Molecular diagnosis of distal renal tubular acidosis in Tunisian patients: proposed algorithm for Northern Africa populations for the ATP6V1B1, ATP6V0A4 and SCL4A1 genes

Background: Primary distal renal tubular acidosis (dRTA) caused by mutations in the genes that codify for the H+ -ATPase pump subunits is a heterogeneous disease with a poor phenotype-genotype correlation. Up to now, large cohorts of dRTA Tunisian patients have not been analyzed, and molecular defects may differ from those described in other ethnicities. We aim to identify molecular defects present in the ATP6V1B1, ATP6V0A4 and SLC4A1 genes in a Tunisian cohort, according to the following algorithm: first, ATP6V1B1 gene analysis in dRTA patients with sensorineural hearing loss (SNHL) or unknown hearing status. Afterwards, ATP6V0A4 gene study in dRTA patients with normal hearing, and in those without any structural mutation in the ATP6V1B1 gene despite presenting SNHL. Finally, analysis of the SLC4A1 gene in those patients with a negative result for the previous studies. Methods: 25 children (19 boys) with dRTA from 20 families of Tunisian origin were studied. DNAs were extracted by the standard phenol/chloroform method. Molecular analysis was performed by PCR amplification and direct sequencing. Results: In the index cases, ATP6V1B1 gene screening resulted in a mutation detection rate of 81.25%, which increased up to 95% after ATP6V0A4 gene analysis. Three ATP6V1B1 mutations were observed: one frameshift mutation (c.1155dupC; p.Ile386fs), in exon 12; a G to C single nucleotide substitution, on the acceptor splicing site (c.175-1G > C; p.?) in intron 2, and one novel missense mutation (c. 1102G > A; p. Glu368Lys), in exon 11. We also report four mutations in the ATP6V0A4 gene: one single nucleotide deletion in exon 13 (c.1221delG; p. Met408Cysfs* 10); the nonsense c.16C > T; p.Arg6*, in exon 3; and the missense changes c.1739 T > C; p.Met580Thr, in exon 17 and c.2035G > T; p.Asp679Tyr, in exon 19. Conclusion: Molecular diagnosis of ATP6V1B1 and ATP6V0A4 genes was performed in a large Tunisian cohort with dRTA. We identified three different ATP6V1B1 and four different ATP6V0A4 mutations in 25 Tunisian children. One of them, c.1102G > A; p.Glu368Lys in the ATP6V1B1 gene, had not previously been described. Among deaf since childhood patients, 75% had the ATP6V1B1 gene c. 1155dupC mutation in homozygosis. Based on the results, we propose a new diagnostic strategy to facilitate the genetic testing in North Africans with dRTA and SNHL.

The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.