Progressive familial heart block type I (PFHBI) is a progressive cardiac bundle branch disease in the His-Purkinje system that exhibits autosomal-dominant inheritance. In 3 branches of a large South African Afrikaner pedigree with an autosomal-dominant form of PFHBI, we identified the mutation c.19G→A in the transient receptor potential cation channel, subfamily M, member 4 gene (TRPM4) at chromosomal locus 19q13.3. This mutation predicted the amino acid substitution p.E7K in the TRPM4 amino terminus. TRPM4 encodes a Ca 2+ -activated nonselective cation (CAN) channel that belongs to the transient receptor potential melastatin ion channel family. Quantitative analysis of TRPM4 mRNA content in human cardiac tissue showed the highest expression level in Purkinje fibers. Cellular expression studies showed that the c.19G→A missense mutation attenuated deSUMOylation of the TRPM4 channel. The resulting constitutive SUMOylation of the mutant TRPM4 channel impaired endocytosis and led to elevated TRPM4 channel density at the cell surface. Our data therefore revealed a gain-of-function mechanism underlying this type of familial heart block.
Background-Isolated cardiac conduction block is a relatively common condition in young and elderly populations. Genetic predisposing factors have long been suspected because of numerous familial case reports. Deciphering genetic predisposing factors of conduction blocks may give a hint at stratifying conduction block carriers in a more efficient way. Methods and Results-One Lebanese family and 2 French families with autosomal dominant isolated cardiac conduction blocks were used for linkage analysis. A maximum combined multipoint lod score of 10.5 was obtained on a genomic interval including more than 300 genes. After screening 12 genes of this interval for mutation, we found a heterozygous missense mutation of the TRPM4 gene in each family (p.Arg164Trp, p.Ala432Thr, and p.Gly844Asp). This gene encodes the TRPM4 channel, a calcium-activated nonselective cation channel of the transient receptor potential melastatin (TRPM) ion channel family. All 3 mutations result in an increased current density. This gain of function is due to an elevated TRPM4 channel density at the cell surface secondary to impaired endocytosis and deregulation of Small Ubiquitin MOdifier conjugation (SUMOylation). Furthermore, we showed by immunohistochemistry that TRPM4 channel signal level is higher in atrial cardiomyocytes than in common ventricular cells, but is highest in Purkinje fibers. Small bundles of highly TRPM4-positive cells were found in the subendocardium and in rare intramural bundles. Conclusions-the TRPM4 gene is a causative gene in isolated cardiac conduction disease with mutations resulting in a gain of function and TRPM4 channel being highly expressed in cardiac Purkinje fibers. (Circ Cardiovasc Genet. 2010;3:374-385.)Key Words: bundle-branch block Ⅲ heart block Ⅲ ion channel Ⅲ sudden death Ⅲ genetics C onduction block is a condition in which the depolarization wave initiated in the sinus node of the heart is slowed down or even blocked on the way to ventricular cardiomyocytes. The position of the block, its completeness (partial or complete), and the number of blocks are largely variable from one individual to the other. Conduction blocks are not rare in the general population either among young people or late in life. Right bundle-branch block (RBBB) has a prevalence of about 0.1% in normal children, with a male predominance. 1 Complete RBBB with normal left ejection fraction and no diagnoses of cardiac disease was observed in 0.3% of individuals in a population of adults with a median age of 64 years in a community-based study lead by Miller et al. 2 The natural evolution of isolated conduction blocks is unpredictable, and deciphering the genetic predisposing factors might help in unmasking those that are dangerous. Rare cases of familial conduction blocks are secondary to mutations in SCN5A 3 or NKX2.5. 4 In the latter gene, the conduction block is often associated with a congenital heart defect (typically an atrial septal defect). Recently, a South African family with cardiac conduction block was reported to carry a ...
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We determine the exact bounds for the length of an arbitrary reduction sequence of a term in the typed λ-calculus with β-, ξ- and η-conversion. There will be two essentially different classifications, one depending on the height and the degree of the term and the other depending on the length and the degree of the term.
This article concerns the second-order systems U
1
2
and V
1
2
of bounded arithmetic, which have proof-theoretic strengths corresponding to polynomial-space and exponential-time computation. We formulate improved witnessing theorems for these two theories by using S
1
2
as a base theory for proving the correctness of the polynomial-space or exponential-time witnessing functions. We develop the theory of nondeterministic polynomial-space computation, including Savitch's theorem, in U
1
2
. Kołodziejczyk et al. [2011] have introduced local improvement properties to characterize the provably total NP functions of these second-order theories. We show that the strengths of their local improvement principles over U
1
2
and V
1
2
depend primarily on the topology of the underlying graph, not the number of rounds in the local improvement games. The theory U
1
2
proves the local improvement principle for linear graphs even without restricting to logarithmically many rounds. The local improvement principle for grid graphs with only logarithmically-many rounds is complete for the provably total NP search problems of V
1
2
. Related results are obtained for local improvement principles with one improvement round and for local improvement over rectangular grids.
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