R E V I E W S

The balance of power between HIV and the immune system

Angela R. McLean

H ow does HIV cause AIDS and why does it take so long? Eleven

years after the first case re- ports ~ this question remains the subject of much debate. Why is it that infected individ- uals initially control their HIV infection, but then after about ten years 2 lose that control? This review concerns the theo- ries that aim to explain this shift in the balance of power between HIV and the immune system.

There are several theories of the pathogenesis of HIV that attempt to explain the long and variable delay

between infection and disease. Here, each theory is reviewed within the context of a

simple mathematical model of the interactions between HIV and the immune

system. From this model, a theoretical index of progression has been derived

that combines elements from each proposed mechanism.

A.R. McLean is in the Zoology Dept, University of Oxford, South Parks Road, Oxford, UK OX1 3PS.

Soon after infection with HIV many patients ex- perience a rapidly growing virus load that peaks as specific immunity against HIV comes into force. The viral burden is then suppressed to very low levels 3 for many years. During these years,, although many patients show no symptoms, there is a steady decline in the number of circulating T helper lymphocytes (HIV infects cells, such as T helper lymphocytes, that express CD4). After a period, which can be as short as two months 4 or longer than a decade, the immune system ceases to keep the HIV population under con- trol, and the viral burden starts to rise again s with the accompanying opportunistic infections and neo- plasms characteristic of full-blown AIDS. This is the pattern of HIV population dynamics within the host that requires explanation. The pattern in the fall of the T helper lymphocyte population is very variable among individuals 6, but the successful use of a linear regression model to predict the onset of AIDS in a haemophiliac cohort r implies that a steady decline in T helper lymphocytes is a good approximation to that pattern.

The six theories for pathogenesis reviewed here are as follows: (1) HIV's growth rate increases be- cause of activation of CD4 + lymphocytes due to immune stimulation by other pathogens8; (2) there is evolution of more virulent strains of HIV9'I°; (3) antigenic diversity in the HIV population renders its replication uncontrollable by the immune systemU; (4) HIV evolves escape mutantsl2-14; (5) the pool of precursor memory T lymphocytes specific to HIV is exhaustedlS; (6) antigen-presenting cells are slowly destroyed 16a7. Each of these theories proposes a mechanism that acts to shift the balance of power between HIV and the immune system. The theories are not mutually exclusive, nor are they necessarily independent of each other.

The interaction between HIV and the immune system is both complex and poorly un- derstood. It is this combina- tion, and the limited nature of observational data, that allows so many different theories to explain the same set of obser- vations. Another consequence of this apparent complexity is the poor ability to give an accurate prognosis for an indi- vidual's disease. One way to address such complexity is through a mathematical model.

Here, I present a mathematical model of the interac- tion between HIV and the immune system. The model, although very simple, can encompass all the proposed mechanisms of the six theories listed above. This allows a classification of the theories and re- solves their apparent superabundance. The model also identifies a composite marker of disease progres- sion that can combine elements of all the proposed mechanisms of HIV's pathogenesis. This theoretical marker may help in the search for biological markers for the prediction of the future course of an individ- ual's disease.

The simplest model ever made Four elements can be identified in the interaction be- tween HIV and the immune system: things that are good for HIV, things that are bad for HIV, things that are good for the immune system, and things that are bad for the immune system. The model describes the rates of change of the HIV population and of the popu- lation of HIV-specific, activated, T helper lympho- cytes. The model has two equations, each with two terms, corresponding to the four elements listed above: HIV's growth rate (good for HIV); the ef- ficiency of the anti-HIV immune response (bad for HIV); the rate of activation of HIV-specific T helper lymphocytes (good for the immune system); and the rate of killing (or disablement) of HIV-specific T helper lymphocytes (bad for the immune system) (see Box 1). The model yields a single expression that summarizes the balance of power between HIV and the immune system 18'19. I call this expression R, the HIV net reproductive number (see Box 2). So long as R is less than 1, the immune system holds the balance of power. If changes in any of the four elements of the interaction are great enough such that R becomes greater than 1, it becomes possible for HIV to grow

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Box 1. HIV pathogenesis: the simplest model ever made

This model summarizes the population dynamics of the interac- tion b e t w e e n HIV and the immune system. Two populations are accounted for: the amount of HIV, V, and the number of HIV- specific, activated T helper lymphocytes, X. The model consists of two equations describing the rates of change of these two popu- lations. The equations represent the following assumptions.

HIV growth: in the absence of specific immunity, HIV grows at a rate proportional to the amount of HIV present, i.e. exponen -

tially. Parameter g represents the intrinsic growth rate of HIV. Immune efficiency: HIV is specifically removed at a rate pro-

portional to the number of HIV-specific T helper lymphocytes. In other words, immune effector lymphocytes (cytotoxic T and B lyre- phocytes) act at a rate that is proportional to the amount of help that they get from HIV-specific T helper lymphocytes. Parameter e represents the efficiency of the immune response (specifically, the rate of removal of HIV per T helper lymphocyte).

Immune activation: HIV-specific T helper lymphocytes are activated at a rate proportional to the amount of HIV present. Parameter a represents the activation rate per virion.

HIV ¢ytopathlclty: T helper lymphocytes (including HIV-specific T helper lymphocytes, X) are removed at a rate proportional to the amount of HIV present. Parameter c represents the cytopathicity of HIV.

These four assumptions are encoded in the two differential equations of the model, as follows.

Population growth rate of activated HIV-specific T lymphocytes:

dX = aV - cVX

d t

activation cytopathicity

Population growth rate of HIV:

d V = g V - eVX

d t growth immune efficiency

(1)

(2)

uncontrollably, leading to the onset of AIDS (Fig. 1). Each theory discussed below proposes a change in one (or two) of the four elements of R that acts to make R larger. The six theories are classified accord- ing to which of the four elements they suggest is changing; each theory can be described in terms of changes over time in the parameters of the simple model (Table 1).

Immune stimulation In vitro studies show that HIV's replication rate is increased in activated host lymphocytes. There is evidence to suggest that activation is necessary for the infection of T helper lymphocytes 2° and the inte- gration of HIV-encoding DNA into the host genome 21. The production of new HIV virions from infected cells is greatly enhanced by activation 22'23. These observations have led to the theory that it is the ac- cumulation of immune stimulation over the years of the incubation period that is responsible for the onset of AIDS 24. In the framework of the simple model, the accumulated immune stimulation theory is classified as an increasing growth rate mechanism (Table 1). A number of mathematical models based upon this hy- pothesis have been published 2s'26. One of the more

extensive studies s addresses interactions between HW and other pathogens that would arise if HIV repli- cation were enhanced by the activation of T helper lymphocytes specific to other pathogens. Three facets of such interactions are addressed: enhanced HW replication due to immune stimulation by other pathogens; modified immune control due to immuno- suppression by HIV; and the spiral of T helper lym- phocyte depletion formed by positive feedback be- tween these two effects. The model predicts that there is a correlation between higher levels of activated T helper lymphocytes and disease progression, and that there is a threshold number of activated T helper lym- phocytes above which the HW-infected immune sys- tem is unable to control pre-established infections. This threshold marks the boundary between a sup- pressed but still functioning immune system and the T helper lymphocyte depletion that marks the final stages of AIDS.

Many cohort studies have identified measures of immune activation, such as levels of activated T lymphocytes 27-29, serum neopterin 3°'31, serum 132- microglobulin 3°-32 and soluble interleukin 2 recep- tors 2s,33, as correlates and predictors of T helper lymphocyte decline or the onset of AIDS. The most convincing of these studies 2s showed that high levels of activated T lymphocytes prior to infection with HIV predicted faster progression to disease. This finding is particularly compelling as it indicates that immune activation that could not have been cadsed by HIV can lead to faster disease progression. Some authors argue 11 that if immune activation by other infectious organisms were an important factor in disease progression, risk groups exposed to larger, numbers of infectious diseases would progress faster to AIDS. Indeed, it has been shown that cyto- megalovirus-infected haemophiliacs develop AIDS faster than those not infected with cytomegalovirus 34. There are extensive data on progression rates among groups of homosexuals and haemophiliacs: some studies find that homosexuals do develop AIDS more rapidly than haemophiliacs 3s-37, but this is not a uni- versal observation. However, since factor VIII is a cause of immunosuppression 3s, it should not be sur- prising that haemophiliacs progress to disease at simi- lar rates to homosexuals, but for different reasons. Haemophiliacs have pre-existing immunosuppres- sion (low a in the model); while in many homosexuals the several other infectious diseases to which they may be exposed cause immune stimulation (and therefore high g in the model).

Evolution of virulence There is great heterogeneity in the HIV population within an infected individual. Growth rates and cyto- pathicity are among the features of viral isolates that

39 are highly variable. Longitudinal studies have shown that individuals in the late stages of disease harbour virus that grows faster and kills host cells more readily 4°. These observations have led to the suggestion that it is the evolution of more virulent strains over the years of the incubation period that

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leads to the onset of AIDS. In terms of the simple model, this theory is classified as increasing growth rate and increasing cytopathicity (Table 1). As with all theories of AIDS pathogenesis, it is difficult to distinguish between correlation and causation when interpreting observed changes through time in the interaction between HIV and the immune system. Recent work showing that the appearance of highly cytopathic isolates is a strong predictor of the onset of AIDS 1° lends weight to this proposed mechanism.

Antigenic diversity The antigenic diversity theory H of HIV pathogenesis calls on this aspect of the biology of HIV as the under- lying cause of AIDS. The heart of this theory is the asymmetric pattern of killing that exists between immunologically distinct strains of HIV and their re- spective clones of T helper lymphocytes. Thus, while each different HIV strain can kill T helper lympho- cytes of any specificity, each specific clone of T helper lymphocytes can only recognize (and orchestrate the killing of) strains of HIV that bear certain MHC class II restricted epitopes. A natural consequence of this asymmetry is a threshold on the number of immunologically distinct strains of HIV that can be controlled.

To understand how the antigenic diversity theory is classified within the framework of the simple model, one must imagine that the simple model's two equations describe the population dynamics of just one strain of HIV and one clone of T helper lymphocytes specific to that strain 41. The term representing cytopathic effects of HIV on T helper lymphocytes (-cVX) has to be changed so that T helper lymphocytes disappear at a rate proportional to the total viral load, not just the load of virus for which that clone is specific. The simplest case would be if n strains were present at identical densities, when -cVX would be replaced by -ncVX. So the per- virion cytopathicity of HIV is proportional to the number of strains present. In this sense, the antigenic diversity theory may be classified as an increasing cyto- pathicity mechanism (Table 1).

Evolution of escape mutants If HIV evolves epitopes that can- not be recognized by current ef- fector lymphocytes (escape mu- tants), no amount of help from T helper lymphocytes will control strains with these epitopes. Re- cent studies ]2 have shown that some HIV-infected individuals do indeed harbour virus with

Box 2. HIV's net reproductive number

The model descr ibed in Box I has equi l ibr ia (points where Vand X are unchanging, i.e. dX/dt= 0 and dV/dt= O) along the line V= O, X = X*, which are stable so long as X* > g/e. So long as g/e is less than a/c, the immune system controls HIV. However, ifg/e is greater than a/c, i t becomes possib le for HIV to grow wi thout l imit (although there are sti l l some star t ing values for X and V tha t will a l low Vto be control led). So AIDS cannot develop so long as:

or

g < a (3) e c

cg < 1 (4) ae

I call the quant i ty cg/ae HIV's net reproduct ive number, R. Its bio- logical interpretat ion is tha t it is the average number of offspring generated by an individual virion. Equation 4 then gives a cri ter ion for the deve lopment of AIDS and so long as it is sat isf ied, the growth of HIV remains control led; once this condi t ion is broken HIV can grow uncontrol lably (Fig. 1). If we recall the def in i t ions of a, c, g a n d e, we can make a biological interpretat ion of Eqn 4 as fol lows:

HIV growth x HIV cytopathici ty < 1 immune act ivat ion x immune efficacy

So Eqn 4 says that so long as the factors that are good for HIV and bad for the immune system are smal l compared to factors tha t are good for the immune system and bad for HIV, the infected indi- vidual will remain well .

'"i E:

2O0OO

50000 -

40000-

31:1000-

20000-

10000-

0

I0000 20000 30000

Activated HIV-specific T helper cells (X)

(b) ~oooo

,5O000

4O0OO

_>3°°°° I

2t:1000

10000

10000

/ /

/

/ , / / " /

2oo0o 3oo00 Activated HIV-specific T helper cells (X)

Rg. 1. The phase plane of X and Vwhen (a) R < I or (b) R > 1. The model in Box I has two types of solution, depending on the size of the HIV net reproductive number, R. If R < 1, a newly intro- duced HIV population first grows but is then controlled by a population of activated HIV-specific T helper cells, and any perturbation leading to a greater HIV population is controlled. However, if any of the four parameters change so that R > 1 (in this example HIV's cytopathicity, c, was doubled) it becomes possible for a new or pre-existing HIV population to grow without control despite the pres- ence of activated HIV-specific T helper cells. However, even if R > 1, there are still stable equilibria along the half-line V = O, X = X* > g/e, so for some starting values of X and V, HIV is still controlled. Thus R > I is a necessary but not a sufficient condition for the development of AIDS. The model can be solved analytically following a method described elsewhere 2s, and this analytic solution also allows the derivation of a closed expression for the seperatrix (in Fig. b, the seperatrix divides values of X and Vthat will eventually lead to AIDS from values that will eventually lead to the con- trol of V). The parameter values used in (a) are: a = 50 000, c = 2, g = 200 000, e = 12. The values used in (b) are: a = 50 000, c = 4, g= 200 000, e = 12. The light lines with arrows are trajectories, the solid heavy lines are isoclines and the broken line is the seperatrix.

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Table 1. A classification of theories of the pathogenesls of HIV

Classification of mechanism

Proposed mechanism of pathogenesls

Immune activation HIV cytopathlclty HIV growth rate Immune efficiency (parameter a) (parameter c) (parameter g) (parameter e) Refs

Accumulated immune stimulation

Evolution of more virulent strains of HIV

Accumulated antigenic diversity

Evolution of epitopes not recognized by current immune responses ('escape mutants')

Exhaustion of HIV-specific naive CD4 ÷ cells ('panergic imnesia')

Slow destruction of antigen- presenting cells

Decreased

Decreased

Increased

Increased

Increased 8, 18, 19, 25, 26

Increased 9, 10, 40

Decreased

11

12, 13

15

16, 17

mutations in epitopes that render them unrecogniz- able to the cytotoxic T lymphocytes in those same patients. Others have found escape mutants with changes in antibody epitopes ~3. If large numbers of such escape mutants were to accumulate over time, without eliciting strong specific immune responses, it could be that the immune system's ability to control HIV would deteriorate, leading to overwhelming growth of HIV. This mechanism can obviously be classified as one of decreasing immune efficiency (Table 1). In order to distinguish the escape mutant theory of pathogenesis from the antigenic diversity theory it is necessary also to specify why the immune system should fail to respond (or respond poorly) to the escape mutants. Two suggested possibilities are" that antigen-presenting germinal centres become satu- rated with viral antigens from the initial viraemic phase~3; or that slowly growing strains of HIV, by

Box 3. A composite surrogate marker for disease progression

The great variability in the course of HIV infections makes it very difficult to predict the future course of any individual's disease. This raises particular problems in planning for future health-care needs and in assessing the impact of drugs. The HIV net reproduc- tive number, R, provides a natural candidate to use as a marker of the extent of an individual's disease: the closer an individual's R rises towards 1, the sooner they are predicted to progress to AIDS. The current best way to predict progression to disease is through the T helper lymphocyte count and a measure of immune

46 activation . in the simple model the T helper lymphocyte count would correspond to the quantity a/c, and measures of immune activation correspond to HIV's growth rate, g. The HIV net repro- ductive number implies that the best way to improve predictions would be to include some way of measuring the efficiency of the immune response in clearing HIV (parameter e), and that further improvements could be made by including a score for virulence (c and g), antigenic diversity (c), and follicular dendritic cell function (a).

preferentially infecting HIV-specific CD4 ÷ T lympho- cytes, disrupt the anti-HIV immune response TM.

Panerglc Imnesla The term 'panergic imnesia' is used to mean the wide- spread immune activation by gp120 (panergy), and the consequent failure to form memory lymphocytes (imnesia). The glycoprotein gp120 occurs on the coat of HIV virions, is shed from them and can bind to the CD4 molecules on the surface of T helper lympho- cytes. The panergic imnesia hypothesis is proposes that this binding delivers an aberrant stimulatory, signal to the lymphocytes, disrupting their ability to generate a pool of memory lymphocytes at the end of an immune response. Thus with each successive exposure to antigen, another set of clones of memory lymphocytes disappears. Eventually the ability to mount a proper anti-HIV response is lost because there are not enough HIV-specific memory T lymphocytes to draw upon. The HIV population then escapes from immune control. In the simple model this can be represented by a slow decrease in parameter a, the per-virion rate of generation of acti- vated, HIV-specific T helper lymphocytes (Table 1).

Destruction of antigen-presenting cells The final theory discussed here concerns a class of cells called follicular dendritic cells. These reside in the germinal centres of lymph nodes and play a cru- cial role in the presentation of antigen to other cells of the immune system. Histological studies 17 of germinal centres from HIV-infected individuals reveal that they contain large amounts of virus and that over the course of the incubation period follicular dendritic cells are lost 16. With the progressive destruction of these cells, activation of T helper lymphocytes be- comes progressively less efficient until HIV growth can no longer be controlled. This mechanism is classi- fied as a decreasing ability to activate HIV-specific T helper lymphocytes (Table 1).

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Apoptosis, superantigens and autoimmunlty The theories reviewed above address the question of why it takes, on average, ten years for AIDS to develop. Most of them do not address the manner in which HIV induces T helper lymphocyte depletion. This is a rich area for investigation. Only a small pro- portion of T helper lymphocytes is infected at any one time, which has led many authors to state that di- rect killing of infected lymphocytes cannot be respon- sible for their depletion. Theoretical and experimen- tal studies of HIV as a superantigen 42, an inducer of programmed cell death (apoptosis) 43 or an inducer of autoimmunity 44 all try to explain how uninfected T helper lymphocytes in HIV-infected individuals are destroyed. These studies have recently been reviewed elsewhere 4s.

Synergy between proposed mechanisms Each of these theories describes a mechanism whereby the balance of power between the immune system and HIV is shifted in HIV's favour. Although there are varying degrees of experimental data to sup- port the different mechanisms, they are not mutually exclusive. There is no reason to believe that any one of them is so potent a mechanism as to render the others unimportant, nor that the same mechanism domi- nates in every individual. These complexities may ex- plain why it has proved so difficulvto find biological markers that will give an accurate prognosis for an in- dividual. The simple model, which encompasses all of these theories, might help to solve this problem. Box 3 discusses some ideas about how R, the HIV net re-

productive number, could be used as the basis for the design of a theoretically motivated, composite surro- gate marker of disease progression.

The model described here summarizes in very broad terms the population dynamics of the interac- tion between HIV and the immune system, and helps an understanding of how the different theories of HIV's pathogenesis relate to each other. If it proves possible to design a surrogate marker of disease pro- gression based on R, the additional accuracy that this could add to predictions of the future course of an in- dividual's disease would be of considerable clinical value.

Acknowledgements I acknowledge the many useful discussions I have had with Professor R.M. May. This work was supported by The Royal Society and by Lady Margaret Hall, Oxford.

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• o f a t o

N ~ ibout

) all you our

ideas.

The winner o f ~ draw for a ~ ~ a r s~scription to the journal ~is:

Carlos J. Santos, Juncos, I~Jerto Rico.

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