The Arabidopsis thaliana checkpoint kinase WEE1 protects against premature vascular differentiation during replication stress

A sessile lifestyle forces plants to respond promptly to factors that affect their genomic integrity. Therefore, plants have developed checkpoint mechanisms to arrest cell cycle progression upon the occurrence of DNA stress, allowing the DNA to be repaired before onset of division. Previously, the WEE1 kinase had been demonstrated to be essential for delaying progression through the cell cycle in the presence of replication-inhibitory drugs, such as hydroxyurea. To understand the severe growth arrest of WEE1-deficient plants treated with hydroxyurea, a transcriptomics analysis was performed, indicating prolonged S-phase duration. A role for WEE1 during S phase was substantiated by its specific accumulation in replicating nuclei that suffered from DNA stress. Besides an extended replication phase, WEE1 knockout plants accumulated dead cells that were associated with premature vascular differentiation. Correspondingly, plants without functional WEE1 ectopically expressed the vascular differentiation marker VND7, and their vascular development was aberrant. We conclude that the growth arrest of WEE1-deficient plants is due to an extended cell cycle duration in combination with a premature onset of vascular cell differentiation. The latter implies that the plant WEE1 kinase acquired an indirect developmental function that is important for meristem maintenance upon replication stress

The fast and accurate computation of eigenvalues and eigenfunctions of time-independent one-dimensional Schrödinger equations

In this paper, we present the basic routines of the C++-program Matslise 3.0, an updated but yet restricted version of the matlab package Matslise 2.0. Matslise 3.0 currently allows the accurate, but in comparison to Matslise 2.0, faster computation of eigenvalues and eigenfunctions of one dimensional time-independent Schrödinger problems. The numerical examples show that speed up factors up to 20 (for the eigenvalues) and 200 (for the eigenfunctions) are obtained. These highly optimized routines will enable us, in the near future, to extend Matslise 3.0 to solve time-independent 2D and 3D as well as time-dependent 1D problems

Determining the index of eigenvalues of an elliptic operator

Abstract: Throughout mathematical physics there are many problems dependent on, or consisting of determining eigenvalues of a linear elliptic operator on a given domain with Dirichlet boundary conditions. Some examples are the Schrödinger equation, the wave equation, the linear theory of elasticity, ... Many researchers have invested time and effort in stating and proving theorems about the spectrum of elliptic operators. In this talk we present a new tool to determine the number of eigenvalues less then a given value. Our theorem will be accompanied with examples and historic context

PySlise : a Python package for solving Schrödinger equations

This is an introduction to a new Python package that is able to solve numerically the one and two-dimensional time independent Schrödinger equation. Accompanying this package there is a web based GUI. The main motivator of this research is modernizing and bringing together existing techniques and proven methods. Matslise is a very effective implementation of CP-methods for the one-dimensional Sturm-Liouville equation. But due to the numerous features, this implementation is not highly optimised for efficiency. For this reason we have reimplemented and optimised the algorithms of Matslise and Matscs in C++. This reimplementation became the computation engine for the Python package and the web based GUI (WebAssembly). The Python package is less feature-rich than the original Matslise and Matscs (only Schrödinger equation, no degenerate case detection...), but a lot more optimised. These optimisations include: very efficient eigenfunction calculations, smarter backward propagation, higher order method for Matscs, on request error calculation, using C++ with Eigen. On top of that there is a unified interface to communicate with Matslise, Matscs and the new code for the two-dimensional case

A replication stress-induced synchronization method for Arabidopsis thaliana root meristems

Synchronized cell cultures are an indispensable tool for the identification and understanding of key regulators of the cell cycle. Nevertheless, the use of cell cultures has its disadvantages, because it represents an artificial system that does not completely mimic the endogenous conditions that occur in organized meristems. Here, we present a new and easy method for Arabidopsis thaliana root tip synchronization by hydroxyurea treatment. A major advantage of the method is the possibility of investigating available Arabidopsis cell-cycle mutants without the need to generate cell cultures. As a proof of concept, the effects of over-expression of a dominant negative allele of the B-type cyclin-dependent kinase CDKB1;1 gene on cell-cycle progression were tested. The previously observed prolonged G(2) phase was confirmed, but was found to be compensated for by a reduced G(1) phase. Furthermore, altered S-phase kinetics indicated a functional role for CDKB1;1 during the replication process