A remark on constrained von Kármán theories.

We derive the Euler-Lagrange equation corresponding to 'non-Euclidean' convex constrained von Kármán theories.

A cooperative mechanism drives budding yeast kinetochore assembly downstream of CENP-A.

Kinetochores are megadalton-sized protein complexes that mediate chromosome-microtubule interactions in eukaryotes. How kinetochore assembly is triggered specifically on centromeric chromatin is poorly understood. Here we use biochemical reconstitution experiments alongside genetic and structural analysis to delineate the contributions of centromere-associated proteins to kinetochore assembly in yeast. We show that the conserved kinetochore subunits Ame1(CENP-U) and Okp1(CENP-Q) form a DNA-binding complex that associates with the microtubule-binding KMN network via a short Mtw1 recruitment motif in the N terminus of Ame1. Point mutations in the Ame1 motif disrupt kinetochore function by preventing KMN assembly on chromatin. Ame1-Okp1 directly associates with the centromere protein C (CENP-C) homologue Mif2 to form a cooperative binding platform for outer kinetochore assembly. Our results indicate that the key assembly steps, CENP-A recognition and outer kinetochore recruitment, are executed through different yeast constitutive centromere-associated network subunits. This two-step mechanism may protect against inappropriate kinetochore assembly similar to rate-limiting nucleation steps used by cytoskeletal polymers.

CENP-T proteins are conserved centromere receptors of the Ndc80 complex.

Centromeres direct the assembly of kinetochores, microtubule-attachment sites that allow chromosome segregation on the mitotic spindle. Fundamental differences in size and organization between evolutionarily distant eukaryotic centromeres have in many cases obscured general principles of their function. Here we demonstrate that centromere-binding proteins are highly conserved between budding yeast and humans. We identify the histone-fold protein Cnn1(CENP-T) as a direct centromere receptor of the microtubule-binding Ndc80 complex. The amino terminus of Cnn1 contains a conserved peptide motif that mediates stoichiometric binding to the Spc24-25 domain of the Ndc80 complex. Consistent with the critical role of this interaction, artificial tethering of the Ndc80 complex through Cnn1 allows mini-chromosomes to segregate in the absence of a natural centromere. Our results reveal the molecular function of CENP-T proteins and demonstrate how the Ndc80 complex is anchored to centromeres in a manner that couples chromosome movement to spindle dynamics.

Molecular architecture and connectivity of the budding yeast Mtw1 kinetochore complex.

Kinetochores are large multiprotein complexes that connect centromeres to spindle microtubules in all eukaryotes. Among the biochemically distinct kinetochore complexes, the conserved four-protein Mtw1 complex is a central part of the kinetochore in all organisms. Here we present the biochemical reconstitution and characterization of the budding yeast Mtw1 complex. Direct visualization by electron microscopy revealed an elongated bilobed structure with a 25-nm-long axis. The complex can be assembled from two stable heterodimers consisting of Mtw1p-Nnf1p and Dsn1p-Nsl1p, and it interacts directly with the microtubule-binding Ndc80 kinetochore complex via the centromere-proximal Spc24/Spc25 head domain. In addition, we have reconstituted a partial Ctf19 complex and show that it directly associates with the Mtw1 complex in vitro. Ndc80 and Ctf19 complexes do not compete for binding to the Mtw1 complex, suggesting that Mtw1 can bridge the microtubule-binding components of the kinetochore to the inner centromere.

Euler-Lagrange equations for variational problems on space curves.

We derive the Euler-Lagrange equations for a large class of variational problems on curves. Our result generalizes a recent result obtained in the literature. Moreover, it is simple and self-contained. It directly yields Euler-Lagrange equations in the form of equilibrium equations for the internal force and moment.

The Dam1 complex confers microtubule plus end-tracking activity to the Ndc80 kinetochore complex.

Kinetochores must remain associated with microtubule ends, as they undergo rapid transitions between growth and shrinkage. The molecular basis for this essential activity that ensures correct chromosome segregation is unclear. In this study, we have used reconstitution of dynamic microtubules and total internal reflection fluorescence microscopy to define the functional relationship between two important budding yeast kinetochore complexes. We find that the Dam1 complex is an autonomous plus end-tracking complex. The Ndc80 complex, despite being structurally related to the general tip tracker EB1, fails to recognize growing ends efficiently. Dam1 oligomers are necessary and sufficient to recruit Ndc80 to dynamic microtubule ends, where both complexes remain continuously associated. The interaction occurs specifically in the presence of microtubules and is subject to regulation by Ipl1 phosphorylation. These findings can explain how the force harvested by Dam1 is transmitted to the rest of the kinetochore via the Ndc80 complex.

Antisaccade performance is related to genetic loading for schizophrenia.

Disturbances of the oculomotor system are promising endophenotypes for schizophrenia. Increased error rates in the antisaccade task and prolonged antisaccade latencies have been found in patients with schizophrenia and their first degree relatives. We investigated oculomotor performance in 41 parents of schizophrenia patients and 22 controls with a prosaccade task and an antisaccade task. Parents were grouped into parents with a positive family history for schizophrenia (N=9) and parents with a negative family history for schizophrenia (N=32). An overlap-paradigm was applied; eye movements were recorded using infrared oculography. The combined group of parents made more antisaccade direction errors than controls (p=0.005) and there was a linear increase in direction errors from controls via negative family history parents to positive family history parents (p=0.008). Antisaccade latencies were prolonged in the combined parent group (p=0.057) compared to controls and there was a linear increase in latency with genetic loading (p=0.018). No group differences were found for prosaccade parameters. These results support the hypothesis that antisaccade impairment is associated with genetic loading for schizophrenia.