Quantification and characterization of P-glycoprotein-substrate interactions

It is generally accepted that P-glycoprotein binds its substrates in the lipid phase of the membrane. Quantification and characterization of the lipid-transporter binding step are, however, still a matter of debate. We therefore selected 15 structurally diverse drugs and measured the binding constants from water to the activating (inhibitory) binding region of P-glycoprotein, K(tw(1)) (K(tw(2))), as well as the lipid-water partition coefficients, K(lw). The former were obtained by measuring the concentrations of half-maximum activation (inhibition), K(1) (K(2)), in living NIH-MDR-G185 mouse embryo fibroblasts using a Cytosensor microphysiometer, and the latter were derived from surface activity measurements. This allowed determination of the membrane concentration of drugs at half-maximum P-glycoprotein activation (C(b(1)) = (0.02 to 67) mmol/L lipid), which is much higher than the corresponding aqueous concentration (K(1) = (0.02 to 376) microM). Moreover we determined the free energy of drug binding from water to the activating binding region of the transporter (DeltaG degrees (tw(1)) = (-30 to -54) kJ/mol), the free energy of drug partitioning into the lipid membrane (DeltaG degrees (lw) = (-23 to -34) kJ/mol), and, as the difference of the two, the free energy of drug binding from the lipid membrane to the activating binding region of the transporter (DeltaG degrees (tl(1)) = (-7 to -27) kJ/mol). For the compounds tested DeltaG degrees (tl(1)) was less negative than DeltaG degrees (lw) but varied more strongly. The free energies of substrate binding to the transporter within the lipid phase, DeltaG degrees (tl(1)), are consistent with a modular binding concept, where the energetically most efficient binding module comprises two hydrogen bond acceptor groups.     

Implicit solvent model studies of the interactions of the influenza hemagglutinin fusion peptide with lipid bilayers

The "fusion peptide," a segment of approximately 20 residues of the influenza hemagglutinin (HA), is necessary and sufficient for HA-induced membrane fusion. We used mean-field calculations of the free energy of peptide-membrane association (DeltaG(tot)) to deduce the most probable orientation of the fusion peptide in the membrane. The main contributions to DeltaG(tot) are probably from the electrostatic (DeltaG(el)) and nonpolar (DeltaG(np)) components of the solvation free energy; these were calculated using continuum solvent models. The peptide was described in atomic detail and was modeled as an alpha-helix based on spectroscopic data. The membrane's hydrocarbon region was described as a structureless slab of nonpolar medium embedded in water. All the helix-membrane configurations, which were lower in DeltaG(tot) than the isolated helix in the aqueous phase, were in the same (wide) basin in configurational space. In each, the helix was horizontally adsorbed at the water-bilayer interface with its principal axis parallel to the membrane plane, its hydrophobic face dissolved in the bilayer, and its polar face in the water. The associated DeltaG(tot) value was approximately -8 to -10 kcal/mol (depending on the rotameric state of one of the phenylalanine residues). In contrast, the DeltaG(tot) values associated with experimentally observed oblique orientations were found to be near zero, suggesting they are marginally stable at best. The theoretical model did not take into account the interactions of the polar headgroups with the peptide and peptide-induced membrane deformation effects. Either or both may overcompensate for the DeltaG(tot) difference between the horizontal and oblique orientations.     

Examining methods for calculations of binding free energies: LRA, LIE, PDLD-LRA, and PDLD/S-LRA calculations of ligands binding to an HIV protease

Several strategies for evaluation of the protein-ligand binding free energies are examined. Particular emphasis is placed on the Linear Response Approximation (LRA) (Lee et. al., Prot Eng 1992;5:215-228) and the Linear Interaction Energy (LIE) method (Aqvist et. al., Prot Eng 1994;7:385-391). The performance of the Protein Dipoles Langevin Dipoles (PDLD) method and its semi-microscopic version (the PDLD/S method) is also considered. The examination is done by using these methods in the evaluating of the binding free energies of neutral C2-symmetric cyclic urea-based molecules to Human Immunodeficiency Virus (HIV) protease. Our starting point is the introduction of a thermodynamic cycle that decomposes the total binding free energy to electrostatic and non-electrostatic contributions. This cycle is closely related to the cycle introduced in our original LRA study (Lee et. al., Prot Eng 1992;5:215-228). The electrostatic contribution is evaluated within the LRA formulation by averaging the protein-ligand (and/or solvent-ligand) electrostatic energy over trajectories that are propagated on the potentials of both the polar and non-polar (where all residual charges are set to zero) states of the ligand. This average involves a scaling factor of 0.5 for the contributions from each state and this factor is being used in both the LRA and LIE methods. The difference is, however, that the LIE method neglects the contribution from trajectories over the potential of the non-polar state. This approximation is entirely valid in studies of ligands in water but not necessarily in active sites of proteins. It is found in the present case that the contribution from the non-polar states to the protein-ligand binding energy is rather small. Nevertheless, it is clearly expected that this term is not negligible in cases where the protein provides preorganized environment to stabilize the residual charges of the ligand. This contribution can be particularly important in cases of charged ligands. The analysis of the non-electrostatic term is much more complex. It is concluded that within the LRA method one has to complete the relevant thermodynamic cycle by evaluating the binding free energy of the "non-polar" ligand, l;, where all the residual charges are set to zero. It is shown that the LIE term, which involves the scaling of the van der Waals interaction by a constant beta (usually in the order of 0.15 to 0.25), corresponds to this part of the cycle. In order to elucidate the nature of this non-electrostatic term and the origin of the scaling constant beta, it is important to evaluate explicitly the different contributions to the binding energy of the non-polar ligand, DeltaG(bind,l;). Since this cannot be done at present (for relatively large ligands) by rigorous free energy perturbation approaches, we evaluate DeltaG(bind,l;) by the PDLD approach, augmented by microscopic calculations of the change in configurational entropy upon binding. This evaluation takes into account the van der Waals, hydrophobic, water penetration and entropic contributions, which are the most important free energy contributions that make up the total DeltaG(bind,l;). The sum of these contributions is scaled by a factor straight theta and it is argued that obtaining a quantitative balance between these contributions should result in straight theta = 1. By doing so we should have a reliable estimate of the value of the LIE beta and a way to understand its origin. The present approach gives straight theta values between 0.5 and 0.73, depending on the approximation used. This is encouraging but still not satisfying. Nevertheless, one might be able to use our PDLD approach to estimate the change of the LIE straight theta between different protein active sites. It is pointed out that the LIE method is quite similar to our original approach where the electrostatic term was evaluated by the LRA method and the non-electrostatic term by the PDLD method (with its vdw, solvation,     

Binding free energy calculations of adenosine deaminase inhibitors

The interactions between four inhibitors and adenosine deaminase (ADA) were examined by calculating their binding free energies after molecular dynamics simulations. A bonded model was used to represent the electrostatic potentials of the zinc coordination site. The charge distribution of the model was derived by using a two-stage electrostatic potential fitting calculations. The calculated binding free energies are in good agreement with the experimental data and the ranking of binding affinities is well reproduced. Notably, our findings suggest that non-polar contributions play an important role for ADA-inhibitor interactions.     

A computer simulation of functional group contributions to free energy in water and a DPPC lipid bilayer

A series of all-atom molecular dynamics simulations has been performed to evaluate the contributions of various functional groups to the free energy of solvation in water and a dipalmitoylphospatidylcholine lipid bilayer membrane and to the free energies of solute transfer (Delta(DeltaG(o))X) from water into the ordered-chain interior of the bilayer. Free energies for mutations of the alpha-H atom in p-toluic acid to six different substituents (-CH3, -Cl, -OCH3, -CN, -OH, -COOH) were calculated by a combined thermodynamic integration and perturbation method and compared to literature results from vapor pressure measurements, partition coefficients, and membrane transport experiments. Convergence of the calculated free energies was indicated by substantial declines in standard deviations for the calculated free energies with increased simulation length, by the independence of the ensemble-averaged Boltzmann factors to simulation length, and the weak dependence of hysteresis effects on simulation length over two different simulation lengths and starting from different initial configurations. Calculated values of Delta(DeltaG(o))X correlate linearly with corresponding values obtained from lipid bilayer transport experiments with a slope of 1.1 and from measurements of partition coefficients between water and hexadecane or decadiene, with slopes of 1.1 and 0.9, respectively. Van der Waals interactions between the functional group of interest and the acyl chains in the ordered chain region account for more than 95% of the overall potential energy of interaction. These results support the view that the ordered chain region within the bilayer interior is the barrier domain for transport and that solvation interactions within this region resemble those occurring in a nonpolar hydrocarbon.     

Phospholipid binding of synthetic talin peptides provides evidence for an intrinsic membrane anchor of talin

Talin, an actin-binding protein, is assumed to anchor at the membrane via an intrinsic amino acid sequence. Three N-terminal talin fragments, 21-39 (S19), 287-304 (H18), and 385-406 (H17) have been proposed as potential membrane anchors. The interaction of the corresponding synthetic peptides with lipid model systems was investigated with CD spectroscopy, isothermal titration calorimetry, and monolayer expansion measurements. The membrane model systems were neutral or negatively charged small unilamellar vesicles or monolayers with a lateral packing density of bilayers (32 mN/m). S19 partitions into charged monolayers/bilayers with a penetration area A(p) = 140 +/- 30 A(2) and a free energy of binding of DeltaG(0) = -5.7 kcal/mol, thereby forming a partially alpha-helical structure. H18 does not interact with lipid monolayers or bilayers. H17 penetrates into neutral and charged monolayers/bilayers with A(p) = 148 +/- 23 A(2) and A(p) = 160 +/- 15 A(2), respectively, forming an alpha-helix in the membrane-bound state. Membrane partitioning is mainly entropy-driven. Under physiological conditions the free energy of binding to negatively charged membranes is DeltaG(0) = -9. 4 kcal/mol with a hydrophobic contribution of DeltaG(h) = -7.8 kcal/mol, comparable to that of post-translationally attached membrane anchors, and an electrostatic contribution of DeltaG(h) = -1.6 kcal/mol. The latter becomes more negative with decreasing pH. We show that H17 provides the binding energy required for a membrane anchor.     

On the role of electrostatic interactions in the design of protein-protein interfaces

Here, the methods of continuum electrostatics are used to investigate the contribution of electrostatic interactions to the binding of four protein-protein complexes; barnase-barstar, human growth hormone and its receptor, subtype N9 influenza virus neuraminidase and the NC41 antibody, the Ras binding domain (RBD) of kinase cRaf and a Ras homologue Rap1A. In two of the four complexes electrostatics are found to strongly oppose binding (hormone-receptor and neuraminidase-antibody complexes), in one case the net effect is close to zero (barnase-barstar) and in one case electrostatics provides a significant driving force favoring binding (RBD-Rap1A). In order to help understand the wide range of electrostatic contributions that were calculated, the electrostatic free energy was partitioned into contributions of individual charged and polar residues, salt bridges and networks involving salt bridges and hydrogen bonds. Although there is no one structural feature that accounts for the differences between the four interfaces, the extent to which the desolvation of buried charges is compensated by the formation of hydrogen bonds and ion pairs appears to be an important factor. Structural features that are correlated with contribution of an individual residue to stability are also discussed. These include partial burial of a charged group in the free monomer, the formation of networks involving charged and polar amino acids, and the formation of partially exposed ion-pairs. The total electrostatic contribution to binding is found to be inversely correlated with buried total and non-polar surface area. This suggests that different interfaces can be designed to exploit electrostatic and hydrophobic forces in very different ways.     

Ionic-strength-dependent effects in protein folding: analysis of rate equilibrium free-energy relationships and their interpretation

The traditional approach to studying protein folding involves applying a perturbation, usually denaturant or mutation, and determining the effect upon the free energy of folding, DeltaG0, and the activation free energy, DeltaG(not equal). Data collected as a function of the perturbation can be used to construct rate equilibrium free-energy relationships, which report on the development of interactions in the transition state for folding. We examine the use of the ionic-strength-dependent rate equilibrium free-energy relationship in protein folding using the N-terminal domain of L9, a small alpha-beta protein, as a model system. Folding is two-state for the range of ionic strength examined, 0.045-1.52 M. The plot of DeltaG(not equal) versus DeltaG0 is linear (r2= 0.918), with a slope equal to 0.45. The relatively low value of the slope indicates that the ionic-strength-dependent interactions are modestly developed in the transition state. The slope is, however, greater than that of a plot of DeltaG(not equal) versus DeltaG0 constructed by varying pH, thus demonstrating directly that ionic-strength-dependent studies probe more than simple electrostatic interactions. Potential transition movement was probed by analysis of the denaturant, ionic strength cross-interaction parameters. The values are small but nonzero and positive, suggesting a small shift of the transition state toward the native state as the protein is destabilized, i.e., Hammond behavior. The complications that arise in the interpretation of ionic-strength-dependent rate equilibrium free-energy relationships are discussed, and it is concluded that the ionic-strength-dependent studies do not provide a reliable indicator of the role of electrostatic interactions. Complications include incomplete screening of electrostatic interactions, specific ion binding, Hofmeister effects, and the potential presence of electrostatic interactions in the denatured state ensemble.     

Prediction of the aqueous solvation free energy of organic compounds by using autocorrelation of molecular electrostatic potential surface properties combined with response surface analysis

Several quantitative structure-property relationship (QSPR) approaches have been explored for the prediction of aqueous solubility or aqueous solvation free energies, DeltaG(sol), as crucial parameter affecting the pharmacokinetic profile and toxicity of chemical compounds. It is mostly accepted that aqueous solvation free energies can be expressed quantitatively in terms of properties of the molecular surface electrostatic potentials of the solutes. In the present study we have introduced autocorrelation molecular electrostatic potential (autoMEP) vectors in combination with nonlinear response surface analysis (RSA) as alternative 3D-QSPR strategy to evaluate the aqueous solvation free energy of organic compounds. A robust QSPR model (r(cv)=0.93) has been obtained by using a collection of 248 organic chemicals. An external test set based on 23 molecules confirmed the good predictivity of the autoMEP/RSA model suggesting its further applicability in the in silico prediction of water solubility of large organic compound libraries.     

Measurement of thermodynamic parameters for hydrophobic mismatch 1: self-association of a transmembrane helix

Membrane partitioning and self-association of transmembrane helices are crucial thermodynamic steps for membrane protein folding, although experimental difficulties have hampered quantitative estimations of related thermodynamic parameters, especially in lipid bilayer environments. This article reports for the first time, the complete set of thermodynamic parameters (DeltaG, DeltaH, DeltaS, and DeltaC(p)) for the formation of the antiparallel dimer of the inert hydrophobic model transmembrane helix X-(AALALAA)(3)-Y (X = 7-nitro-2-1, 3-benzoxadiazol-4-yl (NBD) and Y = NH(2) (I) or X = Ac and Y = NHCH(2)CH(2)-S-N-[4-[[4-(dimethylamino)phenyl]azo]phenyl]maleimide (DABMI) (II)) in dimonounsaturated phosphocholine lipid bilayers with different hydrophobic thicknesses (C14-C22) at 5-55 degrees C, as evaluated by fluorescence resonance energy transfer from I to II. Stronger dimerization was observed in thicker membranes and at lower temperatures (DeltaG = -9 to -26 kJ mol(-)(1)), driven by large negative DeltaH values (-18 to -80 kJ mol(-)(1)). Fourier transform infrared-polarized spectroscopy revealed that the peptide formed a stable transmembrane helix with an orientation angle of approximately 15 degrees in all bilayers without significant effects on lipid structures, suggesting that the depth to which the helix termini penetrate changes depending on the degree of hydrophobic mismatch. The enthalpy changes for helix-helix interactions can be well explained by the electrostatic interactions between helix macrodipoles in different dielectric environments. The new concept of dipole-dipole interaction as a basic driving force of helix dimerization will become a basis for understanding the structural and functional modifications in response to hydrophobic mismatch.     

Interaction between cytochrome c2 and the photosynthetic reaction center from Rhodobacter sphaeroides: effects of charge-modifying mutations on binding and electron transfer.

The electrostatic interactions governing binding and electron transfer from cytochrome c(2) (cyt c(2)) to the reaction center (RC) from the photosynthetic bacteria Rhodobacter sphaeroides were studied by using site-directed mutagenesis to change the charges of residues on the RC surface. Charge-reversing mutations (acid --> Lys) decreased the binding affinity for cyt c(2). Dissociation constants, K(D) (0.3--250 microM), were largest for mutations of Asp M184 and nearby acid residues, identifying the main region for electrostatic interaction with cyt c(2). The second-order rate constants, k(2) (1--17 x 10(8) M(-1) s(-1)), increased with increasing binding affinity (log k(2) vs log 1/K(D) had a slope of approximately 0.4), indicating a transition state structurally related to the final complex. In contrast, first-order electron transfer rates, k(e), for the bound cyt did not change significantly (<3-fold), indicating that electron tunneling pathways were unchanged by mutation. Charge-neutralizing mutations (acid --> amide) showed changes in binding free energies of approximately 1/2 the free energy changes due to the corresponding charge-reversing mutations, suggesting that the charges in the docked complex remain well solvated. Charge-enhancing mutations (amide --> acid) produced free energy changes of the same magnitude (but opposite sign) as changes due to the charge-neutralizing mutations in the same region, indicating a diffuse electrostatic potential due to cyt c(2). A two-domain model is proposed, consisting of an electrostatic docking domain with charged surfaces separated by a water layer and a hydrophobic tunneling domain with atomic contacts that provide an efficient pathway for electron transfer.     

Role of the hydrophobic effect in stability of site-specific protein-DNA complexes

The site-specific binding interaction of lac repressor with a symmetric operator sequence and of EcoRI endonuclease with its specific recognition site both exhibit a characteristic dependence of equilibrium binding constant (Kobs) on temperature, in which Kobs attains a relative maximum in the physiologically relevant temperature range. This behavior, which appears to be quite general for site-specific protein-DNA interactions, is indicative of a large negative standard heat capacity change (delta C0P,obs) in the association process. By analogy with model compound transfer studies and protein folding data, we propose that this delta C0P,obs results primarily from the removal of non-polar surface from water in the association process. From delta C0P,obs we obtain semiquantitative information regarding the change in water-exposed non-polar surface area (delta Anp) and the corresponding hydrophobic driving force for association (delta G0hyd): delta G0hyd approximately equal to 8(+/- 1) x 10(1) delta C0P,obs approximately equal to -22(+/- 5) delta Anp. We propose that removal of non-polar surface from water (the hydrophobic effect) and release of cations (the polyelectrolyte effect) drive the thermodynamically unfavorable process (e.g. conformational distortions) necessary to achieve mutually complementary recognition surfaces (at a steric and functional-group level) in the specific complex.     

Binding free energy calculations of galectin-3-ligand interactions

Galectins show remarkable binding specificity towards beta-galactosides. A recently developed method for calculating binding free energies between a protein and its substrates has been used to evaluate the binding specificity of galectin-3. Five disaccharides and a tetrasaccharide were used as the substrates. The calculated binding free energies agree quite well with the experimental data and the ranking of binding affinities is well reproduced. For all the six protein-ligand complexes it was observed that electrostatic interactions oppose binding whereas the non-polar contributions drive complex formation. The observed binding specificity of galectin-3 for galactosides rather than glucosides is discussed in light of our results.     

Interaction of charged and uncharged calcium channel antagonists with phospholipid membranes. Binding equilibrium, binding enthalpy, and membrane location.

The membrane location and the binding mechanism of two Ca2+ channel antagonists, amlodipine and nimodipine, in pure lipid membranes were investigated with deuterium and phosphorus-31 nuclear magnetic resonance, with thermodynamic methods such as high-sensitivity titration calorimetry, and by measuring the membrane surface charge via the zeta-potential. The two drugs exhibit quite different physical-chemical properties. The noncharged nimodipine is strongly hydrophobic, and selective deuteration of the lipid membrane reveals a homogeneous distribution of nimodipine across the whole hydrocarbon layer, but no interaction at the lipid headgroup level. The membrane behavior of the amiphiphilic amlodipine (electric charge z = +1) is distinctly more complex. Deuterium magnetic resonance demonstrates that amlodipine adopts a well-defined position in the bilayer membrane. In particular, the charged ethanolamine side group of amlodipine is located near the water-lipid interface, interacting with the dipoles of the headgroup region according to a nonspecific, electrostatic mechanism and inducing a reorientation of the phosphocholine dipoles toward the water phase. At the level of the hydrocarbon segment, the nonpolar ring system of amlodipine interacts specifically with the cis double bond of the membrane lipid, forming a weak association complex. With increasing amlodipine concentration the deuterium signal of the cis double bond gradually loses intensity, a phenomenon previously observed only in related studies on protein-lipid interactions. The binding equilibrium of amlodipine to phosphatidylcholine membranes was studied by measuring the electrophoretic mobility of lipid vesicles and with a centrifugation assay. Hydrophobic interactions of the nonpolar ring systems and electrostatic repulsions at the membrane surface contribute to the binding energy.(ABSTRACT TRUNCATED AT 250 WORDS)     

Is lipid bilayer binding a common property of inhibitor cysteine knot ion-channel blockers?

Recent studies of several ICK ion-channel blockers suggest that lipid bilayer interactions play a prominent role in their actions. Structural similarities led to the hypothesis that bilayer interactions are important for the entire ICK family. We have tested this hypothesis by performing direct measurements of the free energy of bilayer partitioning (DeltaG) of several peptide blockers using our novel quenching-enhanced fluorescence titration protocol. We show that various ICK peptides demonstrate markedly different modes of interaction with large unilamellar lipid vesicles. The mechanosensitive channel blocker, GsMTx4, and its active diastereomeric analog, D-GsMTx4, bind strongly to both anionic and zwitterionic membranes. One potassium channel gating modifier, rHpTx2gs, interacts negligibly with both types of vesicles at physiological pH, whereas another, SGTx1, interacts only with anionic lipids. The slope of DeltaG dependence on surface potential is very shallow for both GsMTx4 and D-GsMTx4, indicating complex interplay of their hydrophobic and electrostatic interactions with lipid. In contrast, a cell-volume regulator, GsMTx1, and SGTx1 exhibit a very steep DeltaG dependence on surface potential, resulting in a strong binding only for membranes rich in anionic lipids. The high variability of 5 kcal/mole in observed DeltaG shows that bilayer partitioning is not a universal property of the ICK peptides interacting with ion channels.     

Calculations of antibody-antigen interactions: microscopic and semi-microscopic evaluation of the free energies of binding of phosphorylcholine analogs to McPC603.

The study of antibody-antigen interactions should greatly benefit from the development of quantitative models for the evaluation of binding free energies in proteins. The present work addresses this challenge by considering the test case of the binding free energies of phosphorylcholine analogs to the murine myeloma protein McPC603. This includes the evaluation of the differential binding energy as well as the absolute binding energies and their corresponding electrostatic contributions. Four different approaches are examined: the Protein Dipoles Langevin Dipoles (PDLD) method, the semi-microscopic PDLD (PDLD/S) method, a free energy perturbation (FEP) method based on an adiabatic charging procedure and a linear response approximation that accelerates the FEP calculation. The PDLD electrostatic calculations are augmented by estimates of the relevant hydrophobic and steric contributions. The determination of the hydrophobic energy involves an approach which considers the modification of the effective surface area of the solute by local field effects. The steric contributions are analyzed in terms of the corresponding reorganization energies. This treatment, which considers the protein as a harmonic system, views the steric forces as the restoring forces for the electrostatic interactions. The FEP method is found to give unreliable results with regular cut-off radii and starts to give quantitative results only in very expensive treatment with very large cut-off radii. The PDLD and PDLD/S methods are much faster than the FEP approach and give reasonable results for both the relative and absolute binding energies. The speed and simplicity of the PDLD/S method make it an effective strategy for interactive docking studies and indeed such an option is incorporated in the program MOLARIS. A component analysis of the different energy contributions of the FEP treatment and a similar PDLD analysis indicate that electrostatic effects provide the largest contribution to the differential binding energy, while the hydrophobic and steric contributions are much smaller. This finding lends further support to the idea that electrostatic interactions play a major role in determining the antigen specificity of McPC603.     

Interactions of cationic ligands and proteins with small nucleic acids: analytic treatment of the large coulombic end effect on binding free energy as a function of salt concentration

For nonspecific binding of oligopeptides and other cationic ligands, including proteins, to nucleic acid oligomers, we develop a model capable of quantifying and predicting the salt concentration dependence of the binding free energy (deltaG(o)obs) by way of an analytic treatment of the Coulombic end effect (CEE). Ligands, nucleic acids, and their complexes (species j of valence Zj) are modeled as finite lattices with absolute value(Zj) charged residues; the CEE is quantified by its characteristic length Ne (specified in charged residues) and its consequences for the free energy and ion association of the oligomer. Expressions are developed for the individual site binding constants Ki as a function of position (site number i) of a bound ligand on a nucleic acid and for the observed binding constant Kobs as an ensemble average of Ki. Analysis of deltaG(o)obs = -RT ln Kobs and Sa Kobs identical with (partial differential ln Kobs)/(partial differential ln a(+/-)) for binding of the oligopeptide KWK6 (ZL = +8) to single-stranded (ss) dT(pdT)(absolute value(ZD) oligomers (dT-mers) where ZD = {-6, -10, -11, -14, -15} in the range 0.1-0.25 M Na+ yields Ne = 9.0 +/- 0.8 residues at each end, demonstrating that both KWK6 and the above dT-mers are sufficiently short so that the CEE extends over the entire molecule. The dependences of Kobs and of Sa Kobs on absolute value(ZD) for a given ZL are determined by the difference between 2Ne and the net number of charged residues Q in the complex (Q identical with absolute value(ZD) - ZL). For Q < 2Ne, characteristic of complexes of KWK6 with this set of dT-mers, the distribution of binding free energies deltaG(o)obs = -RT ln Ki for sites along the DNA oligomer is parabolic, and Kobs and Sa Kobs are strongly dependent on absolute value(ZD). For Q > or = 2Ne, the distribution of binding free energies deltaG(o)obs is trapezoidal, and the dependence of Kobs and Sa Kobs on absolute value(ZD) is weaker. Application of the model to nonspecific binding of human DNA polymerase beta to ssDNA demonstrates the significance of the CEE in determining Kobs and Sa Kobs of binding of a cationic site on a protein to a DNA oligomer.     

Free energy of the binding of uridylic acid oligomers with double stranded poly(A) x poly(U)

The binding parameters (K, omega) and the free energy (DeltaG(0)) of triple helix formation have been estimated for complexes of oligo(U)(n) (n = 5, 7-10) with poly(A) . poly(U) on the basis of hypochromicity measurements. The data were treated according to the formula of McGhee and von Hippel [J. Mol. Biol. 86 (1974) 469] by a computer program ALAU [H. Schütz et al., Stud. Biophys. 104 (1984) 23] which takes absorbancies and total concentrations as input. In 1 mM cacodylate buffer pH 7.0 with 10 mM NaCl and 10 mM MgCl(2) at 5 degrees C the free energy of contiguous binding was found to be a linear function of the oligomer length with a slope of DeltaG(c,U)(0) = -0.72 (+/-0.03) kcal x mol(-1) per nucleotide. The mean cooperativity coefficient (omega) was 24.5 (+/- 5.6), and the corresponding free energy of interaction between the neighbouring oligonucleotides in the third strand was DeltaG(0(omega)) = -1.74 (+/-0.13) kcal x mol(-1).     

What determines the van der Waals coefficient beta in the LIE (linear interaction energy) method to estimate binding free energies using molecular dynamics simulations?

Recently a semiempirical method has been proposed by Aqvist et al. to calculate absolute and relative binding free energies. In this method, the absolute binding free energy of a ligand is estimated as deltaGbind = alpha + beta, where Vel(bound) and Vvdw(bound) are the electrostatic and van der Waals interaction energies between the ligand and the solvated protein from an molecular dynamics (MD) trajectory with ligand bound to protein and Vel(free) and Vel(free) and Vvdw(free) are the electrostatic and van der Waals interaction energies between the ligand and the water from an MD trajectory with the ligand in water. A set of values, alpha = 0.5 and beta = 0.16, was found to give results in good agreement with experimental data. Later, however, different optimal values of beta were found in studies of compounds binding to P450cam and avidin. The present work investigates how the optimal value of beta depends on the nature of binding sites for different protein-ligand interactions. By examining seven ligands interacting with five proteins, we have discovered a linear correlation between the value of beta and the weighted non-polar desolvation ratio (WNDR), with a correlation coefficient of 0.96. We have also examined the ability of this correlation to predict optimal values of beta for different ligands binding to a single protein. We studied twelve neutral compounds bound to avidin. In this case, the WNDR approach gave a better estimate of the absolute binding free energies than results obtained using the fixed value of beta found for biotin-avidin. In terms of reproducing the relative binding free energy to biotin, the fixed-beta value gave better results for compounds similar to biotin, but for compounds less similar to biotin, the WNDR approach led to better relative binding free energies.