Extended study on the application of the sextic potential in the frame of X(3)-Sextic

The main aim of the present paper is to study extensively the γ-rigid Bohr Hamiltonian with anharmonic sextic oscillator potential for the variable β and γ = 0. For the corresponding spectral problem, a finite number of eigenvalues are found explicitly, by algebraic means, so-called Quasi-Exact Solvability (QES). The evolution of the spectral and electromagnetic properties by considering higher exact solvability orders is investigated, especially the approximate degeneracy of the ground and first two β bands in the critical point of the shape phase transition from a harmonic to an anharmonic prolate β-soft, also the shape evolution within an isotopic chain. Numerical results are given for 39 nuclei, namely, 98-108Ru, 100-102Mo, 116-130Xe, 180-196Pt, 172Os, 146-150Nd, 132-134Ce, 152-154Gd, 154-156Dy, 150-152Sm, 190Hg and 222Ra. Across this study, it seems that the higher quasi-exact solvability order improves our results by decreasing the rms, mostly for deformed nuclei. The nuclei 100,104Ru, 118,120,126,128Xe, 148Nd and 172Os fall exactly in the critical point.

Tissue folding at the organ–meristem boundary results in nuclear compression and chromatin compaction

Artificial mechanical perturbations affect chromatin in animal cells in culture. Whether this is also relevant to growing tissues in living organisms remains debated. In plants, aerial organ emergence occurs through localized outgrowth at the periphery of the shoot apical meristem, which also contains a stem cell niche. Interestingly, organ outgrowth has been proposed to generate compression in the saddle-shaped organ–meristem boundary domain. Yet whether such growth-induced mechanical stress affects chromatin in plant tissues is unknown. Here, by imaging the nuclear envelope in vivo over time and quantifying nucleus deformation, we demonstrate the presence of active nuclear compression in that domain. We developed a quantitative pipeline amenable to identifying a subset of very deformed nuclei deep in the boundary and in which nuclei become gradually narrower and more elongated as the cell contracts transversely. In this domain, we find that the number of chromocenters is reduced, as shown by chromatin staining and labeling, and that the expression of linker histone H1.3 is induced. As further evidence of the role of forces on chromatin changes, artificial compression with a MicroVice could induce the ectopic expression of H1.3 in the rest of the meristem. Furthermore, while the methylation status of chromatin was correlated with nucleus deformation at the meristem boundary, such correlation was lost in the h1.3 mutant. Altogether, we reveal that organogenesis in plants generates compression that is able to have global effects on chromatin in individual cells.