A statistical rescoring scheme for protein-ligand docking: Consideration of entropic effect

Computational prediction of protein-ligand binding modes provides useful information on the relationship between structure and activity needed for drug design. A statistical rescoring method that incorporates entropic effect is proposed to improve the accuracy of binding mode prediction. A probability function for two sampled conformations to belong to the same broad basin in the potential energy surface is introduced to estimate the contribution of the state represented by a sampled conformation to the configurational integral. The rescoring function is reduced to the colony energy introduced by Xiang et al. (Proc Natl Acad Sci USA 2002;99:7432-7437) when a particular functional form for the probability function is used. The scheme is applied to rescore protein-ligand complex conformations generated by AutoDock. It is demonstrated that this simple rescoring improves prediction accuracy substantially when tested on 163 protein-ligand complexes with known experimental structures. For example, the percentage of complexes for which predicted ligand conformations are within 1 A root-mean-square deviation from the native conformations is doubled from about 20% to more than 40%. Rescoring with 11 different scoring functions including AutoDock scoring functions were also tested using the ensemble of conformations generated by Wang et al. (J Med Chem 2003;46:2287-2303). Comparison with other methods that use clustering and estimation of conformational entropy is provided. Examination of the docked poses reveals that the rescoring corrects the predictions in which ligands are tightly fit into the binding pockets and have low energies, but have too little room for conformational freedom and thus have low entropy.     

Conformational dynamics and thermodynamics of protein-ligand binding studied by NMR relaxation

Protein conformational dynamics can be critical for ligand binding in two ways that relate to kinetics and thermodynamics respectively. First, conformational transitions between different substates can control access to the binding site (kinetics). Secondly, differences between free and ligand-bound states in their conformational fluctuations contribute to the entropy of ligand binding (thermodynamics). In the present paper, I focus on the second topic, summarizing our recent results on the role of conformational entropy in ligand binding to Gal3C (the carbohydrate-recognition domain of galectin-3). NMR relaxation experiments provide a unique probe of conformational entropy by characterizing bond-vector fluctuations at atomic resolution. By monitoring differences between the free and ligand-bound states in their backbone and side chain order parameters, we have estimated the contributions from conformational entropy to the free energy of binding. Overall, the conformational entropy of Gal3C increases upon ligand binding, thereby contributing favourably to the binding affinity. Comparisons with the results from isothermal titration calorimetry indicate that the conformational entropy is comparable in magnitude to the enthalpy of binding. Furthermore, there are significant differences in the dynamic response to binding of different ligands, despite the fact that the protein structure is virtually identical in the different protein-ligand complexes. Thus both affinity and specificity of ligand binding to Gal3C appear to depend in part on subtle differences in the conformational fluctuations that reflect the complex interplay between structure, dynamics and ligand interactions.     

An all atom energy based computational protocol for predicting binding affinities of protein-ligand complexes

We report here a computationally fast protocol for predicting binding affinities of non-metallo protein-ligand complexes. The protocol builds in an all atom energy based empirical scoring function comprising electrostatics, van der Waals, hydrophobicity and loss of conformational entropy of protein side chains upon ligand binding. The method is designed to ensure transferability across diverse systems and has been validated on a heterogenous dataset of 161 complexes consisting of 55 unique protein targets. The scoring function trained on a dataset of 61 complexes yielded a correlation of r=0.92 for the predicted binding free energies against the experimental binding affinities. Model validation and parameter analysis studies ensure the predictive ability of the scoring function. When tested on the remaining 100 protein-ligand complexes a correlation of r=0.92 was recovered. The high correlation obtained underscores the potential applicability of the methodology in drug design endeavors. The scoring function has been web enabled at as binding affinity prediction of protein-ligand (BAPPL) server.     

Pre-existing soft modes of motion uniquely defined by native contact topology facilitate ligand binding to proteins

Modeling protein flexibility constitutes a major challenge in accurate prediction of protein-ligand and protein-protein interactions in docking simulations. The lack of a reliable method for predicting the conformational changes relevant to substrate binding prevents the productive application of computational docking to proteins that undergo large structural rearrangements. Here, we examine how coarse-grained normal mode analysis has been advantageously applied to modeling protein flexibility associated with ligand binding. First, we highlight recent studies that have shown that there is a close agreement between the large-scale collective motions of proteins predicted by elastic network models and the structural changes experimentally observed upon ligand binding. Then, we discuss studies that have exploited the predicted soft modes in docking simulations. Two general strategies are noted: pregeneration of conformational ensembles that are then utilized as input for standard fixed-backbone docking and protein structure deformation along normal modes concurrent to docking. These studies show that the structural changes apparently "induced" upon ligand binding occur selectively along the soft modes accessible to the protein prior to ligand binding. They further suggest that proteins offer suitable means of accommodating/facilitating the recognition and binding of their ligand, presumably acquired by evolutionary selection of the suitable three-dimensional structure.     

Buried surface area,conformational entropy,and protein stability

In this paper, how to calculate the loss of conformational entropy owing to protein folding from data on protein stability, the disulfide bonding pattern and the buried surface area is suggested. The average values of the initiation constant and entropy loss per residue for the helix-coil transition, calculated according to the suggested approach, are in a good agreement with available data. It is shown that the loss of conformational entropy for proteins and protein fragments, thus calculated, can be quite accurately approximated by three straight lines, each representing the loss of conformational entropy in a given range of molecular weights. The first line corresponds to the formation of α helices, the second to proteins with molecular weights below 10,000, and the third to proteins with molecular weights above this value. The standard error varied from 1.3 kcal/mol, for the first region, to between ～3 and 5 kcal/mol for the third. Use of these approximating linear functions is proposed for the calculation of protein stabilities from x-ray data. Such calculations, performed for more than 20 proteins and their fragments, have led to at least qualitative agreement between the calculated stabilities and available data for more than 90% of the cases. While quantitative predictions are at the limit of the method's accuracy, predictions of the probabilities of proteins or their fragments to be stable are expected to give a correct answer in ～95% of the cases.     

Quantification of helix-helix binding affinities in micelles and lipid bilayers

A theoretical approach for estimating association free energies of alpha-helices in nonpolar media has been developed. The parameters of energy functions have been derived from DeltaDeltaG values of mutants in water-soluble proteins and partitioning of organic solutes between water and nonpolar solvents. The proposed approach was verified successfully against three sets of published data: (1) dissociation constants of alpha-helical oligomers formed by 27 hydrophobic peptides; (2) stabilities of 22 bacteriorhodopsin mutants, and (3) protein-ligand binding affinities in aqueous solution. It has been found that coalescence of helices is driven exclusively by van der Waals interactions and H-bonds, whereas the principal destabilizing contributions are represented by side-chain conformational entropy and transfer energy of atoms from a detergent or lipid to the protein interior. Electrostatic interactions of alpha-helices were relatively weak but important for reproducing the experimental data. Immobilization free energy, which originates from restricting rotational and translational rigid-body movements of molecules during their association, was found to be less than 1 kcal/mole. The energetics of amino acid substitutions in bacteriorhodopsin was complicated by specific binding of lipid and water molecules to cavities created in certain mutants.     

153 Wonderful roles of the entropy in protein dynamics,binding and folding

The entropy, which is central to the second law of thermodynamics, determines that the thermal energy always flows spontaneously from regions of higher temperature to regions of lower temperature. In the protein–solvent thermodynamic system, the entropy is defined as a measure of how evenly the thermal energy would distribute over the entire system (Liu et al., 2012). Such tendency to distribute energy as evenly as possible will reduce the state of order of the initial system, and hence, the entropy can be regarded as an expression of the disorder, or randomness of the system (Yang et al., 2012). For a protein–solvent system under a constant solvent condition, the origin of entropy is the thermal energy stored in atoms, which makes atoms jostle around and bump onto one another, thus leading to vibrations of the covalent bonds connecting two atoms (occurring on the fs timescale) and the rotational and translational motions of amino acid side chain groups (occurring on ps timescale) and water molecules. These motions break the noncovalent bonds around structural regions that are weakly constrained thereby triggering the competitive interactions among residues or between residues and water molecules leading ultimately to the loop motions (occurring on ns timescale) around the protein surface. The loop motions can further transmit either through the water network around the protein surface or via specific structural components (such as the hinge-bending regions) over the entire protein molecule leading to large concerted motions (occurring on μs to s timescales) that are most relevant to protein functions (Amadei, Linssen & Berendsen, 1993; Tao, Rao & Liu, 2010). Thus, the multiple hierarchies of the protein dynamics on distinct timescales (Henzler-Wildman & Kern, 2007) are a consequence of the cascade amplification of the microscopic motions of atoms and groups for which the entropy originating from atomic thermal energy is most fundamental. In the case of protein–ligand binding, the importance of the entropy is embodied in the following aspects. (i) The release of the water molecule kinetic energy (which is a process of the solvent entropy maximization) will cause Brownian motions of individual water molecules which result in strong Brownian bombardments to solute molecules causing molecule wanders/diffusions and subsequent accident contacts/collisions between proteins and ligands. (ii) Such collisions will inevitably cause water molecule displacement and, if the contact interfaces are properly complementary, the requirement to increase the solvent entropy would further displace the water network around the binding interfaces thus leading to the formation the initial protein-ligand complex. (iii) In the initial complex, the loose association of the two partners provide the opportunity for protein to increase conformational entropy, thus triggering the conformational adjustments through competitive interaction between protein residues and ligand, leading ultimately to the formation of tightly associated complex (Liu et al., 2012). In the protein folding process, the first stage, i.e. the rapid hydrophobic collapse (Agashe, Shastry & Udgaonkar, 1995; Dill, 1985), is in fact driven by the effect of the solvent entropy maximization. Specifically, the requirement to maintain as many as possible the dynamic hydrogen bonds among the water molecules will squeeze/sequestrate the hydrophobic amino acid side chains into the interior of the folding intermediates and expose the polar/charged side chains onto the intermediate surface. This will minimize the solvent accessible surface area of the folding intermediates and as thus maximize the entropy of the solvent. The resulting molten globule states (Ohgushi & Wada, 1983) may contain a few secondary structural components and native tertiary contacts, while many native contacts, or close residue–residue interactions present in the native state have not yet formed. However, the nature to increase the protein conformational entropy can trigger a further conformational adjustment process, i.e. the conformational entropy increase breaks the transient secondary or tertiary contacts and triggers the competitive interactions among protein residues and between residues and water. This process may repeat many rounds until the negative enthalpy change resulting from the noncovalent formations can overcompensate for protein conformational entropy loss. In summary, we consider that the tendency to maximize the entropy of the protein–solvent system, which originates from the atomic thermal energy, is the most fundamental driving factor for protein folding, binding, and dynamics, whereas the enthalpy reduction, an opposing factor that tends to make the system become ordered, can compensate for the effect of entropy loss to ultimately allow the system to reach equilibrium at the free energy minima, either global or local.     

Conformational constraint in protein ligand design and the inconsistency of binding entropy

It is an accepted practice in ligand design to introduce conformational constraint with the expectation of improving affinity, justified by the theoretical possibility that an unfavorable change in binding entropy will be reduced. This rationale of minimizing the entropic penalty through imposing structural constraints upon a ligand, however, has been voiced more often than verified. Here we examine three modified cyclic peptides, along with multiple versions of their linear control analogs, and determine their thermodynamic parameters when binding the same host, the third PDZ domain (PDZ3) of the mammalian postsynaptic density-95 (PSD-95) protein. To begin a two-stage investigation, the initial evaluation involved solution binding studies with isothermal titration calorimetry (ITC), which provided the changes in Gibbs free energy (DeltaG), enthalpy (DeltaH), and entropy (TDeltaS) upon formation of the protein-ligand complex. In the second stage, a selected macrocycle along with two matched linear controls were subjected to more rigorous analysis by ITC, which included (1) change in heat of buffer ionization (DeltaH(ion)) titrations, to examine the role of proton transfer events; (2) change in heat capacity (DeltaC(p)) determinations, to indirectly probe the nature of the binding surface; and (3) osmotic stress experiments, to evaluate desolvation effects and quantitate water release. Together, these demonstrate that the entropic relationship between a macrocyclic ligand and a linear counterpart can be a complex one that is difficult to rationalize. Further, the addition of constraint can, counterintuitively, lead to a less favorable change in binding entropy. This underscores the need to use matched linear control ligands to assure that comparisons are made in a meaningful manner.     

Predicting protein-ligand binding sites based on an improved geometric algorithm

Knowledge of protein-ligand binding sites is very important for structure-based drug designs. To get information on the binding site of a targeted protein with its ligand in a timely way, many scientists tried to resort to computational methods. Although several methods have been released in the past few years, their accuracy needs to be improved. In this study, based on the combination of incremental convex hull, traditional geometric algorithm, and solvent accessible surface of proteins, we developed a novel approach for predicting the protein-ligand binding sites. Using PDBbind database as a benchmark dataset and comparing the new approach with the existing methods such as POCKET, Q-SiteFinder, MOE-SiteFinder, and PASS, we found that the new method has the highest accuracy for the Top 2 and Top 3 predictions. Furthermore, our approach can not only successfully predict the protein-ligand binding sites but also provide more detailed information for the interactions between proteins and ligands. It is anticipated that the new method may become a useful tool for drug development, or at least play a complementary role to the other existing methods in this area.     

Conformational selection through electrostatics: Free energy simulations of GTP and GDP binding to archaeal initiation factor 2

Archaeal Initiation Factor 2 is a GTPase involved in protein biosynthesis. In its GTP-bound, "ON" conformation, it binds an initiator tRNA and carries it to the ribosome. In its GDP-bound, "OFF" conformation, it dissociates from tRNA. To understand the specific binding of GTP and GDP and their dependence on the conformational state, molecular dynamics free energy simulations were performed. The ON state specificity was predicted to be weak, with a GTP/GDP binding free energy difference of -1 kcal/mol, favoring GTP. The OFF state specificity is larger, 4 kcal/mol, favoring GDP. The overall effects result from a competition among many interactions in several complexes. To interpret them, we use a simpler, dielectric continuum model. Several effects are robust with respect to the model details. Both nucleotides have a net negative charge, so that removing them from solvent into the binding pocket carries a desolvation penalty, which is large for the ON state, and strongly disfavors GTP binding compared to GDP. Short-range interactions between the additional GTP phosphate group and ionized sidechains in the binding pocket offset most, but not all of the desolvation penalty; more distant groups also contribute significantly, and the switch 1 loop only slightly. The desolvation penalty is lower for the more open, wetter OFF state, and the GTP/GDP difference much smaller. Short-range interactions in the binding pocket and with more distant groups again make a significant contribution. Overall, the simulations help explain how conformational selection is achieved with a single phosphate group.     

Protein dynamics and allostery: an NMR view

Allostery, the process by which distant sites within a protein system are energetically coupled, is an efficient and ubiquitous mechanism for activity regulation. A purely mechanical view of allostery invoking only structural changes has developed over the decades as the classical view of the phenomenon. However, a fast growing list of examples illustrate the intimate link between internal motions over a wide range of time scales and function in protein-ligand interactions. Proteins respond to perturbations by redistributing their motions and they use fluctuating conformational states for binding and conformational entropy as a carrier of allosteric energy to modulate association with ligands. In several cases allosteric interactions proceed with minimal or no structural changes. We discuss emerging paradigms for the central role of protein dynamics in allostery.     

A knowledge-guided strategy for improving the accuracy of scoring functions in binding affinity prediction

Background  

Current scoring functions are not very successful in protein-ligand binding affinity prediction albeit their popularity in structure-based drug designs. Here, we propose a general knowledge-guided scoring (KGS) strategy to tackle this problem. Our KGS strategy computes the binding constant of a given protein-ligand complex based on the known binding constant of an appropriate reference complex. A good training set that includes a sufficient number of protein-ligand complexes with known binding data needs to be supplied for finding the reference complex. The reference complex is required to share a similar pattern of key protein-ligand interactions to that of the complex of interest. Thus, some uncertain factors in protein-ligand binding may cancel out, resulting in a more accurate prediction of absolute binding constants.     

Four-body atomic potential for modeling protein-ligand binding affinity: application to enzyme-inhibitor binding energy prediction

Background

Models that are capable of reliably predicting binding affinities for protein-ligand complexes play an important role the field of structure-guided drug design.

Methods

Here, we begin by applying the computational geometry technique of Delaunay tessellation to each set of atomic coordinates for over 1400 diverse macromolecular structures, for the purpose of deriving a four-body statistical potential that serves as a topological scoring function. Next, we identify a second, independent set of three hundred protein-ligand complexes, having both high-resolution structures and known dissociation constants. Two-thirds of these complexes are randomly selected to train a predictive model of binding affinity as follows: two tessellations are generated in each case, one for the entire complex and another strictly for the isolated protein without its bound ligand, and a topological score is computed for each tessellation with the four-body potential. Predicted protein-ligand binding affinity is then based on an empirically derived linear function of the difference between both topological scores, one that appropriately scales the value of this difference.

Results

A comparison between experimental and calculated binding affinity values over the two hundred complexes reveals a Pearson's correlation coefficient of r = 0.79 with a standard error of SE = 1.98 kcal/mol. To validate the method, we similarly generated two tessellations for each of the remaining protein-ligand complexes, computed their topological scores and the difference between the two scores for each complex, and applied the previously derived linear transformation of this topological score difference to predict binding affinities. For these one hundred complexes, we again observe a correlation of r = 0.79 (SE = 1.93 kcal/mol) between known and calculated binding affinities. Applying our model to an independent test set of high-resolution structures for three hundred diverse enzyme-inhibitor complexes, each with an experimentally known inhibition constant, also yields a correlation of r = 0.79 (SE = 2.39 kcal/mol) between experimental and calculated binding energies.

Conclusions

Lastly, we generate predictions with our model on a diverse test set of one hundred protein-ligand complexes previously used to benchmark 15 related methods, and our correlation of r = 0.66 between the calculated and experimental binding energies for this dataset exceeds those of the other approaches. Compared with these related prediction methods, our approach stands out based on salient features that include the reliability of our model, combined with the rapidity of the generated predictions, which are less than one second for an average sized complex.

     

Development, validation, and application of adapted PEOE charges to estimate pKa values of functional groups in protein-ligand complexes

For routine pK(a) calculations of protein-ligand complexes in drug design, the PEOE method to compute partial charges was modified. The new method is applicable to a large scope of proteins and ligands. The adapted charges were parameterized using experimental free energies of solvation of amino acids and small organic ligands. For a data set of 80 small organic molecules, a correlation coefficient of r(2) = 0.78 between calculated and experimental solvation free energies was obtained. Continuum electrostatics pK(a) calculations based on the Poisson-Boltzmann equation were carried out on a validation set of nine proteins for which 132 experimental pK(a) values are known. In total, an overall RMSD of 0.88 log units between calculated and experimentally determined data is achieved. In particular, the predictions of significantly shifted pK(a) values are satisfactory, and reasonable estimates of protonation states in the active sites of lysozyme and xylanase could be obtained. Application of the charge-assignment and pK(a)-calculation procedure to protein-ligand complexes provides clear structural interpretations of experimentally observed changes of protonation states of functional groups upon complex formation. This information is essential for the interpretation of thermodynamic data of protein-ligand complex formation and provides the basis for the reliable factorization of the free energy of binding in enthalpic and entropic contributions. The modified charge-assignment procedure forms the basis for future automated pK(a) calculations of protein-ligand complexes.     

RNA Thermodynamic Structural Entropy

Conformational entropy for atomic-level, three dimensional biomolecules is known experimentally to play an important role in protein-ligand discrimination, yet reliable computation of entropy remains a difficult problem. Here we describe the first two accurate and efficient algorithms to compute the conformational entropy for RNA secondary structures, with respect to the Turner energy model, where free energy parameters are determined from UV absorption experiments. An algorithm to compute the derivational entropy for RNA secondary structures had previously been introduced, using stochastic context free grammars (SCFGs). However, the numerical value of derivational entropy depends heavily on the chosen context free grammar and on the training set used to estimate rule probabilities. Using data from the Rfam database, we determine that both of our thermodynamic methods, which agree in numerical value, are substantially faster than the SCFG method. Thermodynamic structural entropy is much smaller than derivational entropy, and the correlation between length-normalized thermodynamic entropy and derivational entropy is moderately weak to poor. In applications, we plot the structural entropy as a function of temperature for known thermoswitches, such as the repression of heat shock gene expression (ROSE) element, we determine that the correlation between hammerhead ribozyme cleavage activity and total free energy is improved by including an additional free energy term arising from conformational entropy, and we plot the structural entropy of windows of the HIV-1 genome. Our software RNAentropy can compute structural entropy for any user-specified temperature, and supports both the Turner’99 and Turner’04 energy parameters. It follows that RNAentropy is state-of-the-art software to compute RNA secondary structure conformational entropy. Source code is available at https://github.com/clotelab/RNAentropy/; a full web server is available at http://bioinformatics.bc.edu/clotelab/RNAentropy, including source code and ancillary programs.     

Thermodynamic basis of resistance to HIV-1 protease inhibition: calorimetric analysis of the V82F/I84V active site resistant mutant

One of the most serious side effects associated with the therapy of HIV-1 infection is the appearance of viral strains that exhibit resistance to protease inhibitors. The active site mutant V82F/I84V has been shown to lower the binding affinity of protease inhibitors in clinical use. To identify the origin of this effect, we have investigated the binding thermodynamics of the protease inhibitors indinavir, ritonavir, saquinavir, and nelfinavir to the wild-type HIV-1 protease and to the V82F/I84V resistant mutant. The main driving force for the binding of all four inhibitors is a large positive entropy change originating from the burial of a significant hydrophobic surface upon binding. At 25 degrees C, the binding enthalpy is unfavorable for all inhibitors except ritonavir, for which it is slightly favorable (-2.3 kcal/mol). Since the inhibitors are preshaped to the geometry of the binding site, their conformational entropy loss upon binding is small, a property that contributes to their high binding affinity. The V82F/I84V active site mutation lowers the affinity of the inhibitors by making the binding enthalpy more positive and making the entropy change slightly less favorable. The effect on the enthalpy change is, however, the major one. The predominantly enthalpic effect of the V82F/I84V mutation is consistent with the idea that the introduction of the bulkier Phe side chain at position 82 and the Val side chain at position 84 distort the binding site and weaken van der Waals and other favorable interactions with inhibitors preshaped to the wild-type binding site. Another contribution of the V82F/I84V to binding affinity originates from an increase in the energy penalty associated with the conformational change of the protease upon binding. The V82F/I84V mutant is structurally more stable than the wild-type protease by about 1.4 kcal/mol. This effect, however, affects equally the binding affinity of substrate and inhibitors.     

Insights from free-energy calculations: protein conformational equilibrium, driving forces, and ligand-binding modes

Accurate free-energy calculations provide mechanistic insights into molecular recognition and conformational equilibrium. In this work, we performed free-energy calculations to study the thermodynamic properties of different states of molecular systems in their equilibrium basin, and obtained accurate absolute binding free-energy calculations for protein-ligand binding using a newly developed M2 algorithm. We used a range of Asp-Phe-Gly (DFG)-in/out p38α mitogen-activated protein kinase inhibitors as our test cases. We also focused on the flexible DFG motif, which is closely connected to kinase activation and inhibitor binding. Our calculations explain the coexistence of DFG-in and DFG-out states of the loop and reveal different components (e.g., configurational entropy and enthalpy) that stabilize the apo p38α conformations. To study novel ligand-binding modes and the key driving forces behind them, we computed the absolute binding free energies of 30 p38α inhibitors, including analogs with unavailable experimental structures. The calculations revealed multiple stable, complex conformations and changes in p38α and inhibitor conformations, as well as balance in several energetic terms and configurational entropy loss. The results provide relevant physics that can aid in designing inhibitors and understanding protein conformational equilibrium. Our approach is fast for use with proteins that contain flexible regions for structure-based drug design.     

Accounting for Ligand Conformational Restriction in Calculations of Protein-Ligand Binding Affinities

The conformation adopted by a ligand on binding to a receptor may differ from its lowest-energy conformation in solution. In addition, the bound ligand is more conformationally restricted, which is associated with a configurational entropy loss. The free energy change due to these effects is often neglected or treated crudely in current models for predicting binding affinity. We present a method for estimating this contribution, based on perturbation theory using the quasi-harmonic model of Karplus and Kushick as a reference system. The consistency of the method is checked for small model systems. Subsequently we use the method, along with an estimate for the enthalpic contribution due to ligand-receptor interactions, to calculate relative binding affinities. The AMBER force field and generalized Born implicit solvent model is used. Binding affinities were estimated for a test set of 233 protein-ligand complexes for which crystal structures and measured binding affinities are available. In most cases, the ligand conformation in the bound state was significantly different from the most favorable conformation in solution. In general, the correlation between measured and calculated ligand binding affinities including the free energy change due to ligand conformational change is comparable to or slightly better than that obtained by using an empirically-trained docking score. Both entropic and enthalpic contributions to this free energy change are significant.     

Quantitative analyses of bifunctional molecules

Small molecules can be discovered or engineered to bind tightly to biologically relevant proteins, and these molecules have proven to be powerful tools for both basic research and therapeutic applications. In many cases, detailed biophysical analyses of the intermolecular binding events are essential for improving the activity of the small molecules. These interactions can often be characterized as straightforward bimolecular binding events, and a variety of experimental and analytical techniques have been developed and refined to facilitate these analyses. Several investigators have recently synthesized heterodimeric molecules that are designed to bind simultaneously with two different proteins to form ternary complexes. These heterodimeric molecules often display compelling biological activity; however, they are difficult to characterize. The bimolecular interaction between one protein and the heterodimeric ligand (primary dissociation constant) can be determined by a number of methods. However, the interaction between that protein-ligand complex and the second protein (secondary dissociation constant) is more difficult to measure due to the noncovalent nature of the original protein-ligand complex. Consequently, these heterodimeric compounds are often characterized in terms of their activity, which is an experimentally dependent metric. We have developed a general quantitative mathematical model that can be used to measure both the primary (protein + ligand) and secondary (protein-ligand + protein) dissociation constants for heterodimeric small molecules. These values are largely independent of the experimental technique used and furthermore provide a direct measure of the thermodynamic stability of the ternary complexes that are formed. Fluorescence polarization and this model were used to characterize the heterodimeric molecule, SLFpYEEI, which binds to both FKBP12 and the Fyn SH2 domain, demonstrating that the model is useful for both predictive as well as ex post facto analytical applications.