Children growing up in malaria-endemic regions exhibit a gradual accumulation of protective antibodies to different variant surface antigens (VSAs) expressed on parasite-infected erythrocytes. The most well-characterized VSA is PfEMP1 (P. falciparum erythrocyte membrane protein 1), believed to be a major target of naturally acquired immunity (Bull et al. 1998). Each parasite genome contains approximately 60 var genes encoding different PfEMP1 variants (Gardner et al. 2002), and these are expressed sequentially in a mutually exclusive manner during infection. Var genes exhibit extremely high levels of diversity on a population level. This appears to be due to both sexual recombination in the mosquito and frequent ectoptic recombination between var genes on non-homologous chromosomes (Ward et al. 1999; Freitas-Junior et al. 2000; Taylor et al. 2000). Attempts to classify the vastly diverse var genes into meaningful groups based on genomic data have led to the identification of approximately six different var groups based on upstream promoters, direction of transcription and chromosomal position (Kraemer & Smith 2003; Lavstsen et al. 2003, 2005; Kraemer et al. 2007; Kyes et al. 2007). Another study analysing small var sequence ‘tags’ from wild isolates has shown that the proportional representation of these var fragments from different groups (using a slightly different sequence-based classification system) appears to be maintained between different parasite genomes, although their expression patterns in different hosts vary considerably (Bull et al. 2005). Furthermore, analysis of whole var repertoires from three sequenced genomes (Kraemer & Smith 2003; Kraemer et al. 2007) and a considerable number of var sequence tags from wild isolates has revealed a recombination hierarchy that constrains recombination within different groups to some extent (Bull et al. 2008).

Simple mathematical models predict that variant-specific immune responses to P. falciparum may lead to a parasite population that is structured into distinct antigenic types, or strains, with non-overlapping repertoires of var epitopes by means of immune selection (Gupta et al. 1996, 1998). Assuming that the parasite population is composed of discretely circulating strains of varying prevalence and virulence explains several features of malaria epidemiology, including the rapid acquisition of protection against severe disease. This ‘discrete strain’ hypothesis has proved contentious, however, and competing hypotheses range from those suggesting that var genes are completely randomly distributed, to those arguing that significant but variable overlap exists between parasite var repertoires (Giha et al. 1999; Chattopadhyay et al. 2003). Unfortunately, testing these ideas remains extremely challenging for several technical reasons. First of all, the locations of antigenic epitopes within the majority of var genes remain elusive (although see Dahlbäck et al. (2006) and Andersen et al. (2008) for bioinformatic analysis of epitope regions within the conserved var gene associated with placental binding in pregnant women). Furthermore, var diversity makes the design of universal primers problematic, so most sequencing projects focus on the analysis of small sequence fragments rather than whole genes. It is important to note here that simply observing some level of sequence conservation within certain regions of particular var gene families does not contradict the discrete strain hypothesis. Understanding the results of these projects is also hampered by the complex and variable expression patterns of var genes during infection and in vitro. Serological data, by contrast, provide direct information about relationships between the expression of antigenic epitopes and host responses. Here, we attempt to develop a set of tools to dissect these data with a view to extending these methods to eventually allow us to link the genetic structure of var sequence fragments to patterns of parasite recognition among patients from endemic regions.

Numerous studies comparing the antibody responses of hosts to their own (homologous) and others' (heterologous) parasites have addressed the question of population structure at the serological level by exploring levels of cross-reactivity between isolates (Marsh & Howard 1986; Forsyth et al. 1989; Iqbal et al. 1993; Chattopadhyay et al. 2003). The patterns of parasite recognition generated by these comparisons are generally presented in the form of a chequerboard of agglutination assays, measuring the difference in antibody titre at the time of acute disease and during convalescence (see appendix A). The chequerboard from the largest study of this kind, involving Kenyan children (Bull et al. 1999), is shown in figure 1a. Serological studies of this kind have concluded that patients tend to generate antibodies primarily to the VSAs of their own (homologous) parasite, although some cross-reactive responses have been noted (Bull et al. 1999; Chattopadhyay et al. 2003) and certain parasites are particularly well recognized by heterologous sera (Bull et al. 1999, 2000; Nielsen et al. 2004). These observations of both isolate-specific and cross-reactive immune responses have not been satisfactorily linked to the competing hypotheses about parasite population structure described above, however, partly because the relationships between cross-reactive responses are difficult to examine quantitatively using the chequerboard representation of the data.

Both networks were significantly different from random expectations for many of the metrics examined, and showed structural features associated with an interesting ‘source–sink’ pattern of parasite recognition. Table 1 illustrates these features. Both had a significantly lower level of reciprocity and a higher level of transitivity than expected, for example, and were associated with a significantly higher variance in both k_in and k_out as compared with the random networks. In other words patients tended to show both acute and increasing responses to many or few parasites, and particular parasites were either responded to very commonly or very rarely. It is important to note that the interpretations of the acute and response networks are fundamentally different. Acute networks correspond to the existing recognition of parasite isolates at the time of sampling, and we make the assumption that this reflects the previous exposure of patients to particular antigenic determinants. By contrast, response networks are generated by subtracting the pre-existing ‘acute’ response from the ‘convalescent’ response detected 3 weeks later, and represent antibody titres that are stimulated by the presence of particular antigens during current infections.

Our analysis showed that k_out for the response network was significantly positively correlated with multiplicity of infection, or the number of distinct parasite clones identified in the patient (R²=0.45, p=0.022), whereas k_in was not (p=0.609). This is expected since patients harbouring more parasite genotypes are exposed to a larger var pool during infection, generating increasing antibody responses to a broader range of parasites than patients with fewer parasites. The large range of k_in values, on the other hand, can be attributed to three isolates (numbered 1026, 1029 and 1032 in the original study) which have k_in values of 5, 5 and 6, respectively (all other isolates have k_in values of 0 or 1). Although these three isolates have been previously identified as being ‘commonly recognized’ by acute sera (Bull et al. 1999), and display high k_in values within the acute network accordingly, their role in generating the high variance within the response network requires a different explanation and will be discussed further below.

The ordered infection model yielded different network structures from random expectations, whereas the random infection model did not. The ordered model produced networks with extremely low reciprocity, high transitivity, high variance in k_in and k_out, and a significantly higher density of ‘feed-forward’ loops than expected by chance. Table 2 illustrates the difference between the randomly rewired networks and those simulated under the two different infection processes, as well as the striking structural similarities between the networks generated by the ordered model of infection and the acute network. Intuitively, one would expect these characteristics from a hierarchical infection process. As an example, a patient infected by an isolate ‘higher up’ (for example isolate A) in the hierarchy would recognize one ‘lower down’ (isolate B), but this would not be reciprocated (hence low reciprocity). In addition, the patient infected by isolate A would recognize all isolates below B (e.g. isolate C); the patient infected by isolate B would therefore also be expected to recognize isolate C. Thus, the feed-forward loop A→B→C and A→C is found at high densities and transitivity is high.

Three different simplified population structures were examined, as well as the effects of random or ordered expression of different var genes. The population structures modelled were as follows: var repertoires could be (i) discrete with non-overlapping combinations of var genes, in accordance with the theoretical models of Gupta et al. (1996, 1998) described above; (ii) randomly drawn from a global pool of circulating var genes, assuming repertoires have been randomized by recombination; or (iii) an intermediate structure combining both these hypotheses, in which each parasite genotype contains a few ‘common’ var genes that are expressed early in infection (Lavstsen et al. 2005) and are discretely structured due to strong immune selection, and many ‘rare’ var genes drawn randomly from a global pool (this hypothesis is based on ideas generated by Bull et al. (1999, 2000) see electronic supplementary material for further explanation). For each population, it was then assumed that var gene expression occurred either in a particular order or randomly (see appendix A for more details).

For all three populations, the models most compatible with the data were those with ordered rather than random var expression. Without ordered var expression, no source–sink structure occurred and transitivity remained low for all three populations—thus some of the features that the response network shared with the hierarchical infection model described in §4 are in this case due to hierarchical expression patterns. It is important to note that variable infection lengths are also important in generating the structures observed in the real network (see electronic supplementary material).

We propose that there are different levels of immune selection occurring on different groups of var genes, which could lead to the intermediate var repertoire structure described above. Here, relatively common vars will be structured into discrete, non-overlapping combinations by immune selection, since they are expressed first and by many isolates, and only these restricted combinations will be observed. This hypothesis is compatible with the observation that the group A var family appears to be relatively restricted, and it will be testable once the epitope regions of these vars have been elucidated (Jensen et al. 2004). The relative restriction of diversity among the common genes may also be explained by functional constraints with respect to binding particular host receptors—it has been suggested that commonly recognized var genes are optimized for rapid growth among non-immune hosts (Bull et al. 1999), also explaining the apparent association of specific subsets of vars with severe disease (Rottmann et al. 2006; Kyriacou et al. 2007). Under our hypothesis, the remaining var genes within each genome are not under the same immune selection pressure and therefore do not show the same discrete structure, and will be relatively randomly distributed between genotypes. We conjecture that these var genes may also be less functionally constrained, accounting for their diversity.

Bull et al. (2008) have generated networks of var gene fragments, in which each gene fragment is a node and edges connecting genes are exact sequence matches (see figure 6). This network of var sequences forms two main clusters characterized by dense within-cluster links and loose between-cluster connections. The smaller lobe appears to be primarily made up of Group A var genes, which form a dense ‘polymorphic block-sharing group’, whereas the larger lobe appears to be composed of both B and C vars (based on the classification system of Lavstsen et al. (2003) and Kraemer et al. (2007)). The recombination hierarchy evidenced by this structure is consistent with our models. We suggest that if the subset of vars in the group A block-sharing group is expressed often and is highly immunogenic, immune selection may act to structure it into discrete strains. By contrast, the majority of var genes in each repertoire (belonging to groups B and C) may not be expressed to the same extent and would not be under the same level of immune selection. The effects of this type of partitioned var repertoire on the overall level of var diversity and the development of immunity to disease have recently been explored theoretically (Recker et al. 2008). These models showed that the partitioning of var repertoires not only limited the level of diversity achievable through recombination, but could also explain the rapid acquisition of immunity to severe disease despite the vast diversity of var sequences observed. A better understanding of the link between var groups and disease phenotype is needed to confirm the implications of a recombination hierarchy for patterns of immunity and disease, however.

Our analysis also supports the idea that var gene expression patterns within hosts are ordered, to some extent, rather than random. Although theoretical models (for a review see Frank & Barbour 2006) and empirical studies (Horrocks et al. 2002, 2004) have shown that some level of ordering of expression of different var genes is probably needed to maintain antigenic variation within the host, others have concluded that var genes are expressed randomly (for example Fernandez et al. 2002). The hierarchical structure of the response network, and the fact that low reciprocity between heterologous responses was consistently observed in these data, suggest some intrinsic ordering in expression is likely. The role of the host immune system in the orchestration of these expression patterns is not known, however, and probably plays an important part in determining the order of appearance of different variants (Recker et al. 2004).