The effect of multiple binding modes on empirical modeling of ligand docking to proteins.

A popular approach to the computational modeling of ligand/receptor interactions is to use an empirical free energy like model with adjustable parameters. Parameters are learned from one set of complexes, then used to predict another set. To improve these empirical methods requires an independent way to study their inherent errors. We introduce a toy model of ligand/receptor binding as a workbench for testing such errors. We study the errors incurred from the two state binding assumption--the assumption that a ligand is either bound in one orientation, or unbound. We find that the two state assumption can cause large errors in free energy predictions, but it does not affect rank order predictions significantly. We show that fitting parameters using data from high affinity ligands can reduce two state errors; so can using more physical models that do not use the two state assumption. We also find that when using two state models to predict free energies, errors are more severe on high affinity ligands than low affinity ligands. And we show that two state errors can be diagnosed by systematically adding new binding modes when predicting free energies: if predictions worsen as the modes are added, then the two state assumption in the fitting step may be at fault.     

Further consideration of systematic errors present in protein-ligand interactions

Relatively minor systematic errors present during measurements of protein-ligand interaction can lead to large inaccuracies in the calculated values of the equilibrium dissociation constant and the total concentration of the binding protein. These errors, which include binding of the ligand to low affinity material and underestimation of bound ligand, cause the calculation of the concentration of free ligand at equilibrium to be overestimated. We report herein a model of ligandprotein binding which incorporates these errors into the mathematical formulation of the equilibrium binding equation. The effect of these errors on the Scatchard plot is presented.     

High free energy of lipid/protein interaction in biological membranes

The free energy of lipid/protein interaction in biological membranes is still unknown although extensive partitioning and modelling studies have revealed many partial energetic increments. Multiple site binding kinetics are now applied to four well-studied functional membrane proteins, and mean free energy values (+/-S.D.) of -4.23+/-0.49 kcal/mol for single lipid binding sites and of -89.7+/-35.4 kcal/mol for complete lipid substitution are obtained. These high free energy values point to an important bioenergetic role of lipid/protein interaction in membrane functions.     

Correction Approaches for Doubly Labeled Water in Situations of Changing Background Water Abundance

Doubly labeled water (DLW) is an accurate, portable method for measuring free-living energy expenditure. However, under certain conditions shifts in baseline abundance of deuterium and oxygen-18 tracers used in the method may produce errors in derivation of both turnover (k) rates and calculated energy expenditure. Present objectives were to examine during what experimental situations baseline errors arise and to address means of correcting for such baseline shifts so that consequent errors in energy expenditure calculations are minimized. Under conditions where shifts in baseline abundance for deuterium and oxygen-18 parallel abundances corresponding to the natural meteoric water ratio, self-compensating changes in k values for both deuterium and oxygen will result in minimal error to the DLW energy expenditure calculations, provided that the dose ratio of isotopes also mimics the meteoric water line. However, in situations where relative shifts in abundance of each isotope across the measurement period are not in parallel relative to the natural meteoric water line, then the potential for larger DLW errors exists. Optimally, subjects should equilibrate with the new water source. Failing this, correction for shifting baseline can be accomplished by measuring isotopic abundance changes in a control group of subjects not given the DLW dose, but performing similar tasks and consuming the same diet as the group given DLW. Alternatively, theoretically based correction values can be calculated given knowledge of the abundances of the final drinking water and the interval time that subjects consumed the new fluid.     

Ab initio and density functional theoretical design and screening of model crown ether based ligand (host) for extraction of lithium metal ion (guest): effect of donor and electronic induction

The structures, energetic and thermodynamic parameters of model crown ethers with different donor, cavity and electron donating/ withdrawing functional group have been determined with ab initio MP2 and density functional theory in gas and solvent phase. The calculated values of binding energy/ enthalpy for lithium ion complexation are marginally higher for hard donor based aza and oxa crown compared to soft donor based thia and phospha crown. The calculated values of binding enthalpy for lithium metal ion with 12C4 at MP2 level of theory is in good agreement with the available experimental result. The binding energy is altered due to the inductive effect imparted by the electron donating/ withdrawing group in crown ether, which is well correlated with the values of electron transfer. The role of entropy for extraction of hydrated lithium metal ion by different donor and functional group based ligand has been demonstrated. The HOMO-LUMO gap is decreased and dipole moment of the ligand is increased from gas phase to organic phase because of the dielectric constant of the solvent. The gas phase binding energy is reduced in solvent phase as the solvent molecules weaken the metal-ligand binding. The theoretical values of extraction energy for LiCl salt from aqueous solution in different organic solvent is validated by the experimental trend. The study presented here should contribute to the design of model host ligand and screening of solvent for metal ion recognition and thus can contribute in planning the experiments.     

Towards understanding the mechanisms of molecular recognition by computer simulations of ligand-protein interactions

The thermodynamic and kinetic aspects of molecular recognition for the methotrexate (MTX)-dihydrofolate reductase (DHFR) ligand-protein system are investigated by the binding energy landscape approach. The impact of 'hot' and 'cold' errors in ligand mutations on the thermodynamic stability of the native MTX-DHFR complex is analyzed, and relationships between the molecular recognition mechanism and the degree of ligand optimization are discussed. The nature and relative stability of intermediates and thermodynamic phases on the ligand-protein association pathway are studied, providing new insights into connections between protein folding and molecular recognition mechanisms, and cooperativity of ligand-protein binding. The results of kinetic docking simulations are rationalized based on the thermodynamic properties determined from equilibrium simulations and the shape of the underlying binding energy landscape. We show how evolutionary ligand selection for a receptor active site can produce well-optimized ligand-protein systems such as MTX-DHFR complex with the thermodynamically stable native structure and a direct transition mechanism of binding from unbound conformations to the unique native structure.     

Why protein R-factors are so large: a self-consistent analysis

The R-factor and R-free are commonly used to measure the quality of protein models obtained in X-ray crystallography. Well-refined protein structures usually have R-factors in the range of 20-25%, whereas intrinsic errors in the experimental data are usually around 5%. We use molecular dynamics simulations to perform a self-consistent analysis by which we determine the major factors contributing to large values of protein R-factors. The analysis shows that significant R-factor values can arise from the use of isotropic B-factors to model anisotropic protein motions and from coordinate errors. Even in the absence of coordinate errors, the use of isotropic B-factors can cause the R-factors to be around 10%; for coordinate errors smaller than 0.2 A, the two errors types make similar contributions. The inaccuracy of the energy function used and multistate protein dynamics are unlikely to make significant contributions to the large R-factors.     

Non-additivity in protein-protein interactions

The energy of binding between proteins may be seen as the sum of the contributions of the individual amino acid residues. These contributions are additive when the binding energy, due to different amino acid residues, is independent of the interactions between amino acids in the same polypeptide chain. A measure of non-additivity is the coupling free energy. In this communication it is shown that: (1) the coupling free energy is the sum of intramolecular and intermolecular contributions; and (2), when additivity exists, experimentally determined values for the free energy of transfer of amino acids from water to the hydrophobic protein-protein interface are a very good approximation of their contribution to the energy of binding. Additivity cycles can be useful in determining the precise conditions where this approximation holds.     

Probing the effect of point mutations at protein-protein interfaces with free energy calculations

We have studied the effect of point mutations of the primary binding residue (P1) at the protein-protein interface in complexes of chymotrypsin and elastase with the third domain of the turkey ovomucoid inhibitor and in trypsin with the bovine pancreatic trypsin inhibitor, using molecular dynamics simulations combined with the linear interaction energy (LIE) approach. A total of 56 mutants have been constructed and docked into their host proteins. The free energy of binding could be reliably calculated for 52 of these mutants that could unambiguously be fitted into the binding sites. We find that the predicted binding free energies are in very good agreement with experimental data with mean unsigned errors between 0.50 and 1.03 kcal/mol. It is also evident that the standard LIE model used to study small drug-like ligand binding to proteins is not suitable for protein-protein interactions. Three different LIE models were therefore tested for each of the series of protein-protein complexes included, and the best models for each system turn out to be very similar. The difference in parameterization between small drug-like compounds and protein point mutations is attributed to the preorganization of the binding surface. Our results clearly demonstrate the potential of free energy calculations for probing the effect of point mutations at protein-protein interfaces and for exploring the principles of specificity of hot spots at the interface.     

Free Energy Perturbations in Ribonuclease T1 Substrate Binding. A Study of the Influence of Simulation Length,Internal Degrees of Freedom and Structure in Free Energy Perturbations

Abstract

We have studied the reliability of free energy perturbation calculations with respect to simulation protocol and simulation length in a real biological system, the binding of two different ligands to wildtype Ribonuclease T ₁ (RNT1) and to a mutant of RNT1 with Glu-46 replaced by Gln (RNT1-Gln46). The binding of the natural substrate 3′ GMP has been compared with the binding of a fluorescent probe, 2-aminopurine 3′ mono phosphate (2AP3′MP). These simulations predict that the mutant binds 2AP3′MP better than 3′GMP. Four complete free energy perturbations were performed that form a closed loop of four free energy differences, which should sum up to zero. This could be used as a tool for searching for systematic errors that are not detected by standard forward ? backward perturbations. The perturbation between 2AP3′MP and 3′GMP is quite straightforward and similar to what has been done by other groups. The perturbation between Glu46 and Gln46 is much more complex, involving as many as twelve atoms and a change of charge. This perturbation needs much longer simulation time, 500-600 ps, than used in free energy perturbations before. The increased simulation time is needed both to reach an equilibrium and to include several phases of fluctuations of the observed parameters in the production run. The extremely long simulation time is not such a severe problem as much of the work might be done on several different machines in parallel and cheap workstations are excellent for these calculations. Problems may also occur with values of the coupling parameter Λ close to 0 or 1, due to the high mobility of atoms as well as insertion/deletion in a previously unoccupied space involved in the perturbation.     

Thermodynamic cycle-perturbation study of the binding of trifluoroacetyl dipeptide anilide inhibitors with porcine pancreatic elastase

The variety of results of crystallographic studies of the serine proteases complexed with isocoumarin inhibitors presents a challenging problem to modeling methods and molecular energetics. Therefore, the thermodynamic cycle-perturbation technique has been used to study a model system of elastase and two peptidic inhibitors. Using the program AMBER, the technique correctly predicts changes of the binding constants for the trifluoroacetyl dipeptide inhibitors in comparison with available experimental (kinetic and crystallographic) data. However, the absolute values obtained are shown to be sensitive to the specific electrostatic interaction potential parameters used in the simulations. The reader and user are cautioned that thermodynamic cycle-perturbation results may be too optimistic by underestimating the accuracy of free energy values. This is especially a matter of concern for those cases where a direct comparison with experimental values is not possible, viz., (1) the stimulation of binding of novel compounds, (2) structurally uncertain binding sites, or (3) structurally different binding modes. With our best 4-31G* ESP (electrostatic potential) charges we were able to reproduce experimentally determined free energy differences (delta delta A) with an accuracy of about 1.5 kcal/mol. Dynamically induced structural changes in the binding site of elastase, and particularly changes in hydrogen-bond patterns of the binding site, are also reported.     

Solvent accessibility as a predictive tool for the free energy of inhibitor binding to the HIV-1 protease.

We have developed a simple approach for the evaluation of the free energies of inhibitor binding to the protease of the human immunodeficiency virus (HIV-1 PR). Our algorithm is based on the observation that most groups that line the binding pockets of this enzyme are hydrophobic in nature. Based on this fact, we have likened the binding of an inhibitor to this enzyme to its transfer from water to a medium of lower polarity. The resulting expression produced values for the free energy of binding of inhibitors to the HIV-1 PR that are in good agreement with experimental values. The additive nature of this approach has enabled us to partition the free energy of binding into the contributions of single fragments. The resulting analysis clearly indicates the existence of a ranking in the participation of the enzyme's subsites in binding. Although all the enzyme's pockets contribute to binding, the ones that bind the P2-P'2 span of the inhibitor are in general the most critical for high inhibitor potency. Moreover, our method has allowed us to determine the nature of the functional groups that fit into given enzyme binding pockets. Perusal of the energy contributions of single side chains has shown that a large number of hydrophobic and aromatic groups located in the central portion of the HIV-1 PR inhibitors present optimal binding. All of these observations are in agreement with experimental evidence, providing a validation for the physical relevancy of our model.     

Systematic errors in isothermal titration calorimetry: Concentrations and baselines

In the study of 1:1 binding by isothermal titration calorimetry, reagent concentration errors are fully absorbed in the data analysis, giving incorrect values for the key parameters—K, ΔH, and n—with no effect on the least-squares statistics. Reanalysis of results from an interlaboratory study of a selected biochemical process demonstrates that concentration errors are likely responsible for most of the overall statistical error in these parameters. The concentration errors are approximately 10%, greatly exceeding expected levels. Furthermore, examination of selected data sets reveals a surprising sensitivity to the baseline, suggesting a need for great care in treating dilution heats.     

Free energy decomposition of protein-protein interactions.

A free energy decomposition scheme has been developed and tested on antibody-antigen and protease-inhibitor binding for which accurate experimental structures were available for both free and bound proteins. Using the x-ray coordinates of the free and bound proteins, the absolute binding free energy was computed assuming additivity of three well-defined, physical processes: desolvation of the x-ray structures, isomerization of the x-ray conformation to a nearby local minimum in the gas-phase, and subsequent noncovalent complex formation in the gas phase. This free energy scheme, together with the Generalized Born model for computing the electrostatic solvation free energy, yielded binding free energies in remarkable agreement with experimental data. Two assumptions commonly used in theoretical treatments; viz., the rigid-binding approximation (which assumes no conformational change upon complexation) and the neglect of vdW interactions, were found to yield large errors in the binding free energy. Protein-protein vdW and electrostatic interactions between complementary surfaces over a relatively large area (1400--1700 A(2)) were found to drive antibody-antigen and protease-inhibitor binding.     

Free energy perturbation calculations on binding and catalysis after mutating threonine 220 in subtilisin

We present the results of free energy perturbation calculations on binding and catalysis of a tetrapeptide substrate, acetyl-Phe-Ala-Ala-Phe-NMe, by native subtilisin BPN' and a subtilisin BPN' mutant (Thr220----Ala220). The calculated difference in the free energy of binding was 0.70 +/- 0.72 kcal/mol. The calculated difference in the free energy of catalysis was 1.48 +/- 0.89 kcal/mol. These calculated values compare well with the experimental values in which another substrate, succinyl-Ala-Ala-Pro-Phe-p-nitroanilide, was used. These findings suggest that Thr220 is more important for catalysis than substrate binding.     

Prediction of Ras-effector interactions using position energy matrices

MOTIVATION: One of the more challenging problems in biology is to determine the cellular protein interaction network. Progress has been made to predict protein-protein interactions based on structural information, assuming that structural similar proteins interact in a similar way. In a previous publication, we have determined a genome-wide Ras-effector interaction network based on homology models, with a high accuracy of predicting binding and non-binding domains. However, for a prediction on a genome-wide scale, homology modelling is a time-consuming process. Therefore, we here successfully developed a faster method using position energy matrices, where based on different Ras-effector X-ray template structures, all amino acids in the effector binding domain are sequentially mutated to all other amino acid residues and the effect on binding energy is calculated. Those pre-calculated matrices can then be used to score for binding any Ras or effector sequences. RESULTS: Based on position energy matrices, the sequences of putative Ras-binding domains can be scanned quickly to calculate an energy sum value. By calibrating energy sum values using quantitative experimental binding data, thresholds can be defined and thus non-binding domains can be excluded quickly. Sequences which have energy sum values above this threshold are considered to be potential binding domains, and could be further analysed using homology modelling. This prediction method could be applied to other protein families sharing conserved interaction types, in order to determine in a fast way large scale cellular protein interaction networks. Thus, it could have an important impact on future in silico structural genomics approaches, in particular with regard to increasing structural proteomics efforts, aiming to determine all possible domain folds and interaction types. AVAILABILITY: All matrices are deposited in the ADAN database (http://adan-embl.ibmc.umh.es/). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Energetics of interaction of oligopeptide (lac 53-57) with DNA base sequences and origin of sequence-specific recognition

Computer model building with a dynamic energy minimization procedure is used here to study the interaction of a pentapeptide sequence from the lac repressor headpiece (lac 53-57) with different base sequences of DNA. The peptide fragment for this purpose was considered in the classical beta-antiparallel as well as the beta-associated conformation. The model of its interaction with DNA was optimised for various binding positions and base sequences. Partitioning of energy is analysed for different dielectric constant values and the main contributing factors to sequence-specific binding are discussed.     

Prediction of inhibitor binding free energies by quantum neural networks. Nucleoside analogues binding to trypanosomal nucleoside hydrolase

A computational method has been developed to predict inhibitor binding energy for untested inhibitor molecules. A neural network is trained from the electrostatic potential surfaces of known inhibitors and their binding energies. The algorithm is then able to predict, with high accuracy, the binding energy of unknown inhibitors. IU-nucleoside hydrolase from Crithidia fasciculata and the inhibitor molecules described previously [Miles, R. W. Tyler, P. C. Evans, G. Furneaux R. H., Parkin, D. W., and Schramm, V. L. (1999) Biochemistry 38, xxxx-xxxx] are used as the test system. Discrete points on the molecular electrostatic potential surface of inhibitor molecules are input to neural networks to identify the quantum mechanical features that contribute to binding. Feed-forward neural networks with back-propagation of error are trained to recognize the quantum mechanical electrostatic potential and geometry at the entire van der Waals surface of a group of training molecules and to predict the strength of interactions between the enzyme and novel inhibitors. The binding energies of unknown inhibitors were predicted, followed by experimental determination of K(i)() values. Predictions of K(i)() values using this theory are compared to other methods and are more robust in estimating inhibitory strength. The average deviation in estimating K(i)() values for 18 unknown inhibitor molecules, with 21 training molecules, is a factor of 5 x K(i)() over a range of 660 000 in K(i)() values for all molecules. The a posteriori accuracy of the predictions suggests the method will be effective as a guide for experimental inhibitor design.     

Correcting errors in synthetic DNA through consensus shuffling

Although efficient methods exist to assemble synthetic oligonucleotides into genes and genomes, these suffer from the presence of 1–3 random errors/kb of DNA. Here, we introduce a new method termed consensus shuffling and demonstrate its use to significantly reduce random errors in synthetic DNA. In this method, errors are revealed as mismatches by re-hybridization of the population. The DNA is fragmented, and mismatched fragments are removed upon binding to an immobilized mismatch binding protein (MutS). PCR assembly of the remaining fragments yields a new population of full-length sequences enriched for the consensus sequence of the input population. We show that two iterations of consensus shuffling improved a population of synthetic green fluorescent protein (GFPuv) clones from ~60 to >90% fluorescent, and decreased errors 3.5- to 4.3-fold to final values of ~1 error per 3500 bp. In addition, two iterations of consensus shuffling corrected a population of GFPuv clones where all members were non-functional, to a population where 82% of clones were fluorescent. Consensus shuffling should facilitate the rapid and accurate synthesis of long DNA sequences.     

Linear free energy relationships in enzyme binding interactions studied by protein engineering.

Experiments on mutants of tyrosyl-tRNA synthetase have shown that there can be linear free energy relationships (LFERs) between changes in activation free energies and changes in binding energies when groups are deleted that bind to non-reacting parts of the substrate (Fersht et al., 1986, 1987). It has now been proposed (Straub and Karplus, 1990) that such LFERs can occur for the mutation of hydrogen bonding groups only for the limiting examples of Br?nsted beta of 0, 1 or infinity, and that fractional values of beta are not permissible. The reasoning behind this is that the energy of a hydrogen bond is not linear with distance and the (false) premise that an LFER requires that there is a linear relationship between bond energy and distance. We show from a simple model how LFERs can arise for binding interactions and how they can give fractional values of beta, in accord with experimental evidence. An LFER occurs between binding and catalysis when a set of interactions exists in which each member contributes to the binding energy of the transition state the same fraction of the binding energy it contributes to the products (both relative to the ground state).