Dr. Mae-Wan Ho follows the trail of how a bad mathematical model has misled AIDS policies with disastrous consequences, and recent attempts to find a better model
“More than 20 years into the AIDS era, it has become increasingly clear that the current single-virus causation model is lacking in predictive and explanatory power.” This is how Rebecca Culshaw, assistant professor of mathematics at the University of Texas, Tyler, USA, begins her most recent paper published in the winter 2006 issue of the Journal of American Physicians and Surgeons .
Culshaw has announced why she “quit HIV” in March 2006  (On Quitting HIV, this series), and this had lured me onto the fascinating trail of how a bad mathematical model has misguided AIDS policies for so many years worldwide, and more importantly, alerted me to recent attempts to find alternative, more realistic models.
Perhaps quitting HIV is not the same as quitting AIDS, as the world is desperately in need of a good model, to save lives and end human suffering on a gigantic scale.
AIDS disease is generally characterised by a decline in CD4+ T lymphocytes circulating in the blood, which are responsible for cell-mediated immunity. As a result, the patient becomes susceptible to opportunistic infections (those affecting weakened immune systems) such as tuberculosis, pneumonia, meningitis, and other diseases caused by parasites, bacteria and viruses that can enter and multiply in the cells of the body.
But models that assume the human immunodeficiency virus (HIV) plays a central role in disease progression run into considerable difficulties. If the decline in CD4+ cells is due to HIV killing the cells, then there should be a correlation between the ‘viral load’, which estimates the amount of virus in the body, and the CD4+ cell count. But that is not the case. CD4+ cell count is not a reliable indicator of disease progression at all, nor for that matter is viral load  (Chapter 2, Unraveling AIDS, I-SIS Report), and they bear little relationship to each another. This has been confirmed in a recent study on untreated HIV+ individuals .
Although higher viral loads are associated with greater CD4+ cell decline, only a very small proportion of CD4+ cell loss, about 4 – 6 percent, is influenced by viral load. The authors reporting the new study called for future efforts  “to delineate the relative contribution of other mechanisms.” In short, as Culshaw states : “It has been extremely difficult to construct a realistic theoretical model of immune suppression that is entirely mediated by HIV.”
Why is it important to have a realistic model of the disease? A realistic model not only can predict how the disease will progress, it can also help in developing effective treatment and prevention. Since the discovery of HIV, mathematical models have been constructed precisely for those purposes: to determine the rates of progression to AIDS, to define optimal drug regimens for therapy, to develop vaccines, and as a desperate last resort, microbicide vaginal gels  (Concentrating Exclusively on Sexual Transmission of HIV is Misplaced, this series). However, the vast majority of the models lack predictive power because the mechanisms of disease and the fundamental nature of the immune system are both poorly understood. Meanwhile, the consequences of models based on a wrong hypothesis are all too clear, as Culshaw has starkly stated .
The toxicity of HAART treatment is now widely accepted  (Unraveling AIDS, Chapter 7). The scandal of toxic drugs being tested on defenceless foster children in New York City and mothers and babies in Uganda [6-8] (US Foster Children Used in AIDS Drugs Tests; Guinea Pig Kids in AIDS Drugs Trials ; NIH-Sponsored AIDS Drugs Tests on Mothers and Babies ; SiS 27) was widely publicised more recently in Harper’s Magazine . This has reopened the acrimonious debate  between AIDS ‘dissidents’ and the orthodox community of researchers and activists led by Robert Gallo, the controversial co-discoverer of HIV. The litany of vaccine failures has reached epic, controversial proportions  (Unraveling AIDS, Chapters 9-13); and the third large-scale clinical trials of anti-HIV gels has just been terminated because it was not only ineffective, but actually increased the risk of HIV infection . There are many compelling reasons to confront the bad model itself.
The Ho/Shaw model on why “hit hard hit early”
The model of HIV causes AIDS disease that has come to dominate global policies on AIDS, from diagnosis to therapy and prevention, is barely 12 years old. It was created in two high profile papers published in the 12 January 1995 issue of the journal Nature [11, 12]. Two research teams, led respectively by David Ho of the Aaron Diamond AIDS Research Centre NYU School of Medicine, New York, and George Shaw of the University of Alabama at Birmingham, used experimental antiretroviral drugs to follow how HIV viral load and CD4+ cell counts change after drug administration. From the changes, they estimated the rates of viral replication and elimination from the body as well as the rates at which CD4+ cells are killed and replaced by cell proliferation.
The results were astonishing; they were touted as giving a radically new understanding of HIV infection, one in which the immune system is in a constant battle with HIV from the moment of initial infection. As the distinguished late mathematician Serge Lang, a prominent AIDS dissident wrote : “These papers largely provided the justification for the new phase of protease inhibitor and cocktail treatments, as well as for the expanded use of surrogate markers such as “viral load” and CD4 counts for AIDS disease. Each of these represented a significant departure in terms of HIV/AIDS diagnosis, maintenance, treatment, and epidemiological reporting.”
In the Ho study , a protease inhibitor code named ABT-538 was given at 600 to 1 200 mg per day to 20 HIV+ individuals whose pre-treatment CD4+ lymphocyte counts ranged from 36 to 490 per mm3 and viral load, measured by a new quantitative branch polymerase chain reaction from 15 – 554 x 103 virus particles per ml.
Following treatment, every patient had a rapid and dramatic decline in plasma viral load over the first two weeks, between 11 and 275-fold reduction, with a mean of 66-fold, i.e., a 98.5 percent drop. The initial decline was assumed to be exponential, allowing the half time of viral decay (time it takes for half of the virus particles to disappear) to be estimated as 2.1 + 0.4 days. That showed HIV-replication must be “highly productive”, the authors claimed; and the virus particles were cleared as fast as they were produced. In other words, a steady state standoff was established in the body, so that the viral load measured at any time remained roughly the same. The estimated minimum production rate – the same as the minimum clearance rate - averaged 0.68 + 0.13 x 109 virus particles per day, which is really quite modest, considering that each infected cell can produce a hundred virus particles.
The paper was heavily criticised. The estimates depended on the assumption that drug treatment does not affect viral clearance, and that there was a pre-existing steady state between viral production and viral clearance, regardless of the amount of virus in circulation. Curiously, the estimated viral clearance/production rate bore no relationship to the initial viral load or to the CD4+ lymphocyte count, which was difficult to reconcile with the idea that the virus was killing the CD4+ cells by invading the cells to replicate and burst the cells. In that case, the more virus particles and the more cells, the higher should be the production/clearance rate.
After ABT-538 treatment, CD4+ lymphocyte counts rose in each of 18 patients that could be evaluated. Some increases were dramatic and others quite modest. From the slope of the line depicting the rise in CD4+ lymphocyte counts assuming an exponential increase, a doubling time of about 15 days was estimated during the (assumed) pre-treatment steady state. The slopes were inversely correlated with baseline CD4+ cell counts, however, which too was difficult to explain. In patients with lower initial CD4 cell counts, more prominent rises were obtained. Nevertheless, the authors claimed: “This demonstrates convincingly that the CD4+ lymphocyte depletion seen in AIDS is primarily a consequence of the destruction of these cells induced by HIV-1, not a lack of their production.” They explained that such an inverse correlation would be expected if T-cell proliferation were governed by some kind of homeostatic mechanism. From the inverse correlation, it was estimated that the minimum number of CD4+ cells in blood produced or destroyed each day ranged from 4.3 x 106 to 109 x 106, with a mean of 35.1 x 106. As the blood lymphocyte pool is about 2 percent of the total population, the overall CD4+ lymphocytes turnover in the patients was calculated to vary from 0.2 x 109 to 5.4 x 109 cells per day, with a mean of 1.8 x109 cells per day. This number of cells was about the same as the number of putative viruses produced (and cleared) each day, far too many cells killed for the number of viruses produced. Things didn’t add up.
The increase in CD4+ lymphocyte counts following ABT-538 administration was also modelled linearly, and using the same arguments as for the decline in viral load, the minimum estimates of total CD4+ lymphocytes production or destruction rates at baseline were determined to vary between 0.1 x 109 to 7.8 x 109 cells per day with a mean of 2.6 x 109 cells per day, sufficiently close to the estimate above.
The authors commented that the CD4+ lymphocyte depletion seen in advanced HIV-1 infection “may be likened to a sink containing a low water level, with the tap and drain both equally wide open.” As the regenerative capacity of the immune system is not infinite, it is not difficult to see why the sink eventually empties (when CD4+ cells are all depleted).
Now comes the crucial conclusion that has justified the “hit hard, hit early”  strategy of HAART that has gone so disastrously wrong for otherwise healthy HIV+ individuals: “It is also evident from this analogy that our primary strategy to reverse the immunodeficiency ought to be to target virally mediated destruction (plug the drain) rather than to emphasize lymphocyte reconstitution (put in a second tap).”
And: “We believe our new kinetic data have important implications for HIV-1 therapy and pathogenesis. It is self evident that, with rapid turnover of HIV-1, generation of viral diversity and the attendant increased opportunities for viral escape from therapeutic agents are unavoidable sequelae. Treatment strategies, if they are to have a dramatic clinical impact, must therefore be initiated as early in the infection course as possible, perhaps seen during seroconversion…”
The Shaw study  used the protease inhibitors ABT-538, L-735.524, or the non-nucleoside reverse transcriptase inhibitor Nevirepine on a total of 22 patients, as part of a phase I/IIA clinical trial, and came to the same conclusions. In addition, it found drug resistant mutant viruses in all subjects soon after treatment started. The lowest point of viral load was at two weeks in all subjects after treatment started, when the CD4+ cell count rose to a peak. Thereafter, viral load increased rapidly, despite increased drug dosage, and by week four, 100 percent of the virus in blood was drug resistant. The CD4+ cell counts dropped more slowly, and were back to baseline within 6-20 weeks.
Critics faulted the Shaw study for the same unwarranted assumptions that underlie the Ho study. Neither study included a control group. The clinical outcomes of the drugs on the patients were not reported, so it was impossible to tell whether the patients benefited from the transient reduction in viral load or the transient increase in CD4+ cells. The mathematical model had no contact with the observations other than dubious fitting of a straight line through two or three data points .
The Ho/Shaw model began to unravel almost as soon as it was proposed, but the “hit hard hit early” HAART approach continued at least until 2001 when the US government’s expert panel on anti-HIV therapy finally recommended restricting the prescription of anti-HIV drugs for as long as possible for people without symptoms, on account of the serious side effects  (Unraveling AIDS, Chapter 7).
Mario Rodoerer at Stanford University Beckman Center, writing in News and Views of the February 1998 issue of Nature Medicine commented  that two papers published in the same issue [16, 17] “provide the final nails in the coffin for models of T cell dynamics in which a major reason for changes in T cell numbers is the death of HIV-infected cells [i.e., the Ho/Shaw models].”
The papers presented extensive data on the remodelling of the T cell compartment in HIV-infected individuals after treatment with HAART. Throughout the early stages of HIV infection, CD4+ cells decline, whereas the total CD8+ cells expand. However, the application of flow cytometry techniques that accurately identified subsets of T cells showed that this increase in CD8+ cells is made up entirely of memory and activated T cells, while naïve T cells (precursor of memory and activated T cells) declined at the same rate as naïve CD4+ cells (precursor of memory and activated CD4+ cells). Activated T cells are found only in peripheral tissues - the spleen and lymph nodes – and their expansion in the blood in HIV-infected individuals indicated an active immune response even during the later stages of disease.
Within weeks after starting HAART, there were significant increases in the number of B cells, and of CD4+ and CD8+ cell in the blood, but these were only memory cells that can maintain long-term residence in lymph nodes, and not naïve T cells, which do not dwell in lymph nodes and do not immediately respond to HAART.
Essentially, the studies provided evidence for the ‘redistribution hypothesis’: the increase in CD4+ cell counts observed shortly after the start of HAART are T lymphocytes redistributed from the lymph nodes, and not produced by cell proliferation. During active viral replication and the concomitant cellular immune response, a large number of B and T cells may be trapped in peripheral sites (for example, by antigen, cytokine or chemokine signals). After initiation of HAART, when HIV is effectively removed from the system, the immune response begins to resolve and cells pour out of the inflamed lymph nodes back into the blood.
The first study  suggested that the degree of T lymphocyte trapping increases as disease progresses. That would explain why the response to HAART tends to be greater in individuals with lower CD4+ cell counts.
Functional recovery of the T cell compartment is only complete when the repertoire of T cell receptors is restored, so that potentially all antigens can be recognized. The decrease in naïve and memory T cell populations during disease progression means that the repertoire becomes increasingly restricted, finally resulting in immunodeficiency.
The second study  confirmed earlier findings that the T cell receptor repertoire in HIV-infected individuals is significantly different from the normal distribution found in healthy adults. This is due to a loss of unique T cell clones and an expansion of antigen-specific clones caused by an over-representation of certain receptor types.
In individuals responding to HAART, the number of naïve T cells slowly increases over a six-month period after initiation of HAART and a reconstitution of the T cell repertoire can take place (but see later). Notably, this reconstitution occurs only in individuals who show reductions in viral load in response to HAART. It is also likely that failure of HAART, which occurs in many patients over time, will also be accompanied by a re-initiation of cell losses and repertoire restriction.
The use of radioisotope labelling has enabled researchers to identify different populations of T lymphocytes in the human body . There are long-lived and short-lived cells, and the size of the total T lymphocyte pool appears to be regulated mainly at the level of the long-lived cells. During the course of an antigen-driven cell proliferation response, some T cells differentiate into effector cells that clear the antigens from the body, and typically have a short life span. Others become memory T cells, which, by contrast, are long-lived and serve as reservoirs for subsequent activation by antigen to proliferate and produce effector cells. Naïve T cells also have a long life span. In advanced HIV-1 infection, a much higher proportion of T cells are short-lived, compared to healthy controls, and effective HAART tends to restore the values towards the normal. Advanced HIV-1 infection greatly reduces the percentage and total number of CD4+ cells that are long-lived. Because these cells represent the regenerative source of newly formed CD4+ effector T cells, their loss may underlie the immunodeficiency of HIV-1 disease. These abnormalities may not be present in early HIV-1 infection and may represent a marker of disease stage.
However, many questions remain unanswered . Why is HIV so uniquely powerful, among chronic viruses, in inducing a chronic state of immune activation? And why is the HIV- induced immune activation is so disruptive of the proper overall functioning of the immune system?
Of course, there remains the lingering doubt that HIV is not actually causing the disease
None of the models so far has taken into account the role of nutrition in AIDS or AIDS-like diseases, and the ability of good nutrition to reverse or delay disease progression  (Unraveling AIDS, Chapters 15-17). In particular, AIDS is a disease in which the immune system is out of balance, not only in being chronically activated, but also in the predominance of the humoural (type 2) at the expense of cellular (type 1) immunity  (Unraveling AIDS, Chapter 12).
All HIV models so far have considered the CD4+ cells as a single entity. But it has been known for some that the pool of CD4+ cells (commonly known as T-helper or Th cells) contained two different subsets: Th 1, responsible for cell-mediated immunity and Th 2, responsible for extracellular or humoural immunity. The majority of the CD4+ Th 1 cells reside in the peripheral blood and it is their depletion that occurs in the progression to AIDS [1 and references therein]. Th2 cells reside mainly in the bone marrow and to a lesser extent in the lymph nodes, and do not appear to become depleted in the progression to AIDS. If anything they have been observed to increase .
As AIDS progresses there appears to be a gradual shift from Th1- to Th2-dominance, which is why patients experience mainly fungal and mycobacterial infections, but very few “classical” bacterial diseases. Furthermore, elevated levels of antibodies, including autoantibodies, are characteristic of all AIDS patients, as consistent with an increase in Th2 subset. Contrary to what one might expect, HIV is expressed primarily in Th0 (precursor of Th1 and Th2) and Th2 cells and is scarcely
Expressed in the Th1 subset . Yet it is the Th1 cells that are depleted, whereas the cells in which HIV prefers to reside do not decrease. So what mediates the Th1 to Th2 shift, and how can it be prevented or reversed so as to restore balance to the immune system?
Culshaw  suggests using bifurcation theory, a branch of mathematics that deals with changes in critical parameters that determines major or abrupt changes, such as the commitment of Th0 to become either Th1, or Th2.
One crucial component in the Th1 to Th2 shift is the release of nitrous oxide (NO) from the cell-mediated arm of the immune system . NO can diffuse though cell membranes without the help of receptors in cell-cell communication, and nitrogen oxides are regulated by the oxidative state of the immune cells. Excessive oxidation negatively affects immune function through the production of cytokines from the immune cells. Oxidative processes are counterbalanced by reduction, which is accomplished by sulphur-containing molecules that serve as electron donors, the main one is glutathione, a tripeptide consisting of cysteine, glutamine and glycine. Glutathione is found in both the reduced (GSH) and the oxidized (GSSG) form. The ratio of GSH:GSSG has been shown to be important in regulating Th1/Th2 balance [24, 25]. If the GSH:GSSH ratio declines, Th2 cells are preferentially made from Th0, thus resulting in Th2 dominating at the expense of Th1 cells.
HAART causes a transient increase in T-cell counts in the peripheral blood because it damages B-cells as they mature and disrupts antibody production. Unable to make contact with antibody-producing B-cells in the bone marrow, the CD4+ Th2 cells return to the peripheral blood. So, although CD4+ T cell count increases, the cells are ineffective against opportunistic infections. This gives rise to the phenomenon of ‘immune reconstitution syndrome’, in which patients experience the “irony” of an increase in opportunistic infections after initiating HAART therapy .
Culshaw sketches out an alternative mathematical model based on the GSH:GSSG ratio and Th1/Th2 balance, which are crucial in the development of AIDS, and proposes that HIV itself need not even be included as a variable. The proposed model tracks the Th0, Th1 and Th2 subsets of the T-cell pool over time, with the ratio of GSH:GSSG as a possible bifurcation parameter. As GSSG increases, and the ratio declines, a greater proportion of the Th0 cells mature into Th2 cells and are diverted from the Th1 pool. Such a model could enable researchers to determine the critical ratio of GSH:GSSG below which a shift to Th2-dominance occurs.
There are several advantages to such a model. First, it replaces viral load measurements, which have not been shown to have good clinical predictive value as a therapeutic endpoint. Second, determining a critical ratio of GSH:GSSH rather than a critical value gets around the problem of variability among individual patients. Finally, the model explicitly considers the Th1/Th2 ratio, an important measure in the progression to AIDS that has been largely neglected in theoretical modelling.
Circumstance evidence in favour of such a model is that selenium and other antioxidants appear to be effective in preventing and treating AIDS  (Unraveling AIDS, Chapter 17). Another advantage of Culshaw’s new model is that it can make direct contact with nutritional status, an important determinant in disease progression.
Article first published 03/04/07
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