ES/IS: estimation of conformational free energy by combining dynamics simulations with explicit solvent with an implicit solvent continuum model

Anticancer Activity and Mechanism of Action Evaluation of an Acylhydrazone Cu(II) Complex toward Breast Cancer Cells, Spheroids, and Mammospheres

The purpose of this work was to screen the anticancer activity and mechanisms of action of Cu(II)-acylhydrazone complex [Cu(HL)(H₂ O)](NO₃ )⋅H₂ O, (CuHL), to find a potential novel agent for breast chemotherapies. Cytotoxicity studies on MCF7 cells demonstrated that CuHL has stronger anticancer properties than cisplatin over breast cancer cell models. Computational simulations showed that CuHL could interact in the minor groove of the DNA dodecamer, inducing a significant genotoxic effect on both cancer cells from 0.5 to 1 μM. In this sense, molecular docking and molecular dynamics simulations showed that the compound could interact with 20S proteasome subunits. Also, cell proteasome experiments using breast cancer cells revealed that the complex can inhibit proteasomal activity. Moreover, CuHL induced apoptosis in breast cancer cells at very low micromolar concentrations (0.5-2.5 μM) and displayed relevant anticancer activity over spheroids derived from MCF7 cells. Ultimately, CuHL diminished the number of mammospheres formed, disturbing their morphology and size.

Vanillin enones as selective inhibitors of the cancer associated carbonic anhydrase isoforms IX and XII. The out of the active site pocket for the design of selective inhibitors?

New C-glycosides and α,β-unsaturated ketones incorporating the 4-hydroxy-3-methoxyphenyl (vanillin) moiety as inhibitors of carbonic anhydrase (CA, EC 4.2.1.1) isoforms have been investigated. The inhibition profile of these compounds is presented against four human CA (hCA) isozymes, comprising hCAs I and II (cytosolic, ubiquitous enzymes) and hCAs IX and XII (tumour associated isozymes). Docking analysis of the inhibitors within the active sites of these enzymes has been performed and is discussed, showing that the observed selectivity could be explained in terms of an alternative pocket out of the CA active site where some of these compounds may bind. Several derivatives were identified as selective inhibitors of the tumour-associated hCA IX and XII. Their discovery might be a step in the strategy for finding an effective non-sulfonamide CA inhibitor useful in therapy/diagnosis of hypoxic tumours or other pathologies in which CA isoforms are involved.

DNA cleavage mechanism by metal complexes of Cu(II), Zn(II) and VO(IV) with a schiff-base ligand

Metal ions and metal complexes are important components of nucleic acid biochemistry, participating both in regulation of gene expression and as therapeutic agents. Three new transition metal complexes of copper(II), zinc(II) and oxidovanadium(IV) with a ligand derived from o-vanillin and thiophene were previously synthesized and their antitumor properties were studied in our laboratory. To elucidate some molecular mechanisms tending to explain the cytotoxic effects observed over tumor cells, we investigated the interaction of these complexes with DNA by gel electrophoresis, UV-Vis spectroscopy, docking studies and molecular dynamics simulations. Our spectroscopy and computational results have shown that all of them were able to bind to DNA, Cu(II) complex is located in the minor groove while Zn(II) and oxidovanadium(IV) complexes act as major groove binding molecules. Interestingly, only the Cu(II) complex caused double-strand DNA nicks, consistent with its higher cytotoxic activities previously observed in tumor cell lines. We propose that the DNA-complex interaction destabilize the molecule either disrupting the phosphodiester bonds or impairing DNA replication, giving those complexes strong antitumor potential.

Anticancer activity of a new copper(II) complex with a hydrazone ligand. Structural and spectroscopic characterization, computational simulations and cell mechanistic studies on 2D and 3D breast cancer cell models

We report here the synthesis, crystal structure, characterization and anticancer activity of a copper(ii)-hydrazone complex, [Cu(MeBHoVa)(H2O)2](NO3) (for short, CuHL), against human breast cancer cells on monolayer (2D) and spheroids/mammospheres (3D). The solid-state molecular structure of the complex has been determined by X-ray diffraction methods. The conformational space was searched and geometries were optimized both in the gas phase and including solvent effects by computational methods based on DFT. The compound has been characterized in the solid state and in solution by spectroscopic (FTIR, Raman, UV-vis) methods. The results were compared with those obtained for the hydrazone ligand and complemented with DFT calculations. Cell viability assays on MCF7 (IC50(CuHL) = 1.7 ± 0.1 μM, IC50(CDDP) = 42.0 ± 3.2 μM) and MDA-MB-231 (IC50(CuHL) = 1.6 ± 0.1 μM, IC50(CDDP) = 131.0 ± 18 μM) demonstrated that the complex displays higher antitumor activity than cisplatin (CDDP) on 2D and 3D human breast cancer cell models. Molecular docking and molecular dynamics simulations showed that CuHL could interacts with DNA, inducing a significant genotoxic effect on both breast cancer cells from 0.5 to 1 μM. On the other hand, CuHL increases the ROS production and induces cell programmed death on breast cancer cells at very low micromolar concentrations (0.5-1.0 μM). Moreover, the compound decreased the amount of breast CSCs on MCF7 and MDA-MB-231 cells reducing the percentage of CD44+/CD24-/low cells from 0.5 to 1.5 μM. In addition, CuHL overcame CDDP with an IC50 value 65-fold lower against breast multicellular spheroids ((IC50(CuHL) = 2.2 ± 0.3 μM, IC50(CDDP) = 125 ± 4.5 μM)). Finally, CuHL reduced mammosphere formation capacity, hence affecting the size and number of mammospheres and showing that the complex exhibits antitumor properties on monolayer (2D) and spheroids (3D) derived from human breast cancer cells.

In silico and in vitro analysis of FAK/MMP signaling axis inhibition by VO-clioquinol in 2D and 3D human osteosarcoma cancer cells

The study of novel mechanisms of action of vanadium compounds is critical to elucidating the role and importance of these kinds of compounds as antitumor and antimetastatic agents. This work deals with in silico and in vitro studies of one clioquinol oxidovanadium(iv) complex [VO(clioquinol)2], VO(CQ)2, and its regulation of FAK. In particular, we focus on elucidating the relationship of the FAK inhibition, MMP activity and antimetastatic effects of the complex in human bone cancer cells.

On the discovery of a potential survivin inhibitor combining computational tools and cytotoxicity studies

Survivin protein is a metalloprotein member of the inhibitors of apoptosis proteins family, involved in the regulation of programmed cell death. Due to the recent development of antitumor therapies having survivin as molecular target, several strategies to interfere with the expression or function of survivin have emerged. This work describes the discovery of a new potential inhibitor of survivin function using a computer-aided drug design approach. Structure-based virtual screening and molecular dynamic simulations were carried out to select two compounds as possible inhibitors. According to the binding energy, possible ligand localization is in a cavity, close to dimerization interface. Next, cell-based assays were performed on three cell lines: two with tumor phenotype and over-expression of survivin, and another with normal phenotype and low expression of survivin. One of the selected compounds shows a selectively antitumor effect on panel cell lines suggesting that the compound effect could be correlated with the survivin expression.

Detailed potential of mean force studies on host-guest systems from the SAMPL6 challenge

Accurately predicting receptor-ligand binding free energies is one of the holy grails of computational chemistry with many applications in chemistry and biology. Many successes have been reported, but issues relating to sampling and force field accuracy remain significant issues affecting our ability to reliably calculate binding free energies. In order to explore these issues in more detail we have examined a series of small host-guest complexes from the SAMPL6 blind challenge, namely octa-acids (OAs)-guest complexes and Curcurbit[8]uril (CB8)-guest complexes. Specifically, potential of mean force studies using umbrella sampling combined with the weighted histogram method were carried out on both systems with both known and unknown binding affinities. We find that using standard force fields and straightforward simulation protocols we are able to obtain satisfactory results, but that simply scaling our results allows us to significantly improve our predictive ability for the unknown test sets: the overall RMSD of the binding free energy versus experiment is reduced from 5.59 to 2.36 kcal/mol; for the CB8 test system, the RMSD goes from 8.04 to 3.51 kcal/mol, while for the OAs test system, the RSMD goes from 2.89 to 0.95 kcal/mol. The scaling approach was inspired by studies on structurally related known benchmark sets: by simply scaling, the RMSD was reduced from 6.23 to 1.19 kcal/mol and from 2.96 to 0.62 kcal/mol for the CB8 benchmark system and the OA benchmark system, respectively. We find this scaling procedure to correct absolute binding affinities to be highly effective especially when working across a "congeneric" series with similar charge states. It is less successful when applied to mixed ligands with varied charges and chemical characteristics, but improvement is still realized in the present case. This approach suggests that there are large systematic errors in absolute binding free energy calculations that can be straightforwardly accounted for using a scaling procedure. Random errors are still an issue, but near chemical accuracy can be obtained using the present strategy in select cases.

Recent Trends and Applications of Molecular Modeling in GPCR⁻Ligand Recognition and Structure-Based Drug Design

G protein-coupled receptors represent the largest family of human membrane proteins and are modulated by a variety of drugs and endogenous ligands. Molecular modeling techniques, especially enhanced sampling methods, have provided significant insight into the mechanism of GPCR–ligand recognition. Notably, the crucial role of the membrane in the ligand-receptor association process has earned much attention. Additionally, docking, together with more accurate free energy calculation methods, is playing an important role in the design of novel compounds targeting GPCRs. Here, we summarize the recent progress in the computational studies focusing on the above issues. In the future, with continuous improvement in both computational hardware and algorithms, molecular modeling would serve as an indispensable tool in a wider scope of the research concerning GPCR–ligand recognition as well as drug design targeting GPCRs.

Coupled molecular dynamics and continuum electrostatic method to compute the ionization pKa's of proteins as a function of pH. Test on a large set of proteins

A computational method, to predict the pKa values of the ionizable residues Asp, Glu, His, Tyr, and Lys of proteins, is presented here. Calculation of the electrostatic free-energy of the proteins is based on an efficient version of a continuum dielectric electrostatic model. The conformational flexibility of the protein is taken into account by carrying out molecular dynamics simulations of 10 ns in implicit water. The accuracy of the proposed method of calculation of pKa values is estimated from a test set of experimental pKa data for 297 ionizable residues from 34 proteins. The pKa-prediction test shows that, on average, 57, 86, and 95% of all predictions have an error lower than 0.5, 1.0, and 1.5 pKa units, respectively. This work contributes to our general understanding of the importance of protein flexibility for an accurate computation of pKa, providing critical insight about the significance of the multiple neutral states of acid and histidine residues for pKa-prediction, and may spur significant progress in our effort to develop a fast and accurate electrostatic-based method for pKa-predictions of proteins as a function of pH.

KECSA-Movable Type Implicit Solvation Model (KMTISM)

Computation of the solvation free energy for chemical and biological processes has long been of significant interest. The key challenges to effective solvation modeling center on the choice of potential function and configurational sampling. Herein, an energy sampling approach termed the “Movable Type” (MT) method, and a statistical energy function for solvation modeling, “Knowledge-based and Empirical Combined Scoring Algorithm” (KECSA) are developed and utilized to create an implicit solvation model: KECSA-Movable Type Implicit Solvation Model (KMTISM) suitable for the study of chemical and biological systems. KMTISM is an implicit solvation model, but the MT method performs energy sampling at the atom pairwise level. For a specific molecular system, the MT method collects energies from prebuilt databases for the requisite atom pairs at all relevant distance ranges, which by its very construction encodes all possible molecular configurations simultaneously. Unlike traditional statistical energy functions, KECSA converts structural statistical information into categorized atom pairwise interaction energies as a function of the radial distance instead of a mean force energy function. Within the implicit solvent model approximation, aqueous solvation free energies are then obtained from the NVT ensemble partition function generated by the MT method. Validation is performed against several subsets selected from the Minnesota Solvation Database v2012. Results are compared with several solvation free energy calculation methods, including a one-to-one comparison against two commonly used classical implicit solvation models: MM-GBSA and MM-PBSA. Comparison against a quantum mechanics based polarizable continuum model is also discussed (Cramer and Truhlar’s Solvation Model 12).

Improved Efficiency of Replica Exchange Simulations through Use of a Hybrid Explicit/Implicit Solvation Model

The use of parallel tempering or replica exchange molecular dynamics (REMD) simulations has facilitated the exploration of free energy landscapes for complex molecular systems, but application to large systems is hampered by the scaling of the number of required replicas with increasing system size. Use of continuum solvent models reduces system size and replica requirements, but these have been shown to provide poor results in many cases, including overstabilization of ion pairs and secondary structure bias. Hybrid explicit/continuum solvent models can overcome some of these problems through an explicit representation of water molecules in the first solvation shells, but these methods typically require restraints on the solvent molecules and show artifacts in water properties due to the solvation interface. We propose an REMD variant in which the simulations are performed with a fully explicit solvent, but the calculation of exchange probability is carried out using a hybrid model, with the solvation shells calculated on the fly during the fully solvated simulation. The resulting reduction in the perceived system size in the REMD exchange calculation provides a dramatic decrease in the computational cost of REMD, while maintaining a very good agreement with results obtained from the standard explicit solvent REMD. We applied several standard and hybrid REMD methods with different solvent models to alanine polymers of 1, 3, and 10 residues, obtaining ensembles that were essentially independent of the initial conformation, even with explicit solvation. Use of only a continuum model without a shell of explicit water provided poor results for Ala3 and Ala10, with a significant bias in favor of the α-helix. Likewise, using only the solvation shells and no continuum model resulted in ensembles that differed significantly from the standard explicit solvent data. Ensembles obtained from hybrid REMD are in very close agreement with explicit solvent data, predominantly populating polyproline II conformations. Inclusion of a second shell of explicit solvent was found to be unnecessary for these peptides.

Structural and energetic analysis of 2-aminobenzimidazole inhibitors in complex with the hepatitis C virus IRES RNA using molecular dynamics simulations

Despite the many biological functions of RNA, very few drugs have been designed or found to target RNA. Here we report the results of molecular dynamics (MD) simulations and binding energy analyses on hepatitis C virus internal ribosome entry site (IRES) RNA in complex with highly charged 2-aminobenzimidazole inhibitors. Initial coordinates were taken from NMR and crystallography studies that had yielded different binding modes. During MD simulations, the RNA-inhibitor complex is stable in the crystal conformation but not in the NMR conformation. Additionally, we found that existing and standard MD trajectory postprocessing free energy methods, such as the MM-GBSA and MM-PBSA approaches available in AMBER, seem unsuitable to properly rank the binding energies of complexes between highly charged molecules. A better correlation with the experimental data was found using a rather simple binding enthalpy calculation based on the explicitly solvated potential energies. In anticipation of further growth in the use of small molecules to target RNA, we include results addressing the impact of charge assignment on docking, the structural role of magnesium in the IRES-inhibitor complex, the entropic contribution to binding energy, and simulations of a plausible scaffold design for new inhibitors.

Molecular modeling of nucleic acid structure: energy and sampling

An overview of computer simulation techniques as applied to nucleic acid systems is presented. This unit discusses methods used to treat energy and to sample representative configurations. Emphasis is placed on molecular mechanics and empirical force fields.

Analyzing effects of naturally occurring missense mutations

Single-point mutation in genome, for example, single-nucleotide polymorphism (SNP) or rare genetic mutation, is the change of a single nucleotide for another in the genome sequence. Some of them will produce an amino acid substitution in the corresponding protein sequence (missense mutations); others will not. This paper focuses on genetic mutations resulting in a change in the amino acid sequence of the corresponding protein and how to assess their effects on protein wild-type characteristics. The existing methods and approaches for predicting the effects of mutation on protein stability, structure, and dynamics are outlined and discussed with respect to their underlying principles. Available resources, either as stand-alone applications or webservers, are pointed out as well. It is emphasized that understanding the molecular mechanisms behind these effects due to these missense mutations is of critical importance for detecting disease-causing mutations. The paper provides several examples of the application of 3D structure-based methods to model the effects of protein stability and protein-protein interactions caused by missense mutations as well.

Predicting folding free energy changes upon single point mutations

MOTIVATION

The folding free energy is an important characteristic of proteins stability and is directly related to protein's wild-type function. The changes of protein's stability due to naturally occurring mutations, missense mutations, are typically causing diseases. Single point mutations made in vitro are frequently used to assess the contribution of given amino acid to the stability of the protein. In both cases, it is desirable to predict the change of the folding free energy upon single point mutations in order to either provide insights of the molecular mechanism of the change or to design new experimental studies.

RESULTS

We report an approach that predicts the free energy change upon single point mutation by utilizing the 3D structure of the wild-type protein. It is based on variation of the molecular mechanics Generalized Born (MMGB) method, scaled with optimized parameters (sMMGB) and utilizing specific model of unfolded state. The corresponding mutations are built in silico and the predictions are tested against large dataset of 1109 mutations with experimentally measured changes of the folding free energy. Benchmarking resulted in root mean square deviation = 1.78 kcal/mol and slope of the linear regression fit between the experimental data and the calculations was 1.04. The sMMGB is compared with other leading methods of predicting folding free energy changes upon single mutations and results discussed with respect to various parameters.

AVAILABILITY

All the pdb files we used in this article can be downloaded from http://compbio.clemson.edu/downloadDir/mentaldisorders/sMMGB_pdb.rar.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Computational and experimental studies of the interaction between phospho-peptides and the C-terminal domain of BRCA1

The C-terminal domain of BRCA1(BRCT) is involved in the DNA repair pathway by recognizing the pSXXF motif in interacting proteins. It has been reported that short peptides containing this motif bind to BRCA1(BRCT) in the micromolar range with high specificity. In this work, the binding of pSXXF peptides has been studied computationally and experimentally in order to characterize their interaction with BRCA1(BRCT). Elucidation of the contacts that drive the protein-ligand interaction is critical for the development of high affinity small-molecule BRCA1 inhibitors. Molecular dynamics (MD) simulations revealed the key role of threonine at the peptide P+2 position in providing structural rigidity to the ligand in the bound state. The mutation at P+1 had minor effects. Peptide extension at the N-terminal position with the naphthyl amino acid exhibited a modest increase in binding affinity, what could be explained by the dispersion interaction of the naphthyl side-chain with a hydrophobic patch. Three in silico end-point methods were considered for the calculation of binding free energy. The Molecular Mechanics Poisson-Boltzmann Surface Area and the Solvated Interaction Energy methods gave reasonable agreement with experimental data, exhibiting a Pearlman predictive index of 0.71 and 0.78, respectively. The MM-quantum mechanics-surface area method yielded improved results, which was characterized by a Pearlman index of 0.78. The correlation coefficients were 0.59, 0.61 and 0.69, respectively. The ability to apply a QM level of theory within an end-point binding free energy protocol may provide a way for a consistent improvement of accuracy in computer-aided drug design.

Quantum mechanical binding free energy calculation for phosphopeptide inhibitors of the Lck SH2 domain

The accurate and efficient calculation of binding free energies is essential in computational biophysics. We present a linear-scaling quantum mechanical (QM)-based end-point method termed MM/QM-COSMO to calculate binding free energies in biomolecular systems, with an improved description of entropic changes. Molecular dynamics trajectories are re-evaluated using a semiempirical Hamiltonian and a continuum solvent model; translational and rotational entropies are calculated using configurational integrals, and internal entropy is calculated using the harmonic oscillator approximation. As an application, we studied the binding of a series of phosphotyrosine tetrapeptides to the human Lck SH2 domain, a key component in intracellular signal transduction, modulation of which can have therapeutic relevance in the treatment of cancer, osteoporosis, and autoimmune diseases. Calculations with molecular mechanics Poisson-Boltzmann, and generalized Born surface area methods showed large discrepancies with experimental data stemming from the enthalpic component, in agreement with an earlier report. The empirical force field-based solvent interaction energy scoring function yielded improved results, with average unsigned error of 3.6 kcal/mol, and a better ligand ranking. The MM/QM-COSMO method exhibited the best agreement both for absolute (average unsigned error = 0.7 kcal/mol) and relative binding free energy calculations. These results show the feasibility and promise of a full QM-based end-point method with an adequate balance of accuracy and computational efficiency.

Advances in implicit models of water solvent to compute conformational free energy and molecular dynamics of proteins at constant pH

Modern implicit solvent models for macromolecular simulations in water-proton bath are considered. The fundamental quantity that implicit models approximate is the solute potential of mean force, which is obtained by averaging over solvent degrees of freedom. The implicit solvent models suggest practical ways to calculate free energies of macromolecular conformations taking into account equilibrium interactions with water solvent and proton bath, while the explicit solvent approach is unable to do that due to the need to account for a large number of solvent degrees of freedom. The most advanced realizations of the implicit continuum models by different research groups are discussed, their accuracy are examined, and some applications of the implicit solvent models to macromolecular modeling, such as free energy calculations, protein folding, and constant pH molecular dynamics are highlighted.

Computing free energies of protein conformations from explicit solvent simulations

We report a fully general technique addressing a long standing challenge of calculating conformational free energy differences between various states of a polymer chain from simulations using explicit solvent force fields. The main feature of our method is a special mapping variable, a path coordinate, which continuously connects two conformations. The path variable has been designed to preserve locality in the phase space near the path endpoints. We avoid the problem of sampling the unfolded states by creating an artificial confinement "tube" in the phase space that prevents the molecule from unfolding without affecting the calculation of the desired free energy difference. We applied our technique to compute the free energy difference between two native-like conformations of the small protein Trp-cage using the CHARMM force field with explicit solvent. We verified this result by comparing it with an independent, significantly more expensive calculation. Overall, the present study suggests that the new method of computing free energy differences between polymer chain conformations is accurate and highly computationally efficient.

Explicitly solvated ligand contribution to continuum solvation models for binding free energies: selectivity of theophylline binding to an RNA aptamer

To provide more accurate computational estimates of binding free energies in solution from molecular dynamics (MD) simulations, a separate solvation contribution for the binding ligand is determined from a linear response treatment. We use explicit water coordinates for this term and combine with MM-PBSA (molecular mechanics, Poisson-Boltzmann, and surface area contributions) in a new approach (MM-PB/LRA-SA). To assess this method, application to the binding between theophylline and its derivatives to an RNA aptamer was performed and compared with experimental binding affinities. Explicitly solvated MD trajectories were generated with the same parameter set used in the previous work by Gouda et al., who compared the relative binding of these molecules by both the MM-PBSA and thermodynamic integration methods. Substituting the linear response term for the ligand in the MM-PB/LRA-SA approach led to an improvement upon MM-PBSA when compared with experimental and thermodynamic integration results at approximately twice the computational cost. The balance between accuracy and computational expense achieved using this method suggests potential advantages in applying it in the virtual drug-screening process.

Computational evaluation of protein stability change upon mutations

When designing a mutagenesis experiment, it is often crucial to estimate the stability change of proteins induced by mutations (Delta DG). Despite the recent advances in computational methods, it is still challenging to estimate D DG quickly and accurately. We recently developed the Eris protocols for in silico evaluation of the Delta DG. Starting from the tertiary structure of the wide-type protein, the Eris protocols can model the structure of the mutant protein and estimate Delta DG using the structure models. The Eris protocols not only efficiently optimize the side chains conformations, taking advantage of a fast rotamer-based searching algorithm, but also allow protein backbone flexibility during the modeling. As a result, the Eris protocols effectively resolve steric clashes induced by certain mutations and have more accurate Delta DG predictions than a fixed-backbone approach. We discuss the general aspects of computational Delta DG estimations and discuss in detail the principles and methodologies of the Eris protocols.

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.

FAMBE-pH: a fast and accurate method to compute the total solvation free energies of proteins

A fast and accurate method to compute the total solvation free energies of proteins as a function of pH is presented. The method makes use of a combination of approaches, some of which have already appeared in the literature; (i) the Poisson equation is solved with an optimized fast adaptive multigrid boundary element (FAMBE) method; (ii) the electrostatic free energies of the ionizable sites are calculated for their neutral and charged states by using a detailed model of atomic charges; (iii) a set of optimal atomic radii is used to define a precise dielectric surface interface; (iv) a multilevel adaptive tessellation of this dielectric surface interface is achieved by using multisized boundary elements; and (v) 1:1 salt effects are included. The equilibrium proton binding/release is calculated with the Tanford-Schellman integral if the proteins contain more than approximately 20-25 ionizable groups; for a smaller number of ionizable groups, the ionization partition function is calculated directly. The FAMBE method is tested as a function of pH (FAMBE-pH) with three proteins, namely, bovine pancreatic trypsin inhibitor (BPTI), hen egg white lysozyme (HEWL), and bovine pancreatic ribonuclease A (RNaseA). The results are (a) the FAMBE-pH method reproduces the observed pK a's of the ionizable groups of these proteins within an average absolute value of 0.4 p K units and a maximum error of 1.2 p K units and (b) comparison of the calculated total pH-dependent solvation free energy for BPTI, between the exact calculation of the ionization partition function and the Tanford-Schellman integral method, shows agreement within 1.2 kcal/mol. These results indicate that calculation of total solvation free energies with the FAMBE-pH method can provide an accurate prediction of protein conformational stability at a given fixed pH and, if coupled with molecular mechanics or molecular dynamics methods, can also be used for more realistic studies of protein folding, unfolding, and dynamics, as a function of pH.

Fast in silico protein folding by introduction of alternating hydrogen bond potentials

We accelerate protein folding in all-atom molecular dynamics simulations by introducing alternating hydrogen bond potentials as a supplement to the force field. The alternating hydrogen bond potentials result in accelerated hydrogen bond reordering, which leads to rapid formation of secondary structure elements. The method does not require knowledge of the native state but generates the potentials based on the development of the tertiary structure in the simulation. In protein folding, the formation of secondary structure elements, especially alpha-helix and beta-sheet, is very important, and we show that our method can fold both efficiently and with great speed.

Computational chemistry approaches to drug discovery in signal transduction

The advent of therapeutic strategies aimed at targeting specific macromolecular components of deregulated signaling pathways associated with particular disease states has given rise to the idea that it should be possible to design ligands as drug candidates to these targets from first principles. This concept has been beckoning for a long time but structure-based ligand design only became feasible once it was possible to determine the 3-D structures of molecular targets at atomic resolution. However, structure-based design turned out to be difficult, chiefly because under physiological conditions both receptors and ligands are not static but they behave dynamically. While it is possible to design ligands with high steric and electronic complementarity to a receptor site, it is always uncertain how biologically relevant the assumed conformations of both ligand and receptor actually are. The fact that it remains beyond our current abilities to predict with sufficient accuracy the affinity between hypothetical ligand and receptor poses is in part connected with this problem and continues to confound the reliable prediction of drug-like ligands for therapeutic targets. Nevertheless, significant progress has been made and so-called virtual screening methods that use computational methods to dock candidate ligands into receptor sites and to score the resulting complexes are now used routinely as one of the components in drug discovery screening campaigns. Here an overview is given of the underlying principles, implementations, and applications of structure-guided computational design technologies. Although the emphasis is on receptor-based strategies, mention will also be made of some of the more established ligand-based approaches, such as similarity analyses and quantitative structure-activity relationship methods.

Benchmarking implicit solvent folding simulations of the amyloid beta(10-35) fragment

A pathogenetic feature of Alzhemier disease is the aggregation of monomeric beta-amyloid proteins (Abeta) to form oligomers. Usually these oligomers of long peptides aggregate on time scales of microseconds or longer, making computational studies using atomistic molecular dynamics models prohibitively expensive and making it essential to develop computational models that are cheaper and at the same time faithful to physical features of the process. We benchmark the ability of our implicit solvent model to describe equilibrium and dynamic properties of monomeric Abeta(10-35) using all-atom Langevin dynamics (LD) simulations, since Alphabeta(10-35) is the only fragment whose monomeric properties have been measured. The accuracy of the implicit solvent model is tested by comparing its predictions with experiment and with those from a new explicit water MD simulation, (performed using CHARMM and the TIP3P water model) which is approximately 200 times slower than the implicit water simulations. The dependence on force field is investigated by running multiple trajectories for Alphabeta(10-35) using the CHARMM, OPLS-aal, and GS-AMBER94 force fields, whereas the convergence to equilibrium is tested for each force field by beginning separate trajectories from the native NMR structure, a completely stretched structure, and from unfolded initial structures. The NMR order parameter, S2, is computed for each trajectory and is compared with experimental data to assess the best choice for treating aggregates of Alphabeta. The computed order parameters vary significantly with force field. Explicit and implicit solvent simulations using the CHARMM force fields display excellent agreement with each other and once again support the accuracy of the implicit solvent model. Alphabeta(10-35) exhibits great flexibility, consistent with experiment data for the monomer in solution, while maintaining a general strand-loop-strand motif with a solvent-exposed hydrophobic patch that is believed to be important for aggregation. Finally, equilibration of the peptide structure requires an implicit solvent LD simulation as long as 30 ns.

Modeling amyloid fibril formation: a free-energy approach

Amyloid fibrils are structures consisting of many proteins with a well-defined conformation. The formation of these fibrils has been the subject of intense research, largely due to their connection to several diseases. We focus here on the computational studies and discuss these from a free-energy point of view. The fibrillogenic properties of many proteins can be predicted and understood by taking the relevant free energies into account in an appropriate way. This is because both the equilibrium and the kinetic properties of the protein system depend on its free-energy landscape. Advanced simulation techniques can be used to understand the relationship between the free-energy landscape of a protein and its three-dimensional structure and propensity to form amyloid fibrils. We give an overview of existing simulation techniques that operate at a molecular level of detail and that are capable of generating relevant free-energy values. The free energies obtained with these methods can be inserted into a statistical-mechanical or kinetic framework to predict mean fibril properties on length scales and time scales that are inaccessible by molecular-scale simulation methods.

Protein folding: then and now

Over the past three decades the protein folding field has undergone monumental changes. Originally a purely academic question, how a protein folds has now become vital in understanding diseases and our abilities to rationally manipulate cellular life by engineering protein folding pathways. We review and contrast past and recent developments in the protein folding field. Specifically, we discuss the progress in our understanding of protein folding thermodynamics and kinetics, the properties of evasive intermediates, and unfolded states. We also discuss how some abnormalities in protein folding lead to protein aggregation and human diseases.

FALS mutations in Cu, Zn superoxide dismutase destabilize the dimer and increase dimer dissociation propensity: a large-scale thermodynamic analysis

Mutations in the dimeric enzyme Cu, Zn superoxide dismutase (SOD1) leading to its aggregation are implicated in the toxicity in familial amyotrophic lateral sclerosis (FALS). We and others have previously shown that aggregation occurs by a pathway involving dimer dissociation, metal-loss from monomers and multimeric assembly of apo-SOD1 monomers. We postulate that FALS mutations cause enhanced aggregation by affecting one or more steps in the pathway, and computationally test this postulate for 75 known mis-sense FALS mutants of SOD1. Based on an extensive thermodynamic analysis of the stability of apo-dimer and apo-monomer forms of these mutants, we classify the mutations into the following groups: 70 out of 75 mutations in SOD1 lead to (i) decreased dimer stability, and/or (ii) increased dimer dissociation, compared to wild type, and four mutations lead to (iii) decreased monomer stability compared to wild type. Our results suggest that enhanced aggregation of SOD1 in FALS occurs due to an increased population of mutant SOD1 apo-monomers compared to wild type. The dissociation of multimeric proteins induced by diverse mutations may be a common theme in several human diseases.

Computational studies of tryptophanyl-tRNA synthetase: activation of ATP by induced-fit

Catalysis of amino acid activation by Bacillus stearothermophilus tryptophanyl-tRNA synthetase involves three allosteric states: (1) Open; (2) closed pre-transition state (PreTS); and (3) closed products (Product). The interconversions of these states entail significant domain motions driven by ligand binding. We explore the application of molecular dynamics simulations to investigate ligand-linked conformational stability changes associated with this catalytic cycle. Multiple molecular dynamics trajectories (5 ns) for 11 distinct liganded and unliganded monomer configurations show that the PreTS conformation is unstable in the absence of ATP, reverting within approximately 600 ps nearly to the Open conformation. In contrast, Open and Product state trajectories were stable, even without ligands, confirming the previous suggestion that catalysis entails destabilization of the protein conformation, driven by ATP-binding energies developed as the PreTS state assembles during induced-fit. The simulations suggest novel mechanistic details associated with both induced-fit (Open-PreTS) and catalysis (PreTS-Product). Notably, Mg2+ -ATP interactions are coupled to interactions between ATP and active-site lysine side-chains via mechanisms that cannot be captured under the molecular mechanics approximations, and which therefore require restraining potentials for stable simulation. Simulations of Mg2+. ATP-bound PreTS complexes with restraining potentials and with a virtual K111A mutant confirm that these coupling interactions are necessary to sustain the PreTS conformation and, in turn, provide a new model for how the PreTS conformation activates ATP for catalysis. These results emphasize the central role of the PreTS state as a high-energy intermediate structure along the catalytic pathway and suggest that Mg2+ and the KMSKS loop function cooperatively during catalysis.

Coupling between conformation and proton binding in proteins

Interest centers here on whether the use of a fixed charge distribution of a protein solute, or a treatment that considers proton-binding equilibria by solving the Poisson equation, is a better approach to discriminate native from non-native conformations of proteins. In this analysis of the charge distribution of 7 proteins, we estimate the solvation free energy contribution to the total free energy by exploring the 2(zeta) possible ionization states of the whole molecule, with zeta being the number of ionizable groups in the amino acid sequence, for every conformation in the ensembles of 7 proteins. As an additional consideration of the role of electrostatic interactions in determining the charge distribution of native folds, we carried out a comparison of alternative charge assignment models for the ionizable residues in a set of 21 native-like proteins. The results of this work indicate that (1) for 6 out of 7 proteins, estimation of solvent polarization based on the Generalized Born model with a fixed charge distribution provides the optimal trade-off between accuracy, with respect to the Poisson equation, and speed when compared to the accessible surface area model; for the seventh protein, consideration of all possible ionization states of the whole molecule appears to be crucial to discriminate the native from non-native conformations; (2) significant differences in the degree of ionization and hence the charge distribution for native folds are found between the different charge models examined; (3) the stability of the native state is determined by a delicate balance of all the energy components, and (4) conformational entropy, and hence the dynamics of folding, may play a crucial role for a successful ab initio protein folding prediction.

Cooperativity in the self-assembly of porphyrin ladders

Cooperativity is a general feature of intermolecular interactions in biomolecular systems, but there are many different facets of the phenomenon that are not well understood. Positive cooperativity stabilizes a system as progressively more interactions are added, and the origin of the beneficial free energy may be entropic or enthalpic in origin. An "enthalpic chelate effect" has been proposed to operate through structural tightening that improves all of the functional group interactions in a complex, when it is more strongly bound. Here, we present direct calorimetric evidence that no such enthalpic effects exist in the cooperative assembly of supramolecular ladder complexes composed of metalloporphyrin oligomers coordinated to bipyridine ligands. The enthalpic contributions of the individual coordination interactions are 35 kJ.mol(-1) and constant over a range of free energies of self-assembly of -35 to -111 kJ.mol(-1). In rigid well defined systems of this type, the enthalpies of individual interactions are additive, and no enthalpic cooperative effects are apparent. The implication is that in more flexible, less well defined systems such as biomolecular assemblies, the enthalpy contributions available from specific functional group interactions are well defined and constant parameters.

Comparison between Generalized-Born and Poisson-Boltzmann methods in physics-based scoring functions for protein structure prediction

Continuum solvent models such as Generalized-Born and Poisson-Boltzmann methods hold the promise to treat solvation effect efficiently and to enable rapid scoring of protein structures when they are combined with physics-based energy functions. Yet, direct comparison of these two approaches on large protein data set is lacking. Building on our previous work with a scoring function based on a Generalized-Born (GB) solvation model, and short molecular-dynamics simulations, we further extended the scoring function to compare with the MM-PBSA method to treat the solvent effect. We benchmarked this scoring function against seven publicly available decoy sets. We found that, somewhat surprisingly, the results of MM-PBSA approach are comparable to the previous GB-based scoring function. We also discussed the effect to the scoring function accuracy due to presence of large ligands and ions in some native structures of the decoy sets.

Molecular dynamics simulation of amyloid beta dimer formation

Recent experiments with amyloid beta (Abeta) peptide indicate that formation of toxic oligomers may be an important contribution to the onset of Alzheimer's disease. The toxicity of Abeta oligomers depends on their structure, which is governed by assembly dynamics. Due to limitations of current experimental techniques, a detailed knowledge of oligomer structure at the atomic level is missing. We introduce a molecular dynamics approach to study Abeta dimer formation. 1), We use discrete molecular dynamics simulations of a coarse-grained model to identify a variety of dimer conformations; and 2), we employ all-atom molecular mechanics simulations to estimate thermodynamic stability of all dimer conformations. Our simulations of a coarse-grained Abeta peptide model predicts 10 different planar beta-strand dimer conformations. We then estimate the free energies of all dimer conformations in all-atom molecular mechanics simulations with explicit water. We compare the free energies of Abeta(1-42) and Abeta(1-40) dimers. We find that 1), dimer conformations have higher free energies compared to their corresponding monomeric states; and 2), the free-energy difference between the Abeta(1-42) and the corresponding Abeta(1-40) dimer conformation is not significant. Our results suggest that Abeta oligomerization is not accompanied by the formation of thermodynamically stable planar beta-strand dimers.

Potential functions for hydrogen bonds in protein structure prediction and design

Hydrogen bonds are an important contributor to free energies of biological macromolecules and macromolecular complexes, and hence an accurate description of these interactions is important for progress in biomolecular modeling. A simple description of the hydrogen bond is based on an electrostatic dipole-dipole interaction involving hydrogen-donor and acceptor-acceptor base dipoles, but the physical nature of hydrogen bond formation is more complex. At the most fundamental level, hydrogen bonding is a quantum mechanical phenomenon with contributions from covalent effects, polarization, and charge transfer. Recent experiments and theoretical calculations suggest that both electrostatic and covalent components determine the properties of hydrogen bonds. Likely, the level of rigor required to describe hydrogen bonding will depend on the problem posed. Current approaches to modeling hydrogen bonds include knowledge-based descriptions based on surveys of hydrogen bond geometries in structural databases of proteins and small molecules, empirical molecular mechanics models, and quantum mechanics-based electronic structure calculations. Ab initio calculations of hydrogen bonding energies and geometries accurately reproduce energy landscapes obtained from the distributions of hydrogen bond geometries observed in protein structures. Orientation-dependent hydrogen bonding potentials were found to improve the quality of protein structure prediction and refinement, protein-protein docking, and protein design.

Revisiting free energy calculations: a theoretical connection to MM/PBSA and direct calculation of the association free energy

The prediction of absolute ligand-receptor binding affinities is essential in a wide range of biophysical queries, from the study of protein-protein interactions to structure-based drug design. End-point free energy methods, such as the Molecular Mechanics Poisson-Boltzmann Surface Area (MM/PBSA) model, have received much attention and widespread application in recent literature. These methods benefit from computational efficiency as only the initial and final states of the system are evaluated, yet there remains a need for strengthening their theoretical foundation. Here a clear connection between statistical thermodynamics and end-point free energy models is presented. The importance of the association free energy, arising from one molecule's loss of translational and rotational freedom from the standard state concentration, is addressed. A novel method for calculating this quantity directly from a molecular dynamics simulation is described. The challenges of accounting for changes in the protein conformation and its fluctuations from separate simulations are discussed. A simple first-order approximation of the configuration integral is presented to lay the groundwork for future efforts. This model has been applied to FKBP12, a small immunophilin that has been widely studied in the drug industry for its potential immunosuppressive and neuroregenerative effects.

Distinguish protein decoys by Using a scoring function based on a new AMBER force field, short molecular dynamics simulations, and the generalized born solvent model

Recent works have shown the ability of physics-based potentials (e.g., CHARMM and OPLS-AA) and energy minimization to differentiate the native protein structures from large ensemble of non-native structures. In this study, we extended previous work by other authors and developed an energy scoring function using a new set of AMBER parameters (also recently developed in our laboratory) in conjunction with molecular dynamics and the Generalized Born solvent model. We evaluated the performance of our new scoring function by examining its ability to distinguish between the native and decoy protein structures. Here we present a systematic comparison of our results with those obtained with use of other physics-based potentials by previous authors. A total of 7 decoy sets, 117 protein sequences, and more than 41,000 structures were evaluated. The results of our study showed that our new scoring function represents a significant improvement over previously published physics-based scoring functions.

Protein flexibility and computer-aided drug design

Although computational techniques are increasingly being used in computer-aided drug design, the effects due to protein flexibility are still ignored in many applications. This review revisits rigorous statistical mechanical methods for predicting binding affinity, discusses some recent developments for improving their speed and reliability, and examines faster approximate models for facilitating virtual screening and lead optimization.

How well can we predict native contacts in proteins based on decoy structures and their energies?

One strategy for ab initio protein structure prediction is to generate a large number of possible structures (decoys) and select the most fitting ones based on a scoring or free energy function. The conformational space of a protein is huge, and chances are rare that any heuristically generated structure will directly fall in the neighborhood of the native structure. It is desirable that, instead of being thrown away, the unfitting decoy structures can provide insights into native structures so prediction can be made progressively. First, we demonstrate that a recently parameterized physics-based effective free energy function based on the GROMOS96 force field and a generalized Born/surface area solvent model is, as several other physics-based and knowledge-based models, capable of distinguishing native structures from decoy structures for a number of widely used decoy databases. Second, we observe a substantial increase in correlations of the effective free energies with the degree of similarity between the decoys and the native structure, if the similarity is measured by the content of native inter-residue contacts in a decoy structure rather than its root-mean-square deviation from the native structure. Finally, we investigate the possibility of predicting native contacts based on the frequency of occurrence of contacts in decoy structures. For most proteins contained in the decoy databases, a meaningful amount of native contacts can be predicted based on plain frequencies of occurrence at a relatively high level of accuracy. Relative to using plain frequencies, overwhelming improvements in sensitivity of the predictions are observed for the 4_state_reduced decoy sets by applying energy-dependent weighting of decoy structures in determining the frequency. There, approximately 80% native contacts can be predicted at an accuracy of approximately 80% using energy-weighted frequencies. The sensitivity of the plain frequency approach is much lower (20% to 40%). Such improvements are, however, not observed for the other decoy databases. The rationalization and implications of the results are discussed.

The role of the dielectric barrier in narrow biological channels: a novel composite approach to modeling single-channel currents

A composite continuum theory for calculating ion current through a protein channel of known structure is proposed, which incorporates information about the channel dynamics. The approach is utilized to predict current through the Gramicidin A ion channel, a narrow pore in which the applicability of conventional continuum theories is questionable. The proposed approach utilizes a modified version of Poisson-Nernst-Planck (PNP) theory, termed Potential-of-Mean-Force-Poisson-Nernst-Planck theory (PMFPNP), to compute ion currents. As in standard PNP, ion permeation is modeled as a continuum drift-diffusion process in a self-consistent electrostatic potential. In PMFPNP, however, information about the dynamic relaxation of the protein and the surrounding medium is incorporated into the model of ion permeation by including the free energy of inserting a single ion into the channel, i.e., the potential of mean force along the permeation pathway. In this way the dynamic flexibility of the channel environment is approximately accounted for. The PMF profile of the ion along the Gramicidin A channel is obtained by combining an equilibrium molecular dynamics (MD) simulation that samples dynamic protein configurations when an ion resides at a particular location in the channel with a continuum electrostatics calculation of the free energy. The diffusion coefficient of a potassium ion within the channel is also calculated using the MD trajectory. Therefore, except for a reasonable choice of dielectric constants, no direct fitting parameters enter into this model. The results of our study reveal that the channel response to the permeating ion produces significant electrostatic stabilization of the ion inside the channel. The dielectric self-energy of the ion remains essentially unchanged in the course of the MD simulation, indicating that no substantial changes in the protein geometry occur as the ion passes through it. Also, the model accounts for the experimentally observed saturation of ion current with increase of the electrolyte concentration, in contrast to the predictions of standard PNP theory.

Molecular dynamics simulations and thermodynamics analysis of DNA-drug complexes. Minor groove binding between 4',6-diamidino-2-phenylindole and DNA duplexes in solution

An extended set of nanosecond-scale molecular dynamics simulations of DNA duplex sequences in explicit solvent interacting with the minor groove binding drug 4',6-diamidino-2-phenylindole (DAPI) are investigated for four different and sequence specific binding modes. Force fields for DAPI have been parametrized to properly reflect its internal nonplanarity. Sequences investigated include the binding modes observed experimentally, that is, AATT in d(CGCGAATTCGCG)(2) and ATTG in d(GGCCAATTGG)(2) and alternative shifted binding modes ATTC and AATT, respectively. In each case, stable MD simulations are obtained, well reproducing specific hydration patterns seen in the experiments. In contrast to the 2.4 A d(CGCGAATTCGCG)(2) crystal structure, the DAPI is nonplanar, consistent with its gas-phase geometry and the higher resolution crystal structure. The simulations also suggest that the DAPI molecule is able to adopt different conformational substates accompanied by specific hydration patterns that include long-residing waters. The MM_PBSA technology for estimating relative free energies was utilized. The most consistent free energy results were obtained with an approach that uses a single trajectory of the DNA-DAPI complex to estimate all free energy terms. It is demonstrated that explicit inclusion of a subset of bound water molecules shifts the calculated relative binding free energies in favor of both crystallographically observed binding modes, underlining the importance of structured hydration.