Introduction

In a previous study of bipolar disorder, we analyzed 803 SNPs belonging to genes related to signal transmission in the brain [1]. Combinations of three SNP genotypes taken from the 803 SNPs were counted; the theoretical number of such combinations is 2,321,319,627, and we found that the 1355 control persons and 607 patients contained 1,985,613,130 combinations. Of these, 1,719,002,329 were common for the two groups; 208,699,590 were found in control participants only; and 57,911,211 combinations were found exclusively in patients. Among these last combinations, four clusters, each containing about 40 combinations, were found to be significantly associated with bipolar disorder. The four clusters corresponded to four genetic subgroups of patients, one of which was significantly different from the three others with respect to number of manic and depressive episodes [2]. Combinations from the four clusters were present in the genome in 156 of the 607 patients whereas none of the 1355 control participants had such a combination in their genome. For the present study, we used the data from the previous work [1] to answer two questions that computational limitations left us unable to address in the initial analyses.

The first question is whether combinations of four SNP genotypes taken from the same 803 SNPs can reveal more clusters of combinations associated with bipolar disorder? Because the theoretical number of combinations of four SNP genotypes is 1,392,791,776,200, the computational challenge remains considerable, and here we report a way to give a partial answer to this question.

The second question is whether some of the 208,699,590 combinations of three SNP genotypes found exclusively in control participants can be considered as protective or risk reducing regarding bipolar disorder?

Materials and Methods

Results

Theoretically the number of combinations of four SNP genotypes taken from 803 SNPs is 803!/4!(803–4)! × 3⁴ = 1,392,791,776,200. Because of the computational burden, it was not possible to analyze how many of these combinations were present in the 1355 controls and 607 bipolar patients. Instead a selection of combinations of four SNP genotypes was analyzed. The selection was based on statistics as described in Materials and Methods. From the selected group of combinations of four SNP genotypes, those that occurred exclusively in patients were extracted. Using permutation tests it was found that none of these combinations were significantly associated with bipolar disorder. However, among these combinations, a cluster containing 16 combinations was found to be significantly associated with bipolar disorder (p = 0.011 using permutation test, 1000 permutations). The 16 combinations are shown in Table 1, which also shows the number of patients having these combinations in their genome. The total number of patients belonging to the cluster was 73, of whom 20 also were found in the four clusters in the previous study [1]. Of the 73 patients, 18 carried one combination from the cluster, 15 carried two combinations, 40 carried between 3 and 9 combinations.

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Table 1. Cluster containing 16 combinations of four SNP genotypes.

SNP1 = YWHAH_rs1049583² is common for all 16 combinations.

https://doi.org/10.1371/journal.pone.0143432.t001

For all other clusters it was found that similar clusters occurred more than 50 times in the 1000 permutations.

In the previous study [1] 208,699,590 combinations of three SNP genotypes were found exclusively in control persons. A permutation test showed that this number could be a random finding. Also those combinations that were common for many controls could be random findings, because the highest number of controls sharing a combination not present in patients was 40, but such a result or higher than 40 was found more than 700 times in 1000 permutations. Permutation tests also showed that all clusters of combinations of three SNP genotypes found exclusively in controls could be random findings.

Discussion

The genetic basis for polygenic disorders is combinations of genetic variants, if a disorder shows genetic homogeneity this basis consists of only one combination. If the disorder shows genetic heterogeneity several combinations of genetic variants can be basis for the disorder. A combination of genetic variants that is the basis for a polygenic disorder has never been described, probably because analyses of combinations of genetic variants constitute computational and statistical challenges due to the large number of possible combinations, even with moderate numbers of genetic variants [3]. In the present study the number of combinations of only four SNP genotypes taken from 803 SNPs was more than thousand billions four. In order to find one or more combinations significantly associated with a disorder among many billions of combinations calls for various methods and procedures. Obviously, the problem can be addressed by restriction of the analysis to a small number of genetic variants [4,5]. Technically the problem can be attacked by development of fast data-mining methods [1,6,7], and use of specialized hardware, as multiple graphical processing units, to increase scanning speed [8–10]. Such methods has allowed analysis of combinations of genetic variants in studies of esophageal cancer [11], bipolar disorder [1], neuroblastoma [12], and breast cancer [13].

In order to deal with the large number of combinations the statistical analyses can be restricted to the combinations found exclusively in patients, because the chances of finding combinations significantly related to a disorder may be larger in this group of combinations. A further reduction in the number of the patient specific combinations can be obtained by extraction of those combinations that are common to many patients instead of those that are common to few patients.

However, all these methods cannot handle all the combinations of four SNP genotypes taken from 803 SNPs, not to mention the number of combinations of more than four genetic variants taken from studies where thousands of genetic variants have been analyzed. In the present study we have attacked this problem by the use of a selection procedure where not all, but only some combinations have been analyzed. The principle in the procedure is that the distribution between controls and patients for all the genetic variants are analyzed by chi square tests, and those with a low p value are selected. Instead of calculating all possible combinations of two genetic variants, only combinations where at least one genetic variant has a low p value are looked at. And the same principle is used with combinations of three and four genetic variants. By such stepwise selections it is possible to analyze combinations of two, three and four genetic variants, but the cost is that some combinations associated with bipolar disorder but with p values above the threshold may remain undetected. In large data sets as those from genome wide association studies much lower p values may be used in the selection procedure order to obtain numbers of combinations that are manageable. Also biological criteria could have been used in the selection procedure if, e.g., we had reasons to believe that genes for potassium ion channels were particularly important, combinations containing SNP genotypes from such genes could have been used in the selection procedure.

The use of the selection procedure in the present study resulted in exactly the same four clusters of combinations of three SNP genotypes significantly associated to bipolar disorder, as found in the previous study, where all possible combinations were analyzed [1], showing the usefulness of the procedure. Furthermore, the procedure allowed analysis of combinations of four SNP genotypes. No combination of four SNP genotypes found exclusively in patients was significantly associated bipolar disorder, but one cluster of these combinations was found to be significantly associated to bipolar patients. The cluster (Table 1) contained as little as 16 combinations out of more than thousand billion combinations, but 73 patients had one or more of the 16 combinations in their genome. Of the 73 patients, 20 were also among the 156 patients in the four clusters found in the previous study [1]. Thus, 53 patients could be added to the 156 patients, so that 209 out of 607 patients had some of the combinations from the five clusters in their genome. As none of the 1355 control persons had any of these combinations in their genome each of the five clusters may be viewed as general risk factors, and the accumulation of combinations from the clusters in the genome of the single patient may be seen as personal risk factors for bipolar disorder.

All combinations in a cluster contain a common SNP genotype, and in the cluster found in the present study (Table 1), all 16 combinations contained the variant homozygote of YWHAH_rs1049583. In this respect it is interesting that we have found this variant to be associated with bipolar disorder in a study where the present data together with heterogeneous data from genome-wide association studies, protein–protein interaction screens, disease similarity, linkage studies, and gene expression experiments were combined into a multi-layered evidence network [14].

Protective or risk-reducing genes have been found for some diseases [15–17], raising the question whether some of the more than 200 million combinations of three SNP genotypes found exclusively in control persons [1] were significantly associated with not having bipolar disorder; however, we found no such combinations or clusters of combinations. This result does not exclude that combinations of genetic variants may be protective or risk reducing regarding bipolar disorder; because if such combinations are present in small groups of control persons, the present approach may not have identified them. However, the result indicated that specific combinations of SNP genotypes that are protective or risk reducing with respect to bipolar disorder are not present in the genomes of large groups of control persons.

Conclusion

It is generally accepted that the genetic basis for polygenic disorders are combinations of genetic variants, but due to the high number of possible combinations it is difficult to find those that are the genetic basis. Using a procedure where only selections of combinations were analyzed it was possible to find clusters of combinations of SNP genotypes significantly associated to bipolar disorder. The combinations in the clusters were present in the genome of 35% of the patients, but absent in all control subjects. This finding indicates a role for combinations of genetic data in clinical work with diagnosis and estimation of risk of disease, but replication studies are warranted in order to further evaluate the relevance of combinations of genetic data. Such studies may be new, but combinations of genetic variants may also be analyzed in studies already published.

Supporting Information