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Infection and Immunity, December 2007, p. 5651-5662, Vol. 75, No. 12
0019-9567/07/$08.00+0 doi:10.1128/IAI.00970-07
Copyright © 2007, American Society for Microbiology. All Rights Reserved.

Department of Medical Microbiology, University of Nairobi, P.O. Box 19676, Nairobi, Kenya,1 Department of Infectious Disease Epidemiology, Imperial College London, Norfolk Place, London W2 1PG, United Kingdom,2 Department of Epidemiology, Institute of Public Health, University of Copenhagen, Blegdamsvej 2, 2200 Copenhagen, Denmark,3 National Institute for Medical Research, P.O. Box 9653, Dar es Salaam, Tanzania,4 DBL-Institute for Health Research and Development, Jaegersborg Alle 1D, 2920 Charlottenlund, Denmark5
Received 17 July 2007/ Returned for modification 20 August 2007/ Accepted 17 September 2007
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A number of previous workers have examined humoral immune responses to filariasis in areas where this infection is endemic, with the objective of more directly investigating the role of acquired immunity in shaping the epidemiology of infection. These studies unambiguously showed that W. bancrofti infection can induce strong antibody responses (4, 29, 32, 42, 47), but protective responses have not been conclusively identified yet. Recent theoretical analysis and evidence from other helminth infections (3, 9, 27, 28, 35, 36) suggest that one reason for this situation in the study of filariasis could be the paucity of studies that have used an immunoepidemiological perspective to investigate the role of acquired immunity in influencing parasitic infection patterns in host communities in areas where the organism is endemic. In particular, this perspective, which attempts to link observed individual host immune responses to epidemiological patterns, has shown how observation of an increasingly negative correlation between the levels of an immune response and the intensities of infection with increasing host age could indicate a protective role for the response being examined (10, 27, 48-50).
One difficulty in interpreting epidemiological age correlations between specific immune responses and parasite infection levels, however, is that these variables may be related to both age and exposure, which makes distinguishing between purely age effects and exposure-driven gain of protective immunity in immunoepidemiological investigations problematic (6, 27). Recent theoretical work has suggested that protective immunity in lymphatic filariasis may be dependent on the community transmission intensity, such that acquired immunity is manifest only in areas where there is higher transmission (24). Taken together, these observations suggest that (i) age-dependent associations between immune response levels and infection intensities can be expected to vary for communities with different mean transmission intensities and (ii) that taking a comparative immunoepidemiological approach to assessing age copatterns for communities in which transmission intensity differs is necessary for identifying and evaluating the role of protective immunity in regulating filarial infection in humans (3, 14, 16, 17, 24, 25, 27, 28, 48).
We present here results from one such comparative immunoepidemiological analysis in which we focused on comparing observed age relationships between filarial specific antibody responses and W. bancrofti intensity in a community with low parasite transmission intensity in coastal East Africa with the relationships observed in a community in the same region with a higher transmission intensity (25, 39, 43). One feature of the analyses reported here was the use of a combined empirical data analysis and mathematical modeling approach for investigating mechanisms that may underlie the observed differences in the age patterns of parasite-specific antibody responses between communities exposed to different transmission pressures (24, 25, 50, 51). We also contrasted the use of univariate and multivariate statistical methods in the empirical analyses of the data to distinguish between single and combined effects of the antibodies examined in regulating W. bancrofti infection. Our results are discussed below in terms of both the role of humoral responses in the generation of immunity to this important tropical parasitic disease and the design and analysis of studies for investigating acquired immunity to parasitic infections in human communities.
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Parasitological examination. Briefly, blood sampling for parasitological examination started at 2100 h due to the nocturnal mf periodicity in the study area. From each individual, 100 µl of finger prick blood was collected in a heparinized capillary tube and transferred to a tube with 1 ml of 3% acetic acid. Specimens were later examined in a counting chamber with a microscope, and the number of mf/ml was recorded, as described previously (43).
Preparation of serum. Immediately after finger prick blood sampling, 5 ml of venous blood was collected in plain Vacutainer tubes. Serum was separated by centrifugation after overnight clotting in a refrigerator, and sodium azide was added to a concentration of 15 mM as a preservative. Serum was initially frozen at –20°C in the field and was later stored at –80°C in the main laboratory until use. Before further handling and testing of sera, 3 µl/ml tri-N-butyl phosphate (catalog no. T-4908; Sigma) and 10 µl/ml Tween 80 (catalog no. P-1754; Sigma) were added to eliminate lipid-coated virus (33).
CFA.
Serum specimens were examined for the presence of CFA by using a TropBio enzyme-linked immunosorbent assay kit (catalog no. 03-010-01; TropBio Ltd. Pty., Townsville, Australia). The test was performed according to the procedures recommended by the manufacturer and described previously (41). Serum specimens with optical density values of
standard 2 (
32 antigen units) were considered positive for CFA, and specimens with optical density values of
standard 7 were assigned a fixed value of 32,000 CFA units.
Measurement of filaria-specific antibodies. Sera were examined for the presence of filaria-specific immunoglobulin G1 (IgG1), IgG2, IgG3, IgG4, and IgE antibodies with an enzyme-linked immunosorbent assay. The methods used for preparation of antigen from Brugia pahangi adult worms recovered from experimentally infected jirds (Meriones unguiculatus) and for conducting the specific antibody assays have been described in detail previously (13).
Data analysis.
Only data from individuals who were examined for the presence of mf, CFA, and all the filaria-specific antibodies selected for investigation in this study (IgG1, IgG2, IgG3, IgG4, and IgE) were included in the data analysis. All response data (mf, CFA, and specific antibody levels) were log10 transformed (x + 1) to approximate normally distributed residuals before statistical analyses were performed. Description and comparison of age-infection and antibody level patterns within and between the two communities were done by fitting generalized linear models (GLM) with Gaussian distributed errors, using age and community as independent variables and log-transformed mf, CFA, or specific antibody values as responses. Variations in the shape of the age-intensity profiles for each of these responses between the two communities were determined by testing for significance of the age and community interaction term (22). Sequential sums of squares were used in calculating the F values for significance testing (27). We assessed epidemiological age associations between the antibody responses and mf or CFA intensities using two complementary approaches. The first approach was based on univariate statistical methods that essentially attempted to evaluate the effects of one antibody at a time to determine the role that each antibody played independently in regulating Wuchereria infection. This was accomplished via calculation of Pearson partial correlations between infection intensity and antibody variables within five age classes constructed to reflect the age structures of the two study communities (35), with tests for assessing heterogeneity in correlation coefficients between age classes carried out using methods described by Sokal and Rohlf (44). This was followed by an attempt to evaluate all the antibody effects simultaneously to determine their joint contributions to host regulation of worm intensity. This analysis was performed not only to obviate the statistical problems associated with multiple testing of numerous explanatory immunological variables (e.g., the five different antibody types) and with multicolinearity or correlation between multiple explanatory variables (45) but also in recognition of the growing belief that joint effects between multiple immunological parameters are likely to determine the outcome of parasitic infection (2, 15, 26, 40). Multivariate analysis was carried out in this study by performing a principal component regression analysis (23). Essentially, this method entailed reducing the multivariate correlated antibody response data into main independent composite components first and then assessing and comparing the relationship between the derived two or three major components and infection intensity in the young age class (<30 years) versus the older age class (
30 years) in each community, using individual host scores for each of these components as explanatory variables in linear regressions with log CFA levels as the response (5).
Mathematical modeling. We constructed a simple mathematical model using the results and insights gained from the empirical data analyses (described below) to investigate and illustrate how transmission and adult worm intensity variables interacting at the individual host level may generate and hence explain the observed age patterns of specific antifilaria antibody responses in communities in which the organism is endemic with different transmission levels. Given the empirical results regarding the main categories or types of antibody-age response observed in the data (see below), we modeled three major antibody response patterns: (i) a pattern perhaps embodying the observed IgG4 response (antibody response type 1), (ii) a pattern likely shown by the observed IgG3 response (antibody response type 2), and (iii) a pattern perhaps indicated by the IgG1, IgG2, and IgE responses (antibody response type 3). The specific structure of the model, the set of coupled differential equations describing the model, and the parameter values used in the simulations carried out in this report are described in detail in the Appendix.
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TABLE 1. Age-stratified characteristics of the populations in Masaika and Kingwede examined for the presence of filaria-specific antibodies (IgG1, IgG2, IgG3, IgG4, and IgE)
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FIG. 1. Age-specific intensities of (A) mf counts (Mf) and (B) CFA units (AU) observed in different host age classes in Masaika (filled bars) and Kingwede (open bars). The bars indicate geometric means, while the error bars indicate the standard errors of the means. The values for mf counts and CFA units for Kingwede were multiplied by 10 to enable clearer comparisons with the markedly higher infection intensity values obtained for individuals in Masaika. Age class 1, 1 to 4 years; class 2, 5 to 9 years; class 3, 10 to 14 years; class 4, 15 to 19 years; class 5, 20 to 29 years; class 6, 30 to 39 years; class 7, 40 to 49 years; class 8, 50 to 59 years; and class 9, 60 years.
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TABLE 2. Statistical results from Gaussian GLM fits for assessing the effects of community and age on infection and antibody levels: F values and their levels of significance for the main effects of community and age and the community-age interaction effect
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FIG. 2. Age-associated geometric mean filaria-specific IgG1, IgG2, IgG3, IgG4, and IgE levels in Masaika () and Kingwede ( ). Panel F shows the mean IgG4/IgE ratios obtained for each age class in the two study communities. The error bars indicate standard errors of the means. Age classes are defined in the legend for Fig. 1.
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Age associations between individual antibody levels and mf or CFA intensities. The results describing the individual or univariate associations between infection intensity and W. bancrofti-specific antibody levels in relation to the ages of individuals from the two study communities, based on the age-stratified Pearson product moment partial correlation test, are shown in Tables 3 and 4. This test determines the correlation between host infection intensity and a specific antibody level after any joint effects due to the responses of the other antibody isotypes examined are controlled for (13). Hence, it essentially examines the independent effects of each antibody in regulating parasite infection intensity. Correlations were determined for five discrete age classes, chosen both to give adequate sample sizes within each age group and to provide a clear reflection of the study populations in each community (compare Table 1 with Tables 3 and 4), and are shown for specific antibody associations with both mf- and CFA-based infection variables in the case of Masaika and only for CFA levels (see above) for Kingwede. In Masaika (Table 3), the values for the estimated partial correlations indicate that there was a broadly negative association between specific IgG1, IgG2, IgG3, and IgE responses and filarial infection intensity (either mf or CFA) in all age classes examined, with the strength of the negative association rising from the youngest age class and then declining among the older age groups. This pattern, however, was significant only for the specific IgG1 response to either of the worm intensity variables examined (the test of heterogeneity of correlation coefficients was significant for both mf and CFA [Table 3]), although, as expected (given that antibodies in this study were measured against adult worm antigens), there was some indication of a more prominent negative association between specific IgG3 and IgE levels and CFA intensity than between these antibody levels and mf levels. By contrast, specific IgG4 intensities were positively correlated with infection intensity in all age classes, with no apparent age patterns, although again the response was found to be more prominent in relation to CFA than in relation to mf intensity (Table 3). Although the estimated correlations were lower and the age patterns were more variable, a similar pattern of a decreasing negative association between CFA intensity and specific IgG1, IgG2, IgG3, and IgE with increasing mean host age was also observed for Kingwede (Table 4), with the notable difference that this pattern was found to be significant for IgG3 and IgE by comparison with the corresponding findings for these antibodies in Masaika (Table 3). The IgG4 levels and CFA intensity were again positively correlated for all age classes, and there was some indication that the strength of association may increase with mean host age (Table 4).
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TABLE 3. Partial correlation coefficients for filaria-specific antibody levels and individual host infection intensities in different age classes of the examined population in Masaika
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TABLE 4. Partial correlation coefficients for filaria-specific antibody and individual host CFA levels in different age classes of the examined population in Kingwede
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TABLE 5. Results of the principal component analysis of the filaria-specific antibody data
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FIG. 3. Relationship between individual host intensity of CFA and scores for the first three principal components (PCI) in hosts who were less than 30 years old (A, C, and E) and hosts who were 30 years old or older (B, D, and F) in Masaika ( ) and Kingwede ( ). The y axes show the log CFA values, while the x axes indicate individual host scores contributing to principal components 1 (A and B), 2 (C and D). and 3 (E and F) (see text). The lines represent the linear regression model predictions of the relationship between log CFA values and the corresponding principal component scores for hosts from Masaika (solid lines) and Kingwede (dotted lines). The relationship was positive between infection intensity and principal component 1 scores but negative in the case of the relationships for principal component 3 in both communities. For principal component 2, the association was negative for Masaika but positive for Kingwede. Most associations were significant; the only exception was the relationship between CFA and principal component 2, where the observed negative association was significant only in individuals who were 30 years old or older in Masaika (Table 6).
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TABLE 6. Coefficients of linear regression of host CFA intensity (log values) on the first three principal component scores
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FIG. 4. Age-specific IgG4, IgG3, and IgE responses in (A) a low-transmission community and (B) a high-transmission community as a function of transmission intensity and worm burden, as simulated by the model described in the appendix incorporating generative mechanisms suggested by the empirical analyses of the data carried out in this study (see text). Panel C shows the predictions of the model for the expected age-specific IgG4/IgE ratios in each of the communities (solid line, high-transmission community; dashed line, low-transmission community) arising from the proposed mechanisms of generation of these antibody types. In contrast to previous observations, the simulated profiles are in accord with the findings of changes in this ratio in the two study populations.
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However, it is apparent that this differential infection pattern was only weakly observed in this study, supporting our previous conclusion that the transmission intensities observed in the current study communities may be below the threshold required to induce strong population-level protective immune responses (25). Age exposure differences also cannot be totally excluded in confounding the present observations (6, 24, 27, 51), although it is plain that such vector biting patterns would have to be considerably different in the two study communities in order to significantly influence the differences observed in the corresponding age profiles of infection.
The immunoepidemiological rationale for comparing age intensities of infection with corresponding age profiles of specific antibody responses in communities with different transmission intensities is that any intercommunity discordance between such profiles, especially in older subjects, is thought to provide not only a more direct sign of the occurrence of acquired immunity (3, 10, 27, 28, 46, 48) but also identification of which of the specific immune components examined may potentially be a marker of such immunity. More specifically, it is hypothesized that the correlation between immune responses and infection intensity changes with both transmission intensity and host age; the association is expected to be positive in young children because both infection and immune responses reflect exposure, but as the hosts age, the association becomes negative as the immune response gained via cumulative exposure starts to regulate worm intensities (3, 28, 51). Implicit in this hypothesis is that this epidemiological age effect of acquired protective immunity should be manifest or should be greater in communities with higher transmission intensities (1, 48).
Age certainly had a significant effect on the amount of all the specific antibodies examined in Masaika, but it appeared to have a differential effect on antibody production in the low-transmission community, Kingwede. Thus, while in both communities host age affected the specific IgG1, IgG3, and IgG4 responses, it did not influence the generation of specific IgG2 and IgE by hosts in Kingwede. Together with the finding that the mean levels of specific IgG1, IgG2, IgG4, and IgE were also significantly lower in Kingwede, this lack of a host age effect on the generation of IgG2 and IgE in this community may reflect the requirement for a higher cumulative transmission or infection intensity threshold in the age generation of these antibodies compared to the other antibody isotypes (Fig. 2).
Despite this difference in the production of antibodies, a notable finding was that when the age patterns of the specific antibody responses examined were assessed singly, none of them appeared to strongly support expectations for a clear role in fostering acquired immunity to filariasis infection in either study community. Thus, in Masaika, the mean levels of specific IgG1, IgG2, and IgE were higher in the youngest age groups but then declined gradually with age. The mean levels of IgG3 were also generally low and changed only slightly with increasing age. By contrast, the mean levels of specific IgG4 increased with age and reached a plateau in the older age groups. Similarly, in Kingwede, while the mean intensities of specific IgG1 and IgG4 appeared to follow a pattern similar to that seen in Masaika, the age-specific mean levels of IgG2, IgG3, and to a lesser extent IgE either increased linearly with age (IgG3) or increased linearly and reached a plateau in older hosts (IgG2 and IgE). Thus, based on simple assessments of age patterns, either the antibody responses examined in this study appeared to mirror the age profile of infection, as in the case of specific IgG4 or IgG2, IgG3, and IgE responses in Kingwede, or the dominant pattern consisted of a higher response in younger age groups when the mean infection levels were low, which appeared to decline with age even as the infection intensities rose in those age classes (as shown by the IgG1, IgG2, and possibly IgE responses in Masaika). Most previous studies have also generally shown that the specific antifilaria antibody levels are higher in younger age groups than in older age groups, although the differences have rarely been significant (4, 11, 12, 42, 47).
A similar counterintuitive finding regarding the levels and age patterns of the specific antibody response to infection also pertains to the patterns observed for the specific IgG3 response in the present study communities. Thus, while in the high-transmission community the levels of IgG3 appeared to change slightly with age, in the low-transmission community the levels were not only remarkably higher but also increased linearly with age. Furthermore, we also found evidence that despite the lower response in the high-transmission village, these antibodies appeared to have an effect on worm intensity that was more negative than the effect when their levels were much higher under low-transmission conditions (Tables 3, 4, and 6; Fig. 4). The reasons for this striking inverse relationship with exposure intensity and the observed between-community impact of this isotype is not clear, but the data suggest either that the effects of this antibody are manifest only at lower levels coupled with a complex down-regulatory role for exposure intensity under high-transmission conditions or that this finding is an artifact of closely linked changes in some other effective component of the immune response. Further studies, perhaps specifically focusing on specific IgG3 responses in parallel with cellular components known to be associated with the IgG3 response (7) in communities with very different transmission intensities, are warranted if we are to successfully dissect the role of IgG3 in regulating filariasis infection (13).
In contrast to the specific IgG1, IgG2, and IgE responses, the mean levels of IgG4 in both communities increased with age, and the rate of increase was higher in the high-transmission community. This finding clearly mirrors previous observations (12, 20) and is perhaps not surprising since IgG4 levels are generally thought to be positively associated with the presence and intensity of infection (4, 13, 19, 29, 42). The converse age response patterns for specific IgG4 and IgE appear to also underlie the finding in this study that the mean IgG4/IgE intensity ratio varied positively with both transmission intensity and increasing host age, an observation contrary to previous suggestions that in lymphatic filariasis this ratio may be a measure of the strength of immunological resistance to infection and hence expected to be low in the presence of resistance and vice versa (18). If the previous suggestions are correct and the IgG4/IgE ratio is indeed an indicator of resistance, then our findings imply that resistance to infection in bancroftian filariasis is not affected by age. Alternatively, as we have suggested previously, this finding may suggest that the IgG4/IgE ratio may not be a good indicator of resistance to filarial infection (13).
The major finding of interest emerging from carrying out the partial correlation analysis of the effects of the examined filaria-specific antibody responses on parasite intensity is that apart from the overwhelmingly positive specific IgG4 response with infection intensity, the responses of all the other isotypes assessed in both communities were generally found to be negatively associated with host infection intensity irrespective of host age (Tables 3 and 4). This pattern persisted regardless of which infection indicator, mf or CFA intensity, was examined and thus appears to be contrary to theoretical expectations regarding the involvement of antibodies in acquired immunity to filariasis, viz., that antibodies should become more negatively associated with infection intensity as hosts age. Closer inspection of the data also revealed a pattern in which the negative associations with infection observed for each of these isotypes increased from the younger age classes to peak among individuals belonging to the fourth or fifth age decades before declining in the oldest age groups. This nonlinearity appears to support theoretical predictions that interpreting immunity-helminth infection correlations is complicated by specific aspects of the immune response to parasitic infection (50) or that immunity to filariasis infection may be more complex than immunity to other helminths (16, 21, 31, 37, 38, 40). For example, one explanation for the nonlinear negative association of antibody response with infection intensity by host age observed in this study could be that immunity fostered by the specific IgG1, IgG2, IgG3, and IgE response to filariasis may be highest when parasite intensities are either low or moderate during early infection but that as parasite intensities increase with host age, these responses (IgG1, IgG2, and IgE [Fig. 2]) or their impact (IgG3) may be actively suppressed, as has been observed for intestinal nematodes (34). Indeed, such immunological down-regulation with increasing duration of exposure to the parasite (30, 32) has been suggested to be important in filariasis in protecting the host from the more pathological outcomes of infection (16, 17). Interestingly, transmission intensity did not appear to overly influence the individual effects of filaria-specific antibodies, although whether the effects differ in areas with transmission intensities higher than that observed in Masaika remains to be investigated (25).
The above findings give the impression that none of the antibodies studied here are particularly protective or are makers of protective immunity in older individuals. A key finding of this study, however, is that this conclusion, arising from considering only the independent effects of antibody responses, may be premature as it manifestly ignores the influence of interactions and joint effects of the different isotypes that may collectively affect infection intensity (2, 26, 40, 46). Such joint or networked effects among immune components are increasingly thought to be a major factor in determining the outcomes of parasitic infections (15), suggesting that accounting for multivariate immunological effects may be essential for any reliable evaluation of the role of specific antibodies in engendering resistance to filarial infection.
Indeed, our attempt to address this problem by using principal component analysis (5, 46) produced two significant outcomes. First, the results indicated that the specific antibody response to CFA infection (and hence presumably to adult worms) may be dominated by three major response types, including (i) a response reflecting a IgG4 type of reactivity, (ii) a response representing a IgG3 type of reactivity, and (iii) a host phenotype in which higher specific production of IgG1, IgG2, and IgE is countered by lower IgG4-IgG3 generation (Table 5). Second, regression analysis of the relationship between host CFA intensity and the scores obtained for each host for each of these three composite responses confirmed findings from a univariate correlation analysis for the occurrence of a positive association of filarial infection with the IgG4 response and a negative association in individuals exhibiting a heightened specific IgG1, IgG2, and IgE response but a lower specific IgG4 and IgG3 response. The analysis, however, also uncovered two further outcomes that were not revealed by simple correlation analysis. First, the results showed that the specific IgG3 response had a contrasting effect on host CFA levels in the two study communities. Thus, despite the markedly higher levels of specific IgG3 produced by individuals from the low-transmission community (Kingwede), the association of this antibody type with CFA appeared to be positive irrespective of the age class. By contrast, the opposite pattern, a much lower but negative response (which became significant in older individuals), was observed for individuals from Masaika. A second important finding revealed by this analysis, in direct contrast to the results obtained from the correlation analysis, was that the combined IgG1, IgG2, and IgE response was also found to be more negatively associated with worm intensity or CFA levels in older hosts. This and the fact that the magnitude of this association was also higher in the high-transmission community thus indicate that these responses have a role in fostering acquired immunity to filarial (adult) parasites. This is despite the fact that their absolute production declined in older hosts (Fig. 2). These findings provide a key new insight regarding the role of humoral immunity in filariasis, viz., that acquired immunity can be generated through these antibodies but that it perhaps is due more to their composite effects than to separate effects.
The objective of using simple mathematical models in this study to describe the population dynamics of antifilaria antibody responses was not to test or validate the developed model but rather to use it to qualitatively evaluate the mechanistic explanations derived from empirical data analyses regarding the roles of exposure and worm intensity in the generation of these antibodies. This work was predicated primarily on the observation that often mechanistic explanations derived from a purely empirical or statistical analysis of data may not generate observed community patterns owing to problems with scale and the effects of nonlinear interactions between suggested variables that could lead to counterintuitive results at the population level (8). The predictions of our model, which incorporated suggested mechanisms for the production of an IgG4-type response, an IgG3-type response, and an IgE-type response, however, show that in the present case the proposed mechanisms can indeed qualitatively explain the differences in the patterns of these antibody responses observed between our low- and high-transmission communities. In particular, given reasonable parameter values (see Table A1 in the Appendix), the results demonstrate that differences in the linearly increasing age profiles of IgG4 between our communities may arise simply as a direct function of differences in adult worm dynamics, whereas in the case of IgG3 the high linearly increasing age pattern in the low-transmission community compared to the much lower response that varied slightly with age in the high-transmission community was largely due to the effects of negative feedback on antibody production by transmission intensity. In the case of the specific IgE-type response, the simulations suggest that the differences observed between the two study communities, particularly the finding that these antibody types were lower in the low-transmission community and only slightly higher in the high-transmission community with a plateau-type relationship with host age (Fig. 2E and 4A and B), were a function of strong down-regulation of antibody production by high adult worm numbers. We were also able to show that the mechanisms underlying the specific IgG4 and IgE responses can explain the contrary finding of a positively increasing pattern of IgG4/IgE ratios observed in our study communities.
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TABLE A1. Parameter definitions and values used in the simulations shown in Fig. 4
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) and decreases both at a natural per capita rate (µ1) and at rates (ß1 and ß2) reflecting the detrimental effects of antibody response types 2 and 3 on worm survival acting proportional to worm intensity in each case. Antibody response type 1 (IgG4) is modeled simply to increase at a rate (
1) proportional to W and to decrease at a constant natural decay rate (µ2). By contrast, antibody response type 2 (IgG3) is modeled to increase at a rate (
2) proportional to both
and W, but the increase is down-regulated in a nonlinear exponential manner as the transmission rate increases. This antibody response type decreases at a rate (µ3) due to natural decay and as a result of (negative) interaction with W given by the term ß3WG3. Similarly, antibody response type 3 (IgE) increases with age as a linear function of W, and the increase is then down-regulated in an exponential fashion at higher worm loads. The antibody is removed at a natural decay rate (µ3) and through interaction with W according to the term ß4WE. Hence, the full model is:
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This work received financial support from the International Cooperation with Developing Countries Program of the European Communities (contract ERBIC18CT970257 held jointly by P.E.S., E.M., M.N.M., and B.B.A.E.) and the DBL-Institute for Health Research and Development (Denmark). E.M. was supported by a Medical Research Council fellowship (United Kingdom), and W.G.J. was supported by a fellowship from the Danish Agency for Development Assistance (Danida).
Published ahead of print on 1 October 2007. ![]()
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