Fig 1.
A diagram representing the involvement of pH, LEKTI, and KLKs in the desquamation process.
Desmosomes (white ellipses) are converted to corneodesmosomes (green ellipses) as they enter the stratum corneum (SC in figure) from the granular layer (GL in figure). These corneodesmosomes are then degraded by KLKs, first on the horizontal surfaces then the vertical (indicated by the scissors). The degradation process is inhibited by LEKTI, which binds with the KLKs and stops the KLKs from binding with the corneodesmosomes. The local pH regulates the inhibition, and the corneodesmosome degradation rate by KLKs. Arrows with ‘+’ symbols indicate the pH increases the reaction, while ‘⟞’ indicates the pH reduces the rate of the reaction.
Table 1.
The parameter values for the subcellular and multiscale model.
Values are given for the multiscale model and the rate parameters used for the single cell system are given in columns 3 and 5 respectively.
Fig 2.
Solution of the subcellular model for a cell moving at a specified velocity through the pH gradient of the corneum, using an effective concentration of KLK enzyme: s0 = 10 μM, eT = iT = 0.1 nM.
This is a reduction in enzyme by a factor of 10−4 (from 0.7 μM).
Fig 3.
Diagram of the coupling between the multicellular and the subcellular scales.
Cells are coloured by their proportion of remaining corneodesmosome. The cell gets its vertical location, normalised by corneum thickness and start height, (ξi) from the multiscale model, updates the subcellular model parameters and solves for that time step, and then returns the updated proportion of remaining corneodesmosomes (si) to the multicellular model to scale cell-cell adhesion ().
Fig 4.
Model results for normal homeostatic tissue.
(A) An example of the simulation output for one time point. Cells are coloured by their proportion of remaining corneodesmosome (s). A video of this simulation can be found in S1 Video. (B) The tissue thickness over time for 10 simulations. The dashed line shows the mean and the ribbon the minimum and maximum of all realisations over time. Green indicates the overall tissue thickness and blue the corneum thickness (4 CD less than the tissue). (C) Reactant levels for each cell at one time point in one simulation. The dashed black line shows the expected solution of the subcellular model given the expected vertical velocity. The inset shows the detail of the change in free inhibitor (LEKTI) levels as i is defined as iT/s0 and therefore has a maximum possible value of 10−5 when iT = eT = 0.1 nM and s0 = 10 μM. (D) The average vertical velocity over time. The ribbon indicates the range seen across 10 simulations, and the line is the mean of the simulations. The velocity is calculated based on cells in the main tissue and does not include stem cells or cells that are experiencing the desquamation force. (E) Cell turnover time (age at which cells are removed from the system).
Fig 5.
Tissue structure and thickness results for different levels of inhibitor.
(A) Simulation output from one simulation (with no inhibitor) at one time point, showing the level of adhesion protein s in each cell. Note, there is no apparent difference in system dynamics compared to the normal system, just an increased rate of reduced s in time and consequently seen in the vertical direction in the image. A video of this simulation is provided in S2 Video. (B) The steady state thickness values. The points show the mean and the bars indicate the minimum and maximum thickness over the 10 realisations of each setup. The dashed line is a linear fit to the points, with the equation given in the lower right. (C) and (D) Abnormal tissue s and e levels with different levels of inhibitor. The data is taken from the final time point of one simulation for each inhibitor concentration. The dashed lines show the steady state heights for iT = 0 (black) and iT = eT (blue or red).
Fig 6.
(A) The mean vertical cell velocity for different levels of inhibitor. The box plot shows the quartiles, and the error bars give the minimum and maximum across all cells and simulations. The velocity profile is similar across all setups. (B) The cell turnover time, from birth to desquamation, for different levels of inhibitor. The box plot shows the quartiles, and the error bars give the minimum and maximum across all cells and simulations. The box plot shows there are a large number of outlier cells with high turnover times. (C) The steady state against the cell turnover time. The dashed line is a linear fit to the points, with the equation given in the lower right.
Fig 7.
Simulation results for different proportions of normal stem cells (generate cells with normal inhibitor levels) to abnormal stem cells (generate cells with no inhibitor).
(A) Steady state corneum height. The points are the mean and the bars indicate the minimum to maximums for the 10 realisations of each setup. The solid line is a quadratic fit (equation given in legend), and the dotted line shows the expected results for a linear relationship. (B) Reactant levels of each cell at one time point with 50% normal stem cells and 50% abnormal (no) stem cells. The dashed line is the steady state height. The two paths for both s (red) and e (blue) are the different subcellular system dynamics for cells that have normal inhibitor levels (lower e and slower reduction in s) compared to cells with no inhibitor (higher e and faster reduction in s). (C) and (D) Simulation snapshots with cells coloured by their proportion of free enzyme, e (C) or proportion of remaining substrate, s (D). A video of this simulation can be found in S3 Video. (E) Cell velocities. The box plot shows the quartiles, and the error bars give the minimum and maximum across all cells and simulations. The velocity profile is similar across the different proportions. (F) Turnover times of differentiated cells. The box plot shows the quartiles, and the error bars give the minimum and maximum across all cells and simulations.
Table 2.
Parameters used to determine the concentration of KLK5 enzyme.
Table 3.
Parameters used to determine the concentration of corneodesmosome proteins.
Fig 8.
The signed magnitude of the adhesive and repulsive forces (Fij) experienced between two cells (i and j) as a function of rij, the distance between the cell boundaries.
CD: Cell diameters.
Fig 9.
Surface cells experience a vertical desquamation force. Once they detach from the tissue they get removed. Detachment is defined by determining the connected tissue set, starting with the set of attached cells.