1,334 research outputs found
Swap and stop – kinetochores play error correction with microtubules
Correct chromosome segregation in mitosis relies on chromosome biorientation, in which sister kinetochores attach to microtubules from opposite spindle poles prior to segregation. To establish biorientation, aberrant kinetochore–microtubule interactions must be resolved through the error correction process. During error correction, kinetochore–microtubule interactions are exchanged (swapped) if aberrant, but the exchange must stop when biorientation is established. In this article, we discuss recent findings in budding yeast, which have revealed fundamental molecular mechanisms promoting this “swap and stop” process for error correction. Where relevant, we also compare the findings in budding yeast with mechanisms in higher eukaryotes. Evidence suggests that Aurora B kinase differentially regulates kinetochore attachments to the microtubule end and its lateral side and switches relative strength of the two kinetochore–microtubule attachment modes, which drives the exchange of kinetochore–microtubule interactions to resolve aberrant interactions. However, Aurora B kinase, recruited to centromeres and inner kinetochores, cannot reach its targets at kinetochore–microtubule interface when tension causes kinetochore stretching, which stops the kinetochore–microtubule exchange once biorientation is established
Improved bilinear Strichartz estimates with application to the well-posedness of periodic generalized KdV type equations
We improve our previous result [L. Molinet and T. Tanaka, Unconditional
well-posedness for some nonlinear periodic one-dimensional dispersive
equations, J. Funct. Anal. 283 (2022), 109490] on the Cauchy problem for one
dimensional dispersive equations with a quite general nonlinearity in the
periodic setting. Under the same hypotheses that the dispersive operator
behaves for high frequencies as a Fourier multiplier by ,
with , and that the nonlinear term is of the form where is a real analytic function whose Taylor series
around the origin has an infinite radius of convergence, we prove the
unconditional LWP of the Cauchy problem in for with . It is worth noticing that this result is
optimal in the case (generalized KdV equation) in view of the
restriction for the continuous injection of into
. Our main new ingredient is the remplacement of
improved Strichartz estimates by improved bilinear estimates in the treatment
of the worst resonant interactions. Such improved bilinear estimates already
appeared in the work of Hani in the context of Schr\"odinger equations on a
compact manifold. Finally note that this enables us to derive global existence
results for .Comment: 38 pages. Fixed typos. Updated reference
SWAP, SWITCH, and STABILIZE:Mechanisms of Kinetochore–Microtubule Error Correction
For correct chromosome segregation in mitosis, eukaryotic cells must establish chromosome biorientation where sister kinetochores attach to microtubules extending from opposite spindle poles. To establish biorientation, any aberrant kinetochore–microtubule interactions must be resolved in the process called error correction. For resolution of the aberrant interactions in error correction, kinetochore–microtubule interactions must be exchanged until biorientation is formed (the SWAP process). At initiation of biorientation, the state of weak kinetochore–microtubule interactions should be converted to the state of stable interactions (the SWITCH process)—the conundrum of this conversion is called the initiation problem of biorientation. Once biorientation is established, tension is applied on kinetochore–microtubule interactions, which stabilizes the interactions (the STABILIZE process). Aurora B kinase plays central roles in promoting error correction, and Mps1 kinase and Stu2 microtubule polymerase also play important roles. In this article, we review mechanisms of error correction by considering the SWAP, SWITCH, and STABILIZE processes. We mainly focus on mechanisms found in budding yeast, where only one microtubule attaches to a single kinetochore at biorientation, making the error correction mechanisms relatively simpler
WELL-POSEDNESS AND PARABOLIC SMOOTHING EFFECT FOR HIGHER ORDER SCHRO¨ DINGER TYPE EQUATIONS WITH CONSTANT COEFFICIENTS
In this paper, we consider the Cauchy problem of a class of higher order Schr¨odinger type equations with constant coefficients. By employing the energy inequality, we show the L2 well-posedness, the parabolic smoothing and a breakdown of the persistence of regularity. We classify this class of equations into three types on the basis of their smoothing property
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