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Thermodynamic Cycle-Perturbation Approach M Proc. Natl. Acad. Sci. USA Vol. 88, pp. 10287-10291, November 1991 Biophysics Relative differences in the binding free energies of human immunodeficiency virus 1 protease inhibitors: A thermodynamic cycle-perturbation approach M. RAMI REDDYt*, VELLARKAD N. VISWANADHANt§, AND JOHN N. WEINSTEIN§ tAgouron Pharmaceuticals, Inc., 3565 General Atomics Court, San Diego, CA 92121; and 1National Cancer Institute, Laboratory of Mathematical Biology, Building 10, Room 4B-56, National Institutes of Health, Bethesda, MD 20892 Communicated by Robert G. Parr, August 12, 1991 ABSTRACT Peptidomimetic inhibitors of the human im- personal communication) and its analogs, binding constants munodeficiency virus 1 protease show considerable promise for are also available (8, 9). This presents us with an opportunity treatment of AIDS. We have, therefore, been seeking comput- to perform free-energy simulations that might aid in system- er-assisted drug design methods to aid in the systematic design atic design of peptide-based HIV-1-PR inhibitors. of such inhibitors from a lead compound. Here we report Free-energy simulation techniques have been used to thermodynamic cycle-perturbation calculations (using molec- probe a variety ofchemical and biochemical factors including ular dynamics simulations) to compute the relative difference solvation and binding of ions and small molecules (10, 11), in free energy of binding that results when one entire residue relative binding free-energy differences between similar in- (valine) is deleted from one such inhibitor. In particular, we hibitors (13, 14), antigen-antibody complex formation (15), studied the "alchemic" mutation of the inhibitor Ac-Ser-Leu- and subunit association in oligomeric proteins (16). Although Asn-(Phe-Hea-Pro)-Ile-Val-OMe (S1) to Ac-Ser-Leu-Asn-(Phe- the results of many of these simulations show remarkable Hea-Pro)-Ile-OMe (S2), where Hea is hydroxyethylamine, in concordance with experimental measurements, insight into two different (R and S) diastereomeric configurations of the the nature of the interactions has not come easily. hydroxyethylene group. The calculated (averaged for R and S) The objective of the present work is to rationalize the difference in binding free energy [3.3 + 1.1 kcal/mol (mean ± specificities and free energies of binding for peptide-based SD); 1 cal = 4.184 J] is in good agreement with the experi- inhibitors of the HIV-1-PR using a free-energy simulation mental value of 3.8 ± 1.3 kcal/mol, obtained from the method, the thermodynamic cycle-perturbation (TCP) ap- measured K; values for an equilibrium mixture of R and S proach (17-19). Validation of the TCP approach and algo- configurations. Precise testing of our predictions will be pos- rithms, particularly for computing large changes in the ligand sible when binding data become available for the two disaste- structure, is important to computer-assisted drug design reomers separately. The observed binding preference for S1 is because binding data spanning the desired range of chemical explained by the stronger ligand-protein interaction, which structures of interest is usually unavailable. In the present dominates an opposing contribution arising from the large work, we used the TCP approach to simulate a large change desolvation penalty of S1 relative to S2. This calculation in an inhibitor ligand, deletion of the hydrophobic residue suggests that the thermodynamic cycle-perturbation approach valine in the heptapeptide inhibitor Ac-Ser-Leu-Asn-(Phe- can be useful even when a relatively large change in the ligand Hea-Pro)-Ile-Val-OMe (Si) to convert it to the hexapeptide is simulated and supports the use of the thermodynamic Ac-Ser-Leu-Asn-(Phe-Hea-Pro)-Ile-OMe (S2) (where Hea is cycle-perturbation algorithm for screening proposed deriva- hydroxyethylamine), using the TCP approach. Such a sys- tives of a lead inhibitor/drug prior to their synthesis. tematic reduction of the peptide sequence by one amino acid residue at a time is often necessary to determine the minimum The human immunodeficiency virus 1 aspartic protease sequence required for bioactivity (20). (HIV-1-PR) (1) is an important target for anti-AIDS drug Earlier, a model of the dynamical structure of the HIV- design because it mediates a crucial step in the life cycle of 1-PR dimer was developed using "dynamical cross- the HIV-1 retrovirus, namely, the proteolytic processing of correlation" maps (21). In the present free-energy simula- polyprotein precursors encoded by its gag and pol genes. tion, we explore the origins of free-energy differences in Crystallographic structures for recombinant and synthetic binding between two peptidomimetic inhibitors of the HIV- HIV-1-PRs (2-4), some complexes of the HIV-1-PR (refs. 5 1-PR and make predictions of their relative binding affinities and 6 and A. Wlodower, personal communication), and for two possible diastereomeric configurations. related proteases (7) are available. Since the enzymatic mechanism of the PRs requires a transient intermediate to be formed during hydrolysis of the peptide bond, a chemically THEORY stable structure that mimics this tetrahedral intermediate can The TCP approach (17-19, 22) provides a computationally potently inhibit the enzyme's action. This principle has tractable way to evaluate complex thermodynamic free en- motivated inhibitor design efforts in which a hydrolyzable ergies associated with solvation and binding of a ligand in the dipeptide bond within an oligopeptide substrate is replaced aqueous and enzyme-bound states. Fig. 1 shows the schema with a reduced amide, statine analog, hydroxyethylene isos- for computing relative changes in free energy of binding by tere, or hydroxyethyl amine analog [refs. 8 and 9 and refer- construction of a nonphysical path connecting the desired ences therein]. Crystal structures oftwo complexes with such initial and terminal (mutated) states. For two substrates S1 "designer" inhibitors have recently been determined (refs. 5 and S2, the relation between experimentally measured bind- and 6). For one of these complexes (ref. 6 and A. Wlodower, Abbreviations: HIV-1-PR, human immunodeficiency virus 1 aspartic The publication costs of this article were defrayed in part by page charge protease; TCP, thermodynamic cycle-perturbation; Hea, hydroxy- payment. This article must therefore be hereby marked "advertisement" ethylamine; MD, molecular dynamics. in accordance with 18 U.S.C. §1734 solely to indicate this fact. tTo whom reprint requests should be addressed. 10287 Downloaded by guest on September 30, 2021 10288 Biophysics: Reddy et al. Proc. Natl. Acad. Sci. USA 88 (1991) All equilibrium bond lengths, bond angles, and dihedral -G4 S1(aq) + AG1 S1:HIV1-PR(aq) S1(gas) HlV1-PR(aq) angles for nonstandard residues were taken from ab initio (GAUSSIAN88) quantum mechanically optimized geometries. Missing force-field parameters were estimated from similar AGgas CYCLE 1 AGaq CYCLE 2 AGcom chemical species in the AMBER database. (These parameters and the charges on the inhibitor are available from the authors upon request.) To describe the water interactions, we used S2s -AG3 AG2 S2(gas) S2(aq) +HlVl-PR(aq) P- S2:HIV1-PR(aq) the SPC/E rigid geometry model potential (27), which repro- duces bulk properties of water quite accurately (28). FIG. 1. Thermodynamic cycles used in this study. Each "reac- Molecular Dynamics (MD) Calculations. All MD simula- tion" shown in the two cycles is reversible, but the direction of the tions were performed with the GIBBS module of the AMBER arrow indicates that the change in free energy is computed by taking program (23, 24). Newton's equations ofmotion for all atoms the difference between free energy ofthe state at the end ofthe arrow were solved using the Verlet algorithm (29) for integration and that at the point. and the SHAKE algorithm to constrain all bond lengths (30). ing constants (k1 and k2) and free energies (AG1, AG2, AGaq Constant temperature (at T = 298 K) was maintained by and AGcom) is velocity scaling. The initial phase of equilibration consisted of 20 ps of MD simulation. All nonbonded interactions -kBT ln(k2/k1) = AG2 - AG1 involving the inhibitor were computed without any cutoff limit. However, to reduce the computation time, a 10.0-A nonbonded interaction residue-based cutoff was used for = AGcom -AGaq = AAGbind, [1] other interactions that do not directly involve the inhibitor. The nonbonded pair list was updated every 10 MD steps for where kB is the Boltzmann constant and T is the absolute the solvent or 20 MD steps for the ligand-protein complex temperature. simulations. The relative solvation free-energy change for two sub- Mutation of S1 to S2. Fig. 2 shows the atom conversions strates, computed from cycle 1 of Fig. 1, is involved in mutating S1 through an intermediate state S1* to S2. In all free-energy results reported here, the mutation was AG3 -AG4 = AGaq - AGgas = [2] AAGso. accomplished using the GIBBS module ofAMBER, in two steps: The free-energy change for converting S1 into S2 is computed (i) during the first step ofthe transformation (S1 -* S1*) only by transforming or "perturbing" the Hamiltonian of reactant the partial charges were mutated; (it) during the second (S1* state S1 into that of product state S2. This transformation is -- S2), the van der Waal's parameters were mutated and, in a of the terms com- addition, bond stretching, bond angle changes, and torsional accomplished through parametrization were The prising the interaction potentials of the system with a change changes accompanying the mutation simulated. total free-energy change in each step was computed by of state variable A that maps onto reactant and product states summing these incremental free-energy changes in each when A is 0 and 1, respectively. The incremental free-energy window between A = 0 and A = 1. In each step, a total of 51 change between any two successive windows is given by windows was used (AA = 0.02) for the complete mutation.
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