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Keywords:

  • HIV-1 protease;
  • inhibition;
  • molecular dynamics;
  • ligand binding pathways;
  • quantitative structure and property relationship (QSPR);
  • virtual screening

Abstract

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results and Discussion
  5. Conclusions
  6. Acknowledgments
  7. References
  8. Supporting Information

Human immunodeficiency virus type 1 protease (HIV-1 PR) is one of the primary inhibition targets for chemotherapy of AIDS because of its critical role in the replication cycle of the HIV. In this work, a combinatory coarse-grained and atomistic simulation method was developed for dissecting molecular mechanisms and binding process of inhibitors to the active site of HIV-1 PR, in which 35 typical inhibitors were trialed. We found that the molecular size and stiffness of the inhibitors and the binding energy between the inhibitors and PR play important roles in regulating the binding process. Comparatively, the smaller and more flexible inhibitors have larger binding energy and higher binding rates; they even bind into PR without opening the flaps. In contrast, the larger and stiffer inhibitors have lower binding energy and lower binding rate, and their binding is subjected to the opening and gating of the PR flaps. Furthermore, the components of binding free energy were quantified and analyzed by their dependence on the molecular size, structures, and hydrogen bond networks of inhibitors. Our results also deduce significant dynamics descriptors for determining the quantitative structure and property relationship in potent drug ligands for HIV-1 PR inhibition.

HIV-1 protease (HIV-1 PR) continues to be the primary inhibition target of anti-AIDS therapy because of its critical role in processing viral maturation and replication (1–4). However, existing inhibitors have limitations with respect to binding time and effectiveness because they bind to inhibitor-resistant variants (5–7); therefore, new potent inhibitors for HIV-1 PR are always highly sought after. Structurally, HIV-1 PR is a dimeric aspartic protease with each monomer containing 99 residues and the active site being caved by two flexible β-hairpin flaps (see Figure 1). The inhibitors are designed to bind to the active site and block the pathways for the substrate, so that the functionality and activities of the protease are totally inhibited or largely reduced. The design of new HIV-1 PR inhibitors hinges on molecular understanding of the chemical and physical interactions that influence the inhibitor binding process and pathways to PR.

image

Figure 1.  Crystal structures of HIV-1 protease in different conformational states: (A) the semi-open (PDB:1HHP), (B) the opened [obtained from our pervious work (15)], and (C) the closed (with inhibitor Ritonavir (RTV) (PDB:1HXW) occupying the active cavity formed by the two monomers) of the protease. The homodimer is represented as rubber band model possessing a C2 rotational symmetry.

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Much effort has been focused on intrinsic dynamics and flexibility of HIV-1 PR, particularly the opening and closing dynamics of the looping flaps (8–12). Early structural studies showed that the flexible flaps might work as a gate for ligand binding process (13). Atomistic molecular dynamics (MD) simulations revealed the spontaneous opening of the flaps of free protease within 10 nanoseconds (8). However, this fast opening event was questionable because of its insufficient pre-equilibrium (14). Recently, opening events of flaps in MD simulations were found sensitive to implicit aqueous solvent. A complete trajectory of both opening and reclosing events of the flaps was observed using implicit aqueous solvent without any restraints of the system (9). Nonetheless, the use of artificially low solvent viscosity still precludes the direct comparison of MD simulations with the NMR experiments because of the time scale difference. We have performed a series of extensive long-time all-atom MD simulations with explicit-solvent model and found that the rapid, local sub-nanosecond fluctuations of the flap tips trigger its global opening transitions at the 100-ns time scale (15). To overcome the time scale that the all-atomistic MD simulations were limited, McCammon and co-workers (16,17) have firstly proposed a coarse-grained (CG) method for simulating the global opening and closing dynamics of HIV-1 PR and its inhibitors’ binding pathways (18–21).

Major challenges persist in molecular design and simulation of HIV-1 PR inhibitors, for example, in determining the binding pathways and gated association binding rates to PR, as well as in elucidating effective mechanics and dynamics descriptors for virtually screening potent inhibitors. We have performed steered MD simulations and umbrella sampling analysis to the dissociation processes of different types of inhibitors, which indicates that the hydrogen bond network plays important roles in a wide range of dissociation rate constants koff (22). Also, we have applied a CG model to study the binding process of typical inhibitors (23–25), where different binding processes were observed and qualitatively related to the molecular size and geometry of inhibitors. However, the underlying mechanisms of how the size and dynamics of inhibitors affect the driving forces and the binding pathways are still largely unknown. Additionally, for the purpose of structure-based or dynamics-based drug design, we need to quantify the mechanic and dynamic interactions between HIV-1 PR and its inhibitors and thus to validate descriptors for screening PR inhibitors that are highly desirable for rational drug design and development (26,27).

To study the interaction forces between HIV-1 PR and its inhibitors, the fundamental need is to examine the binding energy components and their relationships with the structure and/or chemistry of inhibitors (28). Quantitative analysis from molecular design and simulation of ligand–protein interaction is becoming essential practice in current drug discovery (29). For example, theoretical binding free energy can be used to screen the most promising inhibitors from tens of thousands of ligand candidates (30,31). In addition, individual contributions of residues in binding free energy were widely used for evaluating the structure–resistance correlation in structure-based drug design and became an effective computational protocol for drug resistance prediction (32,33). For the inhibitors binding to HIV-1 PR, the relationship between the binding free energy and the structures of inhibitors should be critically important for computational drug development (27). Nevertheless, previous studies that mainly focused on total binding free energy (23–25,30–33), the contribution of individual components of the binding free energy as well as their dependence on the structure of inhibitors have not been properly investigated. The shortage of this investigation would undermine the molecular understanding of the driving forces and dynamics in the inhibitors’ binding.

In this work, we applied both CG and atomistic MD simulations to a comprehensive database of HIV-1 PR and its 35 potent inhibitors. The inhibitor data set includes not only the FDA-approved drug ligands, but also all other types of potent ligands, such as cyclic urea inhibitors, cyclic sulfamide inhibitors, and substrate analogs. The selected large subset of crystal structures of inhibitor-bound HIV-1 PR complex and the experimental results of their activities (34) allow a complete investigation into the PR–inhibitor interactions responsible for the binding pathways and inhibition functionality. The inhibitors’ binding processes and dynamics were analyzed by the binding free energy, the inhibitor structures, and chemistry diversity, where the binding free energies of inhibitors to PR were calculated by accurate molecular mechanics combining with Poisson–Boltzmann surface area (MM/PBSA) methods. Particularly, we aimed to have better dynamics factors that can describe the inhibitors’ binding processes and dissect its binding energy components, so as to determine the relationship between the association rates and the structures and chemistry of inhibitors. For this purpose, we derived a couple of dynamic descriptors to virtual screening of lead ligands for HIV-1 PR inhibition.

Materials and Methods

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results and Discussion
  5. Conclusions
  6. Acknowledgments
  7. References
  8. Supporting Information

HIV-1 PR structures and the PR–inhibitor complexes

For the HIV-1 PR structures and PR–inhibitor complexes, we have carefully examined Protein Data Bank (PDB) and Drug Bank (35–38) for the PR structures comprising chemically diverse ligands and binding activities. In this work, we designed a data set of totally 35 potent ligands/inhibitors with different types of scaffolds and chemistry (see Table 1 and Supporting Information). These ligands include nine Food and Drug Administration (FDA)-approved inhibitors that currently used in clinical treatment, six analogs of BEA268, seven cyclic urea inhibitors, two cyclic sulfamide inhibitors, six substrates with different sequences, and five other leading inhibitors. The selection of these 35 potent ligands was to incorporate the most important inhibitors that reflected the diversity of the large data set. The criterion of the selection is that these ligands should have both crystal structure and experimental results of the association rate. Details of structures and chemistry of these inhibitors are listed in Table S2 and Figures S1–S6 in Supplementary Information. The inhibitor-bound complex structures were retrieved from Protein Data Bank with respective PDB codes, see Table 1. Both catalytic Asp side chains of the protease were modeled in the non-protonated state according to the solution at pH 7.

Table 1.   HIV-1 PR and its potent 35 ligands investigated in this study
InhibitorsPDB id
  1. aThe structure of BEA268 can be found in reference (34). Details of the chemical structure of the inhibitors used in this study can be found in supplementary Table S2, Figures S1 and S6.

  2. bThe structure of AHA008-bound complex is constructed with AHA001- and DMP323-bound complexes; details can be found in supplementary Figure S7.

  3. cThe modified p2-NC-substrate is also a peptide substrate with cleavage site p2-NC, whose structure is obtained by modifying PDB code 1KJ7. The sequence of the modified p2-NC-substrate can be found in supplementary Table S2.

FDA approved
Saquinavir1HXB
Ritonavir1HXW
Indinavir1HSG
Nelfinavir1OHR
Amprenavir1T7J
Lopinavir1MUI
Atazanavir2AQU
Darunavir3D1Z
Tipranavir2O4P
P1/P1′ analogs of BEA268a
BEA4091EC1
BEA4281EC2
P2/P2′ and central hydroxy analogs of BEA268a
BEA3221EBW
BEA3691EBY
BEA4351D4H
MSA3671EC3
Cyclic urea compounds
AHA0011AJX
AHA0081AJXb
XK2631HVR
DMP3231MES
DMP4501DMP
SD1461QBT
XV6381QBR
Cyclic sulfamide compounds
AHA0061AJV
AHA0471G2K
Substrates
CA-p2 substrate1F7A
RT-TH substrate1KJG
p1-p6-substrate1KJF
p2-NC-substrate1KJ7
Modified p2-NC-substratec1KJ7c
MA-CA-substrate1KJ4
Others
HOE/BAY 7931VIJ
MVT-1014HVP
JG-3657HVP
KNI2721HPX
QF341IZH

Coarse-grained dynamics simulations of HIV-1 PR and inhibitors

To derive the binding free energy, dynamics, and pathways of inhibitors in HIV-1 PR over the long-time dynamics simulation, we adopted and developed a CG dynamics simulation based on the CG model proposed by McCammon and co-workers (16–21). We have tested the CG method by investigating the binding processes of several typical inhibitors to HIV-1 PR (23–25).

In the CG model of HIV-1 PR, each amino acid was represented by one CG bead. The bead was placed at the Cα position of the residue connected by virtual bonds, angles, and dihedrals. The total potential function of the CG force field of HIV-1 PR is a sum of the following interactions (16,17):

  • image(1)

where Ubond, Uangle, and Udihedral are bond, angle, and dihedral interaction functions, respectively; inline image is the electrostatic interaction function; inline image and inline image are the local and non-local non-bonded interaction functions, respectively.

For the inhibitors, we represented the grouped atoms of the molecule by one CG bead, as reported in our previous works (23–25). The CG beads were connected by bond, angle, and dihedral angle potentials, which took harmonic formats (the parameters of the potentials are shown in Table S1 of Supporting Information).

The interactions between HIV-1 PR and inhibitors were treated as a modified Lennard-Jones potential (19), which are defined as

  • image(2)

where the parameter ε defines the interaction energy. The value of ε was determined by fitting the inhibitor–protease binding free energy with the all-atom simulations. rij is the distance from bead i to bead j, while Ri and Rj are the effective radii of bead i in protease and bead j in inhibitor, respectively. The values of the effective radii of beads of the amino acid residues were taken from the widely accepted parameters by Reva et al. (39). For the inhibitors, the effective radii of bead were defined as

  • image(3)

where inline image is the radius of gyration of CG bead i and inline image is the average vdW radii of CH/CH2/CH3 groups that are located at the most outside of the CG beads. inline image is equal to 1.925 Å (40). More details of the CG force field for PR–inhibitor complex can also be referred from our previous studies (23–25).

The binding free energy of inhibitor to PR

We calculated the binding free energy of inhibitors to PR using all-atom molecular mechanics and Poisson–Boltzmann solvation area (MM/PBSA) method (41–43), a widely accepted protocol in determining energetics of ligands binding to protein. In MM/PBSA method, the binding energy, ΔGb, can be calculated by the following formula:

  • image(4)

where ΔGMM is the interaction energy between PR and the inhibitor and ΔGsol is the solvation energy. The term ‘−TΔS’ reflects the conformational entropy changes upon binding. Because the entropies are very close in values for different inhibitors and substrates (31), we could neglect this part of contribution in this study. ΔGMM can be further decomposed into van der Waals (vdW) and electrostatic parts, which can be obtained directly from the all-atom simulations:

  • image(5)

The solvation energy ΔGsol, which consists of two parts – the polar contribution and the non-polar contribution – is defined as

  • image(6)

The polar energy inline image, reflecting the electrostatic solvation energy, was calculated by solving the Poisson–Boltzmann equation using the APBS method (44). Here, the grid size was set to 0.5 Å, the interior dielectric constant was set to 1, and the dielectric constant of water was set to 80. The radii of atoms were taken from the AMBER parameters set by the pdb2pqr package (45). The non-polar contribution corresponding to the burial of the solvent-accessible surface area (SASA) upon binding was calculated by

  • image(7)

where SASA that was calculated by the msms package (46) with a 1.4 Å radius probe sphere; γ and η are constants set to 0.00542 kcal/(mol Å2) and 0.92 kcal/mol (30,47), respectively.

Atomistic molecular dynamics simulations

All-atom MD simulations were performed with the gromacs programs (48,49) using the force field of ffamber99 (50). The all-atom force-field parameters of inhibitors were determined by the ANTECHAMBER and GAFF module (51,52) with AM1-BCC (53) charges (54). The HIV-1 PR and bounded inhibitor complexes were solvated in an 90 × 80 × 80 Å3 TIP3P (55) water box. Appropriate Na and Cl ions were added to neutralize the system. Particle mesh Ewald (56) was used to calculate the long-range electrostatic interactions. The systems were firstly minimized and gradually heated to 300 K and equilibrated for at least 200 pseconds. Positional restraints were firstly used and the restraint force constants were latter ramped down from 2.39 kcal/(mol Å2) to 0 kcal/(mol Å2) in a staged equilibration. All production simulations were performed at 300K at least for 1 ns with a Berendsen controlled (57) pressure of 1 bar. The SHAKE algorithm (58) was applied to constrain the bonds with H-atoms. The time step of the simulations was 2.0 fseconds, and the cut-off of the non-bonded interactions was set to 10 Å. The 1-nanosecond simulation trajectories were saved as 500 frames, and the last 250 snapshots were used for dynamics, energetics, and MM/PBSA calculations. All molecular visualization and trajectory analysis were processed using the vmd program (59).

Calculation of radius of gyration (RG) and hydrogen bonds

To determine promising molecular mechanics and dynamics descriptors for the quantitative structure and property relationship (QSPR), our focuses were narrowed down to two key properties: the radius of gyration and hydrogen bond networks.

The radius of gyration of molecules was calculated by

  • image(8)

where mi is the mass of atom i and ri the position of atom i with respect to the center of mass of the molecule.

For analyzing H-bond, we excluded the H-bonds formed by interwater molecules, interwater and PR, and intra-PR and inhibitors, and thus we obtained the H-bonds formed by PR and inhibitors. For determining the hydrogen bonds (H-bond) formed by donor(s) and acceptor(s), a geometrical criterion was set by both atom distance and bond orientation; namely, the combination of donor D atoms, hydrogen H, and acceptor A atoms with a D-H···A configuration was regarded as a hydrogen bond when the distance between donor D and acceptor A was shorter than 3.5 Å as well as the bond angle H-D···A was smaller than 60.0°.

Results and Discussion

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results and Discussion
  5. Conclusions
  6. Acknowledgments
  7. References
  8. Supporting Information

Binding behavior and pathways of inhibitors

We found from long-time CG MD simulations that HIV-1 PR flaps are opening/closing at 10- to 200-ns time scale, subject to the ligand structures and chemistry. We identified two typical kinds of binding modes/behavior for HIV-1 PR inhibitors, which are shown in the cases of inhibitors XK263 (Figure 2) and saquinavir (SQV, Figure 3), respectively. The binding process was gauged by the position of inhibitor to the protease, namely the distance between the Cα atom of residue ASP25 (bottom of the active site, e.g., of monomer A) and the mass center of the inhibitor, the ASP25A–inhibitor distance. In the case of inhibitor XK263, XK263 firstly diffused to the entrance of the PR cavity (Figure 2D). Then, the molecule rearranged its orientation in order to match the changing cavity geometry (Figure 2E). Under the attractive forces from PR, XK263 could squeeze into the cavity even without full opening of the flap (Figure 2F). Finally, XK263 was fully bound to the active site (Figure 2G) and formed a stable PR–XK263 complex. During the binding process, the interaction energy between the inhibitor and HIV-1 PR dropped about −28 kcal/mol (see Figure 2C). This binding behavior was consistent with all-atom MD simulations (19) that small symmetric inhibitor, such as XK263, can enter the PR cavity without opening of the flaps.

image

Figure 2.  Binding process of XK263 to HIV-1 PR without full opening of the flaps. (A) The changing distances of ILE50A-ILE50B and ASP25A-XK263. (B) The changing distances of ASP25A-ILE50A and ASP25A-XK263. (C) Variation in the free energy during the binding. (D–G) Snapshots of XK263-protease system during the binding process. The initial and current configurations of PR were aligned corresponding to dynamics changes at (D) t = 0.48 nanoseconds; (E) t = 1 nanoseconds; (f) t = 1.7  nanoseconds; (g) t = 3 nanoseconds.

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image

Figure 3.  Binding process of inhibitor SQV to HIV-1 PR needs full opening of the flaps. (A) The changing distances of ILE50A-ILE50B and ASP25A-SQV. (B) The changing distances of ASP25A-ILE50A and ASP25A-SQV. (C) Variation in the free energy during the binding. (D–H) Side-view and top-view snapshots of SQV-protease system during the binding process at (D) t = 0 nanosecond; (E) t = 21.48 nanoseconds; (F) t = 71.96 nanoseconds; (G) t = 125.86 nanoseconds; (H) t = 181.50 nanoseconds. The inhibitor SQV was represented by solid red color.

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In contrast to XK263, the binding process of inhibitor SQV showed a distinctive mode. When SQV diffused to the entrance of the PR cavity, as shown in Figure 3, it could not enter the cavity without the flaps’ opening (Figure 3D). Simply owing to its large size, the inhibitor must wait for the full opening of the flaps (Figure 3E). Besides the inhibitor also needed to find a right orientation to enter the cavity, the flaps may open a few times (indicated by jumping of the tips’ ILE50A–ILE50B distance before SQV entering the cavity in Figure 3A,E) until the inhibitor could access the cavity. Otherwise, it might fail to bind into PR even with flaps’ opening, for example, likely due to its improper orientation. As soon as SQV found the proper direction and the flaps are fully open (Figure 3F), it entered the cavity and bound with PR. Two apparent jumps of total energy during the binding processes (see Figure 3C) correspond to SQV entering the cavity and the formation of PR–SQV complex with the PR flaps closed, respectively. The binding process of SQV confirmed that, for a large-sized ligand (e.g., SQV and the substrates), PR needs the full opening of the flaps and gating of the cavity (60,61).

Association rate constants versus the radius of gyration

XK263 and SQV behaving distinctive binding modes demonstrated that, for HIV-1 PR, the inhibitor binding dynamics and pathways are regulated by its intrinsic structure and chemistry. Key questions are what and how the inhibitors’ physical and chemical factors quantitatively influence the binding process. Given the radius of gyration of XK263 (i.e., 4.98 Å) and SQV (i.e., 5.46 Å), the size and topology/geometry of inhibitors are supposed to be the dominant reason for their different binding behaviors. To prove this hypothesis, we derived the correlations between the association rate constants and the radius of gyration of inhibitors in Figure 4A, where the association rate constants of inhibitors were determined by experimental measurements (34,60,62–65). Figure 4A shows that the association rate constant decreases with increasing radius of gyration. For instance, the cyclic urea inhibitors (e.g., XK263 and DMP323), which have quite small size and symmetric geometry, have three orders of magnitude larger association rate constants than the big-sized SQV and substrates. From the long-time MD simulations (Section A), we learned that the small inhibitor could enter the PR cavity without the opening of the flaps, while the large ones had to wait for the full opening and proper gate direction to bind into cavity (see Figures 2 and 3). Apparently, the smaller the inhibitor, the weaker the gating effect of the flaps and, in contrast, the larger the inhibitor, the stronger the gating effect, which are well consistent with recent CG simulations by Chang and co-workers (61). In addition, for the larger inhibitors, such as SQV, the flaps of the protease need much more time to fully close (e.g., as seen in Figures 2 and 3). This apparently takes much longer time and thus has smaller association rate constant. Interestingly, some other all-atom MD simulations observed similar phenomena (66–68). Remarkably, as a matter of fact, the FDA-approved drugs (e.g., SQV, nelfinavir (NFV), Ritonavir (RTV) and Amprenavir (APV)) fall in a confined region with the radius of gyration of about 4.6–5.6 Å and the association rate constants of about 6.6 × 105–7 × 106 M-1s-1 (Figure 4A, red circle).

image

Figure 4.  (A) Correlation between the association rate constant and the radius of gyration of inhibitors. (B) Correlation between the association rate constant and binding energy of inhibitors. The dash black lines are the trend lines, and the dash red circle highlights the confined region of FDA-approved inhibitors (represented by the solid pink color dots).

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Association rate constants versus the binding energy

The binding free energy is another critical property that enables us to dissect the inhibitor’s binding processes. Figure 4B depicts the correlation between the association rate constants of various potent inhibitors and their binding energies (as determined by the MM/PBSA method). The association rate constant decreases significantly with decreasing absolute value of binding energy. To further understand how the binding energy affects the binding processes, we mimicked the binding energy changes in the CG MD simulations by introducing a dimensionless multiplier factor in the inhibitor–protease interaction potential (eqn 2), that is, ε = ε*ε0, where ε* is the normalized interaction energy, and ε0 was determined according to the PR–inhibitor interaction energy with all-atom MD calculations. We found that, as seen in Figure 5, the variation in binding energy could significantly affect the binding behaviors/modes. For instance in the case of XK263 (Figure 5A), while increasing ε (i.e. ε* > 0.9) apparently reduced the binding time, that dramatically changed the binding behavior of XK263: The inhibitor may need not wait for the flaps’ opening to enter the PR cavity. For the decreased driving forces (i.e. ε* < 0.9), the inhibitor could only enter the cavity with the flaps’ opening. As shown in Figure 5A, the change in binding energy could lead to different binding behaviors/modes, which corresponds to entering the PR cavity with and without the opening of the flaps, respectively.

image

Figure 5.  Dependence of binding time on the dimensionless binding energy ε* calculated by the coarse-grained MD simulations in the cases of (A) XK263 and (B) SQV. The gray region indicates that the inhibitors need to wait for the opening of the flaps to enter the binding cavity. The green region indicates that the inhibitors can enter the cavity without the opening of the flaps. The binding time was defined as the time–course from the start of simulation to the moment of the inhibitor entering the cavity and forming a tight contact with active site and inducing the full closure of flaps.

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For a large-sized inhibitor, such as SQV, increasing the binding energy would dramatically change the binding behavior too (Figure 5B): Before the binding energy was increased above the threshold value, SQV still must wait for the flaps’ opening to enter the PR cavity. However, SQV would enter the cavity without the flaps’ opening if the interaction strength is strong enough. Sadiq et al. (69) showed that mutation-assisted PR can drive SQV out of the cavity by a lateral force without the flaps’ opening. This suggested that as a reverse process of inhibitor being pulled out, it would be possible that the inhibitor could enter the cavity without the flaps’ full opening, for example, by proper mutation to make the driving forces strong enough.

The mechanism behind the effect of binding energy might explain the fundamental difference between XK263 and NFV: They have 5 orders of magnitude difference in their association rate constants of ∼1010 versus ∼105 M-1s-1 (Figure 4B) while having identical molecular size of 4.98 versus 4.95 Å (Figure 4A). According to our all-atom calculations and previous studies (19,23), the binding energy in absolute value of XK263 (i.e., 38.2 kcal/mol) is much larger than that of NFV (i.e., 24.3 kcal/mol). Therefore, XK263 can enter the cavity at higher velocity without the flaps’ opening, but NFV has to wait for the full opening of flaps to enter the cavity at a much lower velocity (23). For another example, the size of inhibitor APV (i.e. 4.57 Å) is smaller than that of XK263 (i.e. 4.98 Å), see Table 2 and Figure 4A. However, the association rate constant of APV (i.e. ∼106 M-1s-1) is four orders of magnitude smaller than that of XK263 because the binding energy of XK263 (i.e., 38.2 kcal/mol) is much larger than that of APV (i.e., 21.6 kcal/mol), see Table 2 and Figure 4B. Similarly, the difference in experimental association rate constant and binding modes for different inhibitors (e.g., Figure 4B) is attributable to the combinatory impacts of radius of gyration and binding energy.

Table 2.   Binding free energies versus dynamics properties and the association rate constant of potent HIV-1 PR inhibitors
InhibitorsΔGMMΔGsolTotal (kcal/mol)Radius of gyration (Å)Number of H-bondsAssociation rate kon (M-1s-1)References of the Association rate
vdW (kcal/mol)Electrostatic (kcal/mol)Non-polar (kcal/mol)Polar (kcal/mol)
  1. aThe values in italic and underlined were from the reference 30.

  2. bThe association rate of modified p2-NC-substrate was from Pietrucci et al.’s (60) explicit-solvent atomistic simulation result.

FDA approved
Saquinavir−59.1 ± 2.5−30.9 ± 2.5−6.7 ± 0.369.2 ± 2.4−27.5 ± 2.75.46 ± 0.103.32 ± 1.368.17 × 105 ± 1.61 × 10534
67.6 ± 0.324.6 ± 1.96.6 ± 0.172.0 ± 2.025.1 ± 0.6a 
Ritonavir−73.5 ± 2.8−34.2 ± 2.5−6.8 ± 0.186.1 ± 3.0−28.4 ± 2.85.90 ± 0.113.67 ± 1.153.92 × 106 ± 1.11 × 10634
80.5 ± 1.038.4 ± 0.56.9 ± 0.1100.8 ± 0.624.9 ± 1.0 
Indinavir−70.8 ± 3.6−35.2 ± 4.0−6.7 ± 0.185.6 ± 3.5−27.1 ± 3.05.33 ± 0.113.12 ± 0.981.53 × 106 ± 2.42 × 10534
70.9 ± 1.831.7 ± 3.86.3 ± 0.186.3 ± 3.522.6 ± 2.2 
Nelfinavir−64.1 ± 3.0−38.5 ± 2.5−6.0 ± 0.384.3 ± 2.5−24.3 ± 2.24.95 ± 0.091.89 ± 0.436.63 × 105 ± 3.04 × 10534
65.3 ± 2.336.8 ± 0.85.7 ± 0.082.8 ± 0.826.8 ± 0.1 
Amprenavir−57.0 ± 2.1−34.1 ± 2.7−5.3 ± 0.174.8 ± 2.5−21.6 ± 2.74.57 ± 0.093.43 ± 1.064.43 × 106 ± 1.25 × 10634
62.6 ± 0.549.6 ± 0.15.1 ± 0.196.5 ± 0.820.8 ± 0.4 
Lopinavir−62.8 ± 3.2−36.1 ± 3.5−6.8 ± 0.280.4 ± 5.8−25.2 ± 3.15.30 ± 0.063.20 ± 0.736.58 × 106 ± 6.18 × 10562
Atazanavir−66.6 ± 2.9−37.0 ± 3.3−6.8 ± 0.179.2 ± 4.8−31.2 ± 3.25.43 ± 0.083.90 ± 0.479.03 × 105 ± 5.82 × 10462
Tipranavir−61.5 ± 3.0−21.4 ± 2.2−5.9 ± 0.162.5 ± 3.4−26.4 ± 3.05.37 ± 0.083.42 ± 0.932.00 × 105 ± 1.00 × 10463
Darunavir−53.9 ± 3.7−39.3 ± 3.8−5.5 ± 0.273.5 ± 4.1−25.2 ± 3.04.79 ± 0.083.88 ± 0.922.20 × 106 ± 8.00 × 10563
P1/P1′ analogs of BEA268
BEA409−82.5 ± 3.9−36.3 ± 5.6−7.4 ± 0.192.7 ± 5.8−33.4 ± 3.86.14 ± 0.113.44 ± 1.203.48 × 105 ± 1.53 × 10534
BEA428−77.9 ± 3.6−41.1 ± 6.0−7.6 ± 0.283.4 ± 5.2−43.2 ± 4.76.26 ± 0.094.53 ± 0.92 
P2/P2′ and central hydroxy analogs of BEA268
BEA322−67.5 ± 3.6−45.9 ± 5.4−6.8 ± 0.189.6 ± 5.3−30.6 ± 3.55.25 ± 0.053.45 ± 0.731.85 × 106 ± 1.39 × 10634
BEA369−69.0 ± 3.9−55.0 ± 5.7−6.7 ± 0.197.9 ± 4.8−32.8 ± 3.55.22 ± 0.063.23 ± 0.806.39 × 10± 3.59 × 10634
BEA435−67.1 ± 3.6−50.4 ± 5.5−6.3 ± 0.397.0 ± 5.5−26.8 ± 4.55.21 ± 0.083.54 ± 1.271.01 × 105 ± 3.08 × 10434
MSA367−79.0 ± 3.6−56.2 ± 4.9−7.5 ± 0.199.7 ± 5.2−42.9 ± 4.15.95 ± 0.145.01 ± 0.88 
Cyclic urea compounds
AHA001−45.5 ± 3.7−39.0 ± 4.5−5.4 ± 0.262.2 ± 5.8−27.7 ± 3.04.51 ± 0.053.37 ± 0.70 
AHA008−64.5 ± 3.9−55.5 ± 5.3−6.1 ± 0.287.7 ± 4.4−38.4 ± 3.74.92 ± 0.106.20 ± 1.337.06 × 109 ± 3.27 × 10934
XK263−72.8 ± 3.4−35.8 ± 3.7−6.0 ± 0.276.3 ± 4.0−38.2 ± 2.54.98 ± 0.043.03 ± 0.682.52 × 1010 ± 9.99 × 10934
DMP323−53.1 ± 3.7−54.8 ± 3.9−6.0 ± 0.176.5 ± 5.1−37.3 ± 3.54.73 ± 0.056.48 ± 1.222.52 × 1010 ± 9.99 × 10934
DMP450−55.1 ± 3.4−43.0 ± 5.7−5.5 ± 0.266.6 ± 5.4−37.0 ± 3.54.46 ± 0.044.25 ± 0.97 
SD146−71.9 ± 4.3−59.2 ± 5.8−7.8 ± 0.297.7 ± 7.3−41.2 ± 4.07.24 ± 0.076.90 ± 1.18 
XV638−68.5 ± 3.7−52.2 ± 4.8−6.8 ± 0.286.7 ± 6.6−40.8 ± 3.96.39 ± 0.066.64 ± 1.13 
Cyclic sulfamide compounds
AHA006−64.4 ± 3.1−47.6 ± 4.1−5.7 ± 0.175.5 ± 3.9−42.2 ± 4.04.70 ± 0.053.86 ± 0.40 
A047−61.4 ± 3.4−52.9 ± 4.4−6.0 ± 0.192.6 ± 4.9−27.6 ± 2.55.06 ± 0.043.95 ± 0.801.88 × 105 ± 1.09 × 10534
Others
HOE/BAY 793−87.4 ± 5.1−58.0 ± 6.1−9.6 ± 0.3100.0 ± 5.9−55.0 ± 5.37.46 ± 0.127.04 ± 0.83 
MVT-101−74.2 ± 4.2−75.3 ± 6.6−7.5 ± 0.2136.0 ± 7.8−21.0 ± 4.96.70 ± 0.128.12 ± 1.511.6 × 105 ± 1.00 × 10465
JG-365−72.2 ± 3.8−72.7 ± 5.7−8.6 ± 0.2127.3 ± 6.3−26.2 ± 4.97.21 ± 0.127.66 ± 1.19  
KNI272−62.6 ± 3.1−33.5 ± 3.0−6.5 ± 0.277.8 ± 2.8−24.8 ± 2.95.33 ± 0.111.86 ± 0.46 
QF34−67.6 ± 2.5−50.1 ± 2.3−7.1 ± 0.297.2 ± 3.0−27.6 ± 3.05.64 ± 0.115.88 ± 1.10 
Substrates
CA-p2 substrate−78.8 ± 4.4−55.4 ± 5.1−8.0 ± 0.2123.4 ± 10.6−18.7 ± 4.08.79 ± 0.166.90 ± 1.122.00 × 10464
RT-TH-substrate−80.0 ± 4.2−113.6 ± 9.3−8.7 ± 0.2194.7 ± 12.3−7.6 ± 5.68.22 ± 0.1112.08 ± 1.50  
p1-p6-substrate−83.1 ± 4.2−109.3 ± 6.1−9.1 ± 0.3173.4 ± 10.8−28.1 ± 5.09.43 ± 0.1511.43 ± 1.21  
p2-NC-substrate−81.4 ± 3.8−60.8 ± 7.9−8.4 ± 0.2130.6 ± 7.3−20.0 ± 5.87.41 ± 0.097.55 ± 1.21  
Modified p2-NC-substrateb−73.3 ± 4.3−78.7 ± 8.2−7.11 ± 0.2135.5 ± 9.8−23.6 ± 4.86.50 ± 0.118.15 ± 1.311.30 × 10660
MA-CA-substrate−87.6 ± 4.5−104.3 ± 7.4−9.0 ± 0.1173.2 ± 7.6−27.7 ± 4.88.59 ± 0.1012.38 ± 1.37  

Analysis of the components of binding free energy

Given that the binding energy has significant impact on the binding behaviors of potent inhibitors, the relationship between the components of binding free energy and the structures of inhibitors needs to be established. According to eqns (4–6), the binding free energy consists of four parts, namely the vdW energy inline image, the electrostatic energy inline image, the non-polar energy inline image, and the polar energy inline image.

The vdW energy inline image is dependent on the intersurface area of PR and inhibitor complex. Meanwhile, the non-polar energy inline image is proportional to the buried SASA upon binding. There should be a dependence of inline image and inline image components on the size of inhibitors (i.e., the radius of gyration of the inhibitor). To prove this, Figure 6A shows that the absolute value of vdW energy increases exponentially with the increase in radius of gyration. Interestingly, we found that vdW for HIV-1 PR inhibitors has an upper limit of about −85 kcal/mol, which corresponds to the radius of gyration of ∼9.5 Å. Similarly, as shown in Figure 6B, the absolute value of the non-polar energy increases versus the radius of gyration and there is also an upper limit of about −9 kcal/mol, which corresponds to the radius of gyration of about 9.5 Å. Adding the inline image and inline image components together (Figure 6C), the results suggested that both the vdW energy and non-polar energy can be enhanced by properly increasing the size of inhibitors.

image

Figure 6.  The relationship between the energy components (the vdW energy and non-polar energy) and the radius of gyration of inhibitors. (A) The vdW energy versus the radius of gyration. (B) The non-polar energy versus the radius of gyration. (C) The summation of the vdW energy and the non-polar energy versus the radius of gyration. The solid lines are the exponential fit trend lines, and the pink-filled dots are referring to the FDA-approved inhibitors.

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However, the existence of upper limits of the vdW energy and non-polar energy indicates something fundamental prevailing. Figure 7 shows snapshots of three different-sized inhibitors tightly bound with PR. It could be concluded that when the inhibitor size is smaller than the topological size of the PR cavity (see Figure 7A,B), the increase in the inhibitor size can effectively increase the vdW contact area between the inhibitor and the protease as well as the SASA. However, when the inhibitor size is bigger than certain value, the vdW and SASA areas will no longer increase (Figure 7C) and contribute no more to the binding energy.

image

Figure 7.  Impact of inhibitor size on the vdW interaction and non-polar interaction, with the snapshots of different size of inhibitors of (A) XK262, (B) HOE/BAY 793, and (C) CA-p2 substrate (see Table 2), binding to the HIV-1 PR cavity. Here, the protease is represented by a solid ribbon model in yellow color, and the inhibitors are represented by transparent vdW surfaces. The red dots indicate the hydrophilic residues of Arg8/108, Asp29/129, and Asp30/130 in PR flaps.

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Different to the inline image and inline image components, the electrostatic energy inline image is strongly dependent on the number of hydrogen bonds (H-bonds) formed at the PR–inhibitor interface. Figure 8A shows that the electrostatic energy linearly depends on the number of H-bonds, with a slope of −6.7 kcal/mol per H-bond. This value falls right in the general H-bond energy range of 5–8 kcal/mol (70). The polar energy inline image (reflecting the electrostatic solvation energy, see eqn 6) also linearly depends on the number of H-bonds, but with a different strength and trend (Figure 8B). From the trend line, we worked out ∼9.8 kcal/mol per H-bond. This energy is the cost of formation of one H-bond between inhibitor and the protease by breaking the H-bond between the water molecules. On top of that, extra works should be carried out to expel the water molecules out of the PR cavity. Taking summation of the electrostatic energy and the polar energy (Figure 8C), these energy components depend on the number of H-bonds. In addition, Figure 8D proves that large inhibitors will have more contacts with the protease, which results in more H-bonds in the PR–inhibitor interface. This observation was consistent with previous studies by Gilson’s group (27).

image

Figure 8.  The relationship between the energy components (the electrostatic energy and the polar energy) and the number of H-bonds and the radius of gyration of inhibitors, respectively. (A) The electrostatic energy versus the number of H-bonds. (B) The polar energy versus the number of H-bonds. (C) The summation of the electrostatic energy and the polar energy versus the number of H-bonds. (D) The number of H-bonds versus the radius of gyration. The solid lines are the fitting trend lines, and the pink-filled dots refer to the FDA-approved inhibitors.

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Breakdown of the energy components indicated that the combined value of the vdW and non-polar energy is negative; therefore, they bring in positive contribution to the binding process. On the other hand, the combination of the electrostatic and polar energy is positive, and they have negative contribution to the binding process. These results prove that the inhibitors binding to HIV-1 PR is a kind of non-covalent association (71), where the association of the PR–inhibitor complex is mainly driven by the favorable non-polar interactions rather than by the polar ones.

Effect of the inhibitors’ stiffness

To further understand the mechanical mechanisms underlying different binding process, we tested the impact of inhibitors’ stiffness from CG MD simulations. We mimicked the stiffness variation in the angle potential of inhibitors kangle through a dimensionless parameter inline image. The variable angle potential now is defined as inline image, where inline image was the original strength of the angle potential and was set to 47.8 kcal/(mol rad2) by fitting to all-atom simulations (see Table S1 of Supporting Information). inline image is a variable between 0 to 1.0, as such a smaller inline image gives a softer angle potential. Similarly, we tuned the bond stiffness by two different bond potentials, that is, kbond = 700 kcal/(mol Å2) for a hard potential and kbond = 70 kcal/(mol Å2) for a soft potential.

Not surprisingly, the changing stiffness of angle potential and bond potential leads to different magnitudes of dynamics flexibility of inhibitors. Figure 9A denotes that the inhibitor flexibility (i.e., in terms of RMS fluctuation) increases with decreasing stiffness of angle potential and bond potential. When we changed bond stiffness from soft to hard potentials, as shown in Figure 9B, the inhibitors’ binding time has dramatically increased (e.g., from 25 to 200 nanoseconds when inline image = 0.6). Dropping the bond stiffness kbond from 700 to 70 kcal/(mol Å2) can make the inhibitor entering PR more easily (Figure 9B). We also observed that when the angle potential stiffness decreased below a threshold value (inline image < 0.3), the inhibitor could enter the PR cavity without the flaps’ opening, likely due to that the inhibitor adaptively changes its geometry (as shown in the inset of Figure 9A) to fit through the PR entrance. In addition, once the inhibitor entered the PR cavity, the inhibitor has constant configuration changes to achieve the most contact with cavity and fit in the active site. This finding verified the same observation by all-atom simulation of the binding process of XK263 (19).

image

Figure 9.  The effect of molecular stiffness on the inhibitors’ flexibility and binding time. (A) The RMSD of inhibitor SQV with different angle and bond stiffness, inline image and kbond, in the coarse-grained MD simulations. The inset was an illustration of the deformation of the inhibitor. (B) The binding time of SQV with different values of inline image and kbond. The red square data points were the results for kbond = 700 kcal/(mol Å2), and the black circle data points were the results for kbond = 70 kcal/(mol Å2). The black and red lines are fitting trend lines.

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The physical meaning for a reduced stiffness is to lower the energy barriers in inhibitors’ conformational changes and at the same time to weaken the steric restriction of protease (especially the entrance contacts) on the inhibitors. This implicates that for an effective binding, namely for a very potent drug inhibitor to HIV-1 PR, the inhibitor needs to have a certain degree of flexibility, not too hard yet not too soft (see Figure 9).

Molecular mechanics and dynamics descriptors for screening potent HIV-1 PR inhibitors

The current state-of-the-art drug discovery heavily relies on virtual screening that can combine traditional structure-based docking with MD simulations, because dynamics simulations can treat naturally occurring explicit solvents and solve the adaptive flexibility and dynamic fluctuations of inhibitor–protein complex, prior to and after the inhibitor docking and binding. Our MD simulations prove that the inhibitors’ structures, dynamic size, and mechanical strength play crucial roles in regulating binding behavior and pathways in HIV-1 PR. Through the dynamic characteristics of 35 potent inhibitors binding to HIV-1 PR, we found that firstly, inhibition binding dynamics are regulated by the molecular size and topology. The small and symmetric inhibitor, such as XK263, enters the cavity via a fast kinetics with a binding time typically at ∼10 nanoseconds [e.g., Figure 2 and reference (23)]. In contrast, the binding time of large inhibitor (such as SQV) is at much larger scale, that is, typically ∼200 nanoseconds (e.g., Figure 3). Experiments showed that the association rate constant of small ligand XK263 is about 109–1010 M-1s-1 (34), which is close to the diffusion-limited rate (1010 M-1s-1), but the association rate constant of SQV is ∼106 M-1s-1 (34). Figure 4A shows that there was a negative correlation between the association rate constant and the inhibitor size – the smaller the size, the higher the association rate constant, or vice versa. The fundamental difference between XK263-like and SQV-like binding lies in that their size and geometry lead to different binding modes, regardless of the opening/gating of the PR flaps. Significantly, the FDA-approved inhibitors have the intermediate molecular size, with radius of gyration falling in 4.6–5.6 Å and the association rate constants of about 6.6 × 105–7 × 106 M-1s-1 (Figure 4A, highlighted by solid pink color dots). This suggests that the radius of gyration can serve as a dynamic descriptor for dynamics screening of potential inhibitors to HIV-1 protease.

Secondly, inhibition binding dynamics are competitively regulated by binding free energy against the inhibitors’ molecular size and flexibility. We learned from Figure 4 that both the molecular size and binding energies determine the association rate constant of inhibitors NFV and APV – a smaller size APV has stronger association rate constant than NFV offset by the smaller binding energy. Also, inhibitors XK263 and NFV have almost same molecular size, but binding energy difference leads to XK263 having larger association rate constants than NFV. Meanwhile, binding energy components showed that van der Waals and non-polar energies mainly drive the inhibitors binding to PR, against the repelling forces from electrostatics and polar energies. Given that the electrostatics and polar energies can be quantified by H-bond numbers (Figure 8C), there is a defined correlation between the radius of gyration and H-bonds (Figure 8D), which is a reflection of hiding rational between the inhibitor dynamic size and its binding free energies. Remarkably enough, as highlighted in Figure 8 by solid pink color dots, the FDA-approved inhibitors fall into a well-defined area of H-bond numbers (i.e., 2–4 H-bonds) against the radius of gyration. This also suggests that the number of H-bonds from MD simulation could serve as a validated descriptor for dynamics-based screening of potential inhibitors to HIV-1 protease.

In terms of computing cost, dynamic radius of gyration and H-bond are much more affordable in calculation from MD trajectories than other properties, such as binding free energy from the MM/PBSA method. This makes them very attractive as the dynamic descriptors, for instance, in coarse-mediated level of dynamics screening. In addition, we showed that the inhibitors’ molecular flexibility has profound impact on the binding behaviors; The quantitative correlation between this property and the experimental binding activities is being investigated, in a hope that molecular flexibility (e.g., mechanical stiffness) could provide another possible dynamic descriptor for screening inhibitors to HIV-1 PR.

Conclusions

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results and Discussion
  5. Conclusions
  6. Acknowledgments
  7. References
  8. Supporting Information

The mechanics and binding dynamics characteristics of potent inhibitors binding to HIV-1 PR were investigated by CG and all-atom MD simulations of a large data set of PR–inhibitor complexes. We found that the molecular structures, dynamic size, and stiffness of the inhibitors play key roles in regulating the binding process. Comparatively, the smaller and more flexible inhibitors have larger association rates, for example, sometimes they even bind into PR without opening the flaps. On the other side, the larger and stiffer inhibitors possess lower binding rates, and their binding is subjected to the opening and gating of the PR flaps. Furthermore, the components of binding free energy were analyzed and quantified by their dependence on the inhibitors’ molecular size, structures, and hydrogen bond networks. We prove that van der Waals and non-polar energies are the major driving forces for inhibitors’ binding to PR. Also we like to propose the radius of gyration and H-bond number as dynamics descriptors for determining the QSPR of potent ligands for HIV-1 PR inhibition. These findings could help to improve our capabilities in dynamics-based molecular design and screening of potent ligands targeting the HIV-1 PR.

Acknowledgments

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results and Discussion
  5. Conclusions
  6. Acknowledgments
  7. References
  8. Supporting Information

BJ thanks support from the National Science Foundation of China (Grant No. 10732050, 10872115, and 11025208). ML acknowledges the support from CSIRO – Advanced Materials TCP and Australian Biotechnology Growth Partnership. DL thanks support from Excellent Young Scholars Research Fund of Beijing Institute of Technology.

References

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results and Discussion
  5. Conclusions
  6. Acknowledgments
  7. References
  8. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. Materials and Methods
  4. Results and Discussion
  5. Conclusions
  6. Acknowledgments
  7. References
  8. Supporting Information

Figure S1. Chemical structures of FDA-approved inhibitors.

Figure S2. Chemical structures of P1/P1’ analogues of BEA268.

Figure S3. Chemical structures of P2/P2’ and central hydroxyl analogues of BEA268.

Figure S4. Chemical structures of cyclic urea inhibitors.

Figure S5. Chemical structures of cyclic sulfamide inhibitors.

Figure S6. Other inhibitors used in this study, namely HOE/BAY 793, MVT-101, JG-365, KNI272 and QF34.

Figure S7. Illustration of modelling the structure of HIV-1 PR-AHA008 complex. (a) The chemical structures of potential inhibitors of AHA001, DMP323 and AHA008. (b) The structure of AHA008 was constructed by substituting the side chain R2 of inhibitor AHA001 by those of inhibitor DMP323. The initial structure of protease was retrieved from the PR structure of PDB code: 1AJX.

Table S1. Parameters of the bonded potentials for inhibitors in the coarse-grained MD models

Table S2. The sequences of substrates as HIV-1 PR inhibitors.

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