Keratins are one of the most abundant proteins in epithelial cells. They form a cytoskeletal filament network whose structural organization seriously conditions its function. Dynamic keratin particles and aggregates are often observed at the periphery of mutant keratinocytes related to the hereditary skin disorder epidermolysis bullosa simplex, which is due to mutations in keratins 5 and 14. To account for their emergence in mutant cells, we extended an existing mathematical model of keratin turnover in wild-type cells and developed a novel 2D phase-field model to predict the keratin distribution inside the cell. This model includes the turnover between soluble, particulate and filamentous keratin forms. We assumed that the mutation causes a slowdown in the assembly of an intermediate keratin phase into filaments, and demonstrated that this change is enough to account for the loss of keratin filaments in the cell’s interior and the emergence of keratin particles at its periphery. The developed mathematical model is also particularly tailored to model the spatial distribution of keratins as the cell changes its shape.

We examined keratin aggregate formation and the possible mechanisms involved. With this aim, we observed the effect that different ratios between mutant and wild-type keratins expressed in cultured keratinocytes may have on aggregate formation in vitro, as well as how keratin aggregate formation affects the mechanical properties of cells at the cell cortex. To this end we prepared clones with expression rates as close as possible to 25%, 50% and 100% of the EGFP-K14 proteins (either WT or R125P and V270M mutants). Our results showed that only in the case of the 25% EGFP-K14 R125P mutant significant differences could be seen. Namely, we observed in this case the largest accumulation of keratin aggregates and a significant reduction in cell stiffness. To gain insight into the possible mechanisms behind this observation, we extended our previous mathematical model of keratin dynamics by implementing a more complex reaction network that considers the coexistence of wild-type and mutant keratins in the cell. The new model, consisting of a set of coupled, non-linear, ordinary differential equations, allowed us to draw conclusions regarding the relative amounts of intermediate filaments and aggregates in cells, and suggested that aggregate formation by asymmetric binding between wild-type and mutant keratins could explain the data obtained on cells grown in culture.

H₂O₂ released to the extracellular space (ECS) regulates diverse physiological processes, yet its concentrations and spatial distribution in tissues remain poorly defined. This uncertainty hampers mechanistic understanding of redox signaling. Here, we used reaction–diffusion modeling to estimate extracellular H₂O₂ concentrations and transport ranges in various scenarios. Idealized analytical models were combined with numerical models incorporating localized NADPH oxidase (NOX) clusters, ECS microstructure, membrane permeability, and the thioredoxin- and GSH-dependent clearance systems. Using maximal neutrophil and NOX O ₂ ^•− /H₂O₂ release rates, we obtained upper bounds for extracellular H₂O₂. Adjacent to isolated average-sized, fully active NOX2 clusters H ₂ O ₂ peaked at ∼540 nM at adhesion cell–cell separations, and decreased radially over ∼50– 100 nm. At the receptor cell surface, peak concentration decreased inversely with intercellular separation, to <5 nM at 1 µm separation. Radial decrease here, for this wide separation, was over ∼2.5 µm. Even the former maximal extracellular concentrations induce just a minimal, highly localized oxidation of the intracellular Prdx, Trx and GSH pools. In turn, maximally activated neutrophils carry ∼2000 such NOX2 clusters, inducing 10’s of µM peak ECS H ₂ O ₂ concentrations. These cause extensive Prdx and Trx oxidation near the exposed membranes. However, the GSH-dependent system still sustains a strong transmembrane gradient if the permeation barrier remains intact, and ECS H ₂ O ₂ concentrations decay to sub-µM within a few µm of the source cell. Extracellular H ₂ O ₂ concentrations scaled linearly with source flux in all the examined conditions. These results establish stringent constraints on autocrine, juxtacrine and next-cell paracrine H₂O₂ signaling.

As they navigate complex extracellular environments, cells and their nuclei undergo extensive deformation. Recent experiments have demonstrated that vascular endothelial cells cultured on microgroove substrates, which mimic the anisotropic topography of the basement membrane, exhibit complex nuclear deformations, leading to partial or even complete nuclear penetration into the microgrooves. Interestingly, the experiments suggest that nuclear entry into the microgrooves is driven mainly by cellular adhesion and spreading rather than by cytoskeleton-mediated pulling and/or pushing forces. In the present work, we develop a phase-field model to describe endothelial cell deformation on microgroove substrates and characterize the conditions necessary for nuclear confinement within the grooves, a process that has been termed "caging" in the experiments. The model introduces a novel non-local term that prevents the cellular body from fragmenting under conditions of strong adhesion and high curvature. Our numerical simulations show that significant nuclear deformation and partial caging occur for strong cell-substrate adhesion and for nuclear membrane stiffness close to or inferior to that of the cell membrane. We further show that the dimensions of the grooves are critical for the caging process, with increasing groove depth and width favoring nuclear penetration into and caging within the grooves. These results are in close agreement with experimental observations, thus corroborating the notion that cell-substrate adhesion forces can drive large-scale nuclear deformations without the need for cytoskeleton-generated forces.