Minimum Sum of Squares Clustering in a Low Dimensional Space

Clustering with a criterion which minimizes the sum of squared distances to cluster centroids is usually done in a heuristic way. An exact polynomial algorithm, with a complexity in O(N ^p+1 logN), is proposed for minimum sum of squares hierarchical divisive clustering of points in a p-dimensional space with small p. Empirical complexity is one order of magnitude lower. Data sets with N = 20000 for p = 2, N = 1000 for p = 3, and N = 200 for p = 4 are clustered in a reasonable computing time.     

Crystal structure of the transfer-RNA domain of transfer-messenger RNA in complex with SmpB

Accurate translation of genetic information into protein sequence depends on complete messenger RNA molecules. Truncated mRNAs cause synthesis of defective proteins, and arrest ribosomes at the end of their incomplete message. In bacteria, a hybrid RNA molecule that combines the functions of both transfer and messenger RNAs (called tmRNA) rescues stalled ribosomes, and targets aberrant, partially synthesized, proteins for proteolytic degradation. Here we report the 3.2-A-resolution structure of the tRNA-like domain of tmRNA (tmRNA(Delta)) in complex with small protein B (SmpB), a protein essential for biological functions of tmRNA. We find that the flexible RNA molecule adopts an open L-shaped conformation and SmpB binds to its elbow region, stabilizing the single-stranded D-loop in an extended conformation. The most striking feature of the structure of tmRNA(Delta) is a 90 degrees rotation of the TPsiC-arm around the helical axis. Owing to this unusual conformation, the SmpB-tmRNA(Delta) complex positioned into the A-site of the ribosome orients SmpB towards the small ribosomal subunit, and directs tmRNA towards the elongation-factor binding region of the ribosome. On the basis of this structure, we propose a model for the binding of tmRNA on the ribosome.     

Trigger factor in complex with the ribosome forms a molecular cradle for nascent proteins

During protein biosynthesis, nascent polypeptide chains that emerge from the ribosomal exit tunnel encounter ribosome-associated chaperones, which assist their folding to the native state. Here we present a 2.7 A crystal structure of Escherichia coli trigger factor, the best-characterized chaperone of this type, together with the structure of its ribosome-binding domain in complex with the Haloarcula marismortui large ribosomal subunit. Trigger factor adopts a unique conformation resembling a crouching dragon with separated domains forming the amino-terminal ribosome-binding 'tail', the peptidyl-prolyl isomerase 'head', the carboxy-terminal 'arms' and connecting regions building up the 'back'. From its attachment point on the ribosome, trigger factor projects the extended domains over the exit of the ribosomal tunnel, creating a protected folding space where nascent polypeptides may be shielded from proteases and aggregation. This study sheds new light on our understanding of co-translational protein folding, and suggests an unexpected mechanism of action for ribosome-associated chaperones.     

De novo mutations revealed by whole-exome sequencing are strongly associated with autism

Multiple studies have confirmed the contribution of rare de novo copy number variations to the risk for autism spectrum disorders. But whereas de novo single nucleotide variants have been identified in affected individuals, their contribution to risk has yet to be clarified. Specifically, the frequency and distribution of these mutations have not been well characterized in matched unaffected controls, and such data are vital to the interpretation of de novo coding mutations observed in probands. Here we show, using whole-exome sequencing of 928 individuals, including 200 phenotypically discordant sibling pairs, that highly disruptive (nonsense and splice-site) de novo mutations in brain-expressed genes are associated with autism spectrum disorders and carry large effects. On the basis of mutation rates in unaffected individuals, we demonstrate that multiple independent de novo single nucleotide variants in the same gene among unrelated probands reliably identifies risk alleles, providing a clear path forward for gene discovery. Among a total of 279 identified de novo coding mutations, there is a single instance in probands, and none in siblings, in which two independent nonsense variants disrupt the same gene, SCN2A (sodium channel, voltage-gated, type II, α subunit), a result that is highly unlikely by chance.     

A peptide deformylase-ribosome complex reveals mechanism of nascent chain processing

Messenger-RNA-directed protein synthesis is accomplished by the ribosome. In eubacteria, this complex process is initiated by a specialized transfer RNA charged with formylmethionine (tRNA(fMet)). The amino-terminal formylated methionine of all bacterial nascent polypeptides blocks the reactive amino group to prevent unfavourable side-reactions and to enhance the efficiency of translation initiation. The first enzymatic factor that processes nascent chains is peptide deformylase (PDF); it removes this formyl group as polypeptides emerge from the ribosomal tunnel and before the newly synthesized proteins can adopt their native fold, which may bury the N terminus. Next, the N-terminal methionine is excised by methionine aminopeptidase. Bacterial PDFs are metalloproteases sharing a conserved N-terminal catalytic domain. All Gram-negative bacteria, including Escherichia coli, possess class-1 PDFs characterized by a carboxy-terminal alpha-helical extension. Studies focusing on PDF as a target for antibacterial drugs have not revealed the mechanism of its co-translational mode of action despite indications in early work that it co-purifies with ribosomes. Here we provide biochemical evidence that E. coli PDF interacts directly with the ribosome via its C-terminal extension. Crystallographic analysis of the complex between the ribosome-interacting helix of PDF and the ribosome at 3.7 A resolution reveals that the enzyme orients its active site towards the ribosomal tunnel exit for efficient co-translational processing of emerging nascent chains. Furthermore, we have found that the interaction of PDF with the ribosome enhances cell viability. These results provide the structural basis for understanding the coupling between protein synthesis and enzymatic processing of nascent chains, and offer insights into the interplay of PDF with the ribosome-associated chaperone trigger factor.     

Structure of the E. coli protein-conducting channel bound to a translating ribosome

Secreted and membrane proteins are translocated across or into cell membranes through a protein-conducting channel (PCC). Here we present a cryo-electron microscopy reconstruction of the Escherichia coli PCC, SecYEG, complexed with the ribosome and a nascent chain containing a signal anchor. This reconstruction shows a messenger RNA, three transfer RNAs, the nascent chain, and detailed features of both a translocating PCC and a second, non-translocating PCC bound to mRNA hairpins. The translocating PCC forms connections with ribosomal RNA hairpins on two sides and ribosomal proteins at the back, leaving a frontal opening. Normal mode-based flexible fitting of the archaeal SecYEbeta structure into the PCC electron microscopy densities favours a front-to-front arrangement of two SecYEG complexes in the PCC, and supports channel formation by the opening of two linked SecY halves during polypeptide translocation. On the basis of our observation in the translocating PCC of two segregated pores with different degrees of access to bulk lipid, we propose a model for co-translational protein translocation.     

L23 protein functions as a chaperone docking site on the ribosome

During translation, the first encounter of nascent polypeptides is with the ribosome-associated chaperones that assist the folding process--a principle that seems to be conserved in evolution. In Escherichia coli, the ribosome-bound Trigger Factor chaperones the folding of cytosolic proteins by interacting with nascent polypeptides. Here we identify a ribosome-binding motif in the amino-terminal domain of Trigger Factor. We also show the formation of crosslinked products between Trigger Factor and two adjacent ribosomal proteins, L23 and L29, which are located at the exit of the peptide tunnel in the ribosome. L23 is essential for the growth of E. coli and the association of Trigger Factor with the ribosome, whereas L29 is dispensable in both processes. Mutation of an exposed glutamate in L23 prevents Trigger Factor from interacting with ribosomes and nascent chains, and causes protein aggregation and conditional lethality in cells that lack the protein repair function of the DnaK chaperone. Purified L23 also interacts specifically with Trigger Factor in vitro. We conclude that essential L23 provides a chaperone docking site on ribosomes that directly links protein biosynthesis with chaperone-assisted protein folding.