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Mathematical modelling of WOX5- and CLE40-mediated columella stem cell homeostasis in Arabidopsis.

Richards S, Wink RH, Simon R - J. Exp. Bot. (2015)

Bottom Line: We have also found that WOX5 contributes to, but is not absolutely necessary for, CSC maintenance.Furthermore, our modelling led us to postulate an additional signalling molecule that promotes CSC maintenance.We propose that this WOX5-independent signal originates in the QC, is targeted by CLE40 signalling and is capable of maintaining CSCs.

View Article: PubMed Central - PubMed

Affiliation: Institute of Developmental Genetics, Heinrich Heine University, 40225 Düsseldorf, Germany.

No MeSH data available.


Graphical and mathematical representations of the C/W/X multi-cell model. The C/W/X model was constructed by adding X to the C/W multi-cell model and giving it the same role as W. (A) C represses W (green) and X (purple). W represses FCC (orange), and X represses FCC (pink). FCC promotes C (teal). Production of W and X is confined to the QC cell (yellow). (B) The model simulates a cell column. The cell with index i=1 is the QC (yellow cell), while the model determines the fates of those distal to it. W, X and C can all diffuse through the cell column and the value of each in cell i are denoted Wi, Xi and Ci. (C) Equations 8, 9, 10, and 11. The production terms of W and X in the yellow box only apply in the QC cell and production of W and X is restricted by the amount of C signalling to the QC (green). Diffusion terms track the fluxes of W, X and C between cell i and its proximal neighbour (dotted underline) and between cell i and its distal neighbour (solid underline). A diffusion term is omitted if the value of i is outside of 1 through 5; there is no flow between the QC and the cell proximal to it and no flow between the 5th cell and the cell distal to it. The value of FCC in cell i (FCC,i) is determined by the sum of Wi and Xi. FCC,i determines the fate of cell i and the production rate of C (teal) in cell i. W and C are degraded at constant rates (grey).
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Figure 8: Graphical and mathematical representations of the C/W/X multi-cell model. The C/W/X model was constructed by adding X to the C/W multi-cell model and giving it the same role as W. (A) C represses W (green) and X (purple). W represses FCC (orange), and X represses FCC (pink). FCC promotes C (teal). Production of W and X is confined to the QC cell (yellow). (B) The model simulates a cell column. The cell with index i=1 is the QC (yellow cell), while the model determines the fates of those distal to it. W, X and C can all diffuse through the cell column and the value of each in cell i are denoted Wi, Xi and Ci. (C) Equations 8, 9, 10, and 11. The production terms of W and X in the yellow box only apply in the QC cell and production of W and X is restricted by the amount of C signalling to the QC (green). Diffusion terms track the fluxes of W, X and C between cell i and its proximal neighbour (dotted underline) and between cell i and its distal neighbour (solid underline). A diffusion term is omitted if the value of i is outside of 1 through 5; there is no flow between the QC and the cell proximal to it and no flow between the 5th cell and the cell distal to it. The value of FCC in cell i (FCC,i) is determined by the sum of Wi and Xi. FCC,i determines the fate of cell i and the production rate of C (teal) in cell i. W and C are degraded at constant rates (grey).

Mentions: To determine if the single-cell model implemented in several cells could describe experimental results, a modified version of the model was implemented in a virtual cell column, with the most proximal cell defined as the W-producing QC cell and the rest allowed to take on either CSC or CC fate. The fate of each cell would still depend on W via FCC as in the single-cell model. With this C/W multi-cell model, W and C could diffuse through the cells, emulating inter-cellular communication. The value of C at the QC determines the production rate of W. The network diagram for the C/W multi-cell model is shown in Fig. 5. We also implemented an alternative model (Supplementary File S1), where values of C at each cell decreased the mobility of WOX5 through that cell, and the results of the alternative model matched the results of the C/W multi-cell model distal to the QC. The alternative C/W multi-cell model, where C regulates W mobility rather than production, is described by the following equations, where the BW term in equation 11 (shown in Fig. 8) only applies in the QC (cell i=1). The equation for FCC,i is identical to equation 7 shown in Fig. 5.


Mathematical modelling of WOX5- and CLE40-mediated columella stem cell homeostasis in Arabidopsis.

Richards S, Wink RH, Simon R - J. Exp. Bot. (2015)

Graphical and mathematical representations of the C/W/X multi-cell model. The C/W/X model was constructed by adding X to the C/W multi-cell model and giving it the same role as W. (A) C represses W (green) and X (purple). W represses FCC (orange), and X represses FCC (pink). FCC promotes C (teal). Production of W and X is confined to the QC cell (yellow). (B) The model simulates a cell column. The cell with index i=1 is the QC (yellow cell), while the model determines the fates of those distal to it. W, X and C can all diffuse through the cell column and the value of each in cell i are denoted Wi, Xi and Ci. (C) Equations 8, 9, 10, and 11. The production terms of W and X in the yellow box only apply in the QC cell and production of W and X is restricted by the amount of C signalling to the QC (green). Diffusion terms track the fluxes of W, X and C between cell i and its proximal neighbour (dotted underline) and between cell i and its distal neighbour (solid underline). A diffusion term is omitted if the value of i is outside of 1 through 5; there is no flow between the QC and the cell proximal to it and no flow between the 5th cell and the cell distal to it. The value of FCC in cell i (FCC,i) is determined by the sum of Wi and Xi. FCC,i determines the fate of cell i and the production rate of C (teal) in cell i. W and C are degraded at constant rates (grey).
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Figure 8: Graphical and mathematical representations of the C/W/X multi-cell model. The C/W/X model was constructed by adding X to the C/W multi-cell model and giving it the same role as W. (A) C represses W (green) and X (purple). W represses FCC (orange), and X represses FCC (pink). FCC promotes C (teal). Production of W and X is confined to the QC cell (yellow). (B) The model simulates a cell column. The cell with index i=1 is the QC (yellow cell), while the model determines the fates of those distal to it. W, X and C can all diffuse through the cell column and the value of each in cell i are denoted Wi, Xi and Ci. (C) Equations 8, 9, 10, and 11. The production terms of W and X in the yellow box only apply in the QC cell and production of W and X is restricted by the amount of C signalling to the QC (green). Diffusion terms track the fluxes of W, X and C between cell i and its proximal neighbour (dotted underline) and between cell i and its distal neighbour (solid underline). A diffusion term is omitted if the value of i is outside of 1 through 5; there is no flow between the QC and the cell proximal to it and no flow between the 5th cell and the cell distal to it. The value of FCC in cell i (FCC,i) is determined by the sum of Wi and Xi. FCC,i determines the fate of cell i and the production rate of C (teal) in cell i. W and C are degraded at constant rates (grey).
Mentions: To determine if the single-cell model implemented in several cells could describe experimental results, a modified version of the model was implemented in a virtual cell column, with the most proximal cell defined as the W-producing QC cell and the rest allowed to take on either CSC or CC fate. The fate of each cell would still depend on W via FCC as in the single-cell model. With this C/W multi-cell model, W and C could diffuse through the cells, emulating inter-cellular communication. The value of C at the QC determines the production rate of W. The network diagram for the C/W multi-cell model is shown in Fig. 5. We also implemented an alternative model (Supplementary File S1), where values of C at each cell decreased the mobility of WOX5 through that cell, and the results of the alternative model matched the results of the C/W multi-cell model distal to the QC. The alternative C/W multi-cell model, where C regulates W mobility rather than production, is described by the following equations, where the BW term in equation 11 (shown in Fig. 8) only applies in the QC (cell i=1). The equation for FCC,i is identical to equation 7 shown in Fig. 5.

Bottom Line: We have also found that WOX5 contributes to, but is not absolutely necessary for, CSC maintenance.Furthermore, our modelling led us to postulate an additional signalling molecule that promotes CSC maintenance.We propose that this WOX5-independent signal originates in the QC, is targeted by CLE40 signalling and is capable of maintaining CSCs.

View Article: PubMed Central - PubMed

Affiliation: Institute of Developmental Genetics, Heinrich Heine University, 40225 Düsseldorf, Germany.

No MeSH data available.