Mihaly Mezei

Molecular Docking: A powerful approach for structure-based drug discovery

Molecular docking has become an increasingly important tool for drug discovery. In this review, we present a brief introduction of the available molecular docking methods, and their development and applications in drug discovery. The relevant basic theories, including sampling algorithms and scoring functions, are summarized. The differences in and performance of available docking software are also discussed. Flexible receptor molecular docking approaches, especially those including backbone flexibility in receptors, are a challenge for available docking methods. A recently developed Local Move Monte Carlo (LMMC) based approach is introduced as a potential solution to flexible receptor docking problems. Three application examples of molecular docking approaches for drug discovery are provided.

Free Energy Simulationsa

Monte Carlo or molecular dynamics simulations involve the numerical determinations of the statistical thermodynamics and related structural, energetic and (in the case of molecular dynamics) dynamic properties of an atomic or molecular assembly on a high-speed digital computer. Applications to molecular systems range from the study of the motions of atoms or groups of atoms of a molecule or macromolecule under the influence of intramolecular energy functions to the exploration of the structure and energetics of condensed fluid phases such as liquid water and aqueous solutions based on intermolecular potentials. The quantities determined in a typical Monte Carlo or molecular dynamics simulation include the average or mean configurational energy (thermodynamic excess internal energy), various spatial distribution functions for equilibrium systems, and time-correlation functions for dynamical systems, along with detailed structural and energetic analyses thereof. Diverse problems in structural and reaction chemistry of molecules in solution, such as solvation potentials, solvent effects on conformational stability and the effect of solvent on chemical reaction kinetics and mechanism via activated complex theory also require a particular knowledge of the configurational free energy, which in principle follows directly from the statistical thermodynamic partition function for the system. Considerations on free energy in molecular simulations take a distinctly different form for intramolecular and intermolecular degrees of freedom. For the intramolecular case, the problem involves vibrational and librational modes of motion on the intramolecular energy surface. We will discuss briefly a t the end of this paper the harmonic and quasiharmonic approximation used to compute vibrational contributions to the free energy, but we will restrict the focus herein to the intermolecular case, where the particles of the system undergo diffusional motion and a harmonic or quasiharmonic treatment breaks down. These considerations apply also in the case of a flexible molecule, where conformational transitions are effectively an intramolecular “diffusional mode.” Conventional Monte Carlo and molecular dynamics procedures for diffusional modes, although firmly grounded in Boltzmann statistical mechanics and dynamics, do not proceed via the direct determination of a partition function because of well-known

Monte Carlo studies of the structure of dilute aqueous sclutions of Li+, Na+, K+, F−, and Cl−

Monte Carlo–Metropolis statistical thermodynamic computer simulations are reported for dilute aqueous solutions of Li+, Na+, K+, F−, and Cl−. The calculations are carried out on systems consisting of one ion and 215 water molecules at 25 °C and experimental densities. The condensed phase environment is modeled using periodic boundary conditions. The configurational energies are developed under the assumption of pairwise additivity by means of potential functions representative of nonempirical quantum mechanical calculations of the ion–water and water–water energies. The internal energies, radial distribution functions, and related thermodynamic properties are calculated for each system. The structure of the local solution environment around each dissolved ion is analyzed in terms of quasicomponent distribution functions. The results are compared with analogous calculations on a smaller system to estimate the effect of long‐range forces in the ion–water potential function on the calculated results.

A cavity-biased (T, V, μ) Monte Carlo method for the computer simulation of fluids

A modified sampling technique is proposed for use in Monte Carlo calculations in the grand canonical ensemble. The new method, called the cavity-biased (T, V, μ) Monte Carlo procedure, attempts insertions of new particles into existing cavities in the system instead of at randomly selected points. Calculations on supercritical Lennard-Jones fluid showed an 8-fold increase in the efficiency of the insertion process using the new method. The highest density that can be successfully treated was raised by 35 per cent, making part of the liquid region of the Lennard-Jones fluid now accessible to theoretical study by this method.

Theoretical studies of hydrogen bonding in liquid water and dilute aqueous solutions

Monte Carlo computer simulations of liquid water and dilute aqueous solutions are analyzed in terms of the nature and extent of intermolecular hydrogen bonding. A geometric definition of the hydrogen bond is used. Calculations on liquid water at 25 °C, 37 °C, and 50 °C, were carried out based on the quantum mechanical MCY potential of Matsuoka, Clementi, and Yoshimine and at 10 °C based on the empirical ST2 potential. The effect of a dissolved solute on aqueous hydrogen bonding was studied for dilute aqueous solutions of Li+, Na+, K+, F−, Cl−, and CH4. The nature of the hydrogen bonding was characterized with quasicomponent distribution functions defined as a function of the intermolecular coordinates relevant to hydrogen bonding. The extent of the hydrogen bonding is described using a network analysis approach developed by Geiger, Stillinger, and Rahman. The results on the quasicomponent distribution functions show that the average hydrogen bond angle deviates with 10 °–25 ° from a linear form, quite ind...

Adaptive umbrella sampling: Self-consistent determination of the non-Boltzmann bias

A self-consistent procedure is described for the determination of the non-Boltzmann bias for the umbrella sampling technique of Valleau, Patey, and Torrie. The new procedure offers more reliable results with less human interference. The problem of matching several differently normalized probability distributions on overlapping domains has been treated in detail. The algorithm has been tested on the calculation of the solvent contribution to the free energy difference between the C7 and αR conformation of the alanine dipeptide, treated earlier with the conventional umbrella sampling technique.

Polyproline II helix is the preferred conformation for unfolded polyalanine in water

Does aqueous solvent discriminate among peptide conformers? To address this question, we computed the solvation free energy of a blocked, 12‐residue polyalanyl‐peptide in explicit water and analyzed its solvent structure. The peptide was modeled in each of 4 conformers: α‐helix, antiparallel β‐strand, parallel β‐strand, and polyproline II helix (PII). Monte Carlo simulations in the canonical ensemble were performed at 300 K using the CHARMM 22 forcefield with TIP3P water. The simulations indicate that the solvation free energy of PII is favored over that of other conformers for reasons that defy conventional explanation. Specifically, in these 4 conformers, an almost perfect correlation is found between a residues solvent‐accessible surface area and the volume of its first solvent shell, but neither quantity is correlated with the observed differences in solvation free energy. Instead, solvation free energy tracks with the interaction energy between the peptide and its first‐shell water. An additional, previously unrecognized contribution involves the conformation‐dependent perturbation of first‐shell solvent organization. Unlike PII, β‐strands induce formation of entropically disfavored peptide:water bridges that order vicinal water in a manner reminiscent of the hydrophobic effect. The use of explicit water allows us to capture and characterize these dynamic water bridges that form and dissolve during our simulations. Proteins 2004.

Grand-canonical ensemble Monte Carlo study of dense liquid Lennard-Jones, soft spheres and water

The cavity biased Monte Carlo method for the (T, V, μ) ensemble has been tested on a system of Lennard-Jones particles near the triple point in the liquid and fluid state, on a system of dense soft spheres and on liquid water at room temperature. We demonstrate that the original (T, V, μ) algorithm of Adams is capable to provide accurate density at much higher densities than it was originally thought possible.

Convergence characteristics of Monte Carlo–Metropolis computer simulations on liquid water

Very long (∼5000 K) Monte Carlo computer simulations are reported for liquid water described in terms of the analytical potential functions of Matsuoka, Clementi, and Yoshimine and Rahman and Stillinger’s empirical ST2 potential. The convergence characteristics of both realizations are fully developed in terms of internal energy, heat capacity molecular distribution functions, and structural indices. A hierarchy in the calculated properties emerges with respect to the degree of computational effort required to obtain reproducible results. Mean energy and radial distribution functions are the most accessible quantities. Fluctuation properties such as heat capacity require roughly twice as many configurations to stabilize as simple orientational averaged quantities. The structural changes over the equilibrated segments of the realization were examined in terms of quasicomponent distribution functions and found to be small in chemical terms.

The finite difference thermodynamic integration, tested on calculating the hydration free energy difference between acetone and dimethylamine in water

A new technique is proposed to compute by Monte Carlo (or molecular dynamics) computer simulation the hydration free energy differences. The method, called finite difference thermodynamic integration, is a combination of the thermodynamic integration and the perturbation method. It was compared with thermodynamic integration over two different paths and the perturbation method on computing the solvation free‐energy difference between the dilute aqueous solution of acetone and dimethyl amine. Finite difference thermodynamic integration was found to have the best convergence characteristics among the methods tested.