WO1995006293A1 - Modelisation moleculaire et conception de medicaments - Google Patents

Modelisation moleculaire et conception de medicaments Download PDF

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Publication number
WO1995006293A1
WO1995006293A1 PCT/IB1994/000257 IB9400257W WO9506293A1 WO 1995006293 A1 WO1995006293 A1 WO 1995006293A1 IB 9400257 W IB9400257 W IB 9400257W WO 9506293 A1 WO9506293 A1 WO 9506293A1
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chemical substance
host
receptor molecule
binding
free energy
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PCT/IB1994/000257
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English (en)
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Carmen Medina
Johan ÅQVIST
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Symbicom Aktiebolag
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Priority to AU73909/94A priority Critical patent/AU7390994A/en
Application filed by Symbicom Aktiebolag filed Critical Symbicom Aktiebolag
Publication of WO1995006293A1 publication Critical patent/WO1995006293A1/fr

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    • C—CHEMISTRY; METALLURGY
    • C07—ORGANIC CHEMISTRY
    • C07K—PEPTIDES
    • C07K1/00—General methods for the preparation of peptides, i.e. processes for the organic chemical preparation of peptides or proteins of any length
    • 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
    • G16C—COMPUTATIONAL CHEMISTRY; CHEMOINFORMATICS; COMPUTATIONAL MATERIALS SCIENCE
    • G16C20/00—Chemoinformatics, i.e. ICT specially adapted for the handling of physicochemical or structural data of chemical particles, elements, compounds or mixtures
    • G16C20/50—Molecular design, e.g. of drugs
    • 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
    • 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

Definitions

  • the present invention relates to a method for assessing the absolute free binding energy between a host or receptor molecule and a chemical substance interacting therewith, e.g. bound thereto, and to a method for assessing the relative free binding energy between a plurality of systems comprising a host or receptor molecule and a chemical substance interacting therewith.
  • thermodynamic cycle If a typical case is considered where it is desired to determine the relative free energy of binding between two compounds, A and B, the problem is described by the thermodynamic cycle:
  • the free energies associated with the two unphysical paths A(w) ⁇ B(w) and A(p) ⁇ B(p) are calculated, corresponding to a "mutation" of A into B (or the creation of B in the case where A is a nil particle).
  • MD (or Monte Carlo) simulations are used to collect ensemble averages along the paths, which must be rather fine grained in order for the free energy to converge properly. If, e.g., two enzyme inhibitors are considered, the path connecting them will involve changes in the molecular charge distribution as well as the creation/annihilation of atoms.
  • the present invention provides a method which makes it possible to assess free energies of binding between a "host or receptor" molecule and a chemical substances, such as a drug candidate, interacting therewith, without the necessity of synthesizing the chemical substances.
  • a chemical substances such as a drug candidate
  • a host or receptor molecule should be understood in a broad sense as any molecule which can interact with a chemical substance, and the interaction of which with a chemical substance or a group or plurality of chemical substances, e.g. drug candidates, is to be studied.
  • the host or receptor molecule may simply be any another chemical compound capable of interacting with the chemical substance, but most often, the host or receptor molecule will be a relatively large molecule, in other words a macromolecule such as a protein or an oligonucleotide, which is relatively large compared to the chemical substance; although the chemical substance interacting with the host or receptor molecule may, of course, in itself be a
  • the host or receptor molecule is a relatively large molecule of natural origin or prepared by recombinant DNA technique and having a particular biological function, e.g. as an enzyme, an antigen, an antibody, a biological receptor, etc.
  • the chemical substance is a synthetic substance of a structure known or believed to interact with or bind to the host or receptor molecule.
  • the method of the invention does not involve "mutational paths", but rather determines the free energy of binding by an approximation, suitably a linear approximation which only involves an average interaction between the chemical substance and its surrounding.
  • the interaction (or potential) energy between the chemical substance (in the following often referred to as the "drug") and its surrounding is divided into a polar (electrostatic) and a non-polar (hydrophobic) contribution, and the absolute free energy of binding is assessed as an adjusted combination of these two contributions.
  • Each of these contributions to the absolute free energy of binding is assessed as the difference between two distinct states, A and B, of interaction between the chemical substance and its surroundings which define the binding process, one state (A) being a state in which the chemical substance is surrounded by solvent, and the other state (B) being a state in which the chemical substance, interacting with (bound to) the host or receptor molecule, is surrounded by solvent.
  • the method of the invention for assessing the absolute free energy of binding between a host or receptor molecule and a chemical substance comprises:
  • the adjusted combination of the above-mentioned energy differen ces comprises about one half of the value of the polar binding energy difference between states B and A, , preferably one half of this value, in accordance with the linear response approximation, e.g. Marcus' theory of electron transfer reactions (Marcus, 1964), to which is added the nonpolar (hydrophobic) contribution, , adjusted by means of an empirical parameter.
  • Equation 1 can thus be written
  • Each of the four averages can be calculated by standard molecular dynamics procedures using suitable computer soft- and hardware.
  • the symbol ⁇ > means molecular dynamics average.
  • the index i-s means compound-solvent (or compound-surrounding), the letter “i” standing for “inhibitor”, which reflects the fact that the relevant compound or drug will often be a compound or drug which is intended to inhibit the function of the host or receptor molecule.
  • the superscript “el” designates the polar or electrostatic energy, while the superscript “vdw” indicates “van der Waals", another designation for the non-polar interac tions.
  • the symbol ⁇ indicates that the quantity in state A is subtracted from the quantity in state B.
  • the parameter ⁇ being determined by empirical calibration. Although, as discussed above, a theoretical prediction of the coefficient for ⁇ Vff s > is 1 ⁇ 2, it may be practically useful to also treat this coefficient as an empirical parameter. This would lead to the free energy of binding being approximated by
  • the assessment of the averages is normally performed by establishing 3-dimensional models or structural representations, using, e.g., suitable standard computer hardware and software, comprising a 3-dimensional structure of the receptor molecule alone and a 3-dimensional structure of the chemical substance "docked therein", and applying molecular dynamics calculations to the 3-dimensional representation.
  • Force field data for use in the molecular dynamics calculations may be from any suitable force field such as publicly available force fields, e.g., AMBER (Weiner et al., 1986), CHARMM (Brooks et al., 1983), GROMOS, OPLS (Jorgensen, 1986), MM2 (Allinger, 1977), etc.
  • the purpose of the molecular dynamics calculation is to be able to explore the available conformations of the system, thereby calculating the average interaction energies. In the simulation, the molecules are allowed to move around to enable exploration of the conformational space.
  • the establishment of the 3-dimensional structural representation may be performed using any method which will result in the establishment of the 3-dimensional coordinates of the molecule or combination in question, including crystallisation and X-ray crystallography, NMR, computer modelling, etc.
  • the term "docked therein” indicates that the chemical substance has been brought to "fit” with the receptor molecule in the 3-dimensional representation; while this does not, in the present context, imply any numerical limitation with respect to the quality of the 3-dimensional fit, it is evident that the binding free energy resulting from the methods will reflect the degree of "fit".
  • molecular dynamics applied to the system comprising the receptor molecule and the compound docked therein will in itself be useful for checking the correctness of the docking in case more than one position and/or more than one orientation is possible.
  • the calculation of the above-mentioned energy averages can, in principle, be performed separately, either manually or (preferably) by means of a computer.
  • the calculation may be performed on the basis of the well-known classical mechanical principles involving simulations on the equations of motion of the relevant molecular systems (molecular dynamics or MD); another principle could be the socalled Monte Carlo simulations, which does not actually solve the equations of motion, but rather calculate the probabilities of different conformations; a still further principle could be energy minimization in which the averages are replaced by minimum energies.
  • molecular dynamics molecular dynamics
  • suitable software preferably software which interfaces or communicates with the stored coordinates of the 3-dimensional models of the receptor molecule and of the receptor molecule with the chemical substance docked therein; such software is available as standard commercial software, e.g. one of the many commercially available types of computer software packages suitable for the purpose.
  • the parameter with which the non-polar and hydrophobic energy difference, , is adjusted is suitably a coefficient representing the result of a calibration established by comparing the results of predictions with actual measured values.
  • the term "representing the result of a calibration” means that the parameter has been established by such calibration, or that the parameter has a value which would have resulted from such calibration against actual measured values; thus, it is not precluded that the parameter, although representing the results, could have been provided, in a particular case, in any other suitable manner.
  • the adjusted parameter may be valid for a relatively broad range of systems, but when working in any particular system, it may be preferred to make a calibration against actual values measured on representatives of the system. Examples of such calibrations are given below.
  • the calibration described in the below Example 1 was found to result in a value of the coefficient ⁇ of about 0.16. It is presumed that the numerical value of ⁇ will be at the most 1.0, and that most values of c. in practice will be at the most 0.5 or preferably at the most 0.3, such as at the most 0.2. While these values are understood to be absolute values, it is believed that ⁇ will in fact be a positive value in most cases.
  • the coefficient for the electronic term is predicted to be 1 ⁇ 2, but may also be treated as an empirical parameter ( ⁇ ) determined by calibration against known data. It is then believed that the parameter ⁇ will assume a value of at most 1.0, and that most values of ⁇ in practice will be about 0.2 - 0.8, such as about 0.3 - 0.7 or preferably about
  • ⁇ will in a most preferred embodiment of the invention have a value of about 0.5. While these values are understood to be absolute values, it is believed (as is the case for the coefficient ⁇ ) that ⁇ will in fact be a positive value in most cases.
  • Equation 1 In some systems, it seems suitable to add an additional constant term to Equation 1, so that the equation becomes
  • ⁇ is a coefficient representing the result of a calibration established by comparing the results of predictions with actual measured values (as described above)
  • c is a constant reflecting extrapolation to zero size of the chemical substance, that is, where the regression line is distinctly offset from origin when moving towards zero size of the chemical substance.
  • the parameter c may also be used to correct for possible systematic errors due to e.g. the neglect of induced polarisation, possible force field deficiencies etc. In these cases, c will normally assume a value between -10 and 10 kcal/mol, typically between -3 and 3 kcal/mol, such as between -2 and 2 kcal/mol, e.g. between -1 and 1 kcal/mol. However, it is anticipated that in many cases, c can suitably be set to zero, as the extent of deviation will be of minor importance for the usefulness of the predicted values.
  • solvent used in the above method is suitably and most often an aqueous solvent like water
  • any other suitable solvent including, e.g., methanol, ethanol, acetone, acetonitrile, chloroform, hexane, etc., or mixtures thereof or combinations of such solvents or mixtures thereof with water.
  • the selection of the solvent will be of little importance to the predicted values as long as the solvent is one which is able to dissolve or solvate the receptor molecule and the substance (in the present context this means that a sufficient amount of the receptor molecule can be homogeneously mixed with the solvent without precipitation so as to allow the determination of binding energies by some suitable method), but there may be cases where it is advantageous to modify the solvent environment (e.g. by modulating the ionic strength) in which the interaction of the substance and the receptor molecule is to take place. If the environment in which the interaction between the chemical substance, such as a drug, and a host or receptor molecule is to take place in the actual use of the drug is the human body, it might be particularly suitable to imitate e.g. human plasma as the solvent.
  • the method of the invention also makes it possible to determine relative values of free energy of binding between a number of chemical substances capable of interacting with a host or receptor molecule.
  • the case may be considered where there are four inhibitors, I 1 , I 2 , I 3 and I 4 .
  • a and a are calculated from molecular dynamics simulations, or Monte Carlo simulations, or simply by energy minimization. For instance, for any particular guess of the parameter ⁇ , it can then be seen how good this guess is by comparing the calculated (from Equation 1) and observed values of ⁇ G bind for each inhibitor. In order to find the best ⁇ , a least-squares optimization can be used, which means that the sum
  • the parameters ⁇ and ⁇ and/or c can be determined by comparing the values (from any of the equations 1b, 2 and 2b) with values and varying the parameters in the pertinent formula until a minimization of the sum of squares is obtained or by determining the parameters analytically by partial differentiation with respect to the parameters of the least squares expression.
  • formula 2b is used and an analytical solution is sought, the partial differentiation of the least square expression with respect to ⁇ , ⁇ and c will e.g. result in three linear equations with the three parameters to be determined.
  • ⁇ G bind (I 1 -I 3 ) AG bind (I 1 ) - ⁇ G bind (I 3 )
  • ⁇ ⁇ G bind (I 1 -I 4 ) ⁇ G bind (I 1 ) - ⁇ G bind (I 4 )
  • ⁇ G bind (I 2 -I 3 ) ⁇ G bind (I 2 ) - ⁇ G bind (I 3 )
  • ⁇ G bind (I 2 -I 4 ) ⁇ G bind (I 2 ) - ⁇ G bind (I 4 )
  • ⁇ G bind (I 3 -I 4 ) ⁇ G bi nd (I 3 ) - ⁇ G bind (I 4 )
  • the ⁇ G bind values would be calculated (by one of the formulas 1 or 2) and their differences taken to obtain the ⁇ G bind values. Then, in the same manner as above, the sum
  • ⁇ and ⁇ could be determined by iterative methods as well as analytically. These parameters are then the ones that gives the best agreement with respect to the relative binding energies (or binding energy differences).
  • N -1 ⁇ 2(n 2 -n)
  • 1 ⁇ 2(n 2 -n) differences in binding energy between inhibitors in a system with n inhibitors One could also imagine a case where, for some reason, the calculations give a systematic error in the absolute ⁇ G bind values. It might then be desirable to try to obtain the best fit of the relative energies instead, and the latter type of the above-described optimization methods would then be preferable.
  • the initial stage could be to establish a possible lead compound by some means, e.g. computer modelling.
  • the method of the invention could then be applied, for example using equation 1 with a value of c. established earlier (for some other system, e.g. the value of a of about 0.16 disclosed herein). If the outcome of the calculations according to the method of the invention would indicate that the binding of the lead compound is good enough, the lead compound could be synthesized, and its actual binding power could be measured.
  • a change of the solvent from e.g. water to methanol may change the optimal value of ⁇ . In any case, for a new system, one would then choose an earlier established value of ⁇ for a similar system.
  • one important utilization of the method of the invention will be a method for identifying a chemical substance capable of interacting with a host or receptor molecule, e.g. binding to the host or receptor molecule, with a predicted binding energy equal to or better than a predetermined threshold value, comprising
  • step 4 if necessary repeating step 4 until the predicted binding free energy determined between the resulting chemical substance, X, and the host or receptor molecule is equal to or better than the predetermined threshold value.
  • One suitable way of calibrating the above-mentioned method could comprise providing a sample of a chemical substance or chemical substances selected from the chemical substances A, B and X and providing a sample of the host or receptor molecule, measuring the binding free energy between the chemical substance or substances and the host or receptor molecule, and if the measured binding free energy between the chemical substance or substances and the host or receptor molecule is not equal or substantially equal to the predicted value, then performing a calibration of the method according to the invention so as increase the predictive value of the method.
  • Fig. 1 Illustration of how the approximation of equation b can be used to estimate the electrostatic contribution to ⁇ G sol in a given environment that can either be water or protein.
  • the state A corresponds to a system with the isolated inhibitor in the gas-phase and a ready-made van der Waals cavity in the condensed system.
  • State B is simply the solvated inhibitor in water or in the protein's active site. These states are given by the two potentials V A and V B .
  • equation b will reduce to since the solvent configuration in state A is uncorrelated with the charge distribution of the solute in state B.
  • Fig. 2. Calculated dependence of the average solute-solvent interaction energy on the length of the carbon chain for n-alkanes solvated in water.
  • Fig. 3. Chemical structures of the inhibitors I 1 . ..., I 5 used in the calculations in Example 1.
  • Fig. 4 Stereo view of the 50 ps average MD structure of the EP-I 1 complex (thin lines) superimposed on the corresponding crystallographic structure (see Example 1). The active site of the enzyme is shown with the bound inhibitor in the centre of the picture.
  • endothiapepsin As a test system, endothiapepsin (EP) was chosen; it belongs to the family of aspartic proteinases (see, e.g., Davies, 1990; Fruton, 1976), a class of enzymes for which numerous studies of inhibitor binding have been reported. Crystal structures of native endothiapepsin and inhibitor complexes have been published by Blundell and coworkers (Foundling et al., 1987; Veerapandian et al., 1990). In the present
  • the atoms within this sphere were free to move while protein atoms beyond 16 A were restrained to their crystallographic positions.
  • An interaction cutoff radius of 8 A was used and the MD time step was 0.001 ps.
  • the equilibration phase of the protein simulations consisted of 5 ps of successive heating of the system and weakening of harmonic positional restraints that were applied to the protein atoms. After this period all restraints within the 16 A sphere were set to zero and the system was further equilibrated at the final temperature of 298 K for another 20 ps.
  • the r.m.s. coordinate deviation for the inhibitor atoms between the following 50 ps MD average structure and the experimental EP-I 1 complex is 0.94 A.
  • Fig. 4 shows a superposition of these two structures, and it can be seen that the agreement is quite satisfactory.
  • the predictive power of the approach was tested by modelling an inhibitor not present in the calibration set.
  • the inhibitor I 5 was chosen; as can be seen from Fig. 3, this inhibitor differs significantly in its chemical structure from any member of the calibration set.
  • This molecule was built into the EP active site and subjected to the same simulation procedure as the other inhibitors.
  • the calculated relative binding free energies with respect to the four inhibitors in the calibration set are given in Table 3, where it can be seen that all the pairwise selectivities involving I 5 are correctly predicted by the simulations, the maximum error in this case being 0.61 kcal/mol.
  • the convergence properties of MD stimulations depend on how far from equilibrium the initial structure is, but judging from the present Example, it seems that one can reach satisfactory convergence within reasonable computing time. For example, by comparing averages over the first and second halves of the MD trajectories, average (over all five inhibitors) errors were obtained of ⁇ 0.35 and ⁇ 0.75 kcal/mol for and , respectively, in the protein; the corresponding errors in water are ⁇ 0.46 and ⁇ 0.62 kcal/mol. This would yield a nominal error range of ⁇ 0.82 kcal/mol in equation 1 originating from the MD convergence uncertainty.
  • equation 1 with the above parameterisation of ⁇ is not an equation for the individual solvation energy terms, since the factor ⁇ represents the combined effect of several energy/free energy relations.
  • the fact that solvation energy differences are always dealt with may also cause some cancellation of possible systematic errors.
  • the formula might be expected to give better results for polar inhibitors, as long as the electrostatic iinear response approximation holds.
  • long range electrostatic effects as well as induced polarisation effects are known to be important, but these problems have not yet been resolved in most available MD programs and force fields.
  • long-range corrections of the Born type see, e.g., Straatsma and Berendsen, 1988; Aqvist, 1990) would obviously become important and may make accurate predictions more difficult
  • the empirical parameter ⁇ is readily transferable to other systems, but it is also possible that it will display some system dependency. Given the fact that the parameterisation of force fields can differ considerably, o. may be found to be force field specific.
  • the aspartic proteinase from the human immunodeficiency virus type 1 (HIV-1) is the target of intense AIDS drug development. This enzyme and three of its inhibitors were chosen as a second test system (Hansson, 1994).
  • Inhibitor 1 acetyl-pepstatin
  • Inhibitor 2 pepstatin This is the N-capped oligopeptide Iva-Val-Val-Sta-Ala-Sta, where Iva is an isovaleryl group; (CH 3 ) 2 CHCH 2 (CO). The only difference from Inhibitor 1 is the added group of three nonpolar carbon atoms (isopropyl group) in the beginning of the molecule (Dreyer et al. 1989). Inhibitor 2 was modeled from Inhibitor 1 by adding the 3 carbon atoms, and rotating around the bonds at the end of the molecule to remove any collisions between atoms .
  • a sphere of radius 20 A of water was added, and any protein atoms outside this sphere were kept fixed.
  • the time step was 1 fs, except for some equilibration steps where noted (2 fs).
  • the temperature was 300 K.
  • the cutoff distance was 15 A in the first set of calculations for all three inhibitors. Then, Inhibitor 3 was tested with 15 A, 10 A and 8 A. Tests of the turning off of charges were performed using 10 A, as were the pH tests described below. A 10 A cutoff was used for the FEP calculations where Inhibitor 2 was changed into Inhibitor 1. These cutoffs apply to interactions between protein groups of zero net charge. Charged protein groups, and all parts of the inhibitor, interact with all other parts of the simulated system, without cutoffs. The molecular dynamics simulations were performed using the program ENZYMIX and the GROMOS potential, with modifications as in Example 1.
  • the protein was in the 'Neut' electric state. Protein simulations started from the end of the 210 ps run reported above for inhibitor 2, and the water simulations started from the end of the corresponding 263 ps run.
  • Inhibitor 1 binds 0.7 kcal/mol tighter than Inhibitor 2. There is a difference between 1 ps and 2 ps calculations, but not so large as to make an even longer calculation worthwhile.
  • equation (1) gives the same relative order of binding strength for the three inhibitors as experimentally observed:
  • Inhibitor 3 > Inhibitor 1 > Inhibitor 2 where '>' means 'binds better than'.
  • the FEP calculation also gives the proper relation between inhibitors 1 and 2.
  • GROMOS Molecular Simulation

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Abstract

Nouveau procédé de détermination de l'énergie libre de liaison entre une molécule hôte ou réceptrice et une substance ligand. Le procédé consiste à déterminer les combinaisons réglées de la différence d'énergie moyenne entre les participations des interactions a) polaires et b) non polaires entre la substance en deux états, à savoir un premier état dans lequel seule la substance est entourée de solvant, et un autre état dans lequel la substance liée à la molécule hôte ou réceptrice est entourée de solvant. De préférence, les participations des interactions polaires et non polaires sont obtenues par des simulations de cinétique moléculaire dérivées de représentations tridimensionnelles de la molécule réceptrice et de la substance. Ce procédé permet le calcul des énergies libres de liaison sans utiliser les techniques de simulation de Monte Carlo ou de perturbation d'énergie libre, et exige, de ce fait, moins de ressources informatiques que les procédés connus. On a également prévu des procédés de sélection/préparation de substances pouvant interagir avec une molécule hôte ou réceptrice.
PCT/IB1994/000257 1993-08-25 1994-08-25 Modelisation moleculaire et conception de medicaments WO1995006293A1 (fr)

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