arXiv subjects

D. Schindler

Publications and source records attributed to D. Schindler.

3 recordsLinked to original sources

arXiv2022

Spontaneous transitions between amoeboid and keratocyte-like modes of migration

The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.

physics.bio-ph↗

arXiv2021

Density of rational points near/on compact manifolds with certain curvature conditions

In this article we establish an asymptotic formula for the number of rational points, with bounded denominators, within a given distance to a compact submanifold $\mathcal{M}$ of $\mathbb{R}^M$ with a certain curvature condition. Our result generalises earlier work of Huang for hypersurfaces [J.-J. Huang, The density of rational points near hypersurfaces, Duke Math. J. 169 (2020), 2045--2077.], as our curvature condition reduces to Gaussian curvature being bounded away from $0$ when $M - dim \mathcal{M} = 1$. An interesting feature of our result is that the asymptotic formula holds beyond the conjectured range of the distance to $\mathcal{M}$. Furthermore, we obtain an upper bound for the number of rational points on $\mathcal{M}$ with additional power saving to the bound in the analogue of Serre's dimension growth conjecture for compact submanifolds of $\mathbb{R}^M$ when $M - dim \mathcal{M} > 1$.

math.NT↗

arXiv2014

Manin's conjecture for certain biprojective hypersurfaces

Using the circle method, we count integer points on complete intersections in biprojective space in boxes of different side length, provided the number of variables is large enough depending on the degree of the defining equations and certain loci related to the singular locus. Having established these asymptotics we deduce asymptotic formulas for rational points on such varieties with respect to the anticanonical height function. In particular, we establish a conjecture of Manin for certain smooth hypersurfaces in biprojective space of sufficiently large dimension.

math.NT↗