Parasitology Today, vol. 8, no. 4, 1992 129

~ e

~o

I 0 I000 2000 3000

hours post infection

Fig. 3. As in Fig. I, except that a high titer of antibodies (2 x 10 a) against two early dominant VSGs pre-exists in the system when the corresponding VSGs begin to emerge.

response. A similar pattern may be obtained by assuming that antibody secretion follows a three-day delay for most, but not all, VSG variants. Displayed in Fig. 3 is the simulation of parasitaemia in a host in which antibody secretion begins three days following immune recognition for all VSGs, except for two early dominant VSGs, for which a high antibody titer pre-exists in the system. As a consequence, parasitaemia decays in less than three months. This result is not trivial, since in our model every individual parasite switches at random and the available repertoire includes 230 different VSGs. That is to say that, even though the emergence of two dominant variants is blocked by the immune system, many other variants do emerge. However, these are unable to sustain parasitaemia for very long, thus

leading to its termination before the VSG repertoire is exhausted. Note that such a pattern and, in fact, any persistent oscillations that are dominated by a few VSGs can be obtained only by assuming the existence of DE intermediates in the large majority of variants. To show this we have repeated the simulations presented in Fig. 3, except for one difference: now the probability that an individual parasite will go through the DE phase is reduced to 0.5 from 0.999, so that half of the population undergoes an instantaneous transition from the expression of one VSG to the next. Under the laker assumption, parasitaemia is characterized by one very high peak containing practically all the available VSG repertoire and a homogenous, slowly decaying infection thereafter (Fig. 4). Such a

~8

o iooo 2ooo 3pop hours post infection

Fig. 4. As in Fig. 3, except that the probability that an individual parasite will go through a brief DE intermediate phase is 0.5.

pattern is not known in real-life parasitaemias of African trypanosomiasis, and implies a role for the DE intermediates in these dynamics.

The theoretical results presented here suggest that host-specific parasitaemia profiles may result from host-specific immune interaction with the DE intermediates. These results further imply that, in some hosts, an early termination of parasitaemia may result from a pre-adaptation of the immune response to a few dominant VSG variants. A plausible explanation for this effect may be that the range of affinity maturation of the humoral response by hypermutation 3'4 is host specific. This hypothesis is now under theoretical examination in our group.

Acknowledgements I thank R. Maizels for helpful discussion, R. Mehr for technical assistance and the John D. and Catherine T. MacArthur Foundation for support.

References I Barry, i.D. and Turner, C.M.R. ( 1991 )

Parasitology Today 7, 207-21 I 2 Agur, Z., Abiri, D. and Van der Ploeg, L.H.T.

(1989) Proc. Natt Acad. Sci. USA 86, 9626-9630

3 Rajewsky. K. et al. (1989) Cold Spring Harbor Symp. Quant. Biol. 54, 209-217

4 Agur, Z., Mazor, G. and Meilijson, I. ( 1991 ) Proc. R. Soc. London Ser. B: 245, 147-150

Zvia Agur Department of Applied Mathematics and

Computer Science The Weizmann Institute of Science Rehovot 76100, Israel

Reply

One of the major goals for those modelling trypanosome infections mathematically is to simulate the rich variety of beqaviour displayed by these parasites. It is encouraging that the recently described model of Agur and colleagues t does demonstrate a rich range of behaviour and it is likely that continual refinement of this model, by incorporation of experimental observation, will lead to increased accuracy of simulation. To try to aid this process of refinement, we suggest that three areas in particular might warrant further investigation.

First, one of the cornerstones of any model of trypanosome growth must be the rate of antigenic variation. This is not 'relatively rare' in the populations that produce the wide range of parasitaemic profiles discussed in our recent paper 2. It is more frequent, by several orders of magnitude, than that measured for laboratory-adapted trypanosome lines 3.

Second, we presented, as merely one example of the variety of parasitaemic profiles recorded in the literature, the course of infection of a cloned trypanosome population in one cow. The extent to which the various model simulations accurately

reflect this parasitaemia is still open to debate. For instance, the simulations shown in the accompanying letter all seem to produce a distinct, sharp first peak of growth, whereas the example given has a complex first peak. The model of Agur and colleagues ~ is strongly influenced by the effect of the immune response on trypanosomes undergoing an antigenic switch and transiently expressing two variant surface glycoproteins (VSGs)(double expressors, or DEs). It is apparent that, to achieve the characteristic differences in parasitaemic profile between different host species, a hitherto unrecognized but somewhat unexpected feature of immune responses is incorporated into the model. This is the possibility that 'host-specific patterns of parasitaemia are due to host- specific interactions between the DE intermediates and the immune system'. In the absence of experimental evidence for such a difference between host species in antigen recognition capability, might it not instead be worth questioning the importance of DEs?

Third, we agree that time delays in the production of variable antigen type (VAT)- specific antibodies directed against a newly emerging VAT are likely to be important determinants of the dynamics of an infection, and Agur provides further

evidence to this effect. However, a comparison of parasitaemias in which the time delay is three and zero days, respectively, may not be as biologically relevant as investigating the effects of rather longer time delays likely to be present in native hosts.

We look forward to seeing a productive interplay between theoretical and experimental analyses developing in the near future, to the mutual benefit of all concerned.

References I Agur, Z., Abiri, D. and Van der Ploeg, L.H.T.

(1989) Proc. Notl Acad SOL USA 86, 9626-9630

2 Barry, J.D. and Turner, C.M.R. (1991) Parasitology Today 7, 207-21 I

3 Turner, C.M.R. and Barry, i.D. (1989) Parasitology 99, 67-75

David Barry Wellcome Unit of Molecular Parasitology and

Institute of Genetics University of Glasgow Church Street Glasgow G I I 5iS, UK

Michael Turner Laboratory for Biochemical Parasitology Department of Zoology University of Glasgow Glasgow G 12 8QQ, UK