A new method for predicting binding free energy between receptor and ligand

A practical method to estimate binding free energy, ΔG_bind, of a given ligand structure to the target receptor has been developed. The method assumes that ΔG_bind is given by the summation of intermolecular interaction energy, ΔG_inter, and partial desolvation energy, ΔG_desolv. ΔG_desolv is calculated from the buried surface area in the complex between the ligand and receptor, based on solvation energy, ΔG_solv, formulated by an equation which can be calibrated with observed values. Then, the method was applied to arabinose-binding protein (ABP) and dihydrofolate reductase (DHFR), after recalibrating the weights for ΔG_inter and each term of ΔG_desolv using observed ΔG_bind data for 29 known ligands to avidin (AV). The usefulness of our method was confirmed by the fact that correlation coefficients between the calculated and observed ΔG_bind's in AV, ABP and DHFR were 0.92, 0.77, and 0.88, whereas the corresponding values obtained by simple force field calculation were 0.79, 0.30, and 0.79, respectively. Further investigations to improve the method and validate the parameters are in progress. Proteins 33:62–73, 1998. © 1998 Wiley-Liss, Inc.     

Hydropathic analysis of the free energy differences in anthracycline antibiotic binding to DNA

Molecular models of six anthracycline antibiotics and their complexes with 32 distinct DNA octamer sequences were created and analyzed using HINT (Hydropathic INTeractions) to describe binding. The averaged binding scores were then used to calculate the free energies of binding for comparison with experimentally determined values. In parsing our results based on specific functional groups of doxorubicin, our calculations predict a free energy contribution of –3.6 ± 1.1 kcal mol^–1 (experimental –2.5 ± 0.5 kcal mol^–1) from the groove binding daunosamine sugar. The net energetic contribution of removing the hydroxyl at position C9 is –0.7 ± 0.7 kcal mol^–1 (–1.1 ± 0.5 kcal mol^–1). The energetic contribution of the 3′ amino group in the daunosamine sugar (when replaced with a hydroxyl group) is –3.7 ± 1.1 kcal mol^–1 (–0.7 ± 0.5 kcal mol^–1). We propose that this large discrepancy may be due to uncertainty in the exact protonation state of the amine. The energetic contribution of the hydroxyl group at C14 is +0.4 ± 0.6 kcal mol^–1 (–0.9 ± 0.5 kcal mol^–1), largely due to unfavorable hydrophobic interactions between the hydroxyl oxygen and the methylene groups of the phosphate backbone of the DNA. Also, there appears to be considerable conformational uncertainty in this region. This computational procedure calibrates our methodology for future analyses where experimental data are unavailable.     

Use of Hoechst fluorescent probe 33258 for quantitative analysis of intracellular binding of anthracycline antibiotics to DNA]

The paper deals with development of a procedure for quantitative determination of the share of anthracycline antibiotics bound in cells directly to DNA. A DNA-specific Hoechst fluorescence dye 33258 was used for the purpose. The level of its quenching on DNA correlated with the quantity of the antibiotic bound to it. It was shown that the quenching of the Hoechst fluorescence dye bound to DNA was not due to the dye competition with the antibiotic for the site of bounding on DNA, as was suggested earlier. It was likely to be defined by reabsorption of the radiation by antibiotic molecules.     

A simple model for predicting the performance of affinity chromatography columns

Summary This paper presents a simple model for affinity chromatography, the approach used is based on the equilibrium stage model introduced by Martin and Synge (1941). The current development eliminates the need for an equilibrium assumption by using a simplified rate equation to describe the adsorption process. Although it is not mathematically rigorous this method has proved useful for the design of column experiments in our laboratory.     

Interaction of anthracycline antibiotics with biopolymers: 7. Equilibrium binding studies on the interaction of iremycin and DNA

We report spectrophotometric equilibrium studies of both the self-association of the new antibiotic iremycin and of its binding to calf thymus DNA in solution (ionic strength 0.2 M; pH 6.0). Iremycin forms dimers in this solution with a dimerization constant K₄=(1.19 ± 0.10) × 10³ M⁻¹. This equilibrium is taken into account in the evaluation of the interaction of iremycin with DNA. The binding behaviour can be completely described by a single binding mechanism of monomeric iremycin to DNA with allowance both for neighbour exclusion and for cooperativity of interaction. The three intrinsic binding parameters for the homogeneous model were determined simultaneously by a least squares fit of the original titration data: equilibrium constant of cooperative binding K = (2.72 ± 0.66) × 10⁵ M⁻¹ cooperativity parameter σ=0.38±3.27 ± 0.32. The binding parameters of iremycin and adriamycin and their microbial activities are compared.     

The solvation contribution to the binding energy of DNA with non-intercalating antibiotics.

The influence of the solvent on the binding energies to DNA of six non-intercalating antibiotics - netropsin, distamycin-3, distamycin-2, SN 18071, berenil and stilbamidine - is evaluated by combining the effect of the first hydration shell with that of bulk water. The first effect is computed by a methodology based on a spherical/point dipole model of water and limited to electrostatic interaction energies. Hydration shells are obtained which are energy optimized with respect to both water-solute and water-water interactions for the complexes and for the isolated DNA oligomers and ligands. The method allows even very large complexes to be studied in reasonable computation times. The second effect is introduced via a cavity treatment. It is shown that if the vacuum interaction energies already predict correctly the preference of the ligands for the minor groove of AT sequences of B-DNA, the introduction of the solvation effect is indispensable for reproducing the order of affinity of the ligands and for bringing the values of the complexation energies into close agreement with experimental data.     

Free energy calculations for the relative binding affinity between DNA and lambda-repressor

The change in the binding free energy between DNA and lambda-repressor resulting from a base substitution, thymine (T)-->deoxyuracil (abbreviated as U), was evaluated by the free energy perturbation method on the basis of molecular dynamics simulations for the DNA-lambda-repressor complex in water with all degrees of freedom and including long-range Coulomb interactions. The binding free energy change that we calculated (1.47 +/- 0.40 kcal/mol) was in good agreement with an experimental value (1.8 kcal/mol). We clarified why the small difference between T and U (CH(3) in T is replaced with H in U) caused such a significant change in the binding free energy: The substitution of CH(3) in T with H in U lowered the dissociated-state free energy level due to the gain of the hydration free energy. Furthermore, the T-->U substitution raised the free energy level in the associated state due to the loss of the favored van der Waals (vdW) interactions with the lambda-repressor amino acid residues. In other words, the amino acid residues of lambda-repressor can recognize the CH(3) in T through the vdW interactions with the CH(3). This recognition is enhanced in a water environment, because the hydrophobic CH(3) prefers the amino acid residues of lambda-repressor to water molecules.     

Insights into protein-protein binding by binding free energy calculation and free energy decomposition for the Ras-Raf and Ras-RalGDS complexes

Absolute binding free energy calculations and free energy decompositions are presented for the protein-protein complexes H-Ras/C-Raf1 and H-Ras/RalGDS. Ras is a central switch in the regulation of cell proliferation and differentiation. In our study, we investigate the capability of the molecular mechanics (MM)-generalized Born surface area (GBSA) approach to estimate absolute binding free energies for the protein-protein complexes. Averaging gas-phase energies, solvation free energies, and entropic contributions over snapshots extracted from trajectories of the unbound proteins and the complexes, calculated binding free energies (Ras-Raf: -15.0(+/-6.3)kcal mol(-1); Ras-RalGDS: -19.5(+/-5.9)kcal mol(-1)) are in fair agreement with experimentally determined values (-9.6 kcal mol(-1); -8.4 kcal mol(-1)), if appropriate ionic strength is taken into account. Structural determinants of the binding affinity of Ras-Raf and Ras-RalGDS are identified by means of free energy decomposition. For the first time, computationally inexpensive generalized Born (GB) calculations are applied in this context to partition solvation free energies along with gas-phase energies between residues of both binding partners. For selected residues, in addition, entropic contributions are estimated by classical statistical mechanics. Comparison of the decomposition results with experimentally determined binding free energy differences for alanine mutants of interface residues yielded correlations with r(2)=0.55 and 0.46 for Ras-Raf and Ras-RalGDS, respectively. Extension of the decomposition reveals residues as far apart as 25A from the binding epitope that can contribute significantly to binding free energy. These "hotspots" are found to show large atomic fluctuations in the unbound proteins, indicating that they reside in structurally less stable regions. Furthermore, hotspot residues experience a significantly larger-than-average decrease in local fluctuations upon complex formation. Finally, by calculating a pair-wise decomposition of interactions, interaction pathways originating in the binding epitope of Raf are found that protrude through the protein structure towards the loop L1. This explains the finding of a conformational change in this region upon complex formation with Ras, and it may trigger a larger structural change in Raf, which is considered to be necessary for activation of the effector by Ras.     

Interaction model for anthracycline activity against DNA topoisomerase II

DNA topoisomerase II (Top2) is an essential nuclear enzyme and a target of very effective anticancer drugs including anthracycline antibiotics. Even though several aspects of drug activity against Top2 are understood, the drug receptor site is not yet known. Several Top2 mutants have altered drug sensitivity and have provided information of structural features determining drug action. Here, we have investigated the sensitivity to three closely related anthracycline derivatives of yeast Top2 bearing mutations in the CAP-like domain and integrated the findings with computer models of ternary drug-enzyme-DNA complexes. The results suggest a model for the anthracycline receptor wherein a drug molecule has specific interactions with the cleaved DNA as well as amino acid residues of the CAP-like domain of an enzyme monomer. The drug molecule is intercalated into DNA at the site of cleavage, and interestingly, drug-enzyme contacts involve one side of the four-ring chromophore and the side chain of the anthracycline molecule. The findings may explain several established structure-activity relationships of antitumor anthracyclines and may thus provide a framework for further developments of effective Top2 poisons.     

Predicting absolute ligand binding free energies to a simple model site

A central challenge in structure-based ligand design is the accurate prediction of binding free energies. Here we apply alchemical free energy calculations in explicit solvent to predict ligand binding in a model cavity in T4 lysozyme. Even in this simple site, there are challenges. We made systematic improvements, beginning with single poses from docking, then including multiple poses, additional protein conformational changes, and using an improved charge model. Computed absolute binding free energies had an RMS error of 1.9 kcal/mol relative to previously determined experimental values. In blind prospective tests, the methods correctly discriminated between several true ligands and decoys in a set of putative binders identified by docking. In these prospective tests, the RMS error in predicted binding free energies relative to those subsequently determined experimentally was only 0.6 kcal/mol. X-ray crystal structures of the new ligands bound in the cavity corresponded closely to predictions from the free energy calculations, but sometimes differed from those predicted by docking. Finally, we examined the impact of holding the protein rigid, as in docking, with a view to learning how approximations made in docking affect accuracy and how they may be improved.     

A simple model for DNA elution from filters

DNA chain scission, induced both in vitro and in vivo by various agents, is an event of great biological relevance. The damage is currently evaluated by empirical membrane separation techniques; the results are quite reproducible and the sensitivity higher than 1 single strand break per 10(9) Daltons. We outline a simple theory of the filtration of coiled macrosolutes, having a random size distribution, through porous membranes, considered as being in quasi-steady flow. The basic transport equation Jj = cj (1 - sigma)Jv is solved by considering that the value of sigma j, the reflection coefficient of component j, (1 less than or equal to j less than or equal to N), is given by (1 - KjRj), where Kj is the partition constant between pore and solution, a function of the conformational entropy loss of the coil, and Rj accounts for the frictional force experienced by a particle moving along the pore. The problem of evaluating the volume Vs filled up with solute has been approached according to a simplified theory of the excluded volume for flexible polymers; the result is Vs = sigma nj4/3 pi(rGj)3 where rGj is the jth radius of gyration. The solution of the resulting set of N differential equations gives nj, the number of molecules of component j remaining on the filter, as a function of the elution volume V. The theory demonstrates that the process is governed by the average dimensions of the coil, so affording a universal calibration of filter elution methods, in excellent agreement with the experiments.     

Quantitative determination of anthracycline antibiotic binding with DNA]

A new method of quantitative intravital assessment of anthracyclines accumulation and binding with DNA in alive cells has been developed. For this purpose DNA specific fluorescent dye Hoechst 33258 was used. Extent of fluorescence quenching of bound with DNA dye correlated with binding of daunomycin with cell DNA after mixing solutions of the drug and cells. It allowed us to determine quantity of drug molecules bound with DNA in the cells during the time.     

Influence of some chromophore substituents on the intercalation of anthracycline antibiotics into DNA

The interaction between some chromopore-modified daunorubicin derivatives and calf thymus DNA was studied using a number of physical techniques in order to investigate the effect substituents on the aromatic ring system have on the capacity to intercalate into DNA and on the DNA binding affinity. The modifications examined include methylation of the hydroxyl groups at the 6 and 11 positions of the B ring and removal of the 11-hydroxyl group. The studies showed that only 11-deoxydaunorubicin retains the ability to bind to DNA by the intercalation mechanism typical of the parent compound, although the structural modification leads to an appreciably weaker binding. In contrast, methylation of any hydroxyl group dramatically reduces the affinity of the drug for DNA. At physiological ionic strength both methyl ether derivatives showed no evidence of intercalation. Structure activity correlations for the intercalation reaction deduced from these studies are in agreement with earlier findings and hypotheses relating to antitumour activity.     

Electrostatic contributions to the binding free energy of the lambdacI repressor to DNA.

A model based on the nonlinear Poisson-Boltzmann (NLPB) equation is used to study the electrostatic contribution to the binding free energy of the lambdacI repressor to its operator DNA. In particular, we use the Poisson-Boltzmann model to calculate the pKa shift of individual ionizable amino acids upon binding. We find that three residues on each monomer, Glu34, Glu83, and the amino terminus, have significant changes in their pKa and titrate between pH 4 and 9. This information is then used to calculate the pH dependence of the binding free energy. We find that the calculated pH dependence of binding accurately reproduces the available experimental data over a range of physiological pH values. The NLPB equation is then used to develop an overall picture of the electrostatics of the lambdacI repressor-operator interaction. We find that long-range Coulombic forces associated with the highly charged nucleic acid provide a strong driving force for the interaction of the protein with the DNA. These favorable electrostatic interactions are opposed, however, by unfavorable changes in the solvation of both the protein and the DNA upon binding. Specifically, the formation of a protein-DNA complex removes both charged and polar groups at the binding interface from solvent while it displaces salt from around the nucleic acid. As a result, the electrostatic contribution to the lambdacI repressor-operator interaction opposes binding by approximately 73 kcal/mol at physiological salt concentrations and neutral pH. A variety of entropic terms also oppose binding. The major force driving the binding process appears to be release of interfacial water from the protein and DNA surfaces upon complexation and, possibly, enhanced packing interactions between the protein and DNA in the interface. When the various nonelectrostatic terms are described with simple models that have been applied previously to other binding processes, a general picture of protein/DNA association emerges in which binding is driven by the nonpolar interactions, whereas specificity results from electrostatic interactions that weaken binding but are necessary components of any protein/DNA complex.     

Theoretical prediction of the binding free energy for mutants of replication protein A

The replication protein A (RPA) is a heterotrimeric (70, 32, and 14 kDa subunits), single stranded DNA (ssDNA) binding protein required for pivotal functions in the cell metabolism, such as chromosomal replication, prevention of hairpin formation, DNA repair and recombination, and signaling after DNA damage. Studies based on deletions and mutations have identified the high affinity ssDNA binding domains in the 70 kDa subunit of RPA, regions A and B. Individually, the domain A and B have a low affinity for ssDNA, while tandems composed of AA, AB, BB, and BA sequences bind the ssDNA with moderate to high affinity. Single and double point mutations on polar residues in the binding domains leads to a reduction in affinity of RPA for ssDNA, in particular when two hydrophilic residues are involved. In view of these results, we performed a study based on molecular dynamics simulation aimed to reproduce the experimental change in binding free energy, ΔΔG, of RPA70 mutants to further elucidate the nature of the protein-ssDNA interaction. The MM-PB(GB)SA methods implemented in Amber10 and the code FoldX were used to estimate the binding free energy. The theoretical and experimental ΔΔG values correlate better when the results are obtained by MM-PBSA calculated on individual trajectories for each mutant. In these conditions, the correlation coefficient between experimental and theoretical ΔΔG reaches a value of 0.95 despite the overestimation of the energy change by one order of magnitude. The decomposition of the MM-GBSA energy per residue allows us to correlate the change of the affinity with the residue polarity and energy contribution to the binding. The method revealed reliable predictions of the change in the affinity in function of mutations, and can be used to identify new mutants with distinct binding properties.     

A simple model predicting individual weight change in humans

Excessive weight in adults is a national concern with over 2/3 of the US population deemed overweight. Because being overweight has been correlated to numerous diseases such as heart disease and type 2 diabetes, there is a need to understand mechanisms and predict outcomes of weight change and weight maintenance. A simple mathematical model that accurately predicts individual weight change offers opportunities to understand how individuals lose and gain weight and can be used to foster patient adherence to diets in clinical settings. For this purpose, we developed a one-dimensional differential equation model of weight change based on the energy balance equation paired to an algebraic relationship between fat-free mass and fat mass derived from a large nationally representative sample of recently released data collected by the Centers for Disease Control. We validate the model's ability to predict individual participants’ weight change by comparing model estimates of final weight data from two recent underfeeding studies and one overfeeding study. Mean absolute error and standard deviation between model predictions and observed measurements of final weights are less than 1.8±1.3 kg for the underfeeding studies and 2.5±1.6 kg for the overfeeding study. Comparison of the model predictions to other one-dimensional models of weight change shows improvement in mean absolute error, standard deviation of mean absolute error, and group mean predictions. The maximum absolute individual error decreased by approximately 60% substantiating reliability in individual weight-change predictions. The model provides a viable method for estimating individual weight change as a result of changes in intake and determining individual dietary adherence during weight-change studies.