F. Macciardi
Institute of Clinical Psychiatry, Milan Medical School, Ospedale S. Paolo, 20142 Milan, Italy
The linkage problem and linkage studies in recent years are a great focus in genetic research, because of their potential importance in giving us the opportunity to better understand the inner genetic mechanisms at the chromosomal level, and thus allowing us to direct our attention to the hypothetical biological basis of the etiological processes of the disease. Segregation analysis may also give us reliable hypotheses about the genetic structure underlying affective disorders (10), but in any case the strongest evidence that they are primarily inherited (as opposed to culturally inherited), short of identifying a specific biochemical gene product, is to demonstrate genetic linkage to a well-defined marker (5). Ideally, the marker is itself an inherited characteristic that is polymorphic (i.e., it exists in two or more discrete forms that could be commonly found in the population), has a well-established and clearly understood mode of inheritance, is stable over time (not state dependent), is reliably detectable, and has been localized to a particular chromosomal region. Genetic linkage, then, is present when two or more loci are in close proximity on the same chromosome, so that genes residing at these loci fail to obey Mendel’s law of independent random assortment, and the degree of linkage is expressed in terms of recombination fraction (THETA). In a simplified way, THETA is a measure of the frequency that homologous chromosomes recombine in the region bounded by the two loci during meiosis. In this chapter we are particularly interested in the possible existence of a linkage between the Manic Depressive Illness (MDI) and the HLA system. The rationale of choosing the HLA system as a marker rests on two main points: (a) the HLA complex satisfies the requirements for a marker system probably better than any other potential marker (15), and (b) different investigators have suggested that one or more loci in the proximity of the HLA complex are capable of increasing susceptibility to affective disorders (13). There is at present a great debate about this point, and we will discuss later the effective role of the HLA complex in eliciting susceptibility to different diseases.
When looking at data describing possible relationships between the HLA system and affective disorders, we can see that population studies, however, show a critical disagreement among various researchers about the existence of such an association (Table 1). Apart from negative results, it should be noted that there is no increase or decrease in common antigens in all the reports cited in Table 1 [modified from Tiwari (15)]. The same results hold true when we try to analyze the data according to partitioning criteria, with the aim to obtain more homogeneous subgroups of the disease. We can see in Tables 2 and 3 [modified from Tiwari (15)] the results regarding the subdivision according to diagnostic criteria, that is, unipolar versus bipolar. The unipolar-bipolar dichotomy introduces the concept of heterogeneity as a main point in data analysis, but it also introduces a theoretical and pragmatical problem: Has the heterogeneity observed at a phenotypic level a corresponding genetic background or must the phenotypic heterogeneity be viewed as a confounding factor that obscures more complex and hidden patterns in which either 
genetic or nongenetic factors play different roles? Thus far, grouping patients into various categories according to different criteria, such as positive or negative family history for the disease, has led to inconclusive results, whereas, on the contrary, we can observe that pooling data from different populations reveals no heterogeneity as depicted in Table 4 [modified from Tiwari (15)]. As a matter of fact, the chi-square for heterogeneity is not significant, with the total chi-square for the relative ratio strongly significant and thus indicating a significant association between MDI and HLA-BW16, even though it is made up by apparently dishomogeneous groups, tested for the presence of a particular antigen in locus В (BW16). In the absence of any specific hypothesis of genetic transmission of the disease, however, the result must be viewed merely as an association of phenotypic characters. At present, population studies really cannot offer unequivocal solutions to the linkage problem that can be best studied with family data and adequate methodologies. When searching for linkage, in fact, we always face the problem that we are not dealing with qualitative data only, such as presence or absence of an all-or-none trait, but that we have to take into account the genetic pattern of
MDI, that is, in practical terms, the formal genetic parameters of a semiquantitative trait. Since the optimal approach to linkage is the Maximum Likelihood Lod-score method that incorporates sequential analysis (7), and given that the exact mode of inheritance for MDI is not fully understood, even though we think that the most likely hypothesis is the presence of a Single Major Locus (SML) (11), we ought to evaluate several assumptions required by the lod-score method before applying the test to our data. Probably the most complete and one of the most precise ways of proceeding with a linkage analysis has been described in an article by Kruger et al. (6); they also were able to find a result strongly supportive of linkage with HLA, obtaining a lod-score of 3.901 with a recombination fraction of 10% (THETA = 0.10). The result was obtained summing the lod-score values for each family studied at the same THETA value, under a series of different assumptions. Obviously the most favorable set of parameters leading to the best result was employed, apart from their adherence to the true biological reality, since the aim of the work was mainly to demonstrate the possibility of having a linkage between MDI and HLA, and not the detection of a specific linkage per se. Thus, regardless of the results obtained, Kruger’s work is frequently seen as a methodological standpoint for decisions related to the choice of an age correction, modeling of the mode of inheritance, and the frequency assumed for the marker haplotypes (items all affecting linkage), more than as a direct experimental approach, mainly since other studies (3,14) failed to find positive results demonstrating linkage. To summarize, methodological problems that could be encountered in a linkage analysis with a lod-score method (2) may be expressed in three issues: (a) the disease may be determined by more than one locus; (b) the association between the disease gene and the marker gene (presence of a genetic disequilibrium); and (c) the errors on parameters (gene frequency and penetrance) affect the lod-score and THETA estimates. The first point is quite obvious; for example, in a two-locus model, if only one of the loci is closely linked to the marker, it may be concluded that linkage is loose or there may not even be evidence for linkage. The second point is especially interesting; ignoring in the analysis the gametic disequilibrium owing to such an association leads to a large underestimation both of the lod-score and THETA. Finally, an incorrect estimate of the parameters des
cribing the susceptibility locus, that is, MDI locus, may, as an extreme, obscure and ignore the presence of a linkage. Alternatively then, many other hypotheses could be made ranging from a low association to an epistatic mode of inheritance. More thorough investigation of these problems related to a strictly formal genetic approach, however, could lead us into a puzzling world of alternative and not easily demonstrable hypotheses that represent the bases of different kinds of studies. Rather, here, it could be more important to ask ourselves why we should continue our efforts to study the HLA complex and its possible linkage with MDI, given all the problems that we have just reviewed. An answer could be derived by biological, biochemical, and also pharma-coimmunological studies. As a matter of fact, we know that "the genes of this complex might well control structures essential for intercellular contact and communication" (12). This statement has now been confirmed by several investigators working in HLA fields at a molecular level: in this way, searching for a linkage between MDI and the HLA complex has a biological reasoning based on membrane molecule properties. An interesting suggestion that we found years ago about the relationship between the HLA system and biological factors involved in affective disorders is that some B-locus antigens, namely B5 and its splits and B35, are strictly related to the individual capacity for lithium accumulation (9). Individuals who expressed these antigens have a greater lithium ratio than others, if they share both a homozygotic or a heterozygotic status, thus following a model of Mendelian transmission for a dominant character. Following these suggestions, our aim is now to evaluate the existence of a linkage between MDI and HLA, focusing our attention to В locus and to the haplotypic structure.