In attempting to deplete the long-lived infected T-cell pool by activation, there is a trade-off between enhanced viral replication (and thus new cell infections) and increased clearance of infected cells in the quiescent cell pool. In the absence of HAART, it is likely that the former process will win, and a net increase in the proportion of infected cells will be seen during T-cell activation treatment. This is because analysis of the pattern of viral load decay following initiation of HAART suggests that whilst highly activated and rapidly dividing cells only form around 1% of the total CD4 T-cell pool, they are responsible for over 99% of viral production prior to initiation of HAART . This implies that increasing T-cell activity results in a net increase in viral production.
Given this trade-off under T-cell activation, we find in the model that the key factor which determines the virological outcome of IAT is the extent to which co-administered HAART inhibits viral replication. If HAART were able to block all replication, IAT would always reduce the prevalence of quiescent infected cells. However, recent analysis indicates that although HAART reduces viral production below the critical threshold required for self-sustaining replication, it may achieve this with only a 50–90% decrease in average viral production per infected cell . It may seem surprising that the rapid clearance of HIV virus associated with HAART can be achieved with such a modest reduction. The rapid time-scale of viral decay is in fact mainly a consequence of the rapid turnover of virus within the activated CD4 T-cell population. The decay profile is to a lesser extent dependent on antiretroviral drug potency, provided that net viral production and re-infection is kept below the critical threshold required for the virus to sustain itself (the basic reproductive number R0 < 1 ). When antiretroviral drug potency is only just above this threshold, HAART alone is observed to be effective; however the addition of IAT can result in HIV viral population growth by increasing viral production back above the critical self-sustaining threshold. This type of threshold effect is typical of non-linear infection processes .
To gain a more quantitative appraisal of the key issues and thus inform the debate on what might constitute an optimal IAT, it is useful to incorporate biological models of T-cell homeostasis [34–37] and viral replication [14,62] into a mathematical framework. This is described in detail in the Appendix. A simpler form of this framework which excluded CD8 T-cell dynamics was used previously to explain simultaneously post-HAART trends in viral load and CD4 T-cell counts and the perturbations in viral load seen following tetanus immunization of untreated HIV-infected patients . We use parameter estimates consistent with that analysis in the present study.
A consequence of our biological model is that increasing the potency of HAART will offer a potential advantage in giving greater freedom for IAT to increase activation (and infected cell clearance rates) and yet keep viral replication below the critical threshold required for new infection of quiescent T-cells to dominate the dynamics. The criterion for HAART to succeed under IAT is more stringent than for success without IAT.
Our analysis indicate that two distinct factors therefore need to be taken into account when measuring the success of IAT – the net changes in total and in infected CD4 T-cell numbers. Figure 4a shows the change in total numbers of HIV-infected CD4 T-cells caused by a single 5-day administration of IAT as a function of HAART potency and the level of activation achieved during IAT, while Fig. 4b shows the long-term effect on total CD4 T-cell numbers. The different shape of these two graphs indicates that for a given antiretroviral drug efficacy, therapy needs to be evaluated both in terms of the effect on T-cell homeostasis and on the infected quiescent T-cell pool, and may not be simultaneously optimal for both effects. Therefore in practice, IAT should aim to deplete the infected cell population as much as possible while not causing a fall in CD4 T-cells. Furthermore, for any antiretroviral drug efficacy, negative (rather than neutral) outcomes are always associated with over-stimulation.
Elimination of reservoirs of infected cells is a long-term goal of treatment of HIV-infected patients on antiretroviral therapy. Immune activation has the potential to help achieve that goal by accelerating the clearance of infected slow-turnover quiescent CD4 T-cells. In this paper we have shown that the outcome of such therapy is critically dependent on two factors: the potency or dose of the immune activating agent administered, and the potency of co-administered HAART. Immune activation that causes non-specific activation of a large proportion of the T-cell pool has the risk of radically depleting both infected and healthy CD4 T-cell populations. Furthermore, as viral production increases as a function of cell turnover, high-level activation may overwhelm the ability of co-administered HAART to control viral replication. In that case, the outcome of therapy might be doubly negative: a net decrease in the size of the CD4 T-cell pool and an increase in the proportion of cells infected.
Some insight can be gained by comparing long-term changes to T-cell homeostasis in HIV-negative kidney transplantation patients treated with OKT3  with changes in the HIV-infected patients treated with OKT3/IL-2 presented here. Results from Müller et al. need to be interpreted cautiously as they report the changes averaged over 13 patients rather than individual patient data. The dose used, 5 mg daily, was the same as in our study, but OKT3 was administered for longer (> 13 days average) and in combination with cyclosporine and prednisolon. The long-term reduction in the CD4/CD8 T-cell ratio was less pronounced in these HIV-negative patients (approximately 40% versus 60% in our HIV-infected patients). As the total T-cell counts remain constant, this suggests that the reduction in CD4 T-cell numbers was 50% larger in HIV-positive patients than in HIV-negative patients, despite the shorter duration of the treatment period. Comparing our model results with those of Müller et al., a daily dose of 5 mg of OKT3 corresponds to a level of T-cell activation where s ≅ 0.35–0.45. This does not take into the account the effect of cyclosporine and prednisolon which could result in a modified value for this parameter. At this dose, the changes to the total CD4 T-cell pool in HIV-positive patients can be accounted for provided that antiretroviral efficacy is approximately 90% (see Fig. 4b). Thus, the discrepancy between HIV-positive and HIV-negative patients may be the result of direct cytopathic effects of residual HIV viral replication under HAART, enhanced by T-cell activation. This interpretation also suggests (from Fig. 4b) that the long-lived T-cell pool infected with replication competent virus was increased several fold by the treatment. This is consistent with our finding that viral RNA in lymph node biopsies tended to increase.
More optimistically, our model suggests that IAT does have the potential to both systematically deplete infected cell reservoirs and even accelerate CD4 T-cell recovery if less potent (e.g., IL-2) immune activants are used [26–29,42–47,65], or the more potent ones (e.g., OKT3 plus IL-2) are administered at lower doses. When more moderate activation is induced, the risks of viral replication exceeding the threshold that can be controlled by HAART is reduced, together with the ferocity of the competition between CD4 and CD8 T-cell pools. Indeed, it appears that subtle differences in the response of these two cell pools to activation may give a window of drug concentrations for which IAT will result in a net increase in the CD4/CD8 ratio. A further clinical advantage of using less potent immune activants is improved tolerability and reduced risk of serious side-effects.
In conclusion, the quantitative analyses presented here predict that optimal viral elimination therapy should consist of the most potent HAART available coupled with extended periodic (or even continuous) low-level IAT. In the longer term, development of tolerable CD4-specific activants may further improve the effectiveness of this type of therapy, offering the potential of not only causing depletion of infected cell reservoirs, but also of restoring CD4/CD8 T-cell ratios to normal levels. However, caution is still required in all use of IAT, as the effect of activants on immune system function is still unknown. Even if IAT were capable of restoring CD4 T-cell populations, memory cell repertoires are still likely to be limited for patients who had reached late-stage disease, and IAT-induced anergy poses a potential risk.
The authors thank S. Jurriaans for excellent technical support.
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To explore the effects of IAT for different doses of T-cell stimulant and anti-viral drug action, a mathematical framework based on coupled differential equations is defined to study the time-evolution of the different subpopulations of T-cells. We are interested in describing two main biological processes: the HIV replication cycle and the nature of T-cell homeostasis.
We call V the free HIV viral load and Zi, Xi and Yi the sizes of the CD8, susceptible CD4 and infected CD4 T-cell subpopulations respectively, where the subscript i takes the values 1 and 2 for quiescent and active T-cells respectively. Cell turnover is assumed to be solely due to division of existing cells rather than recruitment of new cells from precursor populations. It is straightforward to include recruitment terms, even in an age-dependent manner and we find that a low recruitment rate for adults provides a simple explanation for the persistence of changes to the CD4/CD8 balance caused by IAT. Indeed, we would predict that for cases where recruitment of new cells played a significant part in cell turnover, the recovery of the ratio could be substantially accelerated. The equations for the system are:EQUATION where V˙ =dV/dt and so on. The turnover of quiescent T-cells is independent of cell type such that μX1=μZ1=μ, while the turnover of active and proliferating CD8 T-cells μZ2 is somewhat larger than that of their CD4 counterparts μX2. The effect of T-cell activating agents is accounted for by the f functions. There is no effect on the active cell pools, so fX2=fZ2=1, while the effect on the quiescent cell pools is to continuously increase the baseline turnover from μ through to μX or μZ for CD4 and CD8 T-cells respectively. A suitable functional form for CD4 T-cells fX1=1+(μX/μ−1) s/(s +AX50) with an entirely analogous formula for fZi for CD8 T-cells. For low viral loads the force of infection takes the standard form Λ=βV, but to take into account that for high viral loads infection is limited by the complete viral generation time, including the infected cell lifetime, we use the saturating form Λ=μβV/(βV +μ). JOURNAL/aids/04.02/00002030-200004140-00005/ENTITY_OV0398/v/2017-07-25T095608Z/r/image-png = ΣiμXifXiXi is the total turnover of the susceptible CD4 T-cell pool, and a similar definition holds for JOURNAL/aids/04.02/00002030-200004140-00005/ENTITY_OV0388/v/2017-07-25T095608Z/r/image-png for the infected pool. The functions D represent density dependent control of the T-cell pools. The quiescent T-cell pools are jointly regulated by blind homeostasis, so the functions are DX1=DZ1 =TQ/ NQ+C where TQ is the total pool size and NQ is the carrying capacity. The active T-cell pools are regulated specifically at the level of proliferation and so the functions are DX2=(X2+Y2)/ NAX +C, where NAX is the carrying capacity for active CD4 T-cells and DZ2=Z2/ NAZ +C, where NAT is the equivalent for CD8 T-cells. Crowding occurs when the total cell pool size T grows beyond Tmax and acts equally on all cell pools as C =ϕ(1+exp(Tmax/ T)). HAART is included in the equations by a reduction in β (cell infection) and a fraction of virus produced being defective.
Parameter values were determined by fitting the model to the HIV-RNA post-HAART decay curves across a wide spectrum of patients . The model was also shown to be consistent with transient increases in HIV-RNA observed following antigenic challenge of patients not on HAART with vaccines for pathogens other than HIV . Remaining parameters, especially those regarding CD8 T-cell dynamics were set to be consistent with the data on OKT3/IL-2 therapy  and IL-2 therapy alone , but were not fitted as there was not enough data to give meaningful estimates. The aim of the analysis was to illustrate the effect of changing the level of immune stimulation in therapy and also changing the HAART drug efficacy.
We deliberately do not include the transport of cells back and forth from lymph to peripheral blood in this model, as we are more interested in exploring the perturbations to T-cell population sizes during and following therapy than exactly reproducing results from IAT studies. This means that certain transient effects such as the initial rapid rise of CD4 T-cells following HAART observed in some patients as well as the complete peripheral lymphocytopenia observed immediately following OKT3 or high dose IL-2 administration are not captured by the model.
Further follow up of the three patients since this paper was submitted indicates a partial slow recovery of the CD4/CD4 T-cell ratio.