Novel steady state of a microtubule assembly in a confined geometry

We study the steady state of an assembly of microtubules in a confined volume, analogous to the situation inside a cell where the cell boundary forms a natural barrier to growth. We show that the dynamical equations for growing and shrinking microtubules predict the existence of two steady states, with either exponentially decaying or exponentially increasing distribution of microtubule lengths. We identify the regimes in parameter space corresponding to these steady states. In the latter case, the apparent catastrophe frequency near the boundary was found to be significantly larger than that in the interior. Both the exponential distribution of lengths and the increase in the catastrophe frequency near the cell margin is in excellent agreement with recent experimental observations.Comment: 8 pages, submitted to Phys. Rev.

Transport enhancement from incoherent coupling between one-dimensional quantum conductors

We study the non-equilibrium transport properties of a highly anisotropic two-dimensional lattice of spin-1/2 particles governed by a Heisenberg XXZ Hamiltonian. The anisotropy of the lattice allows us to approximate the system at finite temperature as an array of incoherently coupled one-dimensional chains. We show that in the regime of strong intrachain interactions, the weak interchain coupling considerably boosts spin transport in the driven system. Interestingly, we show that this enhancement increases with the length of the chains, which is related to superdiffusive spin transport. We describe the mechanism behind this effect, compare it to a similar phenomenon in single chains induced by dephasing, and explain why the former is much stronger

Weak measurement takes a simple form for cumulants

A weak measurement on a system is made by coupling a pointer weakly to the system and then measuring the position of the pointer. If the initial wavefunction for the pointer is real, the mean displacement of the pointer is proportional to the so-called weak value of the observable being measured. This gives an intuitively direct way of understanding weak measurement. However, if the initial pointer wavefunction takes complex values, the relationship between pointer displacement and weak value is not quite so simple, as pointed out recently by R. Jozsa. This is even more striking in the case of sequential weak measurements. These are carried out by coupling several pointers at different stages of evolution of the system, and the relationship between the products of the measured pointer positions and the sequential weak values can become extremely complicated for an arbitrary initial pointer wavefunction. Surprisingly, all this complication vanishes when one calculates the cumulants of pointer positions. These are directly proportional to the cumulants of sequential weak values. This suggests that cumulants have a fundamental physical significance for weak measurement

Eg5 is static in bipolar spindles relative to tubulin: evidence for a static spindle matrix

We used fluorescent speckle microscopy to probe the dynamics of the mitotic kinesin Eg5 in Xenopus extract spindles, and compared them to microtubule dynamics. We found significant populations of Eg5 that were static over several seconds while microtubules flux towards spindle poles. Eg5 dynamics are frozen by adenylimidodiphosphate. Bulk turnover experiments showed that Eg5 can exchange between the spindle and the extract with a half life of <55 s. Eg5 distribution in spindles was not perturbed by inhibition of its motor activity with monastrol, but was perturbed by inhibition of dynactin with p50 dynamitin. We interpret these data as revealing the existence of a static spindle matrix that promotes Eg5 targeting to spindles, and transient immobilization of Eg5 within spindles. We discuss alternative interpretations of the Eg5 dynamics we observe, ideas for the biochemical nature of a spindle matrix, and implications for Eg5 function

Mitosis: New Roles for Myosin-X and Actin at the Spindle

SummaryRoles for actin and myosin in positioning mitotic spindles in the cell are well established. A recent study of myosin-X function in early Xenopus embryo mitosis now reports that this unconventional myosin is required for pole integrity and normal spindle length by localizing to poles and exerting pulling forces on actin filaments within the spindle

Prc1E and Kif4A control microtubule organization within and between large Xenopus egg asters

© The Author(s), 2018. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Molecular Biology of the Cell 29 (2018): 304-316, doi:10.1091/mbc.E17-09-0540.The cleavage furrow in Xenopus zygotes is positioned by two large microtubule asters that grow out from the poles of the first mitotic spindle. Where these asters meet at the midplane, they assemble a disk-shaped interaction zone consisting of anti-parallel microtubule bundles coated with chromosome passenger complex (CPC) and centralspindlin that instructs the cleavage furrow. Here we investigate the mechanism that keeps the two asters separate and forms a distinct boundary between them, focusing on the conserved cytokinesis midzone proteins Prc1 and Kif4A. Prc1E, the egg orthologue of Prc1, and Kif4A were recruited to anti-parallel bundles at interaction zones between asters in Xenopus egg extracts. Prc1E was required for Kif4A recruitment but not vice versa. Microtubule plus-end growth slowed and terminated preferentially within interaction zones, resulting in a block to interpenetration that depended on both Prc1E and Kif4A. Unexpectedly, Prc1E and Kif4A were also required for radial order of large asters growing in isolation, apparently to compensate for the direction-randomizing influence of nucleation away from centrosomes. We propose that Prc1E and Kif4, together with catastrophe factors, promote “anti-parallel pruning” that enforces radial organization within asters and generates boundaries to microtubule growth between asters

Learning from Minimum Entropy Queries in a Large Committee Machine

In supervised learning, the redundancy contained in random examples can be avoided by learning from queries. Using statistical mechanics, we study learning from minimum entropy queries in a large tree-committee machine. The generalization error decreases exponentially with the number of training examples, providing a significant improvement over the algebraic decay for random examples. The connection between entropy and generalization error in multi-layer networks is discussed, and a computationally cheap algorithm for constructing queries is suggested and analysed.Comment: 4 pages, REVTeX, multicol, epsf, two postscript figures. To appear in Physical Review E (Rapid Communications