The impact of antiretroviral drug-resistance on viral load, CD4+
T cell counts and clinical outcomes is complex. Although the emergence of resistance to protease inhibitors and reverse transcriptase inhibitors clearly affects viral fitness (as defined in vitro and in vivo) 
, its impact on viral load and CD4+
T cell counts is unclear. At comparable plasma viral loads, drug resistant HIV can be associated with more sustained CD4+
T cell gains and reduction of the risk of morbidity and mortality 
than wild-type (drug-sensitive) HIV. To understand the mechanism for this apparent beneficial effect on immunologic and clinical outcomes independent of viremia, we use ENF resistance as a “probe” to explore the impact of fitness on viral and immunologic dynamics in vivo. Although the data linking ENF resistance to viral load, CD4 and clinical outcomes is limited, the preliminary data that does exist is consistent with the more extensive literature pertaining to protease inhibitor resistance. Specifically, despite the emergence of ENF-resistant mutations, CD4+
T cell counts have been observed to increase during therapy as the ENF resistant virus with less capacity to infect T cell replaces the ENF-sensitive virus. A large prospective study has recently been completed in which ENF was given as a “pulse” to determine if the expansion of ENF resistance positively affects CD4+
T cell counts. Preliminary data from 3 individuals has previously been published 
. Given the richness of this data-set, we developed a mathematical model to study the benefits of ENF re-administration after interruption of therapy due to virological failure.
Interruption of ENF after the emergence of ENF resistance results in a rapid decay of the resistant variant 
. One of the key questions is what factors play a role in the waning of the ENF-resistant virus and in determining the time for the ENF-sensitive virus to become dominant. Similar questions arise for the period of ENF re-administration in which ENF-resistant virus rapidly increases and takes over the ENF-sensitive virus. Moreover, despite the rapid turnover of the virus population, the plasma HIV-1 RNA level remains unchanged during ENF interruption raising a question of what determines the plasma viral load. In this study, we took advantage of mathematical models to address these issues.
Our model, which describes the dynamics of ENF-sensitive virus, ENF-resistant virus, target cells, cells infected by ENF-sensitive virus and cells infected by ENF-resistant virus, includes the fitness cost of ENF-resistant virus as well as forward and backward mutations. The model was used to fit data concerning the level of ENF-sensitive viruses, V38A ENF-resistant viruses and the CD4+
T cell count from HIV-1 infected patients, who underwent ENF interruption and subsequent re-administration while continuing to receive the other drugs in their regimen 
. The data fitting during ENF interruption allowed us to estimate the forward mutation rate, the backward mutation rate and the fitness cost of the ENF-resistant virus along with the virus production rate, the infected cell death rate, the infection rate, the source rate of the target cells and the fraction of T cells that were target cells. Moreover, the data fitting allowed us to estimate the ENF efficacy against ENF-sensitive and ENF-resistant viruses during ENF re-administration.
Our parameter estimates, model analysis and numerical simulations produced several interesting observations. First, the magnitude of the backward mutation rate of V38A is approximately the same as that of the forward mutation rate. This indicates that ongoing viral evolution might have some contributions to the loss of ENF-resistance during ENF interruption, supporting the results of phylogenetic analysis in Kitchen et al. 
. However, we observe that backward mutation barely contributes to the loss of drug resistant viruses (26 virions/ml in the first week and 70 virions/ml in the first month post interruption), and thus is not sufficient to achieve the rapid waning of ENF-resistant viruses observed when therapy is interrupted. Outgrowth of the wild-type virus with a fitness advantage in the absence of drug is a more plausible explanation.
Second, we found that the fitness cost of ENF-resistant mutations has a major role in the loss of ENF-resistant virus and the turnover of the virus population during ENF interruption. We estimated that the ENF-resistant virus is 17±3% less fit than the ENF-sensitive virus. This reduced fitness of V38A ENF-resistant virus agrees with the experimental finding of reduced fitness of the V38A mutant virus compared to wild-type virus in vitro 
. Our simulations and analysis showed that the time needed for the sensitive virus to dominate the resistant virus during ENF interruption is mainly determined by the combined effect of fitness cost and the initial ENF-resistant virus proportion. Not surprisingly, the higher the fitness cost, the shorter the turnover time; and the higher the initial ENF-resistant virus proportion, the longer the turnover time (). During ENF re-administration, the ENF efficacy against ENF-resistant virus also plays an important role in determining the time for the resistant virus to outcompete sensitive virus. A higher ENF efficacy against ENF-resistant virus results in a longer turnover time (). Interestingly, there is a negligible effect of the target cell level on determining the turnover time of the virus population ( and ).
Third, we found that the fitness cost and the initial proportion of the ENF-resistant virus do not have any observable role in defining plasma HIV RNA levels. Neither does ENF efficacy during ENF re-administration contribute to setting plasma viral levels. The plasma viral RNA level is determined mainly by the target cell generation rate, λ, the virus production rate, p, the infected cell death rate, δ, and the virus clearance rate, c. A higher value of p or λ and/or a lower value of δ or c give rise to a higher plasma HIV RNA level.
Our next observation is related to the advantage or disadvantage of re-administrating the drug following an interruption. Once the drug is re-administered, the resistant virus rapidly reemerges and becomes dominant over the sensitive virus. This indicates a strong selective pressure of the drug on the virus population. The turnover rate of the virus population is more rapid during the drug re-administration than during the drug interruption. This shows that the advantage of the drug-resistant virus over drug-sensitive virus during the drug re-administration is greater than the disadvantage of the drug-resistant virus over the drug-sensitive virus during the drug interruption. The rapid reemergence of the resistant virus also indicates the persistence of actively replicating resistant virus as suggested in 
. Our parameter estimates indicate that ENF when re-administered is ~29% effective against ENF-resistant virus and ~66% effective against ENF-sensitive virus. This supports the antiviral activity against ENF-resistant viruses observed previously 
. After re-administration of ENF, our model predicts a small transient suppression of viral load followed by a rebound to a higher plasma RNA level, consistent with the pattern shown by the data. This shows that the re-administration of ENF cannot suppress plasma virus for the long term.
One of the most interesting results demonstrated by our model is that despite sustained high levels of viral load, re-administration of ENF helps in maintaining a significantly higher level of CD4+
T cells ( and ). During ENF re-administration patients can achieve more than 35% higher CD4+
T cell count over the period of 3 months compared to the same patients during ENF interruption (). The CD4 count increase predicted by our model (~35%) is consistent with the CD4 count gain in a study on a larger cohort of individuals 
in which the subjects (with the same background regimen as in our study) maintained a 36.8% higher CD4 during ENF treatment than during ENF interruption. This immunologic benefit of ENF occurs even in the presence of high-level ENF resistance, in agreement with the findings in some individuals harboring viruses with ENF-resistance mutations under long-term ENF therapy 
. This outcome on administering ENF can be explained by the presence of resistant viruses with a reduced infection capacity ( and ). The treatment alters the fitness of the virus by selecting the less fit resistant virus that helps in maintaining a higher CD4 count even though it is ineffective in suppressing the viral load. A similar effect has been seen in patients treated with reverse transcriptase and protease inhibitors such as proD30N, rtK65R and rtM184V 
. The benefit of the drug is mediated by changes in both the fitness of the virus and the efficacy of the drug against resistant virus. The CD4+
T cell level during the drug re-administration increases as the efficacy of the drug against resistant virus increases or/and the fitness cost of resistant virus increases.
There are several limitations of this study. The results are based on limited data from only three subjects. Moreover, there are fewer data points available during ENF re-administration, which might produce more uncertainty in the results derived from ENF re-administration. To gain more confidence in the results obtained here, extensive studies with more data are necessary. We have considered the V38A mutant virus as a representative of all ENF-resistant viruses. However, there are many other mutant viruses, which may possess different fitness costs and different mutation rates. It should be noted that in the experiment only the proportion of V38A was measured, and so there might be other mutant virus resistant to ENF that would have been included in the ENF-sensitive viral load. A detailed quasi-species model, as in Murray and Perelson 
, may provide a better explanation of the phenomena and help in estimating a more accurate value of the T-cell benefit. However, such complex models require more detailed data sets in which the population levels of other members of the quasi-species are measured. Currently, such data is unavailable.
In summary, we have used mathematical models to help explain the viral dynamic properties of drug sensitive and resistant viruses in the presence and the absence of the drug ENF. Our results show that even though forward and backward mutations occur during therapy interruption, the primary factor leading to the loss of resistant virus during therapy interruption is the fitness cost of the resistant virus. In the presence of drug, the efficacy of drug against resistant virus is also one of the main factors determining dominance of the drug resistant virus in the population. More importantly, even though the drug is ineffective in suppressing plasma viral load due to the presence of resistant virus, our results support the concept that continued therapy may have a residual immunologic benefit by preserving peripheral blood CD4+ T cell levels.