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. 2020 Apr 9;21(7):2596. doi: 10.3390/ijms21072596

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© 2020 by the authors.

Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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(A) Plot of the filamentous plus particulate keratin concentrations for high values of $K_{P I}$ (wild-type) for different diffusion constants, $D_{I}$ , of the non-soluble filamentous keratin form. From the purple to the yellow line, $D_{I}$ decreases taking the values $D_{S}$ (purple), $0.1 D_{S}$ (teal), $0.02 D_{S}$ (blue), $0.01 D_{S}$ (orange) and $0.005 D_{S}$ (yellow). For all cases $D_{S} = 0.88 μ m^{2} / s^{- 1}$ , and the diffusion constant of the particulate keratin is set equal to the diffusion constant of the filamentous keratin. The advection towards the nucleus dominates diffusion for the lower diffusion constants of the keratin filaments, pushing the filaments into the neighborhood of the nucleus. (B) Plot of the filamentous plus particulate keratin distributions for low values of $K_{P I}$ (mutant), for different diffusion constants, $D_{I}$ , of the filamentous keratin form. From the purple to the yellow line, $D_{I}$ decreases taking the values $D_{S}$ (purple), $0.1 D_{S}$ (teal), $0.02 D_{S}$ (blue), $0.01 D_{S}$ (orange) and $0.005 D_{S}$ (yellow). For all cases $D_{S} = 0.88 μ m^{2} / s^{- 1}$ , and the diffusion constant for the particulate keratin is set equal to the diffusion constant of the filamentous keratin. We always observe an accumulation of particulate keratin at the cell membrane of the mutant cell for values of $D_{S} / D_{I}$ large enough to permit the accumulation of the keratin filaments at the nuclear membrane in the wild-type (blue, orange and yellow lines). (C) Plot of the filamentous plus particulate keratin concentrations for the high (wild-type, orange and blue curves) and low (mutant, green and purple curves) values of $K_{P I}$ . The plots in blue and purple represent the concentrations for constant keratin filament disassembly rate, $K_{S P}$ (in these curves we set $γ_{R} (\vec{r}) = 0.5$ , i.e., independent of the position within the cytoplasm). The orange and green curves are obtained with the keratin filament disassembly rate larger at the cell center, i.e., they are the same results presented in Figure 2D of the manuscript. We observe that in both situations for high values of $K_{P I}$ , the keratin filaments accumulate near the nucleus, while for the low values of $K_{P I}$ the insoluble keratin accumulates near the cell membrane. (D) Diagram representing a more complex model for keratin assembly. In this model the keratin particles are separated in two pools P1 and P2, where only keratin particles P1 can polymerize into filaments. We assume in this case that the mutation increases the reaction rate $K_{P 1 P 2}$ . This model can describe the distinction between different types of the keratin particles but recovers the same keratin particle spatial distribution as the simpler model.