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).
Table 1.
Physiological dNTP levels in different cell types.
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).
Table 2.
Efficacy & fitness.
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 [71], converted to units
by assuming a cell volume of
for resting
T-cells [72]. All utilized parameters are indicated in Tables 1, S1, S2, S3 (supplementary material).
Table 3.
Cell-specific values of AZT-TP for ‘poly-thymidine’ polymerization and susceptibility change by resistance development.
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 [71], converted to units
by assuming a cell volume of
for resting
T-cells [72]. 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 [56], [71], [73], converted to units
by assuming a cell volume of
for resting
T-cells [72]. 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 [56], [71], [73], converted to units
by assuming a cell volume of
for unstimulated
T-cells [72]. All utilized parameters are indicated in Table 1 and Tables S1, S2 (supplementary material).
Table 4.
Estimated in vivo % residual DNA-dependent polymerization for distinct mutants and drug combinations.
Table 5.
Estimated in vivo % residual human mitochondrial polymerase- activity in resting
cells.