Allelic recombination and linkage disequilibrium within Msp-1 of Plasmodium falciparum, the malignant human malaria parasite

The C-terminal, cysteine-rich 19kDa domain of merozoite surface protein-1 (MSP-1) of Plasmodium falciparum is a target of the host's humoral immunity and thus a malaria vaccine candidate. Although variation in the 19kDa domain is limited among parasite isolates, tertiary structure-dependent intramolecular associations between the 19kDa domain and other parts of MSP-1 are suggested to be involved in immune evasion by allowing competitive binding of protective and non-protective antibodies directed to their epitopes, which are conformationally in close proximity but separated at the primary structure. Since allelic recombination can account for the major variability of the Msp-1 gene, we examined whether linkage disequilibrium occurs between polymorphic loci in the 5'- and the 3'-region, the latter encoding the 19kDa domain. From 184 Thai field isolates, we selected 69 isolates with a single allelic type in six variable blocks of Msp-1 as determined by PCR-based allelic typing. All the isolates showed no evidence of recombination in blocks 6 to 16, whereas recombination was apparent in blocks 2 to 6. Sequencing of the 3'-region revealed two potential recombination sites in block 17. Strong linkage disequilibrium was seen between polymorphic loci in the 5'- and 3'-regions. The strength of this disequilibrium did not correlate with distance between loci. We discuss the possible role of epistatic selection on particular association types (haplotypes) of Msp-1.     

Limited recombination events in merozoite surface protein-1 alleles of Plasmodium falciparum on islands.

Intragenic recombination is a principal mechanism for the generation of allelic variation in the merozoite surface protein-1 gene (Msp-1) of the human malaria parasite Plasmodium falciparum. In the present study, linkage disequilibrium between the 5'- and 3'-polymorphic sites was analyzed to determine the frequency of recombination events in Msp-1 in parasite populations on four islands in Vanuatu, the southwestern Pacific, where malaria transmission is moderate and comparable to other mesoendemic areas. Of 141 isolates, whose 5'-haplotypes (Msp-1 blocks 2-6) were determined by PCR-based typing, 138 were successfully sequenced for the 3'-polymorphism (block 17). A total of four distinct 5'-haplotypes and three distinct 3'-sequence types were identified with apparently different frequency distribution among islands. The number of 5'-haplotypes in each island was one to four, far smaller than in other previously studied geographic areas (ten to 21). Associations between the 5'- and 3'-polymorphisms (here termed Msp-1 gene types) were subjected to the R(2) linkage disequilibrium test. The test revealed complete or very strong linkage disequilibrium in all four islands. Mixed infection was unusually rare (2.1%) and the mean number of Msp-1 alleles per person was nearly 1.0. The heterozygosity of the Msp-1 gene type calculated for each island (h=0.41-0.65) was significantly lower than that in other areas of comparable endemicity (h=0.81-0.89) (P<0.01). These results indicate that recombination events in Msp-1 would be extremely limited in Vanuatu, and stress that the frequency of recombination in Msp-1 is determined by not only the intensity of malaria transmission but the frequency of mixed clone infections, the mean number of clones per person and a repertoire of clones in a local area.     

Evolution of recombination due to random drift

In finite populations subject to selection, genetic drift generates negative linkage disequilibrium, on average, even if selection acts independently (i.e., multiplicatively) upon all loci. Negative disequilibrium reduces the variance in fitness and hence, by Fisher's (1930) fundamental theorem, slows the rate of increase in mean fitness. Modifiers that increase recombination eliminate the negative disequilibria that impede selection and consequently increase in frequency by "hitchhiking." Thus, stochastic fluctuations in linkage disequilibrium in finite populations favor the evolution of increased rates of recombination, even in the absence of epistatic interactions among loci and even when disequilibrium is initially absent. The method developed within this article allows us to quantify the strength of selection acting on a modifier allele that increases recombination in a finite population. The analysis indicates that stochastically generated linkage disequilibria do select for increased recombination, a result that is confirmed by Monte Carlo simulations. Selection for a modifier that increases recombination is highest when linkage among loci is tight, when beneficial alleles rise from low to high frequency, and when the population size is small.     

Background selection and population differentiation

A general analytical formula is derived, which predicts the effects of background selection on population differentiation at a neutral locus as a result of its linkage with selected loci of deleterious mutations. The theory is based on the assumptions of random mating, multiplicative fitness, and weak selection in hermaphrodite plants in the island model of population structure. The analytical results show that Fst at the neutral locus increases as a result of the effects of background selection, regardless of the dependence or independence among linked background selective loci. The increment in Fst is closely related to the magnitude of linkage disequilibria between the neutral locus and selected loci, and can be estimated by the ratio of Fst with background selection to Fst without background selection minus one. The steady-state linkage disequilibrium between a neutral locus and a selected locus in subpopulations, primarily attained by gene flow, decreases with the recombination rate, and can be enhanced when there are dependence among linked selected loci. Monte Carlo computer simulations with two- and three-locus models show that the analytical formulae perform well under general conditions. Application of the present theory may aid in analyzing the genome-wide mapping of the effect of background selection in terms of Fst.     

Joint linkage and linkage disequilibrium mapping in natural populations

A new strategy for studying the genome structure and organization of natural populations is proposed on the basis of a combined analysis of linkage and linkage disequilibrium using known polymorphic markers. This strategy exploits a random sample drawn from a panmictic natural population and the open-pollinated progeny of the sample. It is established on the principle of gene transmission from the parental to progeny generation during which the linkage between different markers is broken down due to meiotic recombination. The strategy has power to simultaneously capture the information about the linkage of the markers (as measured by recombination fraction) and the degree of their linkage disequilibrium created at a historic time. Simulation studies indicate that the statistical method implemented by the Fisher-scoring algorithm can provide accurate and precise estimates for the allele frequencies, recombination fractions, and linkage disequilibria between different markers. The strategy has great implications for constructing a dense linkage disequilibrium map that can facilitate the identification and positional cloning of the genes underlying both simple and complex traits.     

Selection for recombination in structured populations

In finite populations, linkage disequilibria generated by the interaction of drift and directional selection (Hill-Robertson effect) can select for sex and recombination, even in the absence of epistasis. Previous models of this process predict very little advantage to recombination in large panmictic populations. In this article we demonstrate that substantial levels of linkage disequilibria can accumulate by drift in the presence of selection in populations of any size, provided that the population is subdivided. We quantify (i) the linkage disequilibrium produced by the interaction of drift and selection during the selective sweep of beneficial alleles at two loci in a subdivided population and (ii) the selection for recombination generated by these disequilibria. We show that, in a population subdivided into n demes of large size N, both the disequilibrium and the selection for recombination are equivalent to that expected in a single population of a size intermediate between the size of each deme (N) and the total size (nN), depending on the rate of migration among demes, m. We also show by simulations that, with small demes, the selection for recombination is stronger than both that expected in an unstructured population (m = 1 - 1/n) and that expected in a set of isolated demes (m = 0). Indeed, migration maintains polymorphisms that would otherwise be lost rapidly from small demes, while population structure maintains enough local stochasticity to generate linkage disequilibria. These effects are also strong enough to overcome the twofold cost of sex under strong selection when sex is initially rare. Overall, our results show that the stochastic theories of the evolution of sex apply to a much broader range of conditions than previously expected.     

The Genetic Structure of Natural Populations of DROSOPHILA MELANOGASTER Xiii. Further Studies on Linkage Disequilibrium

The Raleigh, North Carolina, population of Drosophila melanogaster was examined for linkage disequilibrium in 1974, several years after previous analyses in 1968, 1969, and 1970. alphaglycerol-3-phosphate dehydrogenase-1 (alphaGpdh-1), malate dehydrogenase-1 (Mdh-1), alcohol dehydrogenase (Adh), and hexokinase-C (Hex-C, tentative name, F. M. Johnson, unpublished; position determined by the present authors to be 2-74.5) were assayed for 617 second chromosomes, and esterase-C (Est-C) and octanol dehydrogenase (Odh) were assayed for 526 third chromosomes. In addition, two polymorphic inversions in the second chromosomes [In(2L)t and In(2R)NS] were examined, and the following findings were obtained: (1) No linkage disequilibrium between isozyme genes was detected. Significant linkage disequilibria were found only between the polymorphic inversions and isozyme genes [In(2L)t vs. Adh, and In(2R)NS vs. Hex-C]. Significant disequilibrium was not detected between In(2L)t and alphaGpdh-1, which is included in the inversion, but a tendency toward disequilibrium was consistently found from 1968 to 1974. The frequency of two-strand double crossovers within inversion In(2L)t involving a single crossover on each side of alphaGpdh-1 was estimated to be 0.00022. Thus, the consistent but not significant linkage disequilibrium between the two factors can be explained by recombination after the inversion occurred. (2) Previously existing linkage disequilibrium between Adh and In(2R)NS (the distance is about 30 cM, but the effective recombination value is about 1.75%) was found to have disappeared. (3) No higher-order linkage disequilibrium was detected. (4) Linkage disequilibrium between Odh and Est-C (the distance of which was estimated to be 0.0058 +/- 0.002) could not be detected (chi(2) (df=1) = 0.9).-From the above results, it was concluded that linkage disequilibria among isozyme genes are very rare in D. melanogaster, so that the Franklin-Lewontin model (Franklin and Lewontin 1970) is not applicable to these genes. The linkage disequilibria between some isozyme genes and polymorphic inversions may be explained by founder effect.     

Dynamics of linkage disequilibrium in bacterial genomes undergoing transformation and/or conjugation

Bacteria may undergo recombinational exchange either by conjugation followed by crossing over, or by transformation of small segments of DNA into the cell followed by incorporation into the chromosome by gene conversion. These two forms of recombination may have very different consequences on the patterns of linkage disequilibrium seen within bacterial genomes. In this paper deterministic recursions are obtained for three linked loci in populations having these two forms of recombination. Both neutral genetic variation and the case of one selected gene are considered. It is shown that the two forms of exchange have identical consequences on two-locus linkage disequilibria, but that three-locus disequilibria can have different behaviors. Hitchhiking also has different consequences on the pattern of disequilibrium seen between linked neutral genes in the region of the selected locus. Inference of the relative importance of these two modes of recombination from static samples of DNA sequences will hinge on the relationship between linkage map distance and disequilibria.     

Variances and covariances of squared linkage disequilibria in finite populations

Analysis of linkage disequilibrium D among restriction sites or bases in DNA sequences, arising from mutations in finite populations, depends on a knowledge of the variance-covariance structure of measures such as D2 between different pairs of sites. This requires evaluation of the eighth moments of gene frequencies among two, three, and four loci, and the necessary methodology is derived here and results are computed. While primary emphasis is placed on disequilibrium arising from mutation or gene conversion, the methodology also allows for the joint effects of only drift and recombination. Numerical results confirm that squared linkage disequilibria can have high variances and covariances.     

Linkage Disequilibrium in Natural and Experimental Populations of Drosophila Melanogaster

We have studied linkage disequilibrium in Drosophila melanogaster in two samples from a wild population and in four large laboratory populations derived from the wild samples. We have assayed four polymorphic enzyme loci, fairly closely linked in the third chromosome: Sod Est-6, Pgm, and Odh. The assay method used allows us to identify the allele associations separately in each of the two homologous chromosomes from each male sampled. We have detected significant linkage disequilibrium between two loci in 16.7% of the cases in the wild samples and in 27.8% of the cases in the experimental populations, considerably more than would be expected by chance alone. We have also found three-locus disequilibria in more instances than would be expected by chance. Some disequilibria present in the wild samples disappear in the experimental populations derived from them, but new ones appear over the generations. The effective population sizes required to generate the observed disequilibria by randomness range from 40 to more than 60,000 individuals in the natural population, depending on which locus pair is considered, and from 100 to more than 60,000 in the experimental populations. These population sizes are unrealistic; the fact that different locus-pairs yield disparate estimates within the same population argues against the likelihood that the disequilibria may have arisen as a consequence of population bottlenecks. Migration, or population mixing, cannot be excluded as the process generating the disequilibria in the wild samples, but can in the experimental populations. We conclude that linkage disequilibrium in these populations is most likely due to natural selection acting on the allozymes, or on loci very tightly linked to them.     

Allozymic Variation and Linkage Disequilibrium in Some Laboratory Populations of DROSOPHILA MELANOGASTER

Nine laboratory populations of D. melanogaster were surveyed by starch gel electrophoresis for variation at 17 enzyme loci. A single-fly extract could be assayed for all 17 enzymes, so that the data consist of 17-locus genotypes.--Pairwise linkage disequilibria were estimated from the multilocus genotypic frequencies, using both Burrows' and Hill's methods. Large amounts of linkage disequilibrium were found, in contrast to the results reported for natural populations.-Knowledge of the approximate sizes of these populations was used to compare the observed heterozygosities and linkage disequilibria with predictions of the neutral allele hypothesis. The relatively large amount of linkage disequilibrium is consistent with the small sizes of the populations. However, the levels of heterozygosity in at least some populations suggest that some mechanism has been operating to retard the rate of decay by random drift. Several examples of significant deviation from Hardy-Weinberg frequencies and the large amount of linkage disequilibrum present in these populations indicate that a likely mechanism is selective effects associated with neutral alleles because of linkage disequilibrium with selected loci (e.g., "associative overdominance"). The results are therefore consistent with both neutralist, and selectionist hypotheses, but suggest the importance of considering linkage disequilibrium between neutral and selected loci when attempting to explain the dynamics of enzyme polymorphisms.     

Meiosis and the evolution of recombination at low mutation rates

The classical understanding of recombination is that in large asexual populations with multiplicative fitness, linkage disequilibrium is negligible, and thus there is no selective agent driving an allele for recombination. This has led researchers to recognize the importance of synergistic epistatic selection in generating negative linkage disequilibrium that thereby renders an advantage to recombination. Yet data on such selection is equivocal, and various works have shown that synergistic epistasis per se, when left unquantified in its magnitude or operation, is not sufficient to drive the evolution of recombination. Here we show that neither it, nor any mechanism generating negative linkage disequilibrium among fitness-related loci, is necessary. We demonstrate that a neutral gene for recombination can increase in frequency in a large population under a low mutation rate and strict multiplicative fitness. We work in a parameter range where individuals have, on average, less than one mutation each, yet recombination can still evolve. We demonstrate this in two ways: first, by examining the consequences of recombination correlated with misrepaired DNA damage and, second, by increasing the probability of recombination with declining fitness. Interestingly, the allele spreads without repairing even a single DNA mutation.     

Evidence for Linkage Disequilibrium Maintained by Selection in Two Natural Populations of DROSOPHILA SUBOBSCURA

One island and one mainland population of Drosophila subobscura were found polymorphic at the XDH (xanthine dehydrogenase) and the AO (aldehyde oxidase) loci. It was observed that one allele at the XDH locus, which has a low frequency in both populations, is nonrandomly associated with the alleles at the AO locus. Two lines of evidence support the thesis that this linkage disequilibrium is due to epistasis rather than random drift: (1) D or r, measures of the disequilibrium, have the same sign and magnitude in both populations. (2) The linkage disequilibrium is not due to inversions. Inversions segregating on the chromosome carrying XDH and AO have been separated into two classes, between which exchange of alleles at the two loci is suppressed. Linkage disequilibrium for XDH and AO was observed within each class. In the absence of any exchange of alleles, these disequilibria must have arisen and been maintained independently. The suggestion is made that the epistatic disequilibrium results from the close structural and physiological relationship which exists between the two enzymes.     

A global perspective on genetic variation at the ADH genes reveals unusual patterns of linkage disequilibrium and diversity

Variants of different Class I alcohol dehydrogenase (ADH) genes have been shown to be associated with an effect that is protective against alcoholism. Previous work from our laboratory has shown that the two sites showing the association are in linkage disequilibrium and has identified the ADH1B Arg47His site as causative, with the ADH1C Ile349Val site showing association only because of the disequilibrium. Here, we describe an initial study of the nature of linkage disequilibrium and genetic variation, in population samples from different regions of the world, in a larger segment of the ADH cluster (including the three Class I ADH genes and ADH7). Linkage disequilibrium across approximately 40 kb of the Class I ADH cluster is moderate to strong in all population samples that we studied. We observed nominally significant pairwise linkage disequilibrium, in some populations, between the ADH7 site and some Class I ADH sites, at moderate values and at a molecular distance as great as 100 kb. Our data indicate (1) that most ADH-alcoholism association studies have failed to consider many sites in the ADH cluster that may harbor etiologically significant alleles and (2) that the relevance of the various ADH sites will be population dependent. Some individual sites in the Class I ADH cluster show Fst values that are among the highest seen among several dozen unlinked sites that were studied in the same subset of populations. The high Fst values can be attributed to the discrepant frequencies of specific alleles in eastern Asia relative to those in other regions of the world. These alleles are part of a single haplotype that exists at high (>65%) frequency only in the eastern-Asian samples. It seems unlikely that this haplotype, which is rare or unobserved in other populations, reached such high frequency because of random genetic drift alone.     

The deviation from linkage equilibrium with multiple loci varying in a stepping-stone cline

The balance between the creation of associations between alleles at different loci by immigration and the convergence to linkage equilibrium due to the recombination process is studied in a theoretical model. The geographical structure of the model is a stepping-stone chain of populations linking two genetically constant source populations. The model assumes an arbitrary number of autosomal loci and considers genetic variation (two alleles at each locus) that is not subject to natural selection. The gene frequencies at each locus will then show a linear cline through the stepping-stone chain of populations. The deviation from linkage equilibrium through the stepping-stone cline is characterized by an equation for linear measures that provide the linkage disequilibrium measures for a given set of loci in terms of the gene frequencies and the linkage disequilibria in the source populations and in terms of the linkage disequilibrium measures through the cline for lower numbers of loci. Numerical examples of this iterative solution are given, and it is shown that the build-up of the higher order Bennett-disequilibria through the cline is considerably more pronounced than the build-up of two-locus disequilibria.     

Expected Linkage Disequilibrium for a Neutral Locus Linked to a Chromosomal Arrangement

The expected value of the squared linkage disequilibrium is derived for a neutral locus associated with a chromosomal arrangement that is maintained in the population by strong balancing selection. For a given value of recombination, the expected squared linkage disequilibrium is shown to decrease as the intensity of selection maintaining the arrangement increases. The transient behavior of the expected square linkage disequilibrium is also derived. This theory applies to loci that are closely linked to inversions in Drosophila species and to loci closely linked to the differential segments of the translocation complexes in ring-forming species of Oenothera. In both cases the strong linkage disequilibria that have been observed in natural populations can be explained by random drift.     

Distinguishing recombination and intragenic gene conversion by linkage disequilibrium patterns

Deterministic theory suggests that reciprocal recombination and intragenic, interallelic conversion have different effects on the linkage disequilibrium between a pair of genetic markers. Under a model of reciprocal recombination, the decay rate of linkage disequilibrium depends on the distance between the two markers, while under conversion the decay rate is independent of this distance, provided that conversion tracts are short. A population genetic three-locus model provides a function Q of two-locus linkage disequilibria. Viewed as a random variable, Q is the basis for a test of the relative impact of conversion and recombination. This test requires haplotype frequency data of a sufficiently variable three-locus system. One of the few examples currently available is data from the Human Leukocyte Antigen (HLA) class I genes of three Amerindian populations. We find that conversion may have played a dominant role in shaping haplotype patterns over short stretches of DNA, whereas reciprocal recombination may have played a greater role over longer stretches of DNA. However, in order to draw firm conclusions more independent data are necessary.     

Association studies under general disease models

There is great expectation that the levels of association found between genetic markers and disease status will play a role in the location of disease genes. This expectation follows from regarding association as being proportional to linkage disequilibrium and therefore inversely related to recombination value. For disease genes with more than two alleles, the association measure is instead a weighted average of linkage disequilibria, with the weights depending on allele frequencies and genotype susceptibilities at the disease loci. There is no longer a simple relationship, even in expectation, with recombination. We adopt a general framework to examine association mapping methods which helps to clarify the nature of case-control and transmission/disequilibrium-type tests and reveals the relationship between measures of association and coefficients of linkage disequilibrium. In particular, we can show the consequences of additive and nonadditive effects at the trait locus on the behavior of these tests. These concepts have a natural extension to marker haplotypes. The association of two-locus marker haplotypes with disease phenotype depends on a weighted average of three-locus disequilibria (two markers with each disease locus). It is likely that these two-marker analyses will provide additional information in association mapping studies.     

Simulation of the effect of population size on the evolution of the recombination fraction

A study, by means of computer simulation, has been performed on the evolution of recombination rate modifier genes in a system with three diallelic loci (A, B and C). The locus C, selectively neutral, is responsible for the modification of the recombination fraction between the major loci (A and B) which are subjected to selection. Two models have been analysed, the modifier allele being recessive in one of them, and codominant in the other, with infinite and finite populations. Distinct initial genic frequencies of the major loci and different selection coefficients have been utilised. We have found that the frequency of the allele which favours recombination increases in finite populations, and decreases slightly in infinite populations. These results are consistent with previous theory; presumably, selection favours alleles reducing recombination between epistatically interacting loci in a infinite population, since this reduces the breakup of advantageous combinations of alleles. However, in finite populations, selection favours the breakup of the random linkage disequilibria which are produced by random drift.     

haplotypes identified by DNA polymorphisms at the apolipoprotein A-1 and C-III loci and hypertriglyceridaemia

Summary A Japanese group comprising 40 hypertriglyceridaemic and 35 normolipidaemic subjects were genotyped for two intragenic DNA restriction fragment length polymorphisms (RFLPs) at the A-1 and C-III gene loci. An Sst-1 polymorphism is located at the 3 end of the C-III gene and a Msp-1 polymorphism in the third intron of the A-1 gene. The polymorphic restriction sites are 3.8kb apart. The polymorphism with Sst-1 was present at allelic frequencies of 0.67 (S1 allele) and 0.33 (S2 allele), and the polymorphism with Msp-1 was present at allelic frequencies of 0.55 (M1 allele) and 0.45 (M2 allele). The alleles S1, S2, M1, and M2 are in linkage disequilibrium and three haplotypes were identified S1-M1, S1-M2, and S2-M2. Unlike the previously reported association of the S2 allele with hypertriglyceridaemia found in Caucasians there was no difference in the frequency of S2 allele between normolipidaemic and hyperlipidaemic Japanese. However one of the haplotypes S1-M2 was significantly increased in the hypertriglyceridaemic subjects (32% versus 11% P>0.025). Thus in Japanese there is an association with genotypes at this locus and hypertriglyceridaemia but with a different haplotype than in Caucasians.