Estimating relative free energies from a single ensemble: Hydration free energies

Efficient In Silico Saturation Mutagenesis of a Member of the Caspase Protease Family

Rational-design methods have proven to be a valuable toolkit in the field of protein design. Numerical approaches such as free-energy calculations or QM/MM methods are fit to widen the understanding of a protein-sequence space but require large amounts of computational time and power. Here, we apply an efficient method for free-energy calculations that combines the one-step perturbation (OSP) with the third-power-fitting (TPF) approach. It is fit to calculate full free energies of binding from three different end states only. The nonpolar contribution to the free energies are calculated for a set of chosen amino acids from a single simulation of a judiciously chosen reference state. The electrostatic contributions, on the other hand, are predicted from simulations of the neutral and charged end states of the individual amino acids. We used this method to perform in silico saturation mutagenesis of two sites in human Caspase-2. We calculated relative binding free energies toward two different substrates that differ in their P1' site and in their affinity toward the unmutated protease. Although being approximate, our approach showed very good agreement upon validation against experimental data. 76% of the predicted relative free energies of amino acid mutations was found to be true positives or true negatives. We observed that this method is fit to discriminate amino acid mutations because the rate of false negatives is very low (<1.5%). The approach works better for a substrate with medium/low affinity with a Matthews correlation coefficient (MCC) of 0.63, whereas for a substrate with very low affinity, the MCC was 0.38. In all cases, the combined TPF + OSP approach outperformed the linear interaction energy method.

An Alternative to Conventional λ-Intermediate States in Alchemical Free Energy Calculations: λ-Enveloping Distribution Sampling

Alchemical free energy calculations typically rely on intermediate states to bridge between the relevant phase spaces of the two end states. These intermediate states are usually created by mixing the energies or parameters of the end states according to a coupling parameter λ. The choice of the procedure has a strong impact on the efficiency of the calculation, as it affects both the encountered energy barriers and the phase space overlap between the states. The present work builds on the connection between the minimum variance pathway (MVP) and enveloping distribution sampling (EDS). It is shown that both methods can be regarded as special cases of a common scheme referred to as λ-EDS, which can also reproduce the behavior of conventional λ-intermediate states. A particularly attractive feature of λ-EDS is its ability to emulate the use of soft core potentials (SCP) while avoiding the associated computational overhead when applying efficient free energy estimators such as the multistate Bennett's acceptance ratio (MBAR). The method is illustrated for both relative and absolute free energy calculations considering five benchmark systems. The first two systems (charge inversion and cavity creation in a dipolar solvent) demonstrate the use of λ-EDS as an alternative coupling scheme in the context of thermodynamic integration (TI). The three other systems (change of bond length, change of dihedral angles, and cavity creation in water) investigate the efficiency and optimal choice of parameters in the context of free energy perturbation (FEP) and Bennett's acceptance ratio (BAR). It is shown that λ-EDS allows larger steps along the alchemical pathway than conventional intermediate states.

Alchemical Free-Energy Calculations by Multiple-Replica λ-Dynamics: The Conveyor Belt Thermodynamic Integration Scheme

A new method is proposed to calculate alchemical free-energy differences based on molecular dynamics (MD) simulations, called the conveyor belt thermodynamic integration (CBTI) scheme. As in thermodynamic integration (TI), K replicas of the system are simulated at different values of the alchemical coupling parameter λ. The number K is taken to be even, and the replicas are equally spaced on a forward-turn-backward-turn path, akin to a conveyor belt (CB) between the two physical end-states; and as in λ-dynamics (λD), the λ-values associated with the individual systems evolve in time along the simulation. However, they do so in a concerted fashion, determined by the evolution of a single dynamical variable Λ of period 2π controlling the advance of the entire CB. Thus, a change of Λ is always associated with K/2 equispaced replicas moving forward and K/2 equispaced replicas moving backward along λ. As a result, the effective free-energy profile of the replica system along Λ is periodic of period 2 πK^-1, and the magnitude of its variations decreases rapidly upon increasing K, at least as K^-1 in the limit of large K. When a sufficient number of replicas is used, these variations become small, which enables a complete and quasi-homogeneous coverage of the λ-range by the replica system, without application of any biasing potential. If desired, a memory-based biasing potential can still be added to further homogenize the sampling, the preoptimization of which is computationally inexpensive. The final free-energy profile along λ is calculated similarly to TI, by binning of the Hamiltonian λ-derivative as a function of λ considering all replicas simultaneously, followed by quadrature integration. The associated quadrature error can be kept very low owing to the continuous and quasi-homogeneous λ-sampling. The CBTI scheme can be viewed as a continuous/deterministic/dynamical analog of the Hamiltonian replica-exchange/permutation (HRE/HRP) schemes or as a correlated multiple-replica analog of the λD or λ-local elevation umbrella sampling (λ-LEUS) schemes. Compared to TI, it shares the advantage of the latter schemes in terms of enhanced orthogonal sampling, i.e. the availability of variable-λ paths to circumvent conformational barriers present at specific λ-values. Compared to HRE/HRP, it permits a deterministic and continuous sampling of the λ-range, is expected to be less sensitive to possible artifacts of the thermo- and barostating schemes, and bypasses the need to carefully preselect a λ-ladder and a swapping-attempt frequency. Compared to λ-LEUS, it eliminates (or drastically reduces) the dead time associated with the preoptimization of a biasing potential. The goal of this article is to provide the mathematical/physical formulation of the proposed CBTI scheme, along with an initial application of the method to the calculation of the hydration free energy of methanol.

Saturation Mutagenesis by Efficient Free-Energy Calculation

Single-point mutations in proteins can greatly influence protein stability, binding affinity, protein function or its expression per se. Here, we present accurate and efficient predictions of the free energy of mutation of amino acids. We divided the complete mutational free energy into an uncharging step, which we approximate by a third-power fitting (TPF) approach, and an annihilation step, which we approximate using the one-step perturbation (OSP) method. As a diverse set of test systems, we computed the solvation free energy of all amino acid side chain analogues and obtained an excellent agreement with thermodynamic integration (TI) data. Moreover, we calculated mutational free energies in model tripeptides and established an efficient protocol involving a single reference state. Again, the approximate methods agreed excellently with the TI references, with a root-mean-square error of only 3.6 kJ/mol over 17 mutations. Our combined TPF+OSP approach does show not only a very good agreement but also a 2-fold higher efficiency than full blown TI calculations.

The role of intramolecular nonbonded interaction and angle sampling in single-step free energy perturbation

Single-step free energy perturbation (sFEP) has often been proposed as an efficient tool for a quick free energy scan due to its straightforward protocol and the ability to recycle an existing molecular dynamics trajectory for free energy calculations. Although sFEP is expected to fail when the sampling of a system is inefficient, it is often expected to hold for an alchemical transformation between ligands with a moderate difference in their sizes, e.g., transforming a benzene into an ethylbenzene. Yet, exceptions were observed in calculations for anisole and methylaniline, which have similar physical sizes as ethylbenzene. In this study, we show that such exceptions arise from the sampling inefficiency on an unexpected rigid degree of freedom, namely, the bond angle θ. The distributions of θ differ dramatically between two end states of a sFEP calculation, i.e., the conformation of the ligand changes significantly during the alchemical transformation process. Our investigation also reveals the interrelation between the ligand conformation and the intramolecular nonbonded interactions. This knowledge suggests a best combination of the ghost ligand potential and the dual topology setting, which improves the accuracy in a single reference sFEP calculation by bringing down its error from around 5k_BT to k_BT.

Combination of a Dielectric Continuum Model with Inverse Gas Chromatography for the Characterization of Solid Surfaces

The use of a dielectric continuum model for the characterization of solid surfaces was combined for the first time with inverse gas chromatography. Extension of dielectric continuum models to adsorption from the gaseous phase allowed the distributed surface properties of solid surfaces to be determined. An inverse gas chromatograph was used for the measurement of adsorption equilibria as a quick alternative to time-consuming measurements by gravimetric or volumetric set-ups. Combination of the two techniques allowed the rapid determination of the distributed properties of solid surfaces to be effected and the results were interpreted in a fundamental physical sense. This led to a novel and promising way for the rapid and exact characterization of solid surfaces.

Protein-Ligand Complexes: Computation of the Relative Free Energy of Different Scaffolds and Binding Modes

A methodology for the calculation of the free energy difference between a pair of molecules of arbitrary topology is proposed. The protocol relies on a dual-topology paradigm, a softening of the intermolecular interactions, and a constraint that prevents the perturbed molecules from drifting away from each other at the end states. The equivalence and the performance of the methodology against a single-topology approach are demonstrated on a pair of harmonic oscillators, the calculation of the relative solvation free energy of ethane and methanol, and the relative binding free energy of two congeneric inhibitors of cyclooxygenase 2. The stability of two alternative binding modes of an inhibitor of cyclin-dependent kinase 2 is then investigated. Finally, the relative binding free energy of two structurally different inhibitors of cyclin-dependent kinase 2 is calculated. The proposed methodology allows the study of a range of problems that are beyond the reach of traditional relative free energy calculation protocols and should prove useful in drug design studies.

Thermodynamic characterization of new positive allosteric modulators binding to the glutamate receptor A2 ligand-binding domain: combining experimental and computational methods unravels differences in driving forces

Positive allosteric modulation of the ionotropic glutamate receptor GluA2 presents a potential treatment of cognitive disorders, for example, Alzheimer's disease. In the present study, we describe the synthesis, pharmacology, and thermodynamic studies of a series of monofluoro-substituted 3,4-dihydro-2H-1,2,4-benzothiadiazine 1,1-dioxides. Measurements of ligand binding by isothermal titration calorimetry (ITC) showed similar binding affinities for the modulator series at the GluA2 LBD but differences in the thermodynamic driving forces. Binding of 5c (7-F) and 6 (no-F) is enthalpy driven, and 5a (5-F) and 5b (6-F) are entropy driven. For 5d (8-F), both quantities were equal in size. Thermodynamic integration (TI) and one-step perturbation (OSP) were used to calculate the relative binding affinity of the modulators. The OSP calculations had a higher predictive power than those from TI, and combined with the shorter total simulation time, we found the OSP method to be more effective for this setup. Furthermore, from the molecular dynamics simulations, we extracted the enthalpies and entropies, and along with the ITC data, this suggested that the differences in binding free energies are largely explained by the direct ligand-surrounding enthalpies. Furthermore, we used the OSP setup to predict binding affinities for a series of polysubstituted fluorine compounds and monosubstituted methyl compounds and used these predictions to characterize the modulator binding pocket for this scaffold of positive allosteric modulators.

Structural and dynamic investigation of bovine folate receptor alpha (FOLR1), and role of ultra-high temperature processing on conformational and thermodynamic characteristics of FOLR1-folate complex

The folate receptor alpha (FOLR1) present in milk has widely been studied to investigate the effects of pasteurization, ultra-high temperature (UHT) processing and fermentation on net folate concentration. However, the folate binding mechanism with FOLR1, and effect of temperature on FOLR1-folate complex is poorly explored till now in bovine milk which is a chief resource of folate. Despite of enormous importance of folic acid and the routine intake of bovine milk, folic acid deficiency diseases are common in human race. To understand the folate deficiency in milk after processing, in absence of experimental structure, 3D model of bovine FOLR1 (bvFOLR1) was built followed by 40ns molecular dynamics (MD) simulation. The folate and its derivatives binding sites in bvFOLR1 were anticipated by molecular docking using AutoDock 4.2. Essential MD studies suggested the presence of a longer signal peptide (22 residues) and a short propeptide (7 residues) at the C-terminus that may cleaved during post-translational modification. MD analysis of bvFOLR1-folate complex at 298, 323, 353, 373 and 408K followed by binding energy (BE) calculation showed maximum binding affinity at ∼353K. However, at 373K and UHT (408K), the folate BE is significantly decreased with substantial conformational alteration. Heating at UHT followed by cooling within 298-408K range demoed no structural reformation with temperature reduction, and the folate was displaced from the active site. This study presented the disintegration of folate from bvFOLR1 during high temperature processing and revealed a lower folate concentration in UHT milk and dairy products.

Free energy calculations give insight into the stereoselective hydroxylation of α-ionones by engineered cytochrome P450 BM3 mutants

Previously, stereoselective hydroxylation of α-ionone by Cytochrome P450 BM3 mutants M01 A82W and M11 L437N was observed. While both mutants hydroxylate α-ionone in a regioselective manner at the C3 position, M01 A82W catalyzes formation of trans-3-OH-α-ionone products whereas M11 L437N exhibits opposite stereoselectivity, producing trans-(3S,6S)-OH-α-ionone and cis-(3S,6R)-OH-α-ionone. Here, we explore the stereoselective C3 hydroxylation of α-ionone by Cytochrome P450 BM3 mutants M01 A82W and M11 L437N using molecular dynamics-based free energy calculations to study the interaction between the enzyme and both the substrates and the products. The one-step perturbation approach is applied using an optimized reference state for substrates and products. While the free energy differences between the substrates free in solution amount to ~0 kJ mol(-1), the differences in mutant M01 A82W agree with the experimentally obtained dissociation constants K(d). Moreover, a correlation with experimentally observed trends in product formation is found in both mutants. The trans isomers show the most favorable relative binding free energy in the range of all four possible hydroxylated diastereomers for mutant M01 A82W, while the trans product from (6S)-α-ionone and the cis product from (6R)-α-ionone show highest affinity for mutant M11 L437N. Marcus theory is subsequently used to relate the thermodynamic stability to transition state energies and rates of formation.

The shadow map: a general contact definition for capturing the dynamics of biomolecular folding and function

Structure-based models (SBMs) are simplified models of the biomolecular dynamics that arise from funneled energy landscapes. We recently introduced an all-atom SBM that explicitly represents the atomic geometry of a biomolecule. While this initial study showed the robustness of the all-atom SBM Hamiltonian to changes in many of the energetic parameters, an important aspect, which has not been explored previously, is the definition of native interactions. In this study, we propose a general definition for generating atomically grained contact maps called "Shadow". The Shadow algorithm initially considers all atoms within a cutoff distance and then, controlled by a screening parameter, discards the occluded contacts. We show that this choice of contact map is not only well behaved for protein folding, since it produces consistently cooperative folding behavior in SBMs but also desirable for exploring the dynamics of macromolecular assemblies since, it distributes energy similarly between RNAs and proteins despite their disparate internal packing. All-atom structure-based models employing Shadow contact maps provide a general framework for exploring the geometrical features of biomolecules, especially the connections between folding and function.

Free energy calculations from one-step perturbations

The one-step perturbation approach offers an efficient means to estimate free energy differences. It may be applied to estimate solvation free energies, conformational preferences or relative free energies of binding of series of compounds to a common receptor. Applicability of the method depends on the possibility to define a proper reference state which may in itself be an unphysical molecule. Here, we describe practical considerations and explicit guidelines to define a proper reference state, and to efficiently calculate relative free energies. The strengths and limitations of the method are highlighted and special considerations are noted. The method may be applied using many different simulation programs. Here, analyses are exemplified at the hand of the GROMOS simulation package.

Conformational state-specific free energy differences by one-step perturbation: protein secondary structure preferences of the GROMOS 43A1 and 53A6 force fields

The one-step free energy perturbation approach can be applied to obtain conformational state-specific free energy differences (FEDs) associated with changes in force field parameters, and thus offers the possibility to consider conformational equilibria during force field parameterization. In this work, using the alanine decapeptide in explicit water solution as a model, the α-helical and β-hairpin state-specific FEDs associated with force field changes between two widely used parameter sets of the GROMOS force field, namely, 43A1 and 53A6, were determined using one-step perturbation. The results mostly deviated by only 1 kJ mol(−1) in absolute or a few percent in relative values from thermodynamic integration results, suggesting that the convergence ranges of one-step perturbation were large enough to cover the substantial changes in nonbonded parameters between the two parameter sets. It was also found that one-step perturbation may give larger errors when the changes from the reference state include a large decrease in van der Waals radius, as indicated by the result for the β-hairpin state-specific free energy change going from 53A6 to 43A1. According to the free energy results, the α-helical state of the alanine decapeptide is destabilized by 15 kJ mol(−1), i.e., 1.5 kJ mol(−1) per residue, relative to the β-hairpin state when going from 43A1 to 53A6, in agreement with previous direct simulations in which native α-helices were often found to be unstable in simulations using 53A6, despite that the 53A6 parameters better reproduce a range of thermodynamic properties of small molecular systems. By applying one-step perturbation to analyze the effects of perturbing individual parameters, the differential stabilization of the two secondary structure states can be traced to the changes in van der Waals parameters, especially a van der Waals parameter involved in third-neighbor interactions. This study provides an example of the efficiency of one-step perturbation in force field development, reducing the computational cost by orders of magnitude.

Calculations of binding affinity between C8-substituted GTP analogs and the bacterial cell-division protein FtsZ

The FtsZ protein is a self-polymerizing GTPase that plays a central role in bacterial cell division. Several C8-substituted GTP analogs are known to inhibit the polymerization of FtsZ by competing for the same binding site as its endogenous activating ligand GTP. Free energy calculations of the relative binding affinities to FtsZ for a set of five C8-substituted GTP analogs were performed. The calculated values agree well with the available experimental data, and the main contribution to the free energy differences is determined to be the conformational restriction of the ligands. The dihedral angle distributions around the glycosidic bond of these compounds in water are known to vary considerably depending on the physicochemical properties of the substituent at C8. However, within the FtsZ protein, this substitution has a negligible influence on the dihedral angle distributions, which fall within the narrow range of −140° to −90° for all investigated compounds. The corresponding ensemble average of the coupling constants ³J(C4,H1′) is calculated to be 2.95 ± 0.1 Hz. The contribution of the conformational selection of the GTP analogs upon binding was quantified from the corresponding populations. The obtained restraining free energy values follow the same trend as the relative binding affinities to FtsZ, indicating their dominant contribution.

Efficient free energy calculations for compounds with multiple stable conformations separated by high energy barriers

Compounds with high intramolecular energy barriers represent challenging targets for free energy calculations because of the difficulty to obtain sufficient conformational sampling. Existing approaches are therefore computationally very demanding, thus preventing practical applications for such compounds. We present an enhanced sampling-one step perturbation method (ES-OS) to tackle this problem in a highly efficient way. A single molecular dynamics simulation of a judiciously chosen reference state (using two sets of soft-core interactions) is sufficient to determine conformational distributions of chemically similar compounds and the free energy differences between them. The ES-OS method is applied to a set of five biologically relevant 8-substituted GTP analogs having high energy barriers between the anti and the syn conformations of the base with respect to the ribose part. The reliability of ES-OS is verified by comparing the results to Hamiltonian replica exchange simulations of GTP and 8-Br-GTP and the experimentally determined 3J(C4,H1') coupling constant for GMP in water. Additional simulations in vacuum and octanol allow us to calculate differences in the solvation free energies and in lipophilicities (log P). Free energy contributions from individual conformational regions are also calculated, and their relationship with the overall free energy is derived leading to a set of multiconformational free energy formulas. These relationships are of general applicability and can be used in free energy calculations for a more diverse set of compounds.

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.

The size of the intermolecular energy funnel in protein-protein interactions

Revealing the fundamental principles of protein interactions is essential for the basic knowledge of molecular processes and designing better predictive tools. Protein docking procedures allow systematic sampling of intermolecular energy landscapes, revealing the distribution of energy basins and their characteristics. A systematic search docking procedure GRAMM-X was applied to a comprehensive nonredundant database of nonobligate protein-protein complexes to determine the size of the intermolecular energy funnel. The unbound structures were simulated using rotamer library. The procedure generated grid-based matches, based on a smoothed Lennard-Jones potential, and minimized them off the grid with the same potential. The minimization generated a distribution of distances, based on a variety of metrics, between the grid-based and the minimized matches. The metric selected for the analysis, ligand interface RMSD, provided three independent estimates of the funnel size: based on the distribution amplitude for the near-native matches, deviation from random, and correlation with the energy values. The three methods converge to similar estimates of approximately 6-8 A ligand interface RMSD. The results indicated dependence of the funnel size on the type of the complex (smaller for antigen-antibody, medium for enzyme-inhibitor, and larger for the rest of the complexes) and the funnel size correlation with the size of the interface. Guidelines for the optimal sampling of docking coordinates, based on the funnel size estimates, were explored.

Interaction cutoff effect on ruggedness of protein-protein energy landscape

The concept of the energy landscape is important for better understanding of protein-protein interactions and for designing adequate docking procedures. The intermolecular landscape has a rugged terrain that impedes search procedures. Its inherent ruggedness is related to the conformational characteristics of the molecules and to the form of the potential function--more rugged for short-range potentials and less rugged for "soft," typically long-range potentials. Our study determined that the landscape ruggedness is further substantially exacerbated by truncation of the potentials. This additional ruggedness appears below certain critical interaction ranges that depend on the form of the potential. The theoretical model describing the cutoff effect on the landscape ruggedness is confirmed by the energy calculation on a dataset of protein-protein complexes. The negative effect of the potentials cutoff is well known. However, revealing its physical basis in terms of the energy landscape is important for better understanding of intermolecular interactions.

Mechanism and thermodynamics of binding of the polypyrimidine tract binding protein to RNA

The polypyrimidine tract binding protein (PTB) is involved in many physiological processes, including alternative splicing, internal ribosomal entry side (IRES)-mediated initiation of translation, and polyadenylation, as well as in ensuring mRNA stability. However, the role of PTB in these processes is not fully understood, and this has motivated us to undertake a computational study of the protein. PTB RNA binding domains (RBDs) 3 and 4 and their complexes with oligopyrimidine RNAs were simulated using the GROMOS simulation software using the GROMOS 45A4 force field. First, the stability and fluctuations of the tertiary fold and of the secondary structural elements in individual domains, the combined RBD34 domain, and their complexes with RNA were studied. Second, the simulation results were validated against the experimental NMR NOE data. The analysis of hydrogen bonding patterns, salt bridge networks, and stacking interactions of the RNA to the binding pockets of the protein domains showed that binding is not sequence-specific and that many RNA fragments can bind to them successfully. Further calculations of the relative free energy of binding for different polypyrimidine sequences were carried out using the thermodynamic integration (TI) and single-step perturbation (SSP) methods. It is was not possible to calculate the relative free energies with high accuracy, but the obtained results do give qualitative insights into PTB's affinity for different RNA sequences. Furthermore, the low-energy conformations of the complexes that were found provided additional information about the mechanism of binding.

Pheromone Discrimination by the Pheromone-Binding Protein of Bombyx mori

Pheromone-binding proteins are postulated to contribute to the exquisite specificity of the insect's olfactory system, acting as a filter by preferentially binding only one of the components of the natural pheromone. Here, we investigated the possible discrimination of the two very similar components of the natural pheromone gland from the silk moth, Bombyx mori, bombykol and bombykal, by the only pheromone-binding protein (BmorPBP) known to be expressed in the pheromone-detecting sensilla. Free-energy calculations and virtual docking indicate that both bombykol and bombykal bind to BmorPBP with similar affinity. In addition, in vitro competitive binding assays showed that both bombykol and bombykal were bound by BmorPBP with nearly the same high affinity. While BmorPBP might filter out other physiologically irrelevant compounds hitting the sensillar lymph, discrimination between the natural pheromone compounds must be achieved by molecular interactions with their cognate receptors.

Efficient calculation of many stacking and pairing free energies in DNA from a few molecular dynamics simulations

Through the use of the one-step perturbation approach, 130 free energies of base stacking and 1024 free energies of base pairing in DNA have been calculated from only five simulations of a nonphysical reference state. From analysis of a diverse set of 23 natural and unnatural bases, it appears that stacking free energies and stacking conformations play an important role in pairing of DNA nucleotides. On the one hand, favourable pairing free energies were found for bases that do not have the possibility to form canonical hydrogen bonds, while on the other hand, good hydrogen-bonding possibilities do not guarantee a favourable pairing free energy if the stacking of the bases dictates an unfavourable conformation. In this application, the one-step perturbation approach yields a wealth of both energetic and structural information at minimal computational cost.

Development and testing of an automated approach to protein docking

A new version of GRAMM was applied to Targets 14, 18, and 19 in CAPRI Round 5. The predictions were generated without manual intervention. Ten top-ranked matches for each target were submitted. The docking was performed by a rigid-body procedure with a smoothed potential function to accommodate conformational changes. The first stage was a global search on a fine grid with a projection of a smoothed Lennard-Jones potential. The top predictions from the first stage were subjected to the conjugate gradient minimization with the same smoothed potential. The resulting local minima were reranked according to the weighted sum of Lennard-Jones potential, pairwise residue-residue statistical preferences, cluster occupancy, and the degree of the evolutionary conservation of the predicted interface. For Targets 14 and 18, the conformation of the complex was predicted with root-mean-square deviation (RMSD) of the ligand interface atoms 0.68 A and 1.88 A correspondingly. For Target 19, the interface areas on both proteins were correctly predicted. The performance of the procedure was also analyzed on the benchmark of bound-unbound protein complexes. The results show that, on average, conformations of only 3 side-chains need to be optimized during docking of unbound structures before the backbone changes become a limiting factor. The GRAMM-X docking server is available for public use at http://www.bioinformatics.ku.edu.

The GROMOS software for biomolecular simulation: GROMOS05

We present the latest version of the Groningen Molecular Simulation program package, GROMOS05. It has been developed for the dynamical modelling of (bio)molecules using the methods of molecular dynamics, stochastic dynamics, and energy minimization. An overview of GROMOS05 is given, highlighting features not present in the last major release, GROMOS96. The organization of the program package is outlined and the included analysis package GROMOS++ is described. Finally, some applications illustrating the various available functionalities are presented.

Free energies of ligand binding for structurally diverse compounds

The one-step perturbation approach is an efficient means to calculate many relative free energies from a common reference compound. Combining lessons learned in previous studies, an application of the method is presented that allows for the calculation of relative binding free energies for structurally rather diverse compounds from only a few simulations. Based on the well known statistical-mechanical perturbation formula, the results do not require any empirical parameters, or training sets, only limited knowledge of the binding characteristics of the ligands suffices to design appropriate reference compounds. Depending on the choice of reference compound, relative free energies of binding rigid ligands to the ligand-binding domain of the estrogen receptor can be obtained that show good agreement with the experimental values. The approach presented here can easily be applied to many rigid ligands, and it should be relatively easy to extend the method to account for ligand flexibility. The free-energy calculations can be straightforwardly parallelized, allowing for an efficient means to understand and predict relative binding free energies.

A biomolecular force field based on the free enthalpy of hydration and solvation: the GROMOS force-field parameter sets 53A5 and 53A6

Successive parameterizations of the GROMOS force field have been used successfully to simulate biomolecular systems over a long period of time. The continuing expansion of computational power with time makes it possible to compute ever more properties for an increasing variety of molecular systems with greater precision. This has led to recurrent parameterizations of the GROMOS force field all aimed at achieving better agreement with experimental data. Here we report the results of the latest, extensive reparameterization of the GROMOS force field. In contrast to the parameterization of other biomolecular force fields, this parameterization of the GROMOS force field is based primarily on reproducing the free enthalpies of hydration and apolar solvation for a range of compounds. This approach was chosen because the relative free enthalpy of solvation between polar and apolar environments is a key property in many biomolecular processes of interest, such as protein folding, biomolecular association, membrane formation, and transport over membranes. The newest parameter sets, 53A5 and 53A6, were optimized by first fitting to reproduce the thermodynamic properties of pure liquids of a range of small polar molecules and the solvation free enthalpies of amino acid analogs in cyclohexane (53A5). The partial charges were then adjusted to reproduce the hydration free enthalpies in water (53A6). Both parameter sets are fully documented, and the differences between these and previous parameter sets are discussed.

Effect of methylation on the stability and solvation free energy of amylose and cellulose fragments: a molecular dynamics study

Molecular dynamics (MD) simulations were used to study the stability and solvation of amylose and cellulose fragments. The recently developed gromos carbohydrate force field was further tested by simulating maltose, cellobiose, and maltoheptaose. The MD simulations reproduced fairly well the favorable conformations of disaccharides defined by the torsional angles related with the glycosidic bond and the radius gyration of maltoheptaose. The effects of methylation at different hydroxyl groups on the stability of amylose and cellulose fragments were investigated. The methylations of O-2 and O-3 reduce the stability of a single helix more than methylation at O-6, while the latter reduces the stability of a double helix more. Solvation free-energy differences between the unsubstituted amylose and cellulose fragments and the methylated species were studied using the single-step perturbation method. It was found that methylation at O-2 has the biggest effect, in agreement with experiment.

Estimating entropies from molecular dynamics simulations

While the determination of free-energy differences by MD simulation has become a standard procedure for which many techniques have been developed, total entropies and entropy differences are still hardly ever computed. An overview of techniques to determine entropy differences is given, and the accuracy and convergence behavior of five methods based on thermodynamic integration and perturbation techniques was evaluated using liquid water as a test system. Reasonably accurate entropy differences are obtained through thermodynamic integration in which many copies of a solute are desolvated. When only one solute molecule is involved, only two methods seem to yield useful results, the calculation of solute-solvent entropy through thermodynamic integration, and the calculation of solvation entropy through the temperature derivative of the corresponding free-energy difference. One-step perturbation methods seem unsuitable to obtain entropy estimates.

Free energies of binding of polychlorinated biphenyls to the estrogen receptor from a single simulation

Relative free energies of binding to the ligand-binding domain of the estrogen receptor have been calculated for a series of 17 hydroxylated polychlorinated biphenyls. Because traditional thermodynamic integration or perturbation approaches are hardly feasible for these numbers of compounds, the one-step perturbation approach is applied and is shown to yield accurate results based on only two 2-ns molecular dynamics simulations of an unphysical, judiciously chosen, reference state. The mean absolute difference between the calculated and experimental binding free energies for the 17 compounds is 3.4 kJ/mol, which illustrates the accuracy of the GROMOS biomolecular force field used. Excluding the three largest ligands from the comparison reduces the deviation to 2.0 kJ/mol (i.e., < k(B)T). Apart from the relative free energy, structural information about the binding mode and binding orientation for every compound can also be extracted from the simulation, showing that a ligand bound to its receptor cannot be represented by a single conformation, but it samples an ensemble of different orientations.

Single-step perturbations to calculate free energy differences from unphysical reference states: limits on size, flexibility, and character

Relative free energies for a series of not too different compounds can be estimated accurately from a single simulation of an unphysical reference state that encompasses the characteristic molecular features of the compounds. Previously, this method has been applied to the calculation of free energies of solvation and of ligand binding for small molecules. In the present study we investigate the limits to the accuracy of the method by applying it to a realistic model of the binding of a set of rather large ligands to the protein factor Xa, a key protein in current efforts to design anticoagulation drugs. The evaluation of the binding free energies and conformations of nine derivatives of a biphenylamidino inhibitor leads to insights regarding the effect of the size, flexibility, and character of the unphysical part of the ligand in the reference state on the accuracy of the predicted binding free energies.

Correlated ab initio study of nucleic acid bases and their tautomers in the gas phase, in a microhydrated environment and in aqueous solution. guanine: surprising stabilization of rare tautomers in aqueous solution

Altogether eight keto and enol tautomers of guanine were studied theoretically in the gas phase, in a microhydrated environment (1 and 2 water molecules) and in bulk water. The structures of isolated, as well as mono- and dihydrated tautomers were determined by means of the RI-MP2 method using the extended TZVPP (5s3p2d1f/3s2p1d) basis set. The relative energies of isolated tautomers included the correction to higher correlation energy terms evaluated at the CCSD(T)/aug-cc-pVDZ level. The relative enthalpies at 0 K and relative free energies at 298 K were based on the above-mentioned relative energies and zero-point vibration energies, temperature-dependent enthalpy terms and entropies evaluated at the MP2/6-31G level. The keto form having hydrogen atom at N7 is the global minimum while the canonical form having hydrogen atom at N9 represents the first local minimum at all theoretical levels in vacuo and in the presence of 1 and 2 water molecules. All three unusual rare tautomers having hydrogens at N3 and N7, at N3 and N9, and also at N9 and N7 are systematically considerably less stable and can be hardly detected in the gas phase. The theoretical predictions fully agree with existing theoretical as well as experimental results. The effect of bulk solvent on the relative stability of guanine tautomers was studied by self-consistent reaction field and molecular dynamics free energy calculations using the thermodynamic integration method. Bulk solvent, surprisingly, strongly favored these three rare tautomers over all remaining low-energy tautomers and probably only these forms can exist in water phase. The global minimum (tautomer with hydrogens at N3 and N7) is by 13 kcal/mol more stable than the canonical form (3rd local minimum). Addition of one or two water molecules does not change the relative stability order of isolated guanine tautomers but the respective trend clearly supports the surprising stabilization of three rare forms.

Simulations of the estrogen receptor ligand-binding domain: affinity of natural ligands and xenoestrogens

We have carried out molecular dynamics (MD) simulations and free energy calculations on the alpha-subtype of the human estrogen receptor ligand-binding domain (ERalpha LBD) complexed with a number of known agonists and putative xenoestrogens. Our dynamical simulations of ligand-receptor complexes underscore the highly structured nature of the complex and offer some interesting insights into the structure-activity relationship (SAR) for these ligands. With traditional thermodynamic integration (TI) calculations, we calculate relative binding free energies for three known agonists, in good agreement with experimental values. The sheer number of possible xenoestrogenic compounds makes an approach using traditional free energy calculations unfeasible. Instead, we have made use of a single-step perturbation methodology that allows the calculation of relative free energies for a large number of related polyaromatic hydrocarbons (PAHs) from a single simulation. Our results show good (maximum deviation 3.3 kJ mol(-1)) agreement with experimental data, suggesting the possibility of large-scale xenoestrogen screening in silico to obtain strongly estrogenic compounds for subsequent experimental testing.