MMP-2和Hydroxamate类抑制剂绝对自由能的计算

采用基于线性响应近似的自由能计算方法计算了一类hydroxamate抑制剂和MMP-2的绝对结合自由能。计算中,催化锌离子和MMP-2以及配体之间采用了非键模型。分子动力学模拟结果显示,采用非键模型时,催化Zn离子采用五配位的形式,但配位键的形式和初始结构比较有很大的差别。通过拟合,分别得到了单参数、双参数以及三参数的自由能预测模型,其中,含有常数校正项的三参数模型具有最佳的预测能力,预测自由能和实际自由能之间平均绝对误差仅为2.38kJ/mol。     

Binding free energy, energy and entropy calculations using simple model systems

Free energy differences are calculated for a set of two model host molecules, binding acetone and methanol. Two active sites of different characteristics were constructed based on an artificially extended C60 fullerene molecule, possibly functionalised to include polar interactions in an otherwise apolar, spherical cavity. The model host systems minimise the necessary sampling of conformational space while still capturing key aspects of ligand binding. The estimates of the free energies are split up into energetic and entropic contributions, using three different approaches investigating the convergence behaviour. For these systems, a direct calculation of the total energy and entropy is more efficient than calculating the entropy from the temperature dependence of the free energy or from a direct thermodynamic integration formulation. Furthermore, the compensating surrounding–surrounding energies and entropies are split off by calculating reduced ligand-surrounding energies and entropies. These converge much more readily and lead to properties that are more straightforwardly interpreted in terms of molecular interactions and configurations. Even though not experimentally accessible, the reduced thermodynamic properties may prove highly relevant for computational drug design, as they may give direct insights into possibilities to further optimise ligand binding while optimisation in the surrounding–surrounding energy or entropy will exactly cancel and not lead to improved affinity.     

Binding free energy calculations to rationalize the interactions of huprines with acetylcholinesterase

In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.     

Binding free energy contributions of interfacial waters in HIV-1 protease/inhibitor complexes

Water molecules are commonly observed in crystal structures of protein-ligand complexes where they mediate protein-ligand binding. It is of considerable theoretical and practical importance to determine quantitatively the individual free energy contributions of these interfacial water molecules to protein-ligand binding and to elucidate factors that influence them. The double-decoupling free energy molecular dynamics simulation method has been used to calculate the binding free energy contribution for each of the four interfacial water molecules observed in the crystal structure of HIV-1 protease complexed with KNI-272, a potent inhibitor. While two of these water molecules contribute significantly to the binding free energy, the other two have close to zero contribution. It was further observed that the protonation states of two catalytic aspartate residues, Asp25 and Asp125, strongly influence the free energy contribution of a conserved water molecule Wat301 and that different inhibitors significantly influence the free energy contribution of Wat301. Our results have important implications on our understanding of the role of interfacial water molecules in protein-ligand binding and to structure-based drug design aimed at incorporating these interfacial water molecules into ligands.     

Gamma-point lattice free energy estimates from O1 force calculations

We present a new method for estimating the vibrational free energy of crystal (and molecular) structures employing only a single force calculation, for a particularly displaced configuration, in addition to the calculation of the ground state configuration. This displacement vector is the sum of the phonon eigenvectors obtained from a fast-relative to, e.g., density-functional theory (DFT)-Hessian calculation using interatomic potentials. These potentials are based here on effective charges obtained from a DFT calculation of the ground state electronic charge density but could also be based on other, e.g., empiric approaches.     

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     

Atomic energy levels from configuration interaction calculations with relativistic corrections

It is shown that configuration interaction calculations, with inclusion of the relativistic corrections, constitute an appropriate approach for the prediction of atomic energy levels and that results of experimental accuracy are possible given the availability of large-scale, fast computers. The results obtained for He through F emphasize both the practical difficulties to be encountered and the possibility of predictions with less than 1% error.     

Alchemical free energy calculations and multiple conformational substates

Thermodynamic integration (TI) was combined with (adaptive) umbrella sampling to improve the convergence of alchemical free energy simulations in which multiple conformational substates are present. The approach, which we refer to as non-Boltzmann TI (NBTI), was tested by computing the free energy differences between three five-atomic model systems, as well as the free energy difference of solvation between leucine and asparagine. In both cases regular TI failed to give converged results, whereas the NBTI results were free from hysteresis and had standard deviations well below +/-0.7 kcal/mole. We also present theoretical considerations that make it possible to compute free energy differences between simple molecules, such as the five-atomic model systems, by numerical integration of the partition functions at the respective end points.     

Extending fragment-based free energy calculations with library Monte Carlo simulation: annealing in interaction space

Pre-calculated libraries of molecular fragment configurations have previously been used as a basis for both equilibrium sampling (via library-based Monte Carlo) and for obtaining absolute free energies using a polymer-growth formalism. Here, we combine the two approaches to extend the size of systems for which free energies can be calculated. We study a series of all-atom poly-alanine systems in a simple dielectric solvent and find that precise free energies can be obtained rapidly. For instance, for 12 residues, less than an hour of single-processor time is required. The combined approach is formally equivalent to the annealed importance sampling algorithm; instead of annealing by decreasing temperature, however, interactions among fragments are gradually added as the molecule is grown. We discuss implications for future binding affinity calculations in which a ligand is grown into a binding site.     

Guidelines for the analysis of free energy calculations

Journal of Computer-Aided Molecular Design - Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of...     

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.     

Efficient free energy calculations on small molecule host-guest systems - a combined linear interaction energy/one-step perturbation approach

Two efficient methods to calculate binding affinities of ligands with proteins have been critically evaluated by using sixteen small ligand host-guest complexes. It is shown that both the one-step (OS) perturbation method and the linear interaction energy (LIE) method have complementing strengths and weaknesses and can be optimally combined in a new manner. The OS method has a sound theoretical basis to address the free energy of cavity formation, whereas the LIE approach is more versatile and efficient to calculate the free energy of adding charges to such cavities. The off-term, which is neglected in the original LIE equation, can be calculated without additional costs from the OS, offering a powerful synergy between the two methods. The LIE/OS approach presented here combines the best of two worlds and for the model systems studied here, is more accurate than and as efficient as the original methods. It has a sound theoretical background and no longer requires any empirical parameters. The method appears very well suited for application in lead-optimization programmes in drug research, where the structure and dynamics of a series of molecules is of interest, together with an accurate calculation of the binding free energy.     

Systematic and statistical error in histogram-based free energy calculations

A common technique for the numerical calculation of free energies involves estimation of the probability density along a given coordinate from a set of configurations generated via simulation. The process requires discretization of one or more reaction coordinates to generate a histogram from which the continuous probability density is inferred. We show that the finite size of the intervals used to construct the histogram leads to quantifiable systematic error. The width of these intervals also determines the statistical error in the free energy, and the choice of the appropriate interval is therefore driven by the need to balance the two sources of error. We present a method for the construction of the optimal histogram for a given system, and show that the use of this technique requires little additional computational expense. We demonstrate the efficacy of the technique for a model system, and discuss how the principles governing the choice of discretization interval could be used to improve extended sampling techniques.     

Evaluation of the 1-octanol/water partition coefficient of nucleoside analogs via free energy estimated in quantum chemical calculations

The partition coefficients (logP) of nucleoside analogs determined by the difference in the free energies of hydration and solvation in water-saturated octanol using the thermodynamic integration method are reported. The logP values calculated in this approach are closer to the experimental values compared to other ab initio methods. Solvation free energy in water and octanol, free energy of cavity formation in water and Henry’s constants, and some other parameters are estimated at the density functional theory (DFT) and Hartree-Fock level with 6–31G*, 6–31G, and 6–31+G basis sets. Surface area, mass, refractivity, volume, polarizability, and dipole moment are calculated for some drugs with HF and DFT methods. The results show that log P decreases with the decrease in polarizability and the increase in dipole moment.     

Spectral studies and crystal structures of molybdenum(VI) complexes containing pyridine or picoline as auxiliary ligands: interaction energy calculations and free radical scavenging studies

Transition Metal Chemistry - Three cis-MoO2 complexes [MoO2(CAB)(py)] (1), [MoO2(CAB)(3-pic)] (2) and [MoO2(CAB)(4-pic)] (3) which vary in the nature of the heterocyclic bases in...     

Binding interactions of EDCs to human estrogen-related receptor gamma deciphered by multiple molecular dynamics and energy calculations

Dichloro-diphenyl-trichloroethane (DDT) analogs, classified as environmental endocrine disrupting compounds (EDCs), have been extensively employed as potent insecticides that can cause endocrine system disruption. However, the precise dynamic structural characteristics and interactions between human estrogen-related receptor gamma (hERRγ) and DDT analogs are not yet fully understood. In this study, we comprehensively investigate the impact of these EDCs (DDT, dichloro-diphenyl-dichloroethane (DDD), 2,2-bis(4-chlorophenyl)ethanol (DDOH), O,P′-DDT (2,4′-DDT), 4,4′-dichlorobenzophenone (DCBP), and 4-hydrotamoxifen (4-OHT) on the structural changes of hERRγ and their interaction mechanisms by employing multiple molecular dynamics (MD) simulations coupled with MM-PBSA and SIE approaches. The consequence manifested that overall structures of these six complexes did not transform markedly, but these compounds can affect the local hERRγ structure, leading to essential changes in interactions with pivotal residues nearby L268, V313, L309, Y326, and F435. And van der Waals interactions are the key to how these EDCs interact with hERRγ. These outcomes contribute to our comprehension the risks of DDT analogues to human health.     

L-Enantiomers of transition state analogue inhibitors bound to human purine nucleoside phosphorylase

Human purine nucleoside phosphorylase (PNP) was crystallized with transition-state analogue inhibitors Immucillin-H and DADMe-Immucillin-H synthesized with ribosyl mimics of l-stereochemistry. The inhibitors demonstrate that major driving forces for tight binding of these analogues are the leaving group interaction and the cationic mimicry of the transition state, even though large geometric changes occur with d-Immucillins and l-Immucillins bound to human PNP.     

Rational determination of charge distributions for free energy calculations

Point charges derived from RHF/6-31G* electrostatic potentials are attractive because they tend to exaggerate the polarity of solvated molecules, thereby compensating in an average fashion missing induction effects. In the context of free energy calculations, wherein the molecule is transferred from a polar environment to a nonpolar one, we propose a more rational approach based on a self-consistent reaction field computation at a higher level of theory, supplemented by an estimation of the corresponding distortion energy to account for the change of polarity of the surroundings. Application of this method to the test cases acetamide, acetic acid, methyl acetate and phenol, using multinanosecond molecular dynamics/"umbrella sampling" simulations, yields consistent hydration free energies in reasonably good agreement with experiment.     

Basic ingredients of free energy calculations: A review

Methods to compute free energy differences between different states of a molecular system are reviewed with the aim of identifying their basic ingredients and their utility when applied in practice to biomolecular systems. A free energy calculation is comprised of three basic components: (i) a suitable model or Hamiltonian, (ii) a sampling protocol with which one can generate a representative ensemble of molecular configurations, and (iii) an estimator of the free energy difference itself. Alternative sampling protocols can be distinguished according to whether one or more states are to be sampled. In cases where only a single state is considered, six alternative techniques could be distinguished: (i) changing the dynamics, (ii) deforming the energy surface, (iii) extending the dimensionality, (iv) perturbing the forces, (v) reducing the number of degrees of freedom, and (vi) multi‐copy approaches. In cases where multiple states are to be sampled, the three primary techniques are staging, importance sampling, and adiabatic decoupling. Estimators of the free energy can be classified as global methods that either count the number of times a given state is sampled or use energy differences. Or, they can be classified as local methods that either make use of the force or are based on transition probabilities. Finally, this overview of the available techniques and how they can be best used in a practical context is aimed at helping the reader choose the most appropriate combination of approaches for the biomolecular system, Hamiltonian and free energy difference of interest. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010