arXiv subjects

Marcel Ernst

Publications and source records attributed to Marcel Ernst.

4 recordsLinked to original sources

arXiv2025

Exchange controls coarsening of surface condensates

Biological membranes often exhibit heterogeneous protein patterns, which cells control. Strong patterns, like the polarity spot in budding yeast, can be described as surface condensates, formed by physical interactions between constituents. However, it is unclear how these interactions affect the material exchange with the bulk. To study this, we analyze a thermodynamically consistent model, which reveals that passive exchange generally accelerates the coarsening of surface condensates. Active exchange can further accelerate coarsening, although it can also fully arrest it and induce complex patterns involving various length scales. We reveal how these behaviors are related to non-local transport via diffusion through the bulk, rationalizing the various scaling laws we observe and allowing us to interpret biologically relevant scenarios.

physics.bio-ph↗

arXiv2025

Coarsening model of chromosomal crossover placement

Chromosomal crossovers play a crucial role in meiotic cell division, as they ensure proper chromosome segregation and increase genetic variability. Experiments have consistently revealed two key observations across species: (i) the number of crossovers per chromosome is typically small, but at least one, and (ii) crossovers on the same chromosome are subject to interference, i.e., they are more separated than expected by chance. These observations can be explained by a recently proposed coarsening model, where the dynamics of droplets associated with chromosomes designate crossovers. We provide a comprehensive analysis of the coarsening model, which we also extend by including material exchanges between droplets, the synaptonemal complex, and the nucleoplasm. We derive scaling laws for the crossover count, which allows us to analyze data across species. Moreover, our model provides a coherent explanation of experimental data across mutants, including the wild-type and zyp1-mutant of A. thaliana. Consequently, the extended coarsening model provides a solid framework for investigating the underlying mechanisms of crossover placement.

physics.bio-ph↗

arXiv2021

Stability of convection in dry salt lakes

Dry lakes covered with a salt crust organised into beautifully patterned networks of narrow ridges are common in arid regions. Here, we consider the initial instability and the ultimate fate of buoyancy-driven convection that could lead to such patterns. Specifically, we look at convection in a deep porous medium with a constant through-flow boundary condition on a horizontal surface, which resembles the situation found below an evaporating salt lake. The system is scaled to have only one free parameter, the Rayleigh number, which characterises the relative driving force for convection. We then solve the resulting linear stability problem for the onset of convection. Further exploring the non-linear regime of this model with pseudo-spectral numerical methods, we demonstrate how the growth of small downwelling plumes is itself unstable to coarsening, as the system develops into a dynamic steady state. In this mature state we show how the typical speeds and length-scales of the convective plumes scale with forcing conditions, and the Rayleigh number. Interestingly, a robust length-scale emerges for the pattern wavelength, which is largely independent of the driving parameters. Finally, we introduce a spatially inhomogeneous boundary condition -- a modulated evaporation rate -- to mimic any feedback between a growing salt crust and the evaporation over the dry salt lake. We show how this boundary condition can introduce phase-locking of the downwelling plumes below sites of low evaporation, such as at the ridges of salt polygons.

physics.flu-dyn↗

arXiv2019

Salt polygons and porous media convection

From fairy circles to patterned ground and columnar joints, natural patterns spontaneously appear in many complex geophysical settings. Here, we investigate the origins of polygonally patterned crusts of salt playa and salt pans. These beautifully regular features, approximately a meter in diameter, are found worldwide and are fundamentally important to the transport of salt and dust in arid regions. We show that they are consistent with the surface expression of buoyancy-driven convection in the porous soil beneath a salt crust. By combining quantitative results from direct field observations, analogue experiments and numerical simulations, we further determine the conditions under which salt polygons should form, as well as how their characteristic size emerges.

nlin.PS↗