Deleterious variants in TRAK1 disrupt mitochondrial movement and cause fatal encephalopathy

This is the author accepted manuscript. The final version is available from Oxford University Press via the DOI in this record.The corrigendum to this article is in ORE: http://hdl.handle.net/10871/33588Cellular distribution and dynamics of mitochondria are regulated by several motor proteins and a microtubule network. In neurons, mitochondrial trafficking is crucial because of high energy needs and calcium ion buffering along axons to synapses during neurotransmission. The trafficking kinesin proteins (TRAKs) are well characterized for their role in lysosomal and mitochondrial trafficking in cells, especially neurons. Using whole exome sequencing, we identified homozygous truncating variants in TRAK1 (NM_001042646:c.287-2A > C), in six lethal encephalopathic patients from three unrelated families. The pathogenic variant results in aberrant splicing and significantly reduced gene expression at the RNA and protein levels. In comparison with normal cells, TRAK1-deficient fibroblasts showed irregular mitochondrial distribution, altered mitochondrial motility, reduced mitochondrial membrane potential, and diminished mitochondrial respiration. This study confirms the role of TRAK1 in mitochondrial dynamics and constitutes the first report of this gene in association with a severe neurodevelopmental disorder.D.M.E. and J.K. are supported by the Office of Naval Research (ONR) Grant N000141410538. M.S. is supported by the BBSRC (BB/K006231/1), a Wellcome Trust Institutional Strategic Support Award (WT097835MF, WT105618MA), and a Marie Curie Initial Training Network (ITN) action PerFuMe (316723). M.C.V.M., J.S., H.P., C.F., T.V. and W.A.G. are supported by the NGHRI Intramural Research Program. G.R. is supported by the Kahn Family Foundation and the Israeli Centers of Excellence (I-CORE) Program (ISF grant no. 41/11)

Geometric rank of tensors and subrank of matrix multiplication

Motivated by problems in algebraic complexity theory (e.g., matrix multiplication) and extremal combinatorics (e.g., the cap set problem and the sunflower problem), we introduce the geometric rank as a new tool in the study of tensors and hypergraphs. We prove that the geometric rank is an upper bound on the subrank of tensors and the independence number of hypergraphs. We prove that the geometric rank is smaller than the slice rank of Tao, and relate geometric rank to the analytic rank of Gowers and Wolf in an asymptotic fashion. As a first application, we use geometric rank to prove a tight upper bound on the (border) subrank of the matrix multiplication tensors, matching Strassen's well-known lower bound from 1987

An improved lower bound for arithmetic regularity

The arithmetic regularity lemma due to Green [GAFA 2005] is an analogue of the famous Szemerédi regularity lemma in graph theory. It shows that for any abelian group G and any bounded function f : G → [0, 1], there exists a subgroup H ≤ G of bounded index such that, when restricted to most cosets of H, the function f is pseudorandom in the sense that all its nontrivial Fourier coefficients are small. Quantitatively, if one wishes to obtain that for 1 - ϵ fraction of the cosets, the nontrivial Fourier coefficients are bounded by ϵ, then Green shows that |G/H| is bounded by a tower of twos of height 1/ϵ3. He also gives an example showing that a tower of height Ω(log 1/ϵ) is necessary. Here, we give an improved example, showing that a tower of height Ω(1/ϵ) is necessary

Constructing Near Spanning Trees with Few Local Inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree graph. Given an edge $e$ in $G$ we would like to decide whether $e$ belongs to a connected subgraph $G'$ consisting of $(1+\epsilon)n$ edges (for a prespecified constant $\epsilon >0$), where the decision for different edges should be consistent with the same subgraph $G'$. Can this task be performed by inspecting only a {\em constant} number of edges in $G$? Our main results are: (1) We show that if every $t$-vertex subgraph of $G$ has expansion $1/(\log t)^{1+o(1)}$ then one can (deterministically) construct a sparse spanning subgraph $G'$ of $G$ using few inspections. To this end we analyze a "local" version of a famous minimum-weight spanning tree algorithm. (2) We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of $3$-regular graphs of high girth, in which every $t$-vertex subgraph has expansion $1/(\log t)^{1-o(1)}$