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

Accelerating Alchemical Free Energy Prediction Using a Multistate Method: Application to Multiple Kinases

Alchemical free-energy methods based on molecular dynamics (MD) simulations have become important tools to identify modifications of small organic molecules that improve their protein binding affinity during lead optimization. The routine application of pairwise free-energy methods to rank potential binders from best to worst is impacted by the combinatorial increase in calculations to perform when the number of molecules to assess grows. To address this fundamental limitation, our group has developed replica-exchange enveloping distribution sampling (RE-EDS), a pathway-independent multistate method, enabling the calculation of alchemical free-energy differences between multiple ligands (N > 2) from a single MD simulation. In this work, we apply the method to a set of four kinases with diverse binding pockets and their corresponding inhibitors (42 in total), chosen to showcase the general applicability of RE-EDS in prospective drug design campaigns. We show that for the targets studied, RE-EDS is able to model up to 13 ligands simultaneously with high sampling efficiency, leading to a substantial decrease in computational cost when compared to pairwise methods.

Solvation free energies of alcohols in water: temperature and pressure dependences

Solvation free energies μ* of amphiphilic species, methanol and 1,2-hexanediol, are obtained as a function of temperature or pressure based on molecular dynamics simulations combined with efficient free-energy calculation methods. In general, μ* of an amphiphile can be divided into and , the nonpolar and electrostatic contributions, and the former is further divided into and which are the work of cavity formation process and the free energy change due to weak, attractive interactions between the solute molecule and surrounding solvent molecules. We demonstrate that μ* of the two amphiphilic solutes can be obtained accurately using a perturbation combining method, which relies on the exact expressions for and and requires no simulations of intermediate systems between the solute with strong, repulsive interactions and the solute with the van der Waals and electrostatic interactions. The decomposition of μ* gives us several physical insights including that μ* is an increasing function of T due to , that the contributions of hydrophilic groups to the temperature dependence of μ* are additive, and that the contribution of the van der Waals attraction to the solvation volume is greater than that of the electrostatic interactions.

In silico epitope-based vaccine design against influenza a neuraminidase protein: Computational analysis established on B- and T-cell epitope predictions

Objective

Influenza A virus belongs to the most studied virus and its mutant initiates epidemic and pandemics outbreaks. Inoculation is the significant foundation to diminish the risk of infection. To prevent an incidence of influenza from the transmission, various practical approaches require more advancement and progress. More efforts and research must take in front to enhance vaccine efficacy.

Methods

The present research emphasizes the development and expansion of a universal vaccine for the influenza virus. Research focuses on vaccine design with high efficacy. In this study, numerous computational approaches were used, covering a wide range of elements and ideas in bioinformatics methodology. Various B and T-cell epitopic peptides derived from the Neuraminidase protein N1 are recognized by these approaches. With the implementation of numerous obtained databases and bioinformatics tools, the different immune framework methods of the conserved sequences of N1 neuraminidase were analyzed. NCBI databases were employed to retrieve amino acid sequences. The antigenic nature of the neuraminidase sequence was achieved by the VaxiJen server and Kolaskar and Tongaonkar method. After screening of various B and T cell epitopes, one efficient peptide each from B cell epitope and T cell epitopes was assessed for their antigenic determinant vaccine efficacy. Identical two B cell epitopes were recognized from the N1 protein when analyzed using B-cell epitope prediction servers. The detailed examination of amino acid sequences for interpretation of B and T cell epitopes was achieved with the help of the ABCPred and Immune Epitope Database.

Results

Computational immunology via immunoinformatic study exhibited RPNDKTG as having its high conservancy efficiency and demonstrated as a good antigenic, accessible surface hydrophilic B-cell epitope. Among T cell epitope analysis, YVNISNTNF was selected for being a conserved epitope. T cell epitope was also analyzed for its allergenicity and cytotoxicity evaluation. YVNISNTNF epitope was found to be a non-allergen and not toxic for cells as well. This T-cell epitope with maximum world populace coverages was scrutinized for its association with the HLA-DRB1*0401 molecule. Results from docking simulation analyses showed YVNISNTNF having lower binding energy, the radius of gyration (Rg), RMSD values, and RMSE values which make the protein structure more stable and increase its ability to become an epitopic peptide for influenza virus vaccination.

Conclusions

We propose that this epitope analysis may be successfully used as a measurement tool for the robustness of an antigen-antibody reaction between mutant strains in the annual design of the influenza vaccine.

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.

Toward Automated Free Energy Calculation with Accelerated Enveloping Distribution Sampling (A-EDS)

Free-energy perturbation (FEP) methods are commonly used in drug design to calculate relative binding free energies of different ligands to a common host protein. Alchemical ligand transformations are usually performed in multiple steps which need to be chosen carefully to ensure sufficient phase-space overlap between neighboring states. With one-step or single-step FEP techniques, a single reference state is designed that samples phase-space not only representative of a full transformation but also ideally resembles multiple ligand end states and hence allows for efficient multistate perturbations. Enveloping distribution sampling (EDS) is one example for such a method in which the reference state is created by a mathematical combination of the different ligand end states based on solid statistical mechanics. We have recently proposed a novel approach to EDS which enables efficient barrier crossing between the different end states, termed accelerated EDS (A-EDS). In this work, we further simplify the parametrization of the A-EDS reference state and demonstrate the automated calculation of multiple free-energy differences between different ligands from a single simulation in three different well-described drug design model systems.

Correcting electrostatic artifacts due to net-charge changes in the calculation of ligand binding free energies

Alchemically derived free energies are artifacted when the perturbed moiety has a nonzero net charge. The source of the artifacts lies in the effective treatment of the electrostatic interactions within and between the perturbed atoms and remaining (partial) charges in the simulated system. To treat the electrostatic interactions effectively, lattice-summation (LS) methods or cutoff schemes in combination with a reaction-field contribution are usually employed. Both methods render the charging component of the calculated free energies sensitive to essential parameters of the system like the cutoff radius or the box side lengths. Here, we discuss the results of three previously published studies of ligand binding. These studies presented estimates of binding free energies that were artifacted due to the charged nature of the ligands. We show that the size of the artifacts can be efficiently calculated and raw simulation data can be corrected. We compare the corrected results with experimental estimates and nonartifacted estimates from path-sampling methods. Although the employed correction scheme involves computationally demanding continuum-electrostatics calculations, we show that the correction estimate can be deduced from a small sample of configurations rather than from the entire ensemble. This observation makes the calculations of correction terms feasible for complex biological systems. To show the general applicability of the proposed procedure, we also present results where the correction scheme was used to correct independent free energies obtained from simulations employing a cutoff scheme or LS electrostatics. In this work, we give practical guidelines on how to apply the appropriate corrections easily.

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.

Estimation of relative free energies of binding using pre-computed ensembles based on the single-step free energy perturbation and the site-identification by Ligand competitive saturation approaches

Accurate and rapid estimation of relative binding affinities of ligand-protein complexes is a requirement of computational methods for their effective use in rational ligand design. Of the approaches commonly used, free energy perturbation (FEP) methods are considered one of the most accurate, although they require significant computational resources. Accordingly, it is desirable to have alternative methods of similar accuracy but greater computational efficiency to facilitate ligand design. In the present study relative free energies of binding are estimated for one or two non-hydrogen atom changes in compounds targeting the proteins ACK1 and p38 MAP kinase using three methods. The methods include standard FEP, single-step free energy perturbation (SSFEP) and the site-identification by ligand competitive saturation (SILCS) ligand grid free energy (LGFE) approach. Results show the SSFEP and SILCS LGFE methods to be competitive with or better than the FEP results for the studied systems, with SILCS LGFE giving the best agreement with experimental results. This is supported by additional comparisons with published FEP data on p38 MAP kinase inhibitors. While both the SSFEP and SILCS LGFE approaches require a significant upfront computational investment, they offer a 1000-fold computational savings over FEP for calculating the relative affinities of ligand modifications once those pre-computations are complete. An illustrative example of the potential application of these methods in the context of screening large numbers of transformations is presented. Thus, the SSFEP and SILCS LGFE approaches represent viable alternatives for actively driving ligand design during drug discovery and development. © 2016 Wiley Periodicals, Inc.

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.

Pyranose dehydrogenase ligand promiscuity: a generalized approach to simulate monosaccharide solvation, binding, and product formation

The flavoenzyme pyranose dehydrogenase (PDH) from the litter decomposing fungus Agaricus meleagris oxidizes many different carbohydrates occurring during lignin degradation. This promiscuous substrate specificity makes PDH a promising catalyst for bioelectrochemical applications. A generalized approach to simulate all 32 possible aldohexopyranoses in the course of one or a few molecular dynamics (MD) simulations is reported. Free energy calculations according to the one-step perturbation (OSP) method revealed the solvation free energies (ΔG_solv) of all 32 aldohexopyranoses in water, which have not yet been reported in the literature. The free energy difference between β- and α-anomers (ΔG_β-α) of all d-stereoisomers in water were compared to experimental values with a good agreement. Moreover, the free-energy differences (ΔG) of the 32 stereoisomers bound to PDH in two different poses were calculated from MD simulations. The relative binding free energies (ΔΔG_bind) were calculated and, where available, compared to experimental values, approximated from K_m values. The agreement was very good for one of the poses, in which the sugars are positioned in the active site for oxidation at C1 or C2. Distance analysis between hydrogens of the monosaccharide and the reactive N5-atom of the flavin adenine dinucleotide (FAD) revealed that oxidation is possible at HC1 or HC2 for pose A, and at HC3 or HC4 for pose B. Experimentally detected oxidation products could be rationalized for the majority of monosaccharides by combining ΔΔG_bind and a reweighted distance analysis. Furthermore, several oxidation products were predicted for sugars that have not yet been tested experimentally, directing further analyses. This study rationalizes the relationship between binding free energies and substrate promiscuity in PDH, providing novel insights for its applicability in bioelectrochemistry. The results suggest that a similar approach could be applied to study promiscuity of other enzymes.

Generally, enzymes are perceived as being specific for both their substrates and the reaction they catalyze. This standard paradigm started to shift and currently enzyme promiscuity towards various substrates is perceived rather as the rule than the exception. Enzyme promiscuity seems to be vital for proteins to acquire new functions, and therefore for evolution itself. The driving forces for promiscuity are manifold and consequently challenging to study. Binding free energies, which can be calculated from computer simulations, represent a convenient measure for them. Here, we investigate the binding free energies between the enzyme pyranose dehydrogenase (PDH) and a sugar-substrate by computational means. PDH has an extraordinarily promiscuous substrate-specificity, making it interesting for e.g. bioelectrochemical applications. By introducing modifications to the sugar-structure used for the molecular dynamics simulations, we could simultaneously study all 32 possible aldohexopyranoses from a single simulation. This saves costly computational resources and time for setting up and analyzing the simulations. We could nicely reproduce experimental results and predict so far undetected sugar-oxidation products, directing further experiments. This study gives novel insights into PDH's substrate promiscuity and the enzyme's applicability. A similar approach could be applied to study the promiscuity of other enzymes.

A conformational factorisation approach for estimating the binding free energies of macromolecules

We present a conformational factorization approach. The theory is based on a superposition partition function, decomposed as a sum over contributions from local minima. The factorisation greatly reduces the number of minima that need to be considered, by employing the same local configurations for groups that are sufficiently distant from the binding site. The theory formalises the conditions required to analyse how our definition of the binding site region affects the free energy difference between the apo and holo states. We employ basin-hopping parallel tempering to sample minima that contribute significantly to the partition function, and calculate the binding free energies within the harmonic normal mode approximation. A further significant gain in efficiency is achieved using a recently developed local rigid body framework in both the sampling and the normal mode analysis, which reduces the number of degrees of freedom. We benchmark this approach for human aldose reductase (PDB code 2INE). When varying the size of the rigid region, the free energy difference converges for factorisation of groups at a distance of 14 Å from the binding site, which corresponds to 80% of the protein being locally rigidified.

A tunable coarse-grained model for ligand-receptor interaction

Cell-surface receptors are the most common target for therapeutic drugs. The design and optimization of next generation synthetic drugs require a detailed understanding of the interaction with their corresponding receptors. Mathematical approximations to study ligand-receptor systems based on reaction kinetics strongly simplify the spatial constraints of the interaction, while full atomistic ligand-receptor models do not allow for a statistical many-particle analysis, due to their high computational requirements. Here we present a generic coarse-grained model for ligand-receptor systems that accounts for the essential spatial characteristics of the interaction, while allowing statistical analysis. The model captures the main features of ligand-receptor kinetics, such as diffusion dependence of affinity and dissociation rates. Our model is used to characterize chimeric compounds, designed to take advantage of the receptor over-expression phenotype of certain diseases to selectively target unhealthy cells. Molecular dynamics simulations of chimeric ligands are used to study how selectivity can be optimized based on receptor abundance, ligand-receptor affinity and length of the linker between both ligand subunits. Overall, this coarse-grained model is a useful approximation in the study of systems with complex ligand-receptor interactions or spatial constraints.

The current importance of cell surface receptors as primary targets for drug treatment explains the increasing interest in a mathematical and quantitative description of the process of ligand-receptor interaction. Recently, a new generation of synthetic chimeric ligands has been developed to selectively target unhealthy cells, without harming healthy tissue. To understand these and other types of complex ligand-receptor systems, conventional chemical interaction models often rely on simplifications and assumptions about the spatial characteristics of the system, while full atomistic molecular dynamics simulations are too computationally demanding to perform many particle statistical analysis. In this paper, we describe a novel approach to model the interaction between ligands and receptors based on a coarse grained approximation that includes explicitly both spatial and kinetic details of the interaction, while allowing many-particle simulations and therefore, statistical analysis at biologically relevant time scales. The model is used to study the binding properties of generic chimeric ligands to understand how cell specificity is achieved, its dependence on receptor concentration and the influence of the distance between subunits of the chimera. Overall, this approach proves optimal to study other ligand-receptor systems with complex spatial regulation, such as receptor clustering, multimerization and multivalent asymmetric ligand binding.

Influence of variation of a side chain on the folding equilibrium of a β-peptide: limitations of one-step perturbation

In a recent study (Lin et al., Helv. Chim. Acta 2011, 94, 597), the one-step perturbation method was applied to tackle a challenging computational problem, that is, the calculation of the folding free enthalpies ΔGF,U of six hepta-β-peptides with different, Ala, Val, Leu, Ile, Ser, or Thr, side chains in the fifth residue. The ΔGF,U values obtained using one-step perturbation based on a single molecular dynamics simulation of a judiciously chosen reference state with soft-core atoms in the side chain of the fifth residue showed an overall accuracy of about kB T for the four peptides with nonpolar side chains, but twice as large deviations were observed for the peptides with polar side chains. Here, alternative reference-state Hamiltonians that better cover the conformational space relevant to these peptides are investigated, and post simulation rotational sampling of the χ1 and χ2 torsional angles of the fifth residue is carried out to sample different orientations of the side chain. A reference state with rather soft atoms yields accurate ΔGF,U values for the peptides with the Ser and Thr side chains, but it failed to correctly predict the folding free enthalpy for one peptide with a nonpolar side chain, that is, Leu. Based on the results and those of earlier studies, possible ways to improve the accuracy of the efficient one-step perturbation technique to compute free enthalpies of folding are discussed.

PIP2 controls voltage-sensor movement and pore opening of Kv channels through the S4-S5 linker

Voltage-gated K(+) (Kv) channels couple the movement of a voltage sensor to the channel gate(s) via a helical intracellular region, the S4-S5 linker. A number of studies link voltage sensitivity to interactions of S4 charges with membrane phospholipids in the outer leaflet of the bilayer. Although the phospholipid phosphatidylinositol-4,5-bisphosphate (PIP(2)) in the inner membrane leaflet has emerged as a universal activator of ion channels, no such role has been established for mammalian Kv channels. Here we show that PIP(2) depletion induced two kinetically distinct effects on Kv channels: an increase in voltage sensitivity and a concomitant decrease in current amplitude. These effects are reversible, exhibiting distinct molecular determinants and sensitivities to PIP(2). Gating current measurements revealed that PIP(2) constrains the movement of the sensor through interactions with the S4-S5 linker. Thus, PIP(2) controls both the movement of the voltage sensor and the stability of the open pore through interactions with the linker that connects them.

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.

Structural and dynamic determinants of protein-peptide recognition

Protein-peptide interactions play important roles in many cellular processes, including signal transduction, trafficking, and immune recognition. Protein conformational changes upon binding, an ill-defined peptide binding surface, and the large number of peptide degrees of freedom make the prediction of protein-peptide interactions particularly challenging. To address these challenges, we perform rapid molecular dynamics simulations in order to examine the energetic and dynamic aspects of protein-peptide binding. We find that, in most cases, we recapitulate the native binding sites and native-like poses of protein-peptide complexes. Inclusion of electrostatic interactions in simulations significantly improves the prediction accuracy. Our results also highlight the importance of protein conformational flexibility, especially side-chain movement, which allows the peptide to optimize its conformation. Our findings not only demonstrate the importance of sufficient sampling of the protein and peptide conformations, but also reveal the possible effects of electrostatics and conformational flexibility on peptide recognition.

Site-Specific Fragment Identification Guided by Single-Step Free Energy Perturbation Calculations

The in-silico Site Identification by Ligand Competitive Saturation (SILCS) approach identifies the binding sites of representative chemical entities on the entire protein surface, information that can be applied for computational fragment-based drug design. In this study, we report an efficient computational protocol that uses sampling of the protein-fragment conformational space obtained from the SILCS simulations and performs single step free energy perturbation (SSFEP) calculations to identify site-specific favorable chemical modifications of benzene involving substitutions of ring hydrogens with individual non-hydrogen atoms. The SSFEP method is able to capture the experimental trends in relative hydration free energies of benzene analogues and for two datasets of experimental relative binding free energies of congeneric series of ligands of the proteins α-thrombin and P38 MAP kinase. The approach includes a protocol in which data obtained from SILCS simulations of the proteins is first analyzed to identify favorable benzene binding sites following which an ensemble of benzene-protein conformations for that site is obtained. The SSFEP protocol applied to that ensemble results in good reproduction of experimental free energies of the α-thrombin ligands, but not for P38 MAP kinase ligands. Comparison with results from a P38 full-ligand simulation and analysis of conformations reveals the reason for the poor agreement being the connectivity with the remainder of the ligand, a limitation inherent in fragment-based methods. Since the SSFEP approach can identify favorable benzene modifications as well as identify the most favorable fragment conformations, the obtained information can be of value for fragment linking or structure-based optimization.

Efficient and Accurate Free Energy Calculations on Trypsin Inhibitors

Several combinations of free energy calculation methods have been applied to determine the relative free energies of binding between eight para-substituted benzamidines in complex with the serine protease trypsin. With the aim to improve efficiency and maintain accuracy, the linear response approximation (LRA), linear interaction energy (LIE) and third power fitting (TPF) are combined with the one-step perturbation (OSP) to determine the polar and apolar contributions to the free energy, respectively. It is shown that the combination TPF/OSP gives the most accurate results and is 4.5 times more efficient than the rigorous thermodynamic integration (TI). By projecting the electrostatic preorganization energy from the OSP simulations, an increase in efficiency of a factor 7.5 can even be achieved. Loss of accuracy with respect to the TI data is limited to 3.9 and 5.6 kJ/mol, respectively, making it an attractive approach for lead optimization programs in drug research.

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.

Alchemical free energy methods for drug discovery: progress and challenges

Improved rational drug design methods are needed to lower the cost and increase the success rate of drug discovery and development. Alchemical binding free energy calculations, one potential tool for rational design, have progressed rapidly over the past decade, but still fall short of providing robust tools for pharmaceutical engineering. Recent studies, especially on model receptor systems, have clarified many of the challenges that must be overcome for robust predictions of binding affinity to be useful in rational design. In this review, inspired by a recent joint academic/industry meeting organized by the authors, we discuss these challenges and suggest a number of promising approaches for overcoming them.

NNScore: a neural-network-based scoring function for the characterization of protein-ligand complexes

As high-throughput biochemical screens are both expensive and labor intensive, researchers in academia and industry are turning increasingly to virtual-screening methodologies. Virtual screening relies on scoring functions to quickly assess ligand potency. Although useful for in silico ligand identification, these scoring functions generally give many false positives and negatives; indeed, a properly trained human being can often assess ligand potency by visual inspection with greater accuracy. Given the success of the human mind at protein−ligand complex characterization, we present here a scoring function based on a neural network, a computational model that attempts to simulate, albeit inadequately, the microscopic organization of the brain. Computer-aided drug design depends on fast and accurate scoring functions to aid in the identification of small-molecule ligands. The scoring function presented here, used either on its own or in conjunction with other more traditional functions, could prove useful in future drug-discovery efforts.

Novel naphthalene-based inhibitors of Trypanosoma brucei RNA editing ligase 1

Background

Neglected tropical diseases, including diseases caused by trypanosomatid parasites such as Trypanosoma brucei, cost tens of millions of disability-adjusted life-years annually. As the current treatments for African trypanosomiasis and other similar infections are limited, new therapeutics are urgently needed. RNA Editing Ligase 1 (REL1), a protein unique to trypanosomes and other kinetoplastids, was identified recently as a potential drug target.

Methodology/Principal Findings

Motivated by the urgent need for novel trypanocidal therapeutics, we use an ensemble-based virtual-screening approach to discover new naphthalene-based TbREL1 inhibitors. The predicted binding modes of the active compounds are evaluated within the context of the flexible receptor model and combined with computational fragment mapping to determine the most likely binding mechanisms. Ultimately, four new low-micromolar inhibitors are presented. Three of the four compounds may bind to a newly revealed cleft that represents a putative druggable site not evident in any crystal structure.

Conclusions/Significance

Pending additional optimization, the compounds presented here may serve as precursors for future novel therapies useful in the fight against several trypanosomatid pathogens, including human African trypanosomiasis, a devastating disease that afflicts the vulnerable patient populations of sub-Saharan Africa.

African sleeping sickness is a devastating disease that plagues sub-Saharan Africa. Neglected tropical diseases like African sleeping sickness cause significant death and suffering in the world's poorest countries. Current treatments for African sleeping sickness either have high costs, terrible side effects, or limited effectiveness. Consequently, new medicines are urgently needed. RNA editing ligase 1 is an important protein critical for the survival of Trypanosoma brucei, the unicellular parasite that causes African sleeping sickness. In this paper, we describe our recent efforts to use advanced computer techniques to identify chemicals predicted to prevent RNA editing ligase 1 from functioning properly. We subsequently tested our predicted chemicals and confirmed that a number of them inhibited the protein's function. Additionally, one of the chemicals was effective at stopping the growth of the parasite in culture. Although substantial work remains to be done in order to optimize these chemicals so they are effective and safe to use in human patients, the identification of these parasite-killing compounds is nevertheless a valuable step towards finding a better cure for this devastating disease.

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.

Prediction of protein-ligand binding affinity by free energy simulations: assumptions, pitfalls and expectations

Many limitations of current computer-aided drug design arise from the difficulty of reliably predicting the binding affinity of a small molecule to a biological target. There is thus a strong interest in novel computational methodologies that claim predictions of greater accuracy than current scoring functions, and at a throughput compatible with the rapid pace of drug discovery in the pharmaceutical industry. Notably, computational methodologies firmly rooted in statistical thermodynamics have received particular attention in recent years. Yet free energy calculations can be daunting to learn for a novice user because of numerous technical issues and various approaches advocated by experts in the field. The purpose of this article is to provide an overview of the current capabilities of free energy calculations and to discuss the applicability of this technology to drug discovery.

Alchemical free energy simulations for biological complexes: powerful but temperamental

Free energy simulations compare multiple ligand:receptor complexes by "alchemically" transforming one into another, yielding binding free energy differences. Since their introduction in the 1980s, many technical and theoretical obstacles were surmounted, and the method ("MDFE," since molecular dynamics are often used) has matured into a powerful tool. We describe its current status, its effectiveness, and the challenges it faces. MDFE has provided chemical accuracy for many systems but remains expensive, with significant human overhead costs. The bottlenecks have shifted, partly due to increased computer power. To study diverse sets of ligands, force field availability and accuracy can be a major difficulty. Another difficulty is the frequent need to consider multiple states, related to sidechain protonation or buried waters, for example. Sophisticated, automated methods to sample these states are maturing, such as constant pH simulations. Meanwhile, combinations of MDFE and simpler approaches, like continuum dielectric models, can be very effective. As illustrations, we show how, with careful force field parameterization, MDFE accurately predicts binding specificities between complex tetracycline ligands and their targets. We describe substrate binding to the aspartyl-tRNA synthetase enzyme, where many distinct electrostatic states play a role, and a histidine and a Mg(2+) ion act as coupled switches that help enforce a strict preference for the aspartate substrate, relative to several analogs. Overall, MDFE has achieved a predictive status, where novel ligands can be studied and molecular recognition elucidated in depth. It should play an increasing role in the analysis of complex cellular processes and biomolecular engineering.

Assessment of nonequilibrium free energy methods

One of the factors preventing the general application of free energy methods in rational drug design remains the lack of sufficient computational resources. Many nonequilibrium (NE) free energy methods, however, are easily made embarrassingly parallel in comparison to equilibrium methods and may be conveniently run on desktop computers using distributed computing software. In recent years, there has been a proliferation of NE methods, but the general applicability of these approaches has not been determined. In this study, a subset including only those NE methods which are easily parallelised were considered for examination, with a view to their application to the prediction of protein-ligand binding affinities. A number of test systems were examined, including harmonic oscillator (HO) systems and the calculation of relative free energies of hydration of water-methane. The latter system uses identical potentials to the protein ligand case and is therefore an appropriate model system on which methods may be tested. As well as investigating existing protocols, a replica exchange NE approach was developed, which was found to offer advantages over conventional methods. It was found that Rosenbluth-based approaches to optimizing the NE work values used in NE free energy estimates were not consistent in the improvements in accuracy achieved and that, given their computational cost, the simple approach of taking each work value in an unbiased way is to be preferred. Of the two free energy estimators examined, Bennett's acceptance ratio was the most consistent and is, therefore, to be preferred over the Jarzynski estimator. The recommended protocols may be run very efficiently within a distributed computing environment and are of similar accuracy and precision to equilibrium free energy methods.

Binding of small-molecule ligands to proteins: "what you see" is not always "what you get"

We review insights from computational studies of affinities of ligands binding to proteins. The power of structural biology is in translating knowledge of protein structures into insights about their forces, binding, and mechanisms. However, the complementary power of computer modeling is in showing "the rest of the story" (i.e., how motions and ensembles and alternative conformers and the entropies and forces that cannot be seen in single molecular structures also contribute to binding affinities). Upon binding to a protein, a ligand can bind in multiple orientations; the protein or ligand can be deformed by the binding event; waters, ions, or cofactors can have unexpected involvement; and conformational or solvation entropies can sometimes play large and otherwise unpredictable roles. Computer modeling is helping to elucidate these factors.

AutoGrow: a novel algorithm for protein inhibitor design

Due in part to the increasing availability of crystallographic protein structures as well as rapid improvements in computing power, the past few decades have seen an explosion in the field of computer-based rational drug design. Several algorithms have been developed to identify or generate potential ligands in silico by optimizing the ligand-receptor hydrogen bond, electrostatic, and hydrophobic interactions. We here present AutoGrow, a novel computer-aided drug design algorithm that combines the strengths of both fragment-based growing and docking algorithms. To validate AutoGrow, we recreate three crystallographically resolved ligands from their constituent fragments.

Exploring interactions of endocrine-disrupting compounds with different conformations of the human estrogen receptor alpha ligand binding domain: a molecular docking study

Endocrine-disrupting compounds (EDCs) accumulating in nature are known to interact with nuclear receptors. Especially important is the human estrogen receptor alpha (hERalpha), and several EDCs are either known or suspected to influence the activity of the ligand-binding domain (LBD). We here present a comparative docking study of both well-known hERalpha ligands and small organic compounds, including selected polychlorinated biphenyls (PCBs), plasticizers, and pesticides, that are all potentially endocrine-disrupting,into different conformations of the hERalpha LBD. Three newly found quasi-stable structures of the hERalhpa LBD are examined along with three crystallographic conformations of the protein, either theapo structure or using a protein structure with a bound agonist or antagonist ligand. The possible interactions between the protein and the potentially EDCs are described. It is found that most suspected EDCs can bind in the steroid binding cavity, interacting with at least one of the two hydrophilic ends of the steroid binding site. DDE, DDT, and HPTE are predicted to bind most strongly to the hERalpha LBD. It is predicted that these compounds can interact with the three conformations of hERalpha LBD with comparable affinities.The metabolic hydroxylation of aromatic compounds is found to lead to an increase in the binding affinity of PCBs as well as DDT. Docking into the quasi-stable conformations of the hERalpha LBD leads to computed binding affinities similar to or better than those calculated for the three X-ray structures, revealing that the new structures may be of importance for assessing the function of the influence of EDCs on nuclear receptors.

Protein-ligand binding affinity by nonequilibrium free energy methods

Nonequilibrium (NE) free energy methods are embarrassingly parallel and may be very conveniently run on desktop computers using distributed computing software. In recent years there has been a proliferation of NE methods, but these approaches have barely, if at all, been used in the context of calculating protein-ligand binding free energies. In a recent study by these authors, different combinations of NE methods with various test systems were compared and protocols identified which yielded results as accurate as replica exchange thermodynamic integration (RETI). The NE approaches, however, lend themselves to extensive parallelization through the use of distributed computing. Here the best performing of those NE protocols, a replica exchange method using Bennett's acceptance ratio as the free energy estimator (RENE), is applied to two sets of congeneric inhibitors bound to neuraminidase and cyclooxygenase-2. These protein-ligand systems were originally studied with RETI, giving results to which NE and RENE simulations are compared. These NE calculations were carried out on a large, highly distributed group of low-performance desktop computers which are part of a Condor pool. RENE was found to produce results of a predictive quality at least as good as RETI in less than half the wall clock time. However, non-RE NE results were found to be far less predictive. In addition, the RENE method successfully identified a localized region of rapidly changing free energy gradients without the need for prior investigation. These results suggest that the RENE protocol is appropriate for use in the context of predicting protein-ligand binding free energies and that it can offer advantages over conventional, equilibrium approaches.

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.

Computational prediction of drug binding and rationalisation of selectivity towards cytochromes P450

BACKGROUND

Early in-vitro consideration of metabolism and inhibition of cytochrome P450 has proven its merits over the last 15 years. Simultaneously, many computational drug-design methods have been developed, and are being applied to study the interactions between drug candidates and cytochrome P450 enzymes (P450s).

OBJECTIVE

This review discusses the recent advances of these methods and the implications that are specific for P450s.

METHODS

Mainly focusing on the prediction of binding affinity and ligand selectivity, we outline the applicability of the different methods to answer specific questions. Special emphasis is put on the different levels of theory that are being used in recent computational descriptions of ligand-P450 interactions.

CONCLUSION

P450s offer an additional challenge for computational methods, considering the ambiguities of the catalytic cycle and the significant flexibility of the active site. Different computational methods display different limitations, which is crucial to take into account when choosing the method appropriate to each application.

Hit identification and binding mode predictions by rigorous free energy simulations

The identification of lead molecules using computational modeling often relies on approximate, high-throughput approaches, of limited accuracy. We show here that, with a methodology we recently developed, it is possible to predict the relative binding free energies of structurally diverse ligands of the estrogen receptor-alpha using a rigorous statistical thermodynamics approach. Predictions obtained from the simulations with an explicit solvation model are in good qualitative agreement with experimental data, while simulations with implicit solvent models or rank ordering by empirical scoring functions yield predictions of lower quality. In addition, it is shown that free energy techniques can be used to select the most likely binding mode from a set of possible orientations generated by a docking program. It is suggested that the free energy techniques outlined in this study can be used to rank-order, by potency, structurally diverse compounds identified by virtual screening, de novo design or scaffold hopping programs.