Paradox of schizophrenia genetics: is a paradigm shift occurring?

Schizophrenia (SCZ) is a common and highly heritable form of psychosis associated with a remarkable biological disadvantage [1]. Accordingly, the central paradox of SCZ genetics is how susceptibility genes are preserved in the human gene-pool against a strong negative selection pressure [2–5]. Although recent large-sample epidemiological studies [6–9] have consistently shown that the reproductive fitness of the unaffected female siblings of patients with SCZ is slightly increased (1.02-1.08), it is not large enough to compensate for the gene loss due to the decreased reproductive fitness of patients (0.2-0.3 in males and 0.4-0.5 in females) and their unaffected male siblings (0.9-1.0) in the nuclear genome model (NGM). Furthermore, the latest meta-analysis shows that parents of patients with SCZ have fertility similar to the general population [10]. Therefore, heterozygote advantage does not seem to work in the NGM.

However, it works in the mitochondrial genome model (MGM) because mtDNA is transmitted to the next generation only through females. Indeed, we can see that this slightly elevated fitness of the unaffected female siblings, coupled with the less pronounced decreased fitness of female patients, is sufficient to compensate for the gene loss in the MGM; when we calculate –Δ, the cross-generational reduction of the frequency of females carrying putative pathogenic mtDNA in the general population, using data from the largest-sampled cohort study to date [8], we have $-\Delta <5.06\times {10}^{-3}$[11]. This figure implies that the gene loss can be balanced by de novo mutation in the mtDNA which occurs at a rate of $8.8\times {10}^{-4}\sim 1.3\times {10}^{-2}$ per locus per generation (4.3 × 10^-3 on average) [12].

Thus, in our previous paper [11], we carefully re-examined the necessary conditions for putative nuclear susceptibility genes for SCZ and deduced a criterion (the persistence criterion, or ‘P-criterion’) for nuclear susceptibility genes for SCZ based on the general assumptions of the multifactorial threshold model. Because SCZ must be sustained by mutation-selection balance without heterozygote advantage in the NGM and the mutation rates in the nuclear genome are much lower than in the mitochondrial genome [12–14], the criterion is strong. It demands $0<d<\nu \equiv \frac{(1-sp)\mu }{(1-p)sp}$ (Appendix A), while the principle of association study demands d> 0. Here d μ p and s denote the case–control difference of allele frequencies, the mutation rate at a putative risk locus, and the prevalence and the selection coefficient of the disease respectively. According to epidemiological data collected by Haukka et al. [8]$\left(p=1.29\times {10}^{-2}\text{and}s=6.54\times {10}^{-1}\right)$ν is very small for SCZ. Given the average mutation rate in the autosomes and the X chromosome $\left(\mu =1.48\times {10}^{-5}\right)$, we have $\nu =1.76\times {10}^{-3}$, and given the highest mutation rate $\left(\mu =1.48\times {10}^{-4}\right)$, we have $\nu =1.76\times {10}^{-2}$(Appendix B).

Using this criterion, we can calculate a lower boundary for the sample size required in an association study of a given power (Appendix C). Thus, we can see that more than 29,000 case–control pairs are required in a genome-wide association study (GWAS) with a power of 0.8 to detect a susceptibility variant of the highest mutation rate and a population frequency between 0.005 and 0.995, and that more than 2.9 million case–control pairs are required in a GWAS with a power of 0.8 to detect a susceptibility variant of the average mutation rate and a population frequency between 0.0005 and 0.9995.

In the past two decades, mitochondrial dysfunction (MD) in SCZ has been suggested by several independent lines of evidence [15–18], that include mitochondrial hypoplasia, elevated oxidative stress (OS), disturbed oxidative phosphorylation (OXPHOS), and altered mitochondrial-related gene expression in several cell lines. It is still unknown whether MD in the brains of patients with SCZ is a primary pathogenic change or a secondarily induced process, and the aforementioned inconclusive findings create more questions than answers about the origin of SCZ. We contend, however, that the MGM may very well have the answers.

In the present study, we apply the P-criterion to the results of association studies to date and survey the distribution of SCZ-associated genes that could meet or do not meet the P-criterion. We discuss why those SCZ-associated genes that do not meet the criterion must be protective genes (PGs) for SCZ, and suggest that the MGM can replace the NGM as a basis for genomic research of SCZ. Based on the MGM we propose a new hypothesis that assumes brain-specific antioxidant defenses in which neurotransmissions are involved, and present ten predictions of the hypothesis.

SCZ-associated variants listed in the top 45 in the SZGene Database [19] (the version of the 23^rd December, 2011) were selected. Based on the genotype distributions in the meta-analyses, allele frequencies and the case–control differences were calculated.

Genetic research of SCZ based on the NGM has been one of the most active areas in psychiatry for the past two decades. Although this effort is ongoing, results of association studies based on the NGM have been disappointing, or rather perplexing. No particular susceptibility gene that accounts for a large proportion of heritability has been identified by association studies. The results of association studies have been inconsistent, and SCZ-associated variants including copy number variations differ across populations or even across individuals of the same ethnicity.

The central paradox of SCZ genetics and the results of association studies to date argue against the NGM for SCZ today, and in its place the MGM is emerging as a viable option to account for genomic and pathophysiological research findings involving this enigmatic disorder.

Deduction of the P-criterion is explained in detail elsewhere[11]. Therefore, we present here the essence of the method. At first we describe our three basic assumptions.

where ν is defined as $\nu \equiv \frac{(1-sp)\mu }{(1-p)sp}$.From the observation (A5), we can see that d≥v implies s>s _M for any SCZ-associated variant M which is sustained by mutation-selection balance.

Mutation rates on autosomes and the X chromosome almost always fall within the range between 10^-6 and 10^-4 per locus per generation (usually < 10^-5; one generation = 20 years) [13, 14] and can be approximated by a linear function of the parental age at least under 30 years for maternal age and under 40 years for paternal age [160]. Large-sampled cohort studies in Israel, Sweden and Denmark show that the mean age of parents in the general population is ~ 28 years for mothers and ~31 years for fathers; the mean age of both parents is < 29.6 years [83, 86]. Therefore we can assume: ${10}^{-6}<\mu <\frac{29.6}{20}\times {10}^{-4}=1.48\times {10}^{-4}$. According to the epidemiological data by Haukka et al. [8], the estimated values for p and s are$p=1.29\times {10}^{-2}$and $s=6.54\times {10}^{-1}$. Therefore, we have $\nu =1.76\times {10}^{-3}$for the average mutation rate $\left(1.48\times {10}^{-5}\right)$$\nu =1.76\times {10}^{-2}$for the highest mutation rate $\left(1.48\times {10}^{-4}\right)$, and $\nu =1.76\times {10}^{-4}$for a relatively low mutation rate $\left(1.48\times {10}^{-6}\right)$.

Thus, we have$N\cong \frac{1}{2}{\left(\frac{z{*}_a\sqrt{2x\left(1-x\right)}+z_{\beta }\gamma }{d}\right)}^2\cong {\left(\frac{z{*}_a+z_{\beta }}{d}\right)}^{2}x\left(1-x\right)>{\left(\frac{z{*}_a+z_{\beta }}{v}\right)}^{2}x\left(1-x\right)$.

Let us calculate the required sample size in a GWAS $\left(\alpha =2.5\times {10}^{-7},1-\beta =0.80\right)$. Since we have $z{*}_{0.00000025}+z_{0.2}=5.99$,$N>{\left(\frac{z_{\alpha }^{*}+z_{\beta }}{\nu }\right)}^{2}x(1-x)={\left(\frac{5.99}{1.76\times {10}^{-3}}\right)}^{2}x(1-x)=2.90\times {10}^6$ for x= 0.5. Therefore, more than 2.9 million case–control pairs are required in a genome-wide association study with a power of 0.8 to detect a susceptibility variant of the average mutation rate and a population frequency between 0.0005 and 0.9995.Similarly we can see that more than 29,000 case–control pairs are required in a genome-wide association study with a power of 0.8 to detect a susceptibility variant of the highest mutation rate $\left(\mu =1.48\times {10}^{-4}\right)$ and a population frequency between 0.005 and 0.995.Finally, let us consider the case with a relatively low mutation rate $\mu =1.48\times {10}^{-6}$, which corresponds to $\nu =1.76\times {10}^{-4}$. In this case, more than 290 million case–control pairs are required in a GWAS with a power of 0.8 to detect a susceptibility variant of a population frequency between 0.000005 and 0.999995.