Keratin dynamics: modeling the interplay between turnover and transport

Abstract

Keratin are among the most abundant proteins in epithelial cells. Functions of the keratin network in cells are shaped by their dynamical organization. Using a collection of experimentally-driven mathematical models, different hypotheses for the turnover and transport of the keratin material in epithelial cells are tested. The interplay between turnover and transport and their effects on the keratin organization in cells are hence investigated by combining mathematical modeling and experimental data. Amongst the collection of mathematical models considered, a best model strongly supported by experimental data is identified. Fundamental to this approach is the fact that optimal parameter values associated with the best fit for each model are established. The best candidate among the best fits is characterized by the disassembly of the assembled keratin material in the perinuclear region and an active transport of the assembled keratin. Our study shows that an active transport of the assembled keratin is required to explain the experimentally observed keratin organization.

Fig 1. Keratin network.

Image taken from a time-lapse fluorescence recording of a single hepatocellular carcinoma-derived PLC cell of clone PK18-5 [8] stably expressing fluorescent fusion protein HK18-YFP consisting of human keratin 18 and enhanced yellow fluorescent protein. Bar 10 μm.

Fig 2. Experimental data adapted from [12].

2.1: The spatial distribution of the assembled keratin material. The mean concentration of the keratin material used in the conversion of fluorescence intensities to concentrations is estimated to be equal to 520μM in [15]. Circles represent raw experimental data; curves are fits of experimental data. Details on P(x) and f _final(x) can be found in Appendix 4. 2.2: The speed of the assembled keratin material at 24 hours. 2.3: Regions of assembly and disassembly denoted Sources and Sinks respectively. In all figures, the cell is represented by a one-dimensional cross-section domain centered at the center of the cell; plasma membrane positions are at ±L = ±22.5μm, the nuclear envelope is located at ±7.5μm and the center of the cell is located at zero.

Fig 3. Profiles of the active transport speeds u(x) and v(x) for the insoluble pool both of which are derived from the experimental measurements in [12].

The function u(x) is derived from the profile of speeds and v(x) is approximated as the average value of these speeds. Details on the derivation of u(x) and v(x) are given in Appendix 1.

Fig 4. Possible profiles for the assembly and disassembly rates.

4.1: k _ass = 10⁻³ s ⁻¹ when the linear model is used (resp. μM.s ⁻¹ when the nonlinear model is used) and k _ass(x) is computed using (14). 4.2: k _dis = 10⁻³ s ⁻¹ when the linear model is used (resp. μM.s ⁻¹ when the nonlinear model is used) and k _dis(x) are computed using (15) for Sinks and (16) for Mollify, respectively. Details on the derivation of k _ass(x) and k _dis(x) rates are given in Appendix 2 and Appendix 3, respectively. Parameter values in (14), (15) and (16) are chosen in such a way that their profiles give the same total amount of assembly / disassembly over the spatial domain Ω.

Fig 5. The 36 scenarios to be considered.

Top: Number in parentheses is the scenario index i. Bottom: The numerical value 1 denotes that the process of interest is in Scenario i.

Fig 6. Initial profile of the insoluble pool f ₀(x) defined in (17).

Fig 7. Best fit for each of the 36 scenarios.

Red curve is the response $I_i(x,t_{final},\widehat{p})$ at 48 hours of Scenario i. Black circles are data at 48 hours as in Fig 2.1.

Fig 8. Details about the best model Scenario 21.

8.1: Snapshots from 24 hours (gray) to 48 hours (black) taken every 30 minutes of the profile of the soluble pool over the cell. 8.2: Snapshots from 24 hours (gray) to 48 hours (black) taken every 30 minutes of the profile of the insoluble pool over the cell. 8.3: The distribution of the keratin material between the soluble and insoluble pools over time. 8.4: The profiles of assembly and disassembly maximal rates used with the Michaelis-Menten type turnover terms in Scenario 21. The estimates are k _ass = 9.3819μM/s, k _S = 570.73μM, k _dis = 0.9998μM/s leading to k _max = 1.976μM/s in (16) and k _I = 976.07μM/s.

Fig 9. Estimate of the space-dependent speed.

Estimate of the space-dependent speed given in (13) for the variable speed u(x) of the active transport of the insoluble pool.

Fig 10. Profile for localized assembly rate of type Sources.

The profile for k _ass(x) defined in (14) with k _max = 1, obtained by fitting the profile of assembly regions Sources published in [12] and shown in Fig 2.3.

Fig 11. Profile for localized disassembly rate of type Sinks.

The profile for k _dis(x) defined in (15) and k _max = 1, obtained by fitting the profile of disassembly regions Sinks published in [12] and shown in Fig 2.3.