Equilibrium Model of Drug-Modulated GagPol-Embedded HIV-1 Reverse Transcriptase Dimerization to Enhance Premature Protease Activation

Drug-induced enhancement of HIV-1-mediated cytotoxicity has been pursued as a strategy for rapid elimination of reactivated cells. ¹ Viral protease (PR) is a promising protagonist for inducing cytotoxicity. This is because its overexpression or premature activation within virus producing cells results in cell death, ² likely due to induced apoptosis upon proteolysis of host cell factors. ³ Interestingly, some potent non-nucleoside reverse transcriptase inhibitors (NNRTIs) have shown the ability to increase intracellular processing of Gag and GagPol polyprotein precursors through premature activation of PR. ⁴

NNRTIs are allosteric inhibitors designed to block nucleic acid synthesis in mature reverse transcriptase (RT) that kinetically trap the mature enzyme domains in a dysfunctional open state. ⁵ Mature RT is a heterodimer consisting of subunits p66 and p51. The p66 subunit in RT is composed of p51 and p15 domains, but the two p51 domains in the mature enzyme have distinct quaternary folds. This is extended in the p66 subunit (termed p51e), compact in the p51 subunit (termed p51c). The conformational equilibrium strongly favors p51c over p51e, and p51 homodimers are p51e-p51c asymmetric structural heterodimers, ⁶ despite being sequential homodimers. Furthermore, the NNRTI binding site is structurally close to the heterodimer interface, implicating NNRTIs in either enhancing or disrupting RT stability. ⁷ This supports the observation that NNRTIs also enhance GagPol dimerization ⁸ by stabilizing embedded RT dimers. It also consequently implies a mechanism that NNRTIs that favor mature-like p51e-p51c dimerization in GagPol precursors, in turn, favor juxtaposed PR dimerization and thus act as premature PR autoactivation enhancers (PAEs).

To provide a simple rationalization of this mechanism and to understand its thermodynamic determinants, we analyze an equilibrium model of GagPol-embedded RT heterodimerization in the presence of NNRTIs. The model consists of a protein domain R that exists in two interconvertible conformations R ₁ and R ₂ (analogous to the p51c and p51e conformations in RT, respectively) with conformational equilibrium K_C . Only R ₁ and R ₂ can bind each other (R ₁·R ₂) with dimerization equilibrium constant K_{RN −} in the absence of NNRTI, termed N. Drug N binds R ₂ and R ₁·R ₂ with dissociation constants, K_{D 2} and K_{D 12}, respectively, but not R ₁. Thus R ₁ also binds R ₂·N with dimer equilibrium constant K_{RN +} (Fig. 1A).

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FIG. 1.

Equilibrium model of drug-modulated RT dimerization. (A) Reaction scheme for structurally heterogeneous dimerization of domain R between two interchangeable conformations R ₁ and R ₂ with conformational equilibrium constant K_C and with dimer equilibrium constant K_RN− in the presence of a modulator N that binds R ₂ and R ₁·R ₂ but not R ₁ with relative dissociation constants K_{D 12} and K_{D 2}, respectively. (B) Dependence of the drug-free dimer mole fraction (ρ₀) to changes in K_C and K_{RN −}. The black dot denotes ρ₀ ∼0.0007, based on experimentally known values K_C  = 0.03 and K_{RN −} ∼2.5 × 10⁵ M⁻¹ for RT.⁶ (C) Dependence of ρ to changes in drug concentration [N] and K_{D 2} for (i) a weak drug–dimer binder (K_{D 12} = 10⁵ M) and (ii) efavirenz, EFZ (K_{D 12} = 2.93 × 10⁵ M). ¹⁰ Horizontal dashed lines represent corresponding K_{D 12} values, vertical dashed lines correspond to the 0.1 μM < [N] < 10 μM concentration window. Significant dimer enhancement is only exhibited when K_{D 2} > K_{D 12}. Increasing drug–dimer binding strength shifts the peak enhancement to lower concentrations (black arrow). (iii) EFZ concentration dependence of enhancement relative to drug-free dimerization, ρ/ρ₀, for various values of drug–monomer binding, K_{D 2}. Increase of K_{D 2} increases ρ/ρ₀ but also shifts the peak toward higher drug concentrations. Thus, K_{D 2} and K_{D 12} could be optimized to attain the required enhancement within the desired concentration window. RT, reverse transcriptase. Color images available online at www.liebertpub.com/aid

The concentration of each protein species can be expressed in terms of that of R ₁, [R ₁], and the free drug concentration, [N_f ] from the following equilibrium relations: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} [ {R_2} ] = {K_C}{R_1} , \tag{1} \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} [ { R_2 } \cdot N ] = \frac { 1 } { { { K_ { D2 } } } } [ { R_2 } ] [ { N_f } ] , \tag { 2 } \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} [ {R_1} \cdot {R_2} ] = {K_{RN- }} [ {R_1} ] [ {R_2} ] , \tag{3} \end{align*} \end{document} \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} [ { R_1 } \cdot { R_2 } \cdot N ] = \frac { 1 } { { { K_ { D12 } } } } [ { R_1 } \cdot { R_2 } ] [ { N_f } ] \tag { 4 } \end{align*} \end{document}

where [N_f ] is related to the total drug concentration, [N_t ], by: \documentclass{aastex}\usepackage{amsbsy}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{bm}\usepackage{mathrsfs}\usepackage{pifont}\usepackage{stmaryrd}\usepackage{textcomp}\usepackage{portland, xspace}\usepackage{amsmath, amsxtra}\usepackage{upgreek}\pagestyle{empty}\DeclareMathSizes{10}{9}{7}{6}\begin{document} \begin{align*} [ { N_t } ] = [ { N_f } ] \left( 1 + { \frac { { K_C } } { { K_ { D2 } } } } [ { R_1 } ] + { \frac { { K_ { RN - } } { K_C } } { { K_ { D12 } } } } { [ { R_1 } ] ^2 } \right). \tag { 5 } \end{align*} \end{document}

where [R ₁] exhibits a closed form polynomial solution in terms of the total initial concentration of protein monomers, [R_t ]:

The total dimer concentration [D_t ] is then given by [D_t ] = [R ₁·R ₂] + [R ₁·R ₂·N]. To compare the degree of dimerization for any set of the mentioned parameters, we compute the mole fraction, ρ, of dimeric species, where ρ = [D_t ]/[R_t ] with a maximum theoretical value ρ_max = 0.5.

Sensitivity analysis across a range of dimer equilibrium K_{RN −} and conformational equilibrium K_C constants shows symmetric variation of [D_t ] with K_C in the absence of N (Fig. 1B). Increasing K_{RN −} increases the dimer population, whereas a shift of conformational equilibrium away from unity results in symmetric decrease in [D_t ]. Thus, peak dimer concentration favors equal availability of R ₁ and R ₂ as well as a strong dimer equilibrium between the two. Based on experimentally known parameters: intracellular GagPol concentration ([R_t ] ∼10⁻⁷ M⁻¹), ⁹ the conformational equilibrium between p51e and p51c (K_C ∼0.03),⁶ and the RT dimer equilibrium constant (K_{RN −} ∼2.5 × 10⁵ M⁻¹),⁶ our model yields a small drug-free dimer mole fraction, ρ₀ ∼ 0.0007. Thus, theoretically, the potential exists to enhance intracellular dimerization of GagPol-embedded RT by ∼700-fold.

Previous studies assigned K_{D 2} = K_{D 12} when analyzing the concentration of various species with increasing N ⁶ in a similar model. Here, we relax this constraint to explore the effect of differential drug binding strengths to the monomer versus the dimer. By performing a sensitivity analysis across a parameter space of several orders of magnitude, we find that the effect on the dimer mole fraction ρ upon addition of N crucially depends on the values of drug–monomer and drug–dimer dissociation constants, K_{D 2} and K_{D 12}, respectively. Stronger binding of N to R ₂ than to R ₁·R ₂ (K_{D 2} < K_{D 12}) leads to monotonous decay of ρ upon increasing [N] (Fig. 1C). Significantly enhanced dimerization in contrast is only possible when K_{D 2} > K_{D 12}. In this regime, ρ first peaks across a given concentration range before decaying. However, for a weak drug–dimer dissociation constant (K_{D 12} = 10 μM), this occurs well above [N] = 100 μM (Fig. 1C—i). For decreased values of K_{D 12}, the qualitative profile of the ρ-[N] curve still follows the corresponding ratio of K_{D 2}/K_{D 12}. However, the region within which ρ peaks, shifts toward lower drug concentrations. For K_{D 12} = 2.93 nM, corresponding to the binding affinity of efavirenz (EFZ) to the mature wild type p66-p51 RT dimer, ¹⁰ this peak can be brought within a modest concentration range (100 nM < [N] < 10 μM) (Fig. 1C—ii).

Furthermore, we calculate that even for small increases in K_{D 2} above K_{D 12}, significant drug-induced dimer enhancement is possible relative to the drug-free dimer concentration (ρ/ρ₀). Our model suggests that even for K_{D 2} = 10 nM—within one order of magnitude from the above K_{D 12}—a peak dimer concentration enhancement of ρ/ρ₀ ∼27-fold (occurring at [N] = 390 nM) is possible. For K_{D 2} = 100 nM, this rises to ρ/ρ₀ ∼169 at [N] = 3.16 μM—whereas increasing K_{D 2} excessively increases the peak but also shifts it to higher concentrations (Fig. 1C—iii). Interestingly, EFZ binding affinities are different for varying RT species. One experimental study yielded K_{D 12} = 250, 92, and 7 nM for EFZ binding to p66-p66, p66-p51, and p51-p51 RT, respectively, and K_{D 2} = 2.5 μM for both p66 and p51 EFZ–monomer binding. ¹¹ According to our model, this still yields significant enhancement with ρ/ρ₀ ∼30, 71, and 329, respectively, at [N] = 10 μM.

The model then shows that increasing K_{D 2} relative to K_{D 12} always increases the maximum attainable ρ/ρ₀ within a given drug concentration limit. However, this is asymptotic for K_{D 2} >> K_{D 12}, where the asymptote increases with drug–dimer binding strength. For example, with K_{D 12} = 100 nM and K_{D 2} = 1 μM, we attain a maximum ρ/ρ₀ ∼52 within [N] < 10 μM, where in the regime K_{D 2} >> K_{D 12} we reach an asymptote at ρ/ρ₀ ∼79.

Our analysis rationalizes the observations that EFZ enhances GagPol dimerization by binding monomers of GagPol-embedded p51e less strongly than p51e-p51c within Gag-Pol precursor dimers. More generally, it suggests that NNRTIs could achieve similar or even greater enhancement by having both a strong drug–dimer binding affinity (K_{D 12} < 100 nM) and a relatively weaker drug–monomer binding affinity (K_{D 2}/K_{D 12} > 10). Furthermore, the stronger the drug–dimer binding affinity, the more pronounced the maximum effect of an ever weaker drug–monomer binding affinity.

Development of novel potent NNRTIs is a challenging but feasible pharmacological research effort that benefits from computational simulation-guided synthesis and quantitative evaluation of inhibition for a range of chemical variants. ¹² This includes using structure-based approaches to suggest novel chemical moieties on a given drug scaffold that may increase contributions to binding. Our approach yields a strategy for rationally redesigning NNRTIs as PAEs that is consistent with the mentioned discovery process. First, ideal monomer–drug and dimer–drug binding affinities that enable substantial dimer enhancement within a desired concentration range could be optimized using our model. Chemical moieties on given drug scaffolds that potentially enhance drug–dimer binding, but limit drug–monomer binding, could then be suggested and evaluated by combining the mentioned pipeline ¹² and established cytotoxicity assays. ¹

Similarly, the effects of RT resistance mutations that arise in response to NNRTI therapy can be assessed in our model implicitly as variations in the values of K_{D 2}, K_{D 12}, or both compared with wild type. Although some such mutations (e.g., K103N and Y181C) likely reduce drug binding affinity for the RT dimer, through direct loss of structural interactions with inhibitors, their relative effects on drug–monomer disassociation may not correlate. Therefore, further studies may elucidate drug concentration windows that could take advantage of such differences to preserve functionality of NNRTIs as PAEs for patients in whom NNRTI resistance mutations arise.