HIV-1 polymerase inhibition by nucleoside analogs: cellular- and kinetic parameters of efficacy, susceptibility and resistance selection

Abstract

Nucleoside analogs (NAs) are used to treat numerous viral infections and cancer. They compete with endogenous nucleotides (dNTP/NTP) for incorporation into nascent DNA/RNA and inhibit replication by preventing subsequent primer extension. To date, an integrated mathematical model that could allow the analysis of their mechanism of action, of the various resistance mechanisms, and their effect on viral fitness is still lacking. We present the first mechanistic mathematical model of polymerase inhibition by NAs that takes into account the reversibility of polymerase inhibition. Analytical solutions for the model point out the cellular- and kinetic aspects of inhibition. Our model correctly predicts for HIV-1 that resistance against nucleoside analog reverse transcriptase inhibitors (NRTIs) can be conferred by decreasing their incorporation rate, increasing their excision rate, or decreasing their affinity for the polymerase enzyme. For all analyzed NRTIs and their combinations, model-predicted macroscopic parameters (efficacy, fitness and toxicity) were consistent with observations. NRTI efficacy was found to greatly vary between distinct target cells. Surprisingly, target cells with low dNTP/NTP levels may not confer hyper-susceptibility to inhibition, whereas cells with high dNTP/NTP contents are likely to confer natural resistance. Our model also allows quantification of the selective advantage of mutations by integrating their effects on viral fitness and drug susceptibility. For zidovudine triphosphate (AZT-TP), we predict that this selective advantage, as well as the minimal concentration required to select thymidine-associated mutations (TAMs) are highly cell-dependent. The developed model allows studying various resistance mechanisms, inherent fitness effects, selection forces and epistasis based on microscopic kinetic data. It can readily be embedded in extended models of the complete HIV-1 reverse transcription process, or analogous processes in other viruses and help to guide drug development and improve our understanding of the mechanisms of resistance development during treatment.

Figure 1. DNA-polymerization in the presence of chain terminating nucleoside analogs.

A: The mathematical model defines a Markov jump process: Each state in the model corresponds to the number of incorporated nucleotides: state ‘0’ corresponds to the polymerase enzyme binding to the template, prior to polymerization, states in the model correspond to the condition in which nucleosides have been attached and state corresponds to full-length product, after which the enzyme dissociates from the template/primer. States correspond to the condition, in which a DNA-chain consisting of natural nucleosides has been produced, but where the last nucleoside in the chain is a chain-terminating . At each state , the nascent DNA-chain can either be shortened (pyrophosphorolysis ), -prolonged with a nucleoside (polymerase reaction ) or -terminated by a nucleoside analog (reaction ). If the chain has been terminated (state ), it can get released with rate (excision reaction) to produce a chain of length . B: Sequence context. The reaction rates , , and depend on the nucleoside sequence of the template. In the illustration, the next incoming nucleoside could be either a thymidine or a thymidine-analog (corresponding to position in the template sequence). Therefore, and would refer to thymidine- and thymidine-analog incorporation. The pyrophosphorolysis reaction, on the other hand, would refer to cytosine removal (position in the primer sequence).

Figure 2. DNA-dependent polymerization of a hetero-polymeric sequence by HIV-1 RT in the presence- and absence of a chain terminating adenosine analog (ddATP).

A: Cumulative time for polymerization of a hetero-polymeric sequence in the presence of a chain-terminating nucleoside analog (ddATP). The solid black line (filled dots) indicates the cumulative polymerization time up to sequence position i (the sequence position is indicated at the x-axis) in the absence of inhibitors in the wild type enzyme (calculated using eq. (10)). The dashed blue line (open squares) indicates the time required for polymerization in the presence of ddATP. The dotted red- and green lines (upward and downward pointing triangles) show the time required for polymerization in the ‘K65R’ mutant RT enzyme in the presence- and absence of ddATP. Kinetic parameters are presented in Table 1 and Table S1, S2 (supplementary material) for the wild type and the ‘K65R’ mutant. B: Single nucleoside incorporation time in the absence of ddATP in the wildtype and the ‘K65R’ mutant (solid black and dashed green lines respectively) and in the presence of ddATP in the wild type enzyme (dashed blue line) and in the mutant enzyme (dotted red line), calculated using equation eq. (8).

Figure 3. Factors that modify inhibition of DNA polymerization by nucleoside analogs.

A: Cell-specific factors: Concentration response curve of ddATP for wild type RT during DNA-dependent polymerization (homo-polymeric sequence) in unstimulated T-cells (solid line) and the impact of a 100-fold variation of the the intracellular nucleoside concentrations (dotted line). The illustration was generated by evaluating eq. (19) and typical parameters for DNA-dependent polymerization during HIV-1 reverse transcription and its inhibition by ddATP (all parameters are indicated in Table 1 and Table S1, supplementary material). The corresponding is depicted by a green filled circle. B: Molecular mechanisms of drug resistance and hyper-susceptibility (dashed lines). Impact of (i) selective attrition of inhibitor incorporation and (ii) selective attrition of inhibitor binding to the primer-template on drug susceptibility. Hypersusceptibility is conferred by the opposite change in the indicated parameters. In order to generate the dashed lines, the respective parameters have been increased/decreased by a factor of 100.

Figure 4. RNA- and DNA-dependent polymerization in the presence of intracellular AZT triphosphate in unstimulated T-cells.

The solid blue curves indicate the level of residual polymerization with the wild type enzyme, whereas the dashed lines indicate the residual polymerization with the ‘D67N/K70R/T215Y/K219Q’ mutant. Panels A & B: Residual RNA- and DNA dependent polymerization of a homo-polymeric thymidine sequence (Poly-‘T’). Calculations were obtained by solving eq. (19). Panels C & D: RNA- and DNA polymerization of a hetero-polymeric random sequence of length 500 with 25% respective dNTP content. The illustration was generated using eq. (10). The light grey area indicates the in vivo concentrations range of AZT in purified circulating T-cells from , converted to units by assuming a cell volume of for resting T-cells . All utilized parameters are indicated in Tables 1, S1, S2, S3 (supplementary material).

Figure 5. Molecular mechanisms of HIV-1 resistance development against AZT by ATP-mediated excision.

Potential mechanisms for resistance development against AZT through increasing its excision rate via an ATP-mediated mechanism (see eq. (21)). We calculated residual DNA-dependent polymerization of a Poly-T sequence in unstimulated T-cells using eq. (19) with parameters from Tables 1, S1 and S3 (supplementary material). The solid black line shows residual DNA polymerization in the wild type virus, whereas the dotted red line and the dashed blue line refer to residual polymerization if and were decreased- and increased 100-fold respectively.

Figure 6. Selective advantage of the ‘D67N/K70R/T215Y/K219Q’ mutant against the wild type during RNA- and DNA-dependent polymerization in the presence of AZT-TP.

The solid lines (green = activated cells, blue = unstimulated cells, red = macrophages) indicate the selection parameter , defined in eq. (4), for different levels of intracellular ATZ-TP during RNA- and DNA dependent polymerization (Panels A & B) of a random sequence of length 500 with 25% respective dNTP content. The light grey area indicates the in vivo concentrations range of AZT in purified circulating T-cells from , converted to units by assuming a cell volume of for resting T-cells . The dashed horizontal line indicates the threshold for resistance selection, i.e. . All utilized parameters are indicated in Table 1 and Tables S1, S2, S3 (supplementary material).

Figure 7. Selective advantage of intermediate viral mutants of the Q151M-complex during DNA-dependent polymerization in the presence of TFV-DP.

Dashed blue-, solid green- and dotted magenta line indicate the selective advantage of the Q151M, the multi-drug resistant Q151M-complex (Q151Mc: A62V/V75I/F77L/F116Y/Q151M) and the Q151Mc+K70Q mutation during DNA-dependent polymerization of a random sequence of length 500 with 25% respective dNTP content in unstimulated cells. The light grey area indicates the in vivo concentrations range of TFV-DP from , , , converted to units by assuming a cell volume of for resting T-cells . The dashed horizontal line indicates the threshold for resistance selection, i.e. . Panel A: Selective advantage of the respective mutants with regard to wild type . B: Selective advantage of a succeeding mutants with regard to progenitor in Q151M complex formation . All utilized parameters are indicated in Table 1 and Tables S1, S2 (supplementary material).

Figure 8. Epistatic interactions for DNA-dependent polymerization in the presence of TFV-DP.

Solid blue-, green- and red line indicate epistasis with regard to replication , resistance and fitness as defined in eqs. (5)–(7) for the double mutant ‘K65R/M184V’. The black dashed horizontal line indicates the value, where no epistatic interactions occur. The light grey area indicates the in vivo concentrations range of TFV-DP from , , , converted to units by assuming a cell volume of for unstimulated T-cells . All utilized parameters are indicated in Table 1 and Tables S1, S2 (supplementary material).