INTRODUCTION
Concomitant infection of a host by disparate parasite or pathogen species can pose a multi-pronged challenge for the immune system: how should the cells and molecules of the immune system be allocated amongst the simultaneous responses required by concomitant infection? Experimental immunology has provided a wealth of data on the optimal T-helper cell responses to single-species infections (reviewed in Mosmann & Sad, 1996; Romagnani, 1996; Infante-Duarte & Kamradt, 1999), and, to some extent, on responses to dual infections (e.g. Marshall et al. 1999). Some theoretical work has explored the proliferation of T-helper cells in response to infection (e.g. Morel, Kalagnanam & Morel, 1992; Schweitzer, Swinton & Anderson, 1993; Fishman & Perelson, 1999). There has, however, been no attempt to synthesize the empirical data into a general theory of the optimal allocation of T-helper cells among concomitant infections. The optimality model presented here represents just such an attempt at synthesis. Specifically, the question that the model poses is: can the best T-helper response to concomitant infection (i.e. the response that minimizes host morbidity) be predicted from the empirically-determined optimal T-helper responses to each of the component infections? A test of the model against empirical data is under way.
The induced subset of T-helper cells determines which effector mechanisms will act against infection, so these cells (and their associated cytokines) have an important role in determining immune response efficacy (Infante-Duarte & Kamradt, 1999; Janeway et al. 1999). Generally speaking, for each parasite or pathogen, there is a corresponding ‘optimal’ T-helper/cytokine response that fights infection most efficiently and with least pathology. T-helper type 1 (Th1) cells produce pro-inflammatory cytokines and mediate cytotoxicity by effectors such as killer T cells and macrophages. T-helper type 2 (Th2) cells, on the other hand, produce cytokines that help to stimulate antibody production by B cells and to recruit effectors such as eosinophils. Th1 cells generally work best against intracellular parasites/pathogens, whereas Th2 cells tend to generate effective responses against extracellular parasites/pathogens (Sher & Coffman, 1992; Mosmann & Sad, 1996; Romagnani, 1996) (but see Allen & Maizels, 1997). The empirically-determined optimal T-helper response to a single-species infection is here defined as the response that maximizes host survival or minimizes morbidity in mouse model systems.
The T-helper response might likewise determine the outcome of concomitant infection. Importantly, the T-helper subsets tend to be mutually downregulatory (Sher & Coffman, 1992; Janeway et al. 1999); that is, a Th1 cell produces cytokines that discourage its neighbours from becoming Th2 cells, and vice versa. It is therefore difficult for the immune system to ‘do both’, at least within a given site, and conflicts among T-helper response requirements might arise when different types of responses are required simultaneously. Empirical data suggest that concomitant infection can indeed lead to T-helper response synergies or conflicts, depending on which effector mechanisms are required to clear each infection (Brunet, Dunne & Pearce, 1998). Response synergies (e.g. the induction of Th2-dominated responses by both schistosomes and intestinal nematodes) may decrease the pathological impact of concomitant infection (Curry et al. 1995). Response conflicts (e.g. simultaneous requirements for a Th1-dominated response against Toxoplasma and a Th2-dominated response against Schistosoma), on the other hand, might exacerbate disease (Marshall et al. 1999). Given this potential for T-helper synergy or conflict, how are T-helper cells allocated in a host infected with multiple parasite/pathogen species? Are they allocated in a manner that may be predicted from the optimal responses to each component (single-species) infection?
An optimality model is a useful analytical tool for the exploration of resource allocation problems in biology (Parker & Maynard Smith, 1990). The model proposed here, grounded in empirical data from experimental immunology, generates testable hypotheses about optimal T-helper responses to concomitant infection. Given ‘local’ (single-infection) immune response optima from the empirical database, the model proposes a ‘global’ optimization scheme for the case of concomitant infection. Whether or not this simple model can accurately predict the best T-helper response to concomitant infection, the process of testing optimality hypotheses will inform our understanding of the complexities of the immune system.
MODELLING METHODS AND RESULTS
Summarizing the immune response in one variable
The first step in the modelling process was to formulate a quantitative summary of the complex network of interactions that comprise an immune response. Summarizing an immune response in one variable allows quantitative comparisons among immune responses, across hosts and across infections. Because immune responses actually fall out along a continuum of cytokine and effector combinations rather than into a qualitative (Th1 versus Th2) dichotomy (Allen & Maizels, 1997), a continuous variable may indeed be the best way to characterise a T-helper response to infection.
Here, the summary variable t is defined as the proportional representation of T-helper type 1-associated cytokines in the total cytokine pool. Focusing upon interferon-gamma (IFN-γ) as a driver of Th1 responses and interleukin 4 (IL-4) as a driver of Th2 responses, the systemic T-helper response may be quantified in terms of their relative concentrations:
An IFN-γ-driven (Th1) response will make t approach 1, whereas an IL-4-driven (Th2) response will make t approach 0. The variable t is thus a measure of the extent to which the immune response is skewed toward Th1 or Th2. This formulation of t can be used to summarize the type of immune response mounted against a single-species infection or against a suite of infections.
Establishing a common immunological currency (such as summary variable t) does have costs. One difficulty with t is that it glosses over details of multi-component immune responses (such as the contribution of non-Th cells to the cytokine milieu). The systemic formulation of t also ignores the site specificity of immune responses, although t could easily be scaled down to the organ or tissue level. Finally, t is problematic in that the formulation is sensitive to details of cytokine choice and measurement. Cytokines other than IFN-γ and IL-4 might, for example, better characterize certain immune responses. Any cytokines included in the calculation of t have to be of similar order of magnitude, and all must be measured in metric (rather than antibody manufacturers') units. For all of these reasons, equation (1) may ultimately require refinement. It may even prove better to focus upon cell numbers (via flow cytometric analysis of the T-helper cell populations themselves) rather than cytokine concentrations. As a first attempt, however, t stands as a working summary of immune system action. Empirical data on optimal murine responses to infection may readily be summarized via equation (1) and then incorporated into the model described below.
An optimality model for immune responses to concomitant infection
Can the best T-helper response to concomitant infection (i.e. the response that minimizes morbidity) be predicted from the empirically-determined optimal T-helper responses to each component infection? The model is based on two principles: (a) that an optimal response to concomitant infection will minimize divergence of the joint response from each of the single-infection optima (which would predict a simple average response); and (b) that the divergence of the joint response from each local optimum should be weighted by the consequences of mounting a sub-optimal response to each of the component single infections.
The optimal value of t maximizes survival w(t), as follows:
where n = the number of parasites/pathogens co-infecting a host; ti = the optimal immune response to the ith parasite; and αi = the consequences of a sub-optimal response to the ith parasite. Each ti may be empirically determined in mouse model systems: the value of t that maximizes host survival or minimizes morbidity may be called the optimal response to infection. Alternatively, the mean value of t expressed by hosts could be construed as the optimum, with the standard deviation as a measure of the importance of mounting the correct response to a given parasite. In this way, weighting factor αi may be estimated from data – for example, as the inverse of the variance about the empirically-determined optimum. Another possibility is that αi could be estimated from the relationship between morbidity or mortality and a spectrum of immune responses, t. Data on infected gene-knockout mice could provide this information on the pathological consequences of sub-optimal immune responses (i.e. ones outside the spectrum of Wild-type responses). It is important to note that the magnitude of αi is liable to vary from infection to infection. That is, the importance (to host survival and health) of getting the immune response exactly right is not the same for all parasites/pathogens. Where there is a larger ‘margin for error’, the weighting factor αi would be smaller.
Solving for the optimal t for concomitant infection results in:
The model based on weighted minimization of divergence from local optima thus predicts a weighted average response as the optimal immune response to concomitant infection: the average of all ti weighted by the penalties for getting each response wrong. The weighted-average hypothesis may be tested against empirical data on immune responses in concomitantly-infected mice.
DATA SETS FOR TESTS OF THE MODEL
Some experiments in mouse model systems are targeted at responses to concomitant infection. Uninfected and singly-infected animals serve as controls for the concomitantly-infected animals, and researchers routinely measure cytokine concentrations, Th1/Th2 cell population sizes, and/or cytokine-encoding mRNA quantities, and host survival and morbidity. A single experiment may thus simultaneously generate estimates of ti and αi for single-species infections as well as data on the immune response against concomitant infection (tco) that may be compared with t*.
Concomitant infection by the parasites Schistosoma mansoni and Toxoplasma gondii will provide the first test of the weighted-average hypothesis. The optimal immune response against T. gondii infection is dominated by Th1 cells and Th1-associated cytokines (Denkers & Gazzinelli, 1998). The optimal response to S. mansoni infection, on the other hand, is Th2 dominated (Brunet et al. 1998). For concomitant infection by disparate parasites such as these, the distributions of ti will be non-overlapping. The model described above can generate formalized, quantitative (and hence readily testable) predictions about where the joint response tco will fall along the spectrum of immune responses between the Toxoplasma and Schistosoma extremes. This test of the model is under way.
DISCUSSION
Can immune responses to concomitant infections be understood directly from first principles – the mechanistic understanding of single infection optimal responses – or are there emergent properties? If a simple weighted-average hypothesis (equation (3)) accurately predicts the best response to concomitant infections, then single-infection immune response data may provide sufficient information to enable us to understand the immunology of concomitantly-infected hosts. Experiments on concomitant infections are necessarily more complicated and difficult to carry out than single-species infections. It would be valuable to know whether we can learn about immune responses to concomitant infections by simply combining the results on the component single-species infections. If, on the other hand, the weighted-average hypothesis fails to predict tco mounted against concomitant infections (i.e. there are emergent properties of the infection interaction), then further mathematical analysis can help to tease apart the key factors that might make the dynamics of concomitant infections differ from the sum of their component single infections. Order of infection and the intensity of each infection are particularly likely to affect immune responses to concomitant infection.
Through this optimality modelling approach, we might learn more about the complexities of the immune system, including the extent to which immune response-mediated interactions among infections might affect disease outcome, vaccine or treatment efficacy, and the like. Concomitant Schistosoma-Toxoplasma infections have been shown to exacerbate progression of both diseases, probably via enhanced immunopathology (Marshall et al. 1999). A mathematical investigation of the optimality of immune responses to concomitant Schistosoma-Toxoplasma infections would bring us a step towards a better understanding of emergent immunopathological outcomes of concomitant infection. Much remains to be done to develop this line of thinking, but it appears to be a promising approach to the difficult problem of concomitant infection.
My thanks go to the lab groups of E. Y. Denkers and E. J. Pearce for their many contributions to the development of these ideas. H. K. Reeve and S. E. Roberts were of great assistance in developing the optimality model. I also thank F. E. G. Cox, C. D. Harvell, and A. F. Read for encouraging me in this work. A.L.G. is a pre-doctoral fellow of the Howard Hughes Medical Institute.
