-inhibitor complex, molecular dynamics (MD) simulations were used to investigate the interaction and resistance mechanism directly and dynamically at the atomic level. Nanosecond-level MD simulations were performed on six systems consisting of wild-type or W574L mutant AtAHAS in the complex with three sulfonylurea inhibitors, separately, and binding free energy was calculated for each system using the MM-GBSA method. Comprehensive analyses from structural and energetic aspects confirmed the importance of residue W574, and also indicated that W574L mutation might alert the structural charactersistic of the substrate access channel and decrease the binding affinity of inhibitors, which cooperatively weaken the effective channel-blocked effect and finally result in weaker inhibitory effect of inhibitor and corresponding herbicide resistance of W574L mutant. To our knowledge, it is the first report about MD simulations study on the AHAS-related system, which will pave the way to study the interactions between herbicides and wild-type or mutant AHAS dynamically, and decipher the resistance mechanism at the atomic level for better designing new potent anti-resistance herbicides.     

Insights into photodissociation dynamics of propionyl chloride from ab initio calculations and molecular dynamics simulations

The potential energy surfaces of isomerization, dissociation, and elimination reactions for CH3CH2COCl in the S0 and S1 states have been mapped with the different ab initio calculations. Mechanistic photodissociation of CH3CH2COCl at 266 nm has been characterized through the computed potential energy surfaces, the optimized surface crossing structure, intrinsic reaction coordinate, and ab initio molecular dynamics calculations. Photoexcitation at 266 nm leads to the CH3CH2COCl molecules in the S1 state. From this state, the C-Cl bond cleavage proceeds in a time scale of picosecond in the gas phase. The barrier to the C-Cl bond cleavage on the S1 surface is significantly increased by effects of the matrix and the internal conversion to the ground state prevails in the condensed phase. The HCl eliminations as a result of internal conversion to the ground state become the dominant channel upon photodissociation of CH3CH2COCl in the argon matrix at 10 K.     

Aggregation mechanism of polyglutamine diseases revealed using quantum chemical calculations, fragment molecular orbital calculations, molecular dynamics simulations, and binding free energy calculations

Polyglutamine (polyQ) diseases, including Huntington’s disease (HD), are caused by expansion of polyQ-encoding repeats within otherwise unrelated gene products. The aggregation mechanism of polyQ diseases, the inhibition mechanism of Congo red, and the alleviation mechanism of trehalose were proposed here based on quantum chemical calculations and molecular dynamics simulations. The calculations and simulations revealed the following. The effective molecular bonding is between glutamine (Gln) and Gln (Gln + Gln), between Gln and Congo red (Gln + Congo red), and between Gln and trehalose (Gln + trehalose). The bonding strength is −13.1 kcal/mol for Gln + Gln, −24.4 kcal/mol for Gln + Congo red, and −12.0 kcal/mol for Gln + trehalose. In the polyQ region, both the number of intermolecular Gln + Gln formations and the total calories generated by the Gln + Gln formation are proportional to the number of repetitions of Gln. We propose an aggregation mechanism whose heat generated by the intermolecular Gln + Gln formation causes the pathogeny of polyQ disease. In our aggregation mechanism, this generated heat collapses the host protein and promotes fibrillogenesis. Without contradiction, our mechanism can explain all the experimental results reported to date. Our mechanism can also explain the inhibition mechanism by Congo red as an inhibitor of polyglutamine-induced protein aggregation and the alleviation mechanism by trehalose as an alleviator of that aggregation. The inhibition mechanism by Congo red is explained by the strong interaction with Gln and by the characteristic structure of Congo red.     

Insights into mechanistic photodissociation of acetyl chloride by ab initio calculations and molecular dynamics simulations

The potential energy surfaces of dissociation and elimination reactions for CH(3)COCl in the ground (S0) and first excited singlet (S1) states have been mapped with the different ab inito calculations. Mechanistic photodissociation of CH(3)COCl has been characterized through the intrinsic reaction coordinate and ab initio molecular dynamics calculations. The alpha-C-C bond cleavage along the S1 pathway leads to the fragments of COCl((2)A' ') and CH(3) ((2)A') in an excited electronic state and a high barrier exists on the pathway. This channel is inaccessible in energy upon photoexcitation of the CH(3)COCl molecules at 236 nm. The S1 alpha-C-Cl bond cleavage yields the Cl((2)P) and CH(3)CO(X(2)A') fragments in the ground state and there is very small or no barrier on the pathway. The S1 alpha-C-Cl bond cleavage proceeds in a time scale of picosecond in the gas phase, followed by CH(3)CO decomposition to CH(3) and CO. The barrier to the C-Cl bond cleavage on the S1 surface is significantly increased by effects of the argon matrix. The S1 alpha-C-Cl bond cleavage in the argon matrix becomes inaccessible in energy upon photoexcitation of CH(3)COCl at 266 nm. In this case, the excited CH(3)COCl(S1) molecules cannot undergo the C-Cl bond cleavage in a short period. The internal conversion from S1 to S0 becomes the dominant process for the CH(3)COCl(S1) molecules in the condensed phase. As a result, the direct HCl elimination in the ground state becomes the exclusive channel upon 266 nm photodissociation of CH(3)COCl in the argon matrix at 11 K.     

Insights into uranyl chemistry from molecular dynamics simulations

First-principles and purely classical molecular dynamics (MD) simulations for complexes of the uranyl ion (UO(2)(2+)) are reviewed. Validation of Car-Parrinello MD simulations for small uranyl complexes in aqueous solution is discussed. Special attention is called to the mechanism of ligand-exchange reactions at the uranyl centre and to effects of solvation and hydration on coordination and structural properties. Large-scale classical MD simulations are surveyed in the context of liquid-liquid extraction, with uranyl complexes ranging from simple hydrates to calixarenes, and nonaqueous phases from simple organic solvents and supercritical CO(2) to ionic liquids.     

Adaptively biased molecular dynamics for free energy calculations

We present an adaptively biased molecular dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using nonequilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters and an O(t) numerical cost with molecular dynamics time t. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.     

Revealing binding selectivity of inhibitors toward bromodomain-containing proteins 2 and 4 using multiple short molecular dynamics simulations and free energy analyses

ABSTRACT

Emerging evidences indicate bromodomain-containing proteins 2 and 4 (BRD2 and BRD4) play critical roles in cancers, inflammations, cardiovascular diseases and other pathologies. Multiple short molecular dynamics (MSMD) simulations combined with molecular mechanics generalized Born surface area (MM-GBSA) method were applied to investigate the binding selectivity of three inhibitors 87D, 88M and 89G towards BRD2 over BRD4. The root-mean-square fluctuation (RMSF) analysis indicates that the structural flexibility of BRD4 is stronger than that of BRD2. Moreover the calculated distances between the C_α atoms in the centres of the ZA_loop and BC_loop of BRD4 are also bigger than that of BRD2. The rank of binding free energies calculated using MM-GBSA method agrees well with that determined by experimental data. The results show that 87D can bind more favourably to BRD2 than BRD4, while 88M has better selectivity on BRD4 over BRD2. Residue-based free-energy decomposition method was utilized to estimate the inhibitor-residue interaction spectrum and the results not only identify the hot interaction spots of inhibitors with BRD2 and BRD4, but also demonstrate that several common residues, including (W370, W374), (P371, P375), (V376, V380) and (L381, L385) belonging to (BRD2, BRD4), generate significant binding difference of inhibitors to BRD2 and BRD4.     

Computation of binding free energy with molecular dynamics and grand canonical Monte Carlo simulations

The binding of a ligand to a receptor is often associated with the displacement of a number of bound water molecules. When the binding site is exposed to the bulk region, this process may be sampled adequately by standard unbiased molecular dynamics trajectories. However, when the binding site is deeply buried and the exchange of water molecules with the bulk region may be difficult to sample, the convergence and accuracy in free energy perturbation (FEP) calculations can be severely compromised. These problems are further compounded when a reduced system including only the region surrounding the binding site is simulated. To address these issues, we couple molecular dynamics (MD) with grand canonical Monte Carlo (GCMC) simulations to allow the number of water to fluctuate during an alchemical FEP calculation. The atoms in a spherical inner region around the binding pocket are treated explicitly while the influence of the outer region is approximated using the generalized solvent boundary potential (GSBP). At each step during thermodynamic integration, the number of water in the inner region is equilibrated with GCMC and energy data generated with MD is collected. Free energy calculations on camphor binding to a deeply buried pocket in cytochrome P450cam, which causes about seven water molecules to be expelled, are used to test the method. It concluded that solvation free energy calculations with the GCMC/MD method can greatly improve the accuracy of the computed binding free energy compared to simulations with fixed number of water.     

FEW: A workflow tool for free energy calculations of ligand binding

In the later stages of drug design projects, accurately predicting relative binding affinities of chemically similar compounds to a biomolecular target is of utmost importance for making decisions based on the ranking of such compounds. So far, the extensive application of binding free energy approaches has been hampered by the complex and time‐consuming setup of such calculations. We introduce the free energy workflow (FEW) tool that facilitates setup and execution of binding free energy calculations with the AMBER suite for multiple ligands. FEW allows performing free energy calculations according to the implicit solvent molecular mechanics (MM‐PB(GB)SA), the linear interaction energy, and the thermodynamic integration approaches. We describe the tool's architecture and functionality and demonstrate in a show case study on Factor Xa inhibitors that the time needed for the preparation and analysis of free energy calculations is considerably reduced with FEW compared to a fully manual procedure. © 2013 Wiley Periodicals, Inc.     

Insights into the phosphoryl-transfer mechanism of cAMP-dependent protein kinase from quantum chemical calculations and molecular dynamics simulations

To investigate the molecular details of the phosphoryl-transfer mechanism catalyzed by cAMP-dependent protein kinase, we performed quantum mechanical (QM) calculations on a cluster model of the active site and molecular dynamics (MD) simulations of a ternary complex of the protein with Mg(2)ATP and a 20-residue peptide substrate. Overall, our theoretical results confirm the participation of the conserved aspartic acid, Asp(166), as an acid/base catalyst in the reaction mechanism catalyzed by protein kinases. The MD simulation shows that the contact between the nucleophilic serine side chain and the carboxylate group of Asp(166) is short and dynamically stable, whereas the QM study indicates that an Asp(166)-assisted pathway is structurally and energetically feasible and is in agreement with previous experimental results.     

Overcoming free energy barriers using unconstrained molecular dynamics simulations

Association of unconstrained molecular dynamics (MD) and the formalisms of thermodynamic integration and average force [Darve and Pohorille, J. Chem. Phys. 115, 9169 (2001)] have been employed to determine potentials of mean force. When implemented in a general MD code, the additional computational effort, compared to other standard, unconstrained simulations, is marginal. The force acting along a chosen reaction coordinate xi is estimated from the individual forces exerted on the chemical system and accumulated as the simulation progresses. The estimated free energy derivative computed for small intervals of xi is canceled by an adaptive bias to overcome the barriers of the free energy landscape. Evolution of the system along the reaction coordinate is, thus, limited by its sole self-diffusion properties. The illustrative examples of the reversible unfolding of deca-L-alanine, the association of acetate and guanidinium ions in water, the dimerization of methane in water, and its transfer across the water liquid-vapor interface are examined to probe the efficiency of the method.     

Fast and flexible gpu accelerated binding free energy calculations within the amber molecular dynamics package

Alchemical free energy (AFE) calculations based on molecular dynamics (MD) simulations are key tools in both improving our understanding of a wide variety of biological processes and accelerating the design and optimization of therapeutics for numerous diseases. Computing power and theory have, however, long been insufficient to enable AFE calculations to be routinely applied in early stage drug discovery. One of the major difficulties in performing AFE calculations is the length of time required for calculations to converge to an ensemble average. CPU implementations of MD‐based free energy algorithms can effectively only reach tens of nanoseconds per day for systems on the order of 50,000 atoms, even running on massively parallel supercomputers. Therefore, converged free energy calculations on large numbers of potential lead compounds are often untenable, preventing researchers from gaining crucial insight into molecular recognition, potential druggability and other crucial areas of interest. Graphics Processing Units (GPUs) can help address this. We present here a seamless GPU implementation, within the PMEMD module of the AMBER molecular dynamics package, of thermodynamic integration (TI) capable of reaching speeds of >140 ns/day for a 44,907‐atom system, with accuracy equivalent to the existing CPU implementation in AMBER. The implementation described here is currently part of the AMBER 18 beta code and will be an integral part of the upcoming version 18 release of AMBER. © 2018 Wiley Periodicals, Inc.     

Free energy calculations using flexible-constrained, hard-constrained and non-constrained molecular dynamics simulations.

A comparison of different treatments of bond-stretching interactions in molecular dynamics simulation is presented. Relative free energies from simulations using rigid bonds maintained with the SHAKE algorithm, using partially rigid bonds maintained with a recently introduced flexible constraints algorithm, and using fully flexible bonds are compared in a multi-configurational thermodynamic integration calculation of changing liquid water into liquid methanol. The formula for the free energy change due to a changing flexible constraint in a flexible constraint simulation is derived. To allow for a more direct comparison between these three methods, three different pairs of models for water and methanol were used: a flexible model (simulated without constraints and with flexible constraints), a rigid model (simulated with standard hard constraints), and an alternative flexible model (simulated with flexible constraints and standard hard constraints) in which the ideal or constrained bond lengths correspond to the average bond lengths obtained from a short simulation of the unconstrained flexible model. The particular treatment of the bonds induces differences of up to 2 % in the liquid densities, whereas (excess) free energy differences of up to 5.7 (4.3) kJ mol(-1) are observed. These values are smaller than the differences observed between the three different pairs of methanol/water models: up to 5 % in density and up to 8.5 kJ mol(-1) in (excess) free energy.     

Some practical aspects of free energy calculations from molecular dynamics simulation

In this work, we address two critical aspects of calculation of the free energy differences in molecular systems from molecular simulations. The first aspect involves checking whether the calculated free energy difference depends significantly on the extent of perturbation used for accomplishment of a given transformation. The second aspect of interest is to verify if the sampling errors in calculating the free energy differences between the wild-type molecule and a mutated one in its free state and in a complex are similar, or not, for a finite-length dynamic simulation. The reliability of the free energy estimates obtained from molecular simulations using thermodynamic cycles depends in part on this fact. For investigating these aspects, we use a self-transformation scheme in which a transformation of a part of a molecular system into itself is considered. We perform MD simulations of DNA fragments in which a part of a specific base is subjected to such a self-transformation. Results indicate that the estimated free energy differences do not depend significantly on the extent of perturbation used to achieve the transformation. Interestingly, the variation in the cumulative free energy difference, ΔA, with the coupling parameter, λ, depends significantly on the extent of perturbation. We examine the physical basis of the observed nature of the variation of the accumulated free energy difference, ΔA, against the λ value in the case of a self-transformation. In a thermodynamic cycle, the sampling errors due to the finite-length simulation for the molecular system are found to be similar to each other for the two perturbations (free and in a complex) justifying the use of such approach in calculating ΔΔA in molecular complexes. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 877–885, 1999     

A negative cooperativity mechanism of human CYP2E1 inferred from molecular dynamics simulations and free energy calculations

Human cytochrome P450 2E1 (CYP2E1) participates in the metabolism of over 2% of all the oral drugs. A hallmark peculiar feature of this enzyme is that it exhibits a pronounced negative cooperativity in substrate binding. However the mechanism by which the negative cooperativity occurs is unclear. Here, we performed molecular dynamics simulations and free energy calculations on human CYP2E1 to examine the structural differences between the substrate-free and the enzymes with one and two aniline molecules bound. Our results indicate that although the effector substrate does not bind in the active site cavity, it still can directly interact with the active site residues of human CYP2E1. The interaction of the effector substrate with the active site leads to a reorientation of active site residues, which thereby weakens the interactions of the active substrate with this site. We also identify a conserved residue T303 that plays a crucial role in the negative cooperative binding on the short-range effects. This residue is a key factor in the positioning of substrates and in proton delivery to the active site. Additionally, a long-range effect of the effector substrate is identified in which F478 is proposed to play a key role. As located in the interface between the active and effector sites, this residue structurally links the active and effector sites and is found to play a significant role in affecting substrate access and ligand positioning within the active site. In the negative cooperative binding, this residue can decrease the interactions of the active substrate with the active site by π-π stacking which then lowers the hydroxylation activity for the active substrate. These findings are in agreement with previous experimental observations and thus provide detailed atomistic insight into the poorly understood mechanism of the negative cooperativity in human CYP2E1.     

Computational studies on pseudorotaxanes by molecular dynamics and free energy perturbation simulations

A computational scheme that comprises the utilization of the AMBER force field with RESP charges and an explicit solvent model for acetonitrile proved to be useful for studying the structures and energetics of pseudorotaxanes of benzidine and 4,4'-biphenol with cyclobis(paraquat-p-phenylene). The scheme can be further utilized for modeling [2]rotaxanes.     

Minimum free energy pathways and free energy profiles for conformational transitions based on atomistic molecular dynamics simulations

An efficient method for the calculation of minimum free energy pathways and free energy profiles for conformational transitions is presented. Short restricted perturbation-targeted molecular dynamics trajectories are used to generate an approximate free energy surface. Approximate reaction pathways for the conformational change are constructed from one-dimensional line segments on this surface using a Monte Carlo optimization. Accurate free energy profiles are then determined along the pathways by means of one-dimensional adaptive umbrella sampling simulations. The method is illustrated by its application to the alanine "dipeptide." Due to the low computational cost and memory demands, the method is expected to be useful for the treatment of large biomolecular systems.     

Studies of the mechanism of selectivity of protein tyrosine phosphatase 1B (PTP1B) bidentate inhibitors using molecular dynamics simulations and free energy calculations

Bidentate inhibitors of protein tyrosine phosphatase 1B (PTP1B) are considered as a group of ideal inhibitors with high binding potential and high selectivity in treating type II diabetes. In this paper, the binding models of five bidentate inhibitors to PTP1B, TCPTP, and SHP-2 were investigated and compared by using molecular dynamics (MD) simulations and free energy calculations. The binding free energies were computed using the Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) methodology. The calculation results show that the predicted free energies of the complexes are well consistent with the experimental data. The Molecular Mechanics/Generalized Born Surface Area (MM/GBSA) free energy decomposition analysis indicates that the residues ARG24, ARG254, and GLN262 in the second binding site of PTP1B are essential for the high selectivity of inhibitors. Furthermore, the residue PHE182 close to the active site is also important for the selectivity and the binding affinity of the inhibitors. According to our analysis, it can be concluded that in most cases the polarity of the portion of the inhibitor that binds to the second binding site of the protein is positive to the affinity of the inhibitors while negative to the selectivity of the inhibitors. We expect that the information we obtained here can help to develop potential PTP1B inhibitors with more promising specificity.