Protein Engineering, Vol. 12, No. 6, 469-474,
June 1999
© 1999 Oxford University Press
Molecular mechanics analysis of drug-resistant mutants of HIV protease
Department of Microbiology and Immunology, Kimmel Cancer Center, Thomas Jefferson University, Philadelphia, PA 19107, USA.E-mail: weber{at}asterix.jci.tju.edu
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Abstract |
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Drug-resistant mutants of HIV-1 protease limit the long-term effectiveness of current anti-viral therapy. In order to study drug resistance, the wild-type HIV-1 protease and the mutants R8Q, V32I, M46I, V82A, V82I, V82F, I84V, V32I/I84V and M46I/I84V were modeled with the inhibitors saquinavir and indinavir using the program AMMP. A new screen term was introduced to reproduce more correctly the electron distribution of atoms. The atomic partial charge was represented as a delocalized charge distribution instead of a point charge. The calculated protease–saquinavir interaction energies showed the highly significant correlation of 0.79 with free energy differences derived from the measured inhibition constants for all 10 models. Three different protonation states of indinavir were evaluated. The best indinavir model included a sulfate and gave a correlation coefficient of 0.68 between the calculated interaction energies and free energies from inhibition constants for nine models. The exception was R8Q with indinavir, probably due to differences in the solvation energy. No significant correlation was found using the standard molecular mechanics terms. The incorporation of the new screen correction resulted in better prediction of the effects of inhibitors on resistant protease variants and has potential for selecting more effective inhibitors for resistant virus.
Keywords: drug resistance/HIV protease/indinavir/molecular mechanics/saquinavir
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Introduction |
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AIDS is a fast-growing epidemic and the World Health Organization predicted that 30–40 million people worldwide will be infected by the human immunodeficiency virus type 1 (HIV-1) by the year 2000. The replication of HIV-1 is inhibited by HIV-1 protease inhibitors, such as the drugs ritonavir, indinavir, saquinavir and nelfinavir. Clinically, protease inhibitors are more effective than previous anti-HIV drugs in lowering the level of virus in the blood of infected patients. However, the long-term therapeutic efficacy is limited by the rapid selection of inhibitor-resistant variants of the protease (Condra et al., 1995
; Boucher, 1996; Schinazi et al., 1997). Most of the nearly 50 known drug-resistant mutants of HIV-1 protease involve conservative substitutions of hydrophobic residues, such as Val to Ile (Schinazi et al., 1997). The activity of selected resistant mutants of HIV-1 protease on selected substrates and inhibitors has been studied (Gulnik et al., 1995; Maschera et al., 1996; Pazhanisamy et al., 1996). The protease mutants generally show reduced affinity for inhibitors. It is expected that the protease affinity for a specific inhibitor is reduced by the resistant mutation, while the mutant protease retains sufficient activity on the polyprotein substrates for the replication of virus. Moreover, it is not obvious how any particular mutation acts to reduce the affinity for a specific inhibitor. Overcoming drug resistance will require detailed knowledge of the molecular basis for the specificity of the protease for its inhibitors. Therefore, we have analyzed the structures and interaction energies of 10 HIV-1 protease mutants with two different inhibitors using molecular mechanics.
The HIV-1 protease is essential for the production of infectious virus particles. The protease catalyzes the hydrolysis of specific sequences in the precursor polyproteins to release itself and the other mature structural and functional viral proteins (Debouck et al., 1987; Darke et al., 1988). The 99 residue HIV-1 protease is a member of the aspartic protease family and is enzymatically active as a homodimer. Crystal structures of the uninhibited HIV-1 protease and of the protease in complex with numerous inhibitors have been determined (for a review, see Wlodawer and Erickson, 1993). The binding of inhibitors to wild-type HIV-1 protease has been analyzed by molecular mechanics calculations. These calculations provide a simple and rapid method to estimate the trends in the free energy of binding different ligands to a protein of known structure (reviewed in Weber and Harrison, 1998). Generally, the contributions of entropy and solvation are neglected in these calculations. However, several successful calculations have been reported. Holloway et al. (1995) obtained correlation coefficients R = 76–88.5% between the protease–inhibitor interaction energies and the differences in free energy derived from inhibition constants using the MM2X force field in OPTIMOL. A combination of molecular mechanics estimation of the interaction energy and heuristic estimation of entropy gave a correlation coefficient of 75.5% for 13 inhibitors of HIV protease (Head et al., 1996). In addition, we have shown that molecular mechanics calculations with AMMP (Harrison, 1993) can evaluate the trends in catalytic efficiency for peptide substrates of HIV-1 protease. Calculations on HIV protease with the tetrahedral intermediate of 21 peptide substrates related by single amino acid substitutions in positions P4–P3' gave a correlation coefficient of 0.64 between the interaction energies and the differences in free energy derived from kinetic measurements (Weber and Harrison, 1996). The calculations on 14 substrates with changes in the P2–P2' positions gave a highly significant correlation of 0.86. The calculations also gave a significant correlation with kinetic measurements for the related protease from Rous sarcoma virus with similar peptide substrates (Weber and Harrison, 1997). Here, this method is extended to drug-resistant mutants of HIV-1 protease with two clinical inhibitors. The molecular mechanics calculations are shown to be capable of predicting the relative inhibition of protease mutants by saquinavir and indinavir.
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Materials and methods |
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Energy minimization calculation
The minimization and molecular dynamics were run using the program AMMP (Harrison, 1993) that incorporates an algorithm to increase the speed and allow the calculation of non-bonded and electrostatic terms without the use of a cut-off radius. AMMP is available from http://asterix.jci.tju.edu. The calculations were run on a DEC AlphaStation 233. The molecular mechanics calculations used the UFF potential set (Rappe et al., 1992) with parameters modified as described in Weber and Harrison (1996, 1997) (parameter set sp4). In addition, the force constants for the planarity terms of the carbonyl and aromatic carbon atoms were increased from 6 to 150 and 100 kcal/mol.Å, respectively. This change significantly improved the agreement between the calculated normal mode frequencies and observed infrared absorptions for formaldehyde and benzene. Charges for the non-standard groups were generated as described previously (Weber and Harrison, 1996). The positions for the non-hydrogen atoms were initially fixed in order to calculate and minimize the hydrogen atom positions. No screening dielectric term or bulk solvent correction was included. A constant dielectric of one was used. No cut-off was applied for non-bonded and electrostatic terms. These terms were calculated with an algorithm that amortizes or spreads the cost of calculation over many simpler calculations which results in lower average cost, as described in Harrison and Weber (1994). This algorithm, when used in conjunction with the fast multipole method as implemented in AMMP, brings the cost of the calculation without cut-offs below the cost of using a cut-off of 8–10 Å with standard approaches.
The models were based on the starting crystal structures of wild-type HIV-1 protease with saquinavir (Krohn et al., 1991) and indinavir (Protein Database entry 1HSG; Chen et al., 1994). The hydrogen atoms were generated by minimization for the wild-type protease, inhibitor and the water molecules observed in the crystal structures. Saquinavir was given an overall charge of zero. For indinavir, different protonation states were considered with an overall charge of 0, +1 and +2. The partial charges for the inhibitor atoms were generated by a method of moments calculation, as described for the tetrahedral reaction intermediate of HIV protease (Weber and Harrison, 1996). Each mutation was made by stripping the two residues in each dimer down to the Cß atom, except for the mutant R8Q where the C
atoms were also kept, since this side chain is long and on the protein surface. The new atoms for each substituted residue were created by minimizing on the bond, angle, hybrid and torsion geometrical terms. Each of the side chain torsion angles for the mutated residues was rotated through 360° in steps of 15° to search for alternative conformations. This torsion search finds the angle(s) that have a minimum in the non-bonded and electrostatic energy terms. Finally, the modeled protease–inhibitor complex was optimized by a longer minimization using 100 steps of conjugate gradients followed by 16 cycles of alternating 30 steps of conjugate gradients and short runs of molecular dynamics (20 steps of 1 fs at 300 K). The protease–inhibitor interaction energy was calculated using the standard non-bonded and electrostatic terms and also using the screen correction described below.
Screen correction
One potential defect in the standard point charge model for atomic interactions is the inability of a point charge to account correctly for the spread of the electron cloud. While the typical distribution of electrons is highly peaked at the nucleus, the electrostatic potential of a set of orbitals can be significantly different from a point charge model at short distances (<5–6 Å). The difference is readily visible when the electrostatic potential from a 1s orbital is compared with the potential around a point charge. The electrostatic potential between 1s orbitals is shallower than the potential of point charges at short interatomic distances. Therefore, a new term was introduced to correct for the electron distribution in atoms which are represented as point charges in the standard terms. The atomic partial charge was represented as a delocalized charge distribution. As a first approximation, the charge was assumed to be distributed approximately as a 1s hydrogen orbital with an arbitrary radial scale. A major reason for using a 1s hydrogen orbital was the availability of an analytical expression for the electrostatic potential. The coulomb interaction between atoms i and j (Vij) is given by (Wallace, 1984)
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this expression reduces to the standard 1/r potential. A radial scale value of 0.20 was found by empirical tests to give the best correlation of calculated and experimental energies. This empirical value for the radial scale is probably affected by energetic terms, such as solvation energies, that have been neglected in these calculations. A more rigorous determination of radial scale values will require direct fitting to molecular electrostatic potentials determined from ab initio quantum mechanics calculations on small molecules. The radial screen is not equivalent to a simple dielectric correction, because the interaction energy converges to the 1/r term at intermediate ranges, not 1/
r as would be the case with a dielectric. The radial screen damps the interaction energy only at short distances, resulting in a `softer' non-bonded potential. |
Results |
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Molecular mechanics calculations of interaction energy were applied to mutants of HIV-1 protease with different inhibitors in order to understand the molecular basis for the development of drug resistance. Kinetic measurements of inhibition constants were available for the series of drug-resistant mutants R8Q, V32I, M46I, V82A, V82I, V82F, I84V, V32I/I84V and M46I/I84V with the inhibitors saquinavir and indinavir that are in use as anti-viral drugs (Gulnik et al., 1995
). This set of measurements was chosen because a relatively large number of mutants were analyzed compared with other studies and crystal structures were available for complexes of these two inhibitors with the wild-type HIV-1 protease.
The molecular mechanics interaction energy is an estimate of the internal energy difference between separate and bound states and does not include the entropic contribution or solvation terms. Therefore, the calculated interaction energy will only show correlation with the relative binding free energy derived from inhibition constants, 
G = RTln(Kimu/Kiwt), where subscript mu refers to mutant and wt to wild-type protease, if the differences in entropy and solvation are similar for all the tested protease mutants. In addition, there will be no correlation if the wild-type and mutant proteases have different conformational changes on binding the same inhibitor. In fact, conformational differences near the site of mutation were observed in the crystal structure of the V82A mutant protease with inhibitor (Baldwin et al., 1995).
The complexes were built starting from the crystal structures of wild-type HIV-1 protease with the inhibitors, saquinavir (Krohn et al., 1991) or indinavir (Chen et al., 1994). The chemical structures of the inhibitors are shown in Figure 1. The minimized complexes included the protease dimer, bound inhibitor and water molecules from the crystal structures. The positions of the non-hydrogen protease atoms in the minimized complexes were compared with those in the crystal structures of wild-type protease. The minimized complex with saquinavir had root mean square (r.m.s.) differences compared with the crystal structure of 0.36 Å for C
atoms, 0.46 Å for main chain atoms, 0.69 Å for side chain atoms and 0.58 Å for all atoms. Similarly, the minimized complex of HIV-1 protease with indinavir gave r.m.s. differences of 0.34 Å for C atoms, 0.41 Å for main chain atoms, 0.61 Å for side chain atoms and 0.52 Å for all atoms compared with the 1HSG crystal structure. These values are well within the range of 0.16–0.79 Å for r.m.s. differences observed between main chain atoms in different crystal forms of the same protein (Zegers et al., 1994) and close to the average value of 0.40 Å for C atoms (Flores et al., 1993). There are no crystal structures available for mutant proteases with saquinavir or indinavir. When the crystal structures of all HIV protease mutants in the Protein Database (Bernstein et al., 1977) were compared with the wild-type structure, the average r.m.s. deviation was 0.56 Å for C atoms. A similar variation (0.6 Å) has been reported for the structures of wild-type protease with different inhibitors (Wlodawer and Erickson, 1993). Therefore, the differences due to minimization with AMMP are within the range of experimental differences in HIV protease crystal structures and in other protein structures and indicate the accuracy of the potentials and minimization procedure.
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The molecular mechanics analysis of 10 models of HIV-1 protease variants with saquinavir gave calculated interaction energies that are summarized in Table I
. The interaction energy was calculated using either the standard non-bond and electrostatic terms or the new screening term and is represented as the difference in calculated interaction energy for the mutant minus the wild-type complex. The screening term corrects for the charge distribution of real atoms that are not point charges, but have a cloud of electrons orbiting around a nucleus. When the 10 minimized models were analyzed using the standard terms, there was no correlation between the calculated interaction energies and the energies derived from inhibition constants. However, nine of the 10 models had a correlation of 0.694 between the calculated interaction energy and the free energy derived from inhibition constants. The calculated interaction energy for the double mutant V32I/I84V did not correlate with the free energy differences derived from the measured Ki values. This result was promising, especially since double mutants may be more difficult to model owing to the greater number of degrees of freedom for the substituted side chains. Therefore, the interaction energy was calculated using the screen term, which gave a correlation coefficient of 0.789 for all 10 models, as shown in Figure 2, with a significance of more than 0.995 by Student's t-test (Press et al., 1992). This level of significance means that the correlation can arise by chance in less than 0.5% of cases. Therefore, the inclusion of the screen term leads to highly significant correlation of the calculated interaction energy with the measured free energy difference for models of the wild-type and all nine protease mutants with saquinavir.
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The modeling of HIV protease with indinavir was performed for three protonation states of indinavir; the neutral IND0, the mono-protonated IND+1 and the diprotonated indinavir INDS. Protonation was considered for the N1 and N2 nitrogens in the pterazine ring and the N3 nitrogen in the pyridine ring of indinavir (Figure 1B
). The observed pKas of dimethylpterazine suggest that on average only one nitrogen, either N1 or N2, will be protonated. The question is which of the two possible monoprotonated forms is more stable in the complex with the protease. In the protease complex, the catalytic aspartic acids are closer to the N1 nitrogen than to the N2 nitrogen of indinavir, which suggests that N1 is preferentially protonated. This result was confirmed by density functional quantum calculations (Harrison, 1998) that showed a decided preference for a proton on N1 rather than N2 in the protease–indinavir complex. Therefore, only the N1 monoprotonated state was considered. In addition, protonation of the pyridinal N3 was considered for the diprotonated indinavir. The pKa of pyridine and the second protonation of dimethylpiperazine are nearly the same, so factors such as solvent accessibility and the presence of counterions would determine which nitrogen is protonated in the protease complex. The N3 atom of indinavir lies close to the positively charged guanidium group of Arg8 in the HIV protease crystal structure. Examination of this region of the crystal structure showed that one solvent molecule was positioned within hydrogen bonding distance of both N3 of indinavir and the guanidium nitrogen of Arg8. Since solvent ions are often indistinguishable from water molecules in crystal structures, this arrangement suggested that the solvent molecule between Arg8 and N3 of indinavir was actually a negative ion. The kinetic assays were performed in 1.2 M ammonium sulfate (Kageyama et al., 1993); therefore, a sulfate ion SO42– was modeled in place of the water molecule and interacting with positive charges on both Arg8 and N3. The sulfate atoms were not restrained during minimization. The diprotonated model designated INDS had positive charges on N1 and N3 of indinavir and included a sulfate ion with good ionic interactions with both N3 of indinavir and the side chain nitrogens of Arg8, as shown in Figure 3. The three models were evaluated by comparing the correlation coefficients between the calculated interaction energies and the free energy differences derived from kinetic data for the wild-type and mutant proteases (Table II). The interaction energies calculated with the standard terms, omitting values for R8Q, gave correlation coefficients of 0.20, 0.29 and 0.50 for the uncharged IND0, the monoprotonated IND+1 and diprotonated INDS models, respectively. These values were not significant by the Student's t-test. Even the best INDS models gave a correlation with only modest significance at the 0.90 level, which may arise by chance in 10% of trials. The calculations with the screen term gave better correlation than the standard calculations in all cases. Using all nine protease models, except for R8Q, the correlation coefficient with the screen correction was 0.64 for the uncharged IND0 model, 0.65 for the IND+1 model with N1 protonated and 0.68 for the INDS model with both N1 and N3 protonated and the sulfate ion introduced. Therefore, the INDS model with the screen correction was selected as giving the best representation of the indinavir–protease complex and the highest correlation coefficient for nine complexes (Figure 4) with significance at greater than the 0.975 level. This correlation may arise by chance in 1–2.5% of cases.
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The interaction energy calculated for the R8Q mutant with indinavir did not correlate well with the results for other mutants, whichever protonation state was used for indinavir. The disagreement of the calculations for the R8Q mutant probably arises from several factors, including changes in protease conformation, charge and solvation due to this particular mutation. The R8Q mutant is likely to have a different conformation from the wild-type or other mutants owing to the substitution of the uncharged Gln for the charged Arg8. In addition, Arg8 has solvent-mediated interactions with the indinavir in the crystal structure and these interactions will be altered by the substitution of Gln for Arg. The solvent structure around the side chain of residue 8 will also be altered by the substitution of an uncharged for a basic side chain. However, the calculations for other tested protonation states of indinavir did not give any better agreement with the free energy difference from inhibition constants for the R8Q mutant. This difficulty in modeling the R8Q mutant suggests that improvements are needed in the treatment of charge and solvent in order to apply these calculations to enzyme–inhibitor complexes that involve changes in charged groups.
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Discussion |
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The inhibition of different protease variants by the clinical drugs saquinavir and indinavir has been analyzed by molecular mechanics calculations. Significant correlation with trends in the observed inhibition constants was obtained by application of the new screen correction for the delocalized electron distribution in atoms which are approximately represented as point charges in the standard terms. The screen correction is not equivalent to a simple dielectric correction of 1/
r, as seen by examination of Equation 1, but damps the interaction energy only at short distances. The lack of quantitative agreement between the calculated differences in interaction energy and the observed free energy differences arises from the absence of estimates for the entropy and energy of solvation. The calculated interaction energy is a single point estimate of the difference in the internal energy for a specific molecular conformation. This point estimate is not the same as the free energy difference, which is a thermodynamic average over many conformations. Analysis by statistical mechanics showed that the effect of using a point estimate rather than an average over a distribution is to overestimate the free energy difference (Weber and Harrison, 1996, 1997). This overestimation is observed for the calculations with the screen correction.
The calculations for the R8Q mutant did not show agreement with the relative inhibition constant for any of the tested models of indinavir. The lack of agreement may arise from a different or larger conformational change on binding indinavir to R8Q, a different charged state for the R8Q–indinavir complex or larger changes in the ignored entropic and solvent contributions. The most likely possibility is the existence of a different charged state and solvent structure in the R8Q–indinavir complex compared with the complexes with the other mutants. However, the calculations gave significant agreement for the R8Q–saquinavir complex in which the inhibitor was uncharged. Moreover, the calculations apparently were able to accommodate the effect of the conformational change that was observed in the crystal structure of the V82A mutant (Baldwin et al., 1995) and the effects of double mutants. The agreement of the trends in predicted compared with calculated energies suggested that drug resistance is due to small changes in the internal energy of the protease–inhibitor complex including both van der Waals and electrostatic changes. Similar conclusions were reached by other groups from analysis of crystal structures (Pazhanisamy et al., 1996; Ala et al., 1997). One caveat is that the tested mutants all alter residues in the inhibitor binding site, whereas some common drug-resistant mutations, such as L90M and N88D, alter residues that are not in direct contact with inhibitor (Schinazi et al., 1997). Their mode of action is not understood.
Prolonged exposure to saquinavir results in the resistant mutants L90M and G48V (Boucher, 1996), although these particular mutants were not included in the available kinetic measurements. This pattern of resistance differs from those arising with other protease inhibitors. Exposure to indinavir results in the mutation of V82, followed by changes at M46, V84 and other positions (Condra et al., 1995; Schinazi et al., 1997). The calculations predict that saquinavir will be most effective on mutants V32I, V82F and M46I and least effective on the three mutants containing I84V. Similarly, indinavir is predicted to be most effective on V82I and M46I mutants and least effective on V82A and M46I/I84V. However, the relative effectiveness of the two drugs cannot be predicted for a particular mutant, since the calculations do not give absolute values for the binding free energies.
The physical and chemical properties of the mutants of HIV-1 protease have been reproduced in the molecular mechanics calculations for 19 out of 20 complexes. The inclusion of the new screen correction has allowed the extension of molecular mechanics calculations from predicting the effects of changes in the ligand (Xu et al., 1995; Weber and Harrison, 1996, 1997) to predicting the effects of mutations in the protein. The current calculations only include the ordered water molecules that are observed in the crystal structures of the wild-type protease. In the future, the molecular mechanics calculations will be improved by reparameterization, particularly of charged atom types, and better treatment of solvent. The calculations were best for changes involving neutral groups. However, the majority of drug-resistant mutations involve conservative substitutions of hydrophobic residues and alterations in charge are relatively rare (13% of all substitutions) (Schinazi et al.,1997). Therefore, the calculations can be applied to select the best protease inhibitor to use for particular drug-resistant variants found in AIDS patients. The same technique is also applicable to design modifications of the inhibitors to improve their effectiveness for resistant variants of HIV-1 protease.
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Acknowledgments |
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We thank Charles Reed for help with Figure 3
. This work was supported in part by United States Public Health Service Grant AI41380. |
Notes |
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1 To whom correspondence should be addressed
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Received July 10, 1998; revised October 10, 1998; accepted February 25, 1999.
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