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US20100273664A1 - Method For The Determination Of Intra- And Intermolecular Interactions In Aqueous Solution - Google Patents

Method For The Determination Of Intra- And Intermolecular Interactions In Aqueous Solution Download PDF

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US20100273664A1
US20100273664A1 US12/446,659 US44665907A US2010273664A1 US 20100273664 A1 US20100273664 A1 US 20100273664A1 US 44665907 A US44665907 A US 44665907A US 2010273664 A1 US2010273664 A1 US 2010273664A1
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water
proteins
bond
wat
sat
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Gudrun Lange
Robert Klein
Juergen Albrecht
Matthias Rarey
Ingo Reulecke
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Bayer CropScience AG
Universitaet Hamburg
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Universitaet Hamburg
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    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C10/00—Computational theoretical chemistry, i.e. ICT specially adapted for theoretical aspects of quantum chemistry, molecular mechanics, molecular dynamics or the like
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16B—BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
    • G16B15/00—ICT specially adapted for analysing two-dimensional or three-dimensional molecular structures, e.g. structural or functional relations or structure alignment
    • G16B15/30—Drug targeting using structural data; Docking or binding prediction
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16B—BIOINFORMATICS, i.e. INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR GENETIC OR PROTEIN-RELATED DATA PROCESSING IN COMPUTATIONAL MOLECULAR BIOLOGY
    • G16B15/00—ICT specially adapted for analysing two-dimensional or three-dimensional molecular structures, e.g. structural or functional relations or structure alignment
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
    • Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
    • Y10T436/00—Chemistry: analytical and immunological testing
    • Y10T436/14—Heterocyclic carbon compound [i.e., O, S, N, Se, Te, as only ring hetero atom]
    • Y10T436/142222—Hetero-O [e.g., ascorbic acid, etc.]
    • Y10T436/143333—Saccharide [e.g., DNA, etc.]

Definitions

  • the present invention relates to the determination of the interaction between molecules in aqueous solution.
  • the obtained results can be used for the prediction if and to what extent two molecules of various origin fit to each other. This can be used for the identification of agrochemicals and pharmaceuticals.
  • the water molecules form a network connected by transient H-bonds in which individual H-bonds are continuously made and broken. Accordingly, there is a perpetual change of the H-bond network formed by the water molecules even though the number of made and broken H-bonds remains constant in the course of time.
  • water still has a remarkable preference for H-bonds with HOH . . . O distances close to 1.8 A and angles between 160 and 180° and tetrahedral H-bonded arrangements seem still to be strongly preferred structural elements in water, however transient they may be.
  • the hydrophobic effect can be analyzed by looking at the H-bonds within the water network around hydrophobic moieties (Silverstein, J. Am. Chem. Soc. 2000, 122: 8037-41).
  • Various theories based on Paulings calculation have been put forward involving made and broken water H-bonds around hydrophobic moieties. They are still fiercely disputed and seem not to describe the phenomenon ‘hydrophobic effect’ satisfactorily (Abraham et al., J. Am. Chem. Soc. 2002, 124: 7853-56).
  • Recent neutron scattering experiments have confirmed that water retains its tetrahedral structure and forms an H-bonded network in solutions.
  • the present invention relates to a method for the determination of intra- or intermolecular interactions in an aqueous solution, said method comprising the steps of:
  • the present invention relates to a method for the determination of intra- or intermolecular interactions in an aqueous solution, said method consisting of:
  • the present invention particularly relates to a method, wherein the dehydration is quantified by:
  • the present invention more particularly relates to a method, wherein f sat and f unsat are defined in pure bulk water by the terms as listed under (a) and (b) of the before
  • the invention preferably relates to a method, wherein in case of polar functions a relationship between the dehydration term and the hydrogen bond energy ( ⁇ ° pol . . . wat ) involving f sat is used.
  • the invention preferably relates to a method, wherein in case of polar functions the relationship
  • the invention relates to a method, wherein f sat is within a range 0.75 to 0.90, more preferably f sat is within a range 0.82 to 0.88, most preferably f sat is within a range of 0.84 to 0.87.
  • the invention also relates to the use of a method for the determination of intra- or intermolecular interactions in an aqueous solution, said method comprising the steps of:
  • the target molecule is selected from the group consisting of proteins, nucleic acid molecules, or lipids
  • the target molecule is selected from the group consisting of cell wall proteins, membrane bound proteins, water soluble proteins, cellular proteins, enzymatic proteins, regulatory proteins, ion channel proteins, carrier proteins, aquaporins, vacuolar proteins, golgi apparatus proteins, cytoskeleton proteins, DNA- or RNA-replication proteins, DNA- or RNA-recombination proteins, viral proteins, mitochondrial proteins, plastid proteins involved in the respiration and photorespiration apparatus, proteins belonging to the signal transduction pathway, receptors, G-proteins, senescence proteins, plant stress proteins (including abiotic and biotic plant stress proteins), HMG-proteins (high mobility group proteins), LMG-proteins (low mobility group proteins), Terpenoid synthesis proteins, DNA-molecules, RNA-molecules, transcriptions factors, phospholipids, galactosylglycerides, glucocerebroside
  • the interacting molecule is selected from the group consisting of proteins, enzyme inhibitors, agonist, antagonists, small weight compounds (molecular weight ⁇ 600 g/mol) and fragments of the latter.
  • the invention also relates to the use of a method for the determination of intra- or intermolecular interactions in an aqueous solution, said method comprising the steps of:
  • the invention also relates to the use of a method for the determination of intra- or intermolecular interactions in an aqueous solution, said method comprising the steps of:
  • FIG. 1A shows the thermodynamic cycle which is used to calculate f sat and f unsat .
  • FIG. 1B shows f sat (squares) and f unsat (triangles) as a function of temperature.
  • FIG. 2A shows the average enthalpy H (squares) and entropy term ⁇ TS contribution (triangles) of the four H-bond functions per water molecule towards the Gibbs free energy of the water network as a function of the temperature.
  • FIG. 2B shows the difference in enthalpy ( ⁇ H, squares), entropy term ( ⁇ TS, triangles) and Gibbs free energy ( ⁇ G, crosses) between water at temperature T and water at 373K as a function of temperature T.
  • FIG. 3B shows ⁇ H (squares), ⁇ T ⁇ S (triangles) and ⁇ G (stars) in kJ/mol for generating an additional unsatisfied H-bond function in the water network as a function of the temperature T.
  • the values for ⁇ H, ⁇ T ⁇ S and ⁇ G at 298K are indicated by arrows.
  • FIG. 3C shows f unsat (triangles) and the term characterizing the lack of enthalpy/entropy term compensation (1 ⁇ T/373) (squares) as a function of the temperature in the water network.
  • FIG. 4 shows ⁇ G i,j two ideal protein water H-bonds are replaced with an interfacial H-bond of different quality as a function of temperature assuming that ⁇ polar1 . . . polar2 is 27.1 kJ/mol (squares), 22.5 kJ/mol (triangles), 15 kJ/mol (diamonds), or 0 kJ/mol (stars).
  • FIG. 5 shows ⁇ G i,j for generating a CH . . . OR contact pair in an interface as a function of temperature assuming that the water was bound to the H-bond function with either 27.1 (squares), 20 (triangles) or 15 (diamonds) kJ/mol.
  • FIG. 7 shows that the folded protein state becomes more unfavorable with higher temperature since ⁇ G i,j for the formation of an additional ideal interfacial H-bond (squares) becomes more favorable and the unfavorable ⁇ G i,j for the exposure of an apolar moiety to water (triangles) becomes less severe. Their sum (diamonds) shows that both effects annihilate each other at 313K.
  • FIG. 8 shows a comparison between the contributions predicted for ‘ideal functional’ groups according to examples 1-3, the values extracted according to example 5 and the respective published experimental data.
  • FIG. 9A shows the calculated contributions to ⁇ G bound/unbound of individual ligand atoms in the protein ligand interface of the estrogen receptor and raloxifene calculated based on the published structure (Brzozowski et al., Nature 1997, 389:753-758).
  • FIG. 9B shows the calculated contributions to ⁇ G bound/unbound of individual ligand atoms in the protein ligand interface of the estrogen receptor and modified raloxifene.
  • FIG. 9C shows the calculated contributions to ⁇ G bound/unbound of individual ligand atoms in the protein ligand interface of the SH2 domain of src and Ru79181 (J. Med. Chem 2002 45: 2915-22). The ligand atoms O28 and N19 are marked.
  • FIG. 10A shows the enrichment calculations for Acc.
  • the enrichment is shown for the following scoring functions: FlexX2.0, HYDE, ChemScore, G-Score, PMF-Score and ScreenScore.
  • FIG. 10B shows the enrichment calculations for the estrogen receptor.
  • the enrichment is shown for the following scoring functions: FlexX2.0, HYDE, ChemScore, G-Score, PMF-Score and ScreenScore.
  • FIG. 10C shows the enrichment calculations for CDK2.
  • the enrichment is shown for the following scoring functions: FlexX2.0, HYDE, ChemScore, G-Score, PMF-Score and ScreenScore.
  • FIG. 10D shows the enrichment calculations for thrombin.
  • the enrichment is shown for the following scoring functions: FlexX2.0, HYDE, ChemScore, G-Score, PMF-Score and ScreenScore.
  • FIG. 11A shows the number of identified hits and false positives with a HYDE score better than ⁇ 25 kJ/mol for the four targets accase, estrogen receptor, CDK2 and Thrombin.
  • FIG. 11B shows the number of identified hits with a score above ⁇ 25 kJ/mol and the number of those compounds which are hits but were not identified (false negatives).
  • FIG. 11C shows the number of identified hits and false positives for the top scored compounds using FlexX2.0 and the same number of compounds as found for the HYDE score
  • FIG. 11D shows the number of identified hits and the number of those compounds which are hits but were not identified (false negatives) using FlexX2.0 and the same number of compounds as those found for the HYDE score.
  • FIG. 11E shows the number of identified hits and false positives for the top scored compounds using Chemscore and the same number of compounds as found for the HYDE score
  • FIG. 11F shows the number of identified hits and the number of those compounds which are hits but were not identified (false negatives) using Chemscore and the same number of compounds as those found for the HYDE score.
  • FIG. 11G shows the number of identified hits and false positives for the top scored compounds using Gscore and the same number of compounds as found for the HYDE score
  • FIG. 11H shows the number of identified hits and the number of those compounds which are hits but were not identified (false negatives) using Gscore and the same number of compounds as those found for the HYDE score.
  • FIG. 11I shows the number of identified hits and false positives for the top scored compounds using PMF-Score and the same number of compounds as found for the HYDE score
  • FIG. 11J shows the number of identified hits and the number of those compounds which are hits but were not identified (false negatives) using PMF Score and the same number of compounds as those found for the HYDE score.
  • FIG. 11K shows the number of identified hits and false positives for the top scored compounds using ScreenScore and the same number of compounds as found for the HYDE score
  • FIG. 11L shows the number of identified hits and the number of those compounds which are hits but were not identified (false negatives) using ScreenScore and the same number of compounds as those found for the HYDE score.
  • FIG. 12 shows the number of identified hits and false positives if the scoring function HYDE is used and additionally a filter for the internal conformational energy of 60 kJ/mol is applied.
  • FIG. 13A shows a table showing the FlexX2.0 score, the root mean square deviations between atomic positions in the crystal structure and the respective docked pose, the Hyde score and the stabilizing and destabilizing contributions calculated using our approach for the experimental crystal structure and the first 25 docking solution calculated using FlexX2.0.
  • FIG. 13B shows the stabilizing versus the destabilizing contributions for the crystal structure (triangle) and the docking solutions (crosses). It becomes obvious that only the crystal structure has considerable more stabilizing than destabilizing contributions and none of the docked poses will be observed in experiments
  • the corresponding thermodynamic cycle is shown in FIG. 1A .
  • the total energy needed to break the four H-bonds in ice and transfer water into the vapor state is 54.18 kJ/mol.
  • the fraction of satisfied and unsatisfied H-bond functions in the water network can be calculated as follows:
  • FIG. 1B shows the fraction of satisfied and unsatisfied H-bond functions within the water network.
  • the percentage of unsatisfied H-bond functions has increased to roughly 17% while at the boiling point (373K) 25% of the H-bond functions are unsatisfied in the water network. This means that the interface between liquid water and vapor is characterized by water molecules which have in average one unsatisfied and three satisfied H-bond functions.
  • a further reduction of satisfied H-bond functions within the water network to an average value below three satisfied H-bond functions per water molecule causes a breakdown of the three-dimensional water network and liquid water is evaporating.
  • This can be rationalized since three linear independent vectors, i.e. three directed H-bonds are needed to span a three-dimensional space.
  • the calculated fraction of unsatisfied H-bond functions at the liquid/vapor interface at 373K is identical to the fraction of made/broken H-bonds which had been estimated for surfaces (Luzar, Chemical Physics Letter 1983, 96: 485-90; Wernet, Science 2004, 304: 995-999).
  • the potential of a directed interaction such as an H-bond has distinct minima for certain distances and angles. As a result, the interacting atoms are orientated towards each other with a well defined geometry.
  • the H-bond energy ⁇ o is only realized at the ideal geometry while deviations from the ideal distance between donor X—H and acceptor Y or from the ideal angle X—H . . . Y forced upon the system by external constraints give rise to a weaker interaction energy ⁇ with ⁇ o .
  • F sat (T) seems to give a temperature dependent estimate on how much the average H-bond within the water network is weakened due to the temperature dependent deviation from ideal geometry within the network.
  • ⁇ wat . . . wat f sat (T) ⁇ 0 wat . . . wat .
  • the statistical average is the same if at one extreme the fraction f sat is considered locally as being ideally made and other H-bonds within the water network not at all or if at the other extreme they are all made with the same lower quality. It should be pointed out, that assigning H-bond energies to individual water molecules or looking at clusters of a limited size instead of looking at the whole statistical ensemble gives rise to serious discrepancies with the experimental data as has been experienced by Wernet et al. (Science 2004, 304: 995-999).
  • f unsat (T) gives an estimate of the entropy term contribution ( ⁇ T ⁇ S) in the water network due to the presence of the H-bonds.
  • Breaking H-bonds within a network is an endothermic process ( ⁇ H ⁇ 0) while at the same time the entropy term, the product of the temperature with entropy, increases (T ⁇ S>0).
  • Making H-bonds is an exothermic process ( ⁇ H>0) while at the same time the entropy term decreases (T ⁇ S ⁇ 0).
  • FIG. 2A shows the enthalpy and entropy term contribution of the four H-bonds per water molecule towards the Gibbs free energy of the water network as a function of the temperature.
  • FIG. 2B shows the difference in enthalpy ( ⁇ H), Gibbs free energy ( ⁇ G) and entropy term ( ⁇ S)) between the water network at temperature T and water at 373K for different temperatures T.
  • ⁇ G dehydration and ⁇ G hydration for a polar function can be calculated as:
  • the H-bond energy ⁇ polar . . . wat as a function of the distance and angle can be calculated using various methods and has its maximal value ⁇ 0 only at ideal geometry.
  • FIG. 3A shows ⁇ G dehydration polar for a polar function as function of temperature assuming that ⁇ polar . . . wat equals 27.1, 20, or 15 kJ/mol, respectively.
  • ⁇ G dehydration polar is positive if the polar function had interacted reasonable well with the water network. Isolated H-bond functions are easily accessible to the water network and thus the H-bonds between these polar functions and the water network can be realized with ideal geometry.
  • the ‘—CH . . . O H-bond’ is with ⁇ 0 ⁇ 1-3 kJ/mol (Gu et al., J. Am. Chem. Soc. 1999, 121: 9411-9422) very weak compared to the H-bond between individual water molecules.
  • the water H-bond function interacting with the ‘—CH’-function can be considered to be unsatisfied.
  • ⁇ H is endothermic at any temperature, and only partly compensated by a favorable ⁇ T ⁇ S term.
  • the removal of an unsatisfied H-bond function within the water network i.e. the dehydration of an apolar function results in a favorable ⁇ G of the same size.
  • the hydrophobic effect correlates with the difference of unsatisfied water H-bond functions in the presence and absence of apolar functions and thus will be lower if the fraction of unsatisfied water H-bonds in an aqueous solution is higher than in pure water due to additives.
  • the presence of organic additives leads to a larger fraction of unsatisfied water H-bond functions, f unsat′ at temperature T compared to that present in pure water at temperature T.
  • ⁇ H and T ⁇ S for the generation of an additional unsatisfied water H-bond function by an apolar function can be calculated if T′ is the temperature at which the fraction of unsatisfied water H-bond functions is f unsat′ in pure water:
  • the water specific Gibbs free desolvation energy has an unexpected impact on the interaction between molecules in aqueous solution.
  • Functional groups from different molecules come close to each other in an intermolecular interface. Different pairings of isolated functional groups can occur: (1) two isolated polar functions forming an intermolecular H-bond, (2) two isolated apolar functions forming an apolar contact pair, (3) an isolated polar and an apolar function e.g. a CH . . . O contact pair and (d) those pairings involving functions for which ⁇ 0 wat . . . wat ⁇ 0 func . . . wat ⁇ 0 such as —C—F functions. These pairs contribute differently to ⁇ G bound/unbound .
  • ⁇ G i,j for the formation of an interfacial H-bond can be calculated by combining the Gibbs free dehydration energy of the polar functions ( ⁇ G dehydration polar ) with the vacuum H-bond energy of the interfacial H-bond ( ⁇ polar1 . . . polar2 ).
  • the contribution of an individual interfacial H-bond ⁇ G i,j to ⁇ G bound/unbound thus depends strongly on the difference in quality between the interfacial H-bond and the H-bonds that the polar functions can form with the water network. In general, if the H-bonds are of similar quality, ⁇ G i,j is weakly stabilizing. If the new interfacial H-bond is worse than the H-bonds between the polar functions and the water network, ⁇ G i,j is a destabilizing contribution to ⁇ G bound/unbound . If the new interfacial H-bond is much better, ⁇ G i,j becomes a strongly stabilizing contribution to ⁇ G bound/unbound .
  • H-bonds make H-bonds to the water network with ideal geometry and it can be assumed that ⁇ polar1 . . . wat ⁇ polar2 . . . wat ⁇ 0 wat . . . wat . If this is true for both H-bond functions which form an interfacial H-bond, the contribution of this H-bond is the following:
  • FIG. 4A shows that an interfacial H-bond contributes weakly stabilizing to ⁇ G bound/unbound only if it has an ideal geometry. In all other cases an interfacial H-bond contribute either not at all or in most cases destabilizing.
  • a closer analysis of the H-bonds which the conserved water molecule forms to the HIV-protease shows that the distances and the angles are ideal.
  • Tubulin forms well defined hollow cylinders, the microtubuli, upon temperature increase.
  • Calorimetric measurements have shown that these temperature driven self-assembly processes are entropy driven. Since it seems difficult to comprehend that the formation of well ordered supramolecular structures from individual protein molecules results in an increase of entropy, it was assumed that the increase in entropy was due to not understood processes within the water (Oosawa and Asakura, Thermodynamics of the Polymerization of Protein 1976, Publisher: Academic, London).
  • interfacial H-bonds With ideal geometry become more stabilizing. These H-bonds orient two molecules well due to their restrictive H-bond geometry thereby giving rise to well-ordered structures. As a consequence of these stronger stabilizing contributions at higher temperature, the equilibrium is shifted towards the aggregated state with a substantial number of interfacial H-bonds and well ordered supramolecular structures are formed. The importance of interfacial H-bonds in the aggregation of tubulin is reflected in the 3D structure of tubulin.
  • the size of the apolar surface which gives rise to an unsatisfied water H-bond function can be estimated based on geometrical considerations. It corresponds to the surface of the cone of a water H-bond function and can be calculated assuming a distance of 1.6 ⁇ (H-bond distance between oxygen and next water hydrogen) and an angle of 60° for the —O—H . . . O angle. This surface is roughly 24 ⁇ 2 and very similar to the size of a —C—H group.
  • the removal of an additional unsatisfied water H-bond function due to the removal of a surface from the size of a —C—H group from the water network releases 2.9 kJ/mol or 113 J/mol ⁇ 2 at 298K, 2.1 kJ/mol or 88 J/mol ⁇ 2 at 313K and 1.3 kJ/mol or 54 J/mol ⁇ 2 at 333K.
  • the contribution of an apolar contact pair in the intermolecular interface is 5.9 kJ/mol at 298K, 4.2 kJ/mol at 313K and 2.5 kJ/mol at 333K. If the apolar function has a larger surface than a —CH moiety, it will leave more water H-bond functions unsatisfied and induce a larger hydrophobic effect.
  • hydrophobic compounds have a higher solubility in the presence of organic additives. As observed in daily life and predicted by present invention correctly, the hydrophobic effect decreases and thus the solubility of hydrophobic compounds increases at higher temperatures and/or in the presence of organic solutes due the predicted better enthalpy/entropy term compensation at higher temperatures.
  • FIG. 5A shows ⁇ G i,j as function of temperature for creating a —CH . . .
  • Specificity/recognition means that the system has to be able to distinguish between correct and wrong ligands. This can be achieved by favoring those compounds which make stabilizing interactions but also by disfavoring ligands with destabilizing interactions. As seen in x-ray structures, selectivity seems to be conferred by ideal interfacial H-bonds which were formed after an ideally bound water has been replaced. According to present invention, the contribution of a protein ligand H-bond towards stabilization of a protein ligand complex is at best app ⁇ 4.0 kJ/mol at 298K which gives rise to a modest 5-10 fold increased affinity.
  • each unsatisfied interfacial H-bond function disfavors complex formation by up to +11.5 kJ/mol at 298K giving rise to a net destabilization of 8.8 kJ/mol for ‘—CH . . . O H-bonds’ and 20 kJ/mol for interfacial ‘H-bonds’ with bad H-bond geometry.
  • this leads to a 10-50 fold destabilization while the destabilization in the latter case is 5000 fold.
  • ⁇ G i,j for the formation of an apolar contact pair is ⁇ 2.5 kJ/mol while the contribution of an ideal interfacial H-bond is ⁇ 5.4 kJ/mol.
  • the formation of an H-bond between two tertiary butanol molecule has a similar preference than the formation of an apolar contact pair which explains the experimental observation.
  • ⁇ G bound/unbound becomes temperature dependent if either polar or apolar functions strongly dominate the molecular interface. If the interface is dominated by H-bonds, ⁇ G bound/unbound will become more favorable with increasing temperature. This is the case for temperature induced self-assemblies (see example 1). If the interface is dominated by apolar contact pairs, ⁇ G bound/unbound will become less favorable with increasing temperature and/or presence of organic additives.
  • Scoring functions are used in order to calculate the interaction between two molecules in a more automatic fashion. Most scoring functions sum up individual terms for intermolecular interactions such as H-bonds, ‘hydrophobic interaction’, and ‘CH . . . O’ interactions. The physical meaning of the terms ⁇ G i,j described in examples 1-3 compare directly with the terms used in most scoring functions. However, the size and the sign of the contributions calculated according to present invention differ significantly from those used in other scoring function. For instance, the scoring function used in docking programs such as FlexX (Rarey et al., J. Mol. Biol. 1996, 261: 470-489,) rewards the formation of interfacial H-bonds much higher than contributions due to the hydrophobic effect.
  • An interaction propensity based on its partial log P o/w was assigned to each atom in a molecule.
  • the interaction score between two atoms in the interface is calculated via an empirical mathematical function treating all interaction types on purpose identical.
  • a logic function derived from ‘common understanding’ determines if the interaction pair contributes stabilizing (hydrophobic hydrophobic interaction or acid-base interaction) or destabilizing (hydrophobic polar, base-base or acid-acid) contribution to the free binding energy. Additional empirical terms for considering the ‘increased entropy in water due to released water molecules’ and a calibration for each molecular system has been shown to be necessary in order to explain the experimental results with sufficient accuracy (Cozzini et al., J. Med. Chem.
  • the hydrophobic effect is for the first time quantitatively described as the Gibbs free dehydration energy of apolar functions.
  • ⁇ G dehydration the dehydration of the interacting molecular interfaces
  • ⁇ i the vacuum H-bonds energies between interacting H-bond functions
  • ⁇ G A and ⁇ G B the changes in the Gibbs free energy of molecule A and B upon binding
  • the Gibbs free energy of dehydration may be included either directly into the intermolecular interactions such as the H-bonds (I) or calculated independently and added to the contributions from the H-bonds (II).
  • H-bond energies can be either estimated using experimental approaches such as Raman spectroscopy and IR spectroscopy. Alternatively, it is possible to calculate H-bond energies for instance using quantum mechanical methods. The calculation of the Gibbs free dehydration energy can be done using different approaches considering either the whole molecule or using an incremental approach. This includes the use of geometrical calculations in analogy to Eisenberg and MacLachlan (Nature 1986, 319: 199-203), free energy analyses based on force fields (Radmer and Kollman, J. Comp.-Aided Mol. Des. 1998, 12: 215-227) and the calculation of the chemical potential in aqueous solution.
  • Approximate dehydration free enthalpies may be derived from molecular dynamics (MD) or Monte Carlo (MC) simulations which take all interacting moieties, i.e. both molecules and solvent, explicitly into account.
  • Another approach to approximate dehydration free enthalpies is provided by the program COSMO-RS theory which describes the interactions in a solvent as local contact interactions of molecular surfaces (Klamt et al., J. Comp.-Aided Mol. Des. 2001, 15: 355-365).
  • the problem of interacting molecules is reduced to pairs of interacting surfaces characterized by so-called ⁇ -profiles which can be calculated by quantum mechanical methods. For the calculation of free energy-related entities, the least demanding approaches in terms of computational effort are incremental methods.
  • c log P BioByte Inc., California, USA
  • a log P Ghose and Crippen, J. Comp. Chem. 1988, 9: 80-90
  • C log P is based upon the recognition of molecular fragments within a molecule and summation of their group contributions to the partition coefficient while A log P adds up contributions related to the individual atom types present in a particular molecule.
  • the atom type contributions were determined via a regression using a representative set of molecules with experimentally known log P values.
  • the log P value of a compound is the decadic logarithm of its partition coefficient K octanol/water between n-octanol and water. Assuming that the Gibbs free dehydration energy of a molecule is small in octanol compared to that in water, the log P value can be also used as a measure of the Gibbs free dehydration energy of a given molecule:
  • occ k A is the occurrence of geometry type k in molecule A and p log P k occ is its increment which can be determined by solving the system of linear equations by multi-linear regression.
  • the molecular vector contains a solvent accessibility dependent value f acc,k of the corresponding geometry types instead of their occurrence.
  • the calculated log P is then:
  • f acc,k A depends on the accessibilities acc k of all atoms of geometry type k in molecule A.
  • the derived p log P k acc therefore is dependent not only on the occurrence of an atom type but on its accessibility to the solvent as well.
  • the accessibility value can be calculated as the sum over all atoms i of geometry type k in molecule A:
  • f acc , k A ⁇ i ⁇ wsas i wsas k , mean ⁇ i ⁇ : ⁇ ⁇ atoms ⁇ ⁇ of ⁇ ⁇ geometry ⁇ ⁇ type ⁇ ⁇ k ⁇ ⁇ in ⁇ ⁇ molecule ⁇ ⁇ A
  • wsas i is the weighted solvent accessible surface area of atom i and wsas k,mean is the mean accessibility of geometry type k in the parameterization dataset.
  • wsas i is calculated according to Lee and Richards (J. Mol. Biol. 1971, 55: 379-400).
  • the SAS algorithm was modified such that it takes directional effects of polar function into account. The surface regions which would make good H-bonds to water contribute more strongly to wsas compared to those which do not form good H-bond to water (e.g. perpendicular to the amide binding plane).
  • the surface-weighted contribution model has the additional advantage that the algorithm providing the solvent accessible surface area of the atoms can directly be used to calculate the dehydration energy of an interface.
  • the latter represents those parts of the surface area which where previously solvent accessible but which are no longer accessible after the molecular interface is formed.
  • the Gibbs free dehydration energy of atom i of molecule A in the interface is:
  • ⁇ f acc is the difference in the accessibility of atom i between the bound and the unbound state.
  • p log P i acc is the partial dehydration increment according to the geometry type of atom i.
  • the calculation of the H-bond energy can be done using the relationship between the H-bond energy and the Gibbs free dehydration energy for an ideal polar function.
  • the Gibbs free dehydration energy for polar molecules is reduced by the factor f sat .
  • the Gibbs free dehydration energy for this function has to be divided by f sat and can be calculated as:
  • ⁇ f ia describes the changes in the interacting surface and equals 1 if it is reasonable large indicating that the H-bond has a reasonable good geometry.
  • the H-bond energy between any atom i and any atom j can be calculated as the sum of their individual contributions towards the H-bond energy:
  • FIG. 8 shows a comparison between (a) the contributions obtained for the ‘ideal functions’ according to examples 1-3, (b) the corresponding contributions extracted according to example 5 and (c) the known experimental data (Eisenberg et al., Nature 1986, 319: 199-203; Reynolds et al., Proc. Natl. Acad. Sci. U.S.A. 1974, 71: 2925-7; Jeffrey, An Introduction to Hydrogen Bonding 1997, Publisher: Oxford Univ Press, Oxford; Fersht et al. Nature 1985, 314: 235-8; Savage et al. J. Chem. Soc.
  • FIG. 9A shows the contribution towards ⁇ G bound/unbound for each atom in the protein ligand interface of raloxifene (Brzozowski et al., Nature 1997, 389:753-758) bound to the Estrogen receptor.
  • the size of the individual atomic contribution varies between ⁇ 5.3 and 1.6 kJ/mol. Small changes within the interacting molecule lead to a significant altered affinity. For instance, replacing the nitrogen N29 with a carbon changes the contribution of this atom from ⁇ 4.0 to +2.9 kJ. The change of 6.9 kJ corresponds to a 100 fold reduced change affinity ( FIG. 9B ).
  • Another example is the binding of Ru79181 (J. Med. Chem 2002 45: 2915-22) to the SH2 domain of src.
  • the method according to present invention allows an analysis if a particular atom in an experimental or a calculated molecular interface contributes either favorably or unfavorably to ⁇ G bound/unbound and also what type of changes are needed in order to improve the affinity between molecules.
  • Scoring functions are often used to estimate the affinity between molecules in aqueous solutions in a high-throughput manner whereby the fit of thousands of molecules to a molecular target is calculated (virtual screening).
  • the quality of a scoring function is often demonstrated in so called enrichment plots.
  • Molecules of a library consisting of compounds with proven affinity to the investigated protein (‘hits’) and compounds which do not bind to that protein (‘Random’) are scored using this scoring function and ranked according to their score. The plot of the rank versus the sum of the identified hits up to this rank is shown in the enrichment plots.
  • the enrichments calculated using different scoring functions are shown in FIG.
  • ACCase proprietary crystal structure
  • Estrogen receptor identifier 1err from Protein data bank, Berman et al., Nucleic Acids Research 2000, 28: 235-242
  • CDK2 identifier 1di8 from protein data bank Berman et al., Nucleic Acids Research 2000, 28: 235-242
  • thrombin identifier 1k22 from protein data bank, Berman et al., Nucleic Acids Research 2000, 28: 235-242).
  • the scoring functions include (a) HYDE, (b) FlexX2.0 (c) Chemscore, (d) GScore, (e) PMF and (f) ScreenScore (program suite Sybyl 7.2, commercially available from Tripos Ltd. St. Louis).
  • ACCase 51 hits were added to a random set of 1000 compounds, in case of the estrogen receptor 53 hits, in case of CDK2, 72 hits and in case of thrombin 144 hits. All structures were prepared according to the requirements of FlexX2.0. FlexX2.0 was used in order to generate the poses i.e. the conformation in which the compound may bind to the protein. The best 50 poses were stored for all compounds and scored with the respective scoring function. Looking at FIG.
  • HYDE is the only scoring function which gives a reasonable enrichment for all four targets. All other scoring functions give rise to good enrichments for some targets but very poor enrichments for at least one other target. FlexX2.0, for instance gives rise to a very good enrichment in case of thrombin, while the enrichments in case of CDK2 and ACCase is poor.
  • Chemscore performs very well for the estrogen receptor but only poorly for ACCase, CDK2 and thrombin while PMF performs well for ACCase and poorly for the other targets. ScreenScore performs poorly for ACCase while GScore performs poorly in all four cases.
  • the purpose of virtual screening is the identification of compounds which bind to the target protein from compound libraries which may consist of up to several million molecules.
  • the compounds are docked into the target protein and scored using a scoring function.
  • the likelihood that a chosen molecule selected using a particular scoring function is indeed binding to the target protein reflects the quality of that scoring function.
  • this cut-off score has to be defined for each protein individually. In many cases this cutoff score is defined based on criteria which include that a certain percentage of the ‘hits’ are identified up to this cutoff score.
  • docking not always produces the correct pose.
  • a more stringent upper limit ⁇ 25 kJ/mol corresponding to an affinity of roughly 10 ⁇ 6 M can be used.
  • the cutoff value ⁇ 25 kJ/mol we calculated the number of ‘hits’ and false positive for the four different targets. Looking at FIG. 11A it becomes clear that in all cases a significant probability exists that a ligand with a score better than ⁇ 25 kJ/mol belongs to the group of ‘hits’. The probability that a compound with a score better than ⁇ 25 kJ/mol is indeed a ‘hit’ ranges from 19% in case of CDK2 to 74% in case of thrombin. Interestingly, not all ‘hits’ have a score better than the cutoff score.
  • the number of identified ‘hits’ within these top ranked compounds is in many cases quite small compared to the total number of ‘hits’ within the data set. Defining the cut-off score using a percentage of identified hits such as 50% would very much increase the number of compounds better than this cutoff score. Thereby the percentage of ‘hits’ would be significantly diluted and the probability that a ligand better than the cut-off score is indeed a ‘hit would be significantly reduced.
  • FIG. 12 shows the likelihood that a certain compound which binds to the respective protein according to HYDE and has an internal conformational energy with less than 60 kJ/mol is indeed a hit. The likelihood ranges from 88% in case of thrombin to 28% in case of CDK2.
  • FIG. 13A shows the FlexX2.0 and the HYDE score for the pose observed in the experimental x-ray structure and the docking poses which were generated using FlexX2.0.
  • FIG. 13B shows the stabilizing versus the destabilizing contributions for the experimental structure and the first 25 docking solutions.
  • the stabilizing contribution consists of the sum of the H-bond contributions and the hydrophobic effect arising due to ligand binding while the destabilizing contributions consists of the Gibbs free dehydration energy of the polar atoms and of those apolar atoms pointing towards the aqueous solution.
  • HYDE allows to distinguish between correct and wrong positioning of a ligand. This is required in order to determine which portion of the interacting molecule contributes favorably or unfavorably to ⁇ G bound/unbound .

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CN112334985A (zh) * 2018-03-19 2021-02-05 达索系统德国公司 COSMOplex：自组织系统的自洽模拟
TWI760967B (zh) * 2020-12-14 2022-04-11 國立中興大學 異質材料之接合面結構的預測方法
TWI805455B (zh) * 2022-07-20 2023-06-11 國立中興大學 異質界面接合結構的預測系統
US11710543B2 (en) * 2017-10-19 2023-07-25 Schrödinger, Inc. Methods for predicting an active set of compounds having alternative cores, and drug discovery methods involving the same

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CN104293877B (zh) * 2014-09-28 2016-05-25 山东大学 一种gpr120激动剂的快速筛选方法
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US11710543B2 (en) * 2017-10-19 2023-07-25 Schrödinger, Inc. Methods for predicting an active set of compounds having alternative cores, and drug discovery methods involving the same
CN112334985A (zh) * 2018-03-19 2021-02-05 达索系统德国公司 COSMOplex：自组织系统的自洽模拟
US12451218B2 (en) 2018-03-19 2025-10-21 Dassault Systemes Americas Corp. Cosmoplex: self-consistent simulation of self-organizing systems
TWI760967B (zh) * 2020-12-14 2022-04-11 國立中興大學 異質材料之接合面結構的預測方法
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