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The importance of structured noise in the generation of self-organizing tissue patterns through contact-mediated cell-cell signalling.

Cohen M, Baum B, Miodownik M - J R Soc Interface (2010)

Bottom Line: Here, we develop a general model of protrusion-based patterning to analyse the role of noise in this process.By analysing the effects of introducing thresholds required for signal detection in this model of lateral inhibition, our study shows how filopodia-mediated cell-cell communication can generate complex patterns of spots and stripes, which, in the presence of signalling noise, align themselves across a patterning field.Thus, intermittent protrusion-based signalling has the potential to yield robust self-organizing tissue-wide patterns without the need to invoke diffusion-mediated signalling.

View Article: PubMed Central - PubMed

Affiliation: CoMPLEX, University College London, London, UK. m.cohen@ucl.ac.uk

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Patterns of stripes align owing to signal noise. (a,b) Simulations of inhibitory signalling with a signalling range of two cells, an inhibitory threshold, T = 9, and temporal signalling noise, Nt = 0.01. The active signalling cells and the neighbourhood of inactive cells are labelled according to the colour key in (e). The number of simulations steps and total events (in brackets) is shown progressing from left to right. In (a), where a small array of 20 × 20 cells was used, the initial pattern of randomly orientated stripes can be seen to align, over time, with the array boundaries where there is no signal. In (b), where a larger array of 100 × 100 cells (with toroidal boundaries) was used, distinct zones of aligned stripes are formed as a result of the signalling noise. See also the electronic supplementary material, movie 2. (c) Graphical visualization of the patterning process. The figure shows the cumulative proportion of each cell type (as defined in the colour key in (e)) obtained from data averaged over 10 simulations with the conditions specified in (b). The process of stripe alignment correlates with a transition from n = T and n = T + 1 cells to n = T + 2 cells. Also plotted are the number of events per time step and the CV in the pattern spacing. With stripe alignment there is no change in the CV of the pattern spacing. (d) A comparison of the final pattern state achieved after 10 000 steps with different amounts of signal noise. The figures show the mean values obtained after 10 simulations at a signal range of two cells and a threshold, T = 9. Optimized patterns are achieved with noise levels in the range 0.001 < Nt <0.01. Similar results (data not shown) were obtained when spatial noise was used instead of (or in addition to) temporal noise. NB: Standard errors (95% confidence intervals) in the mean values plotted in (c,d) were less than 1% (left-hand y-axis) and less than 0.01 (right-hand y-axis) and so were not visible on this scale.
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RSIF20100488F6: Patterns of stripes align owing to signal noise. (a,b) Simulations of inhibitory signalling with a signalling range of two cells, an inhibitory threshold, T = 9, and temporal signalling noise, Nt = 0.01. The active signalling cells and the neighbourhood of inactive cells are labelled according to the colour key in (e). The number of simulations steps and total events (in brackets) is shown progressing from left to right. In (a), where a small array of 20 × 20 cells was used, the initial pattern of randomly orientated stripes can be seen to align, over time, with the array boundaries where there is no signal. In (b), where a larger array of 100 × 100 cells (with toroidal boundaries) was used, distinct zones of aligned stripes are formed as a result of the signalling noise. See also the electronic supplementary material, movie 2. (c) Graphical visualization of the patterning process. The figure shows the cumulative proportion of each cell type (as defined in the colour key in (e)) obtained from data averaged over 10 simulations with the conditions specified in (b). The process of stripe alignment correlates with a transition from n = T and n = T + 1 cells to n = T + 2 cells. Also plotted are the number of events per time step and the CV in the pattern spacing. With stripe alignment there is no change in the CV of the pattern spacing. (d) A comparison of the final pattern state achieved after 10 000 steps with different amounts of signal noise. The figures show the mean values obtained after 10 simulations at a signal range of two cells and a threshold, T = 9. Optimized patterns are achieved with noise levels in the range 0.001 < Nt <0.01. Similar results (data not shown) were obtained when spatial noise was used instead of (or in addition to) temporal noise. NB: Standard errors (95% confidence intervals) in the mean values plotted in (c,d) were less than 1% (left-hand y-axis) and less than 0.01 (right-hand y-axis) and so were not visible on this scale.

Mentions: To further investigate the dynamics of this process, we carried out simulations at different lattice sizes and boundary types. Figure 6 shows the results of when noisy signalling was implemented with second neighbour shell communication and an inhibition threshold of nine signalling cells (see also electronic supplementary material, movie M2). In the smaller array with fixed boundaries (figure 6a), the stripes align themselves to the cell boundaries (at which there was no signal). In a large array with toroidal boundaries (figure 6b), regions of alignment emerge. This demonstrates that the tendency for stripes to locally align is an inherent property of the system that is not boundary dependent. However, in the smaller array, the fixed boundaries bias the orientation of this local effect. Note that when simulations were implemented in a large array with fixed boundaries (data not shown) stripes close to boundaries aligned with them; however, stripes in the central field aligned themselves in arbitrary directions within distinct regions (as in figure 6b). We think it probable that, based upon the scale of most biological patterns [3,40], boundary effects will be significant in most developmental systems (as in figure 6a).Figure 6.


The importance of structured noise in the generation of self-organizing tissue patterns through contact-mediated cell-cell signalling.

Cohen M, Baum B, Miodownik M - J R Soc Interface (2010)

Patterns of stripes align owing to signal noise. (a,b) Simulations of inhibitory signalling with a signalling range of two cells, an inhibitory threshold, T = 9, and temporal signalling noise, Nt = 0.01. The active signalling cells and the neighbourhood of inactive cells are labelled according to the colour key in (e). The number of simulations steps and total events (in brackets) is shown progressing from left to right. In (a), where a small array of 20 × 20 cells was used, the initial pattern of randomly orientated stripes can be seen to align, over time, with the array boundaries where there is no signal. In (b), where a larger array of 100 × 100 cells (with toroidal boundaries) was used, distinct zones of aligned stripes are formed as a result of the signalling noise. See also the electronic supplementary material, movie 2. (c) Graphical visualization of the patterning process. The figure shows the cumulative proportion of each cell type (as defined in the colour key in (e)) obtained from data averaged over 10 simulations with the conditions specified in (b). The process of stripe alignment correlates with a transition from n = T and n = T + 1 cells to n = T + 2 cells. Also plotted are the number of events per time step and the CV in the pattern spacing. With stripe alignment there is no change in the CV of the pattern spacing. (d) A comparison of the final pattern state achieved after 10 000 steps with different amounts of signal noise. The figures show the mean values obtained after 10 simulations at a signal range of two cells and a threshold, T = 9. Optimized patterns are achieved with noise levels in the range 0.001 < Nt <0.01. Similar results (data not shown) were obtained when spatial noise was used instead of (or in addition to) temporal noise. NB: Standard errors (95% confidence intervals) in the mean values plotted in (c,d) were less than 1% (left-hand y-axis) and less than 0.01 (right-hand y-axis) and so were not visible on this scale.
© Copyright Policy - open-access
Related In: Results  -  Collection

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RSIF20100488F6: Patterns of stripes align owing to signal noise. (a,b) Simulations of inhibitory signalling with a signalling range of two cells, an inhibitory threshold, T = 9, and temporal signalling noise, Nt = 0.01. The active signalling cells and the neighbourhood of inactive cells are labelled according to the colour key in (e). The number of simulations steps and total events (in brackets) is shown progressing from left to right. In (a), where a small array of 20 × 20 cells was used, the initial pattern of randomly orientated stripes can be seen to align, over time, with the array boundaries where there is no signal. In (b), where a larger array of 100 × 100 cells (with toroidal boundaries) was used, distinct zones of aligned stripes are formed as a result of the signalling noise. See also the electronic supplementary material, movie 2. (c) Graphical visualization of the patterning process. The figure shows the cumulative proportion of each cell type (as defined in the colour key in (e)) obtained from data averaged over 10 simulations with the conditions specified in (b). The process of stripe alignment correlates with a transition from n = T and n = T + 1 cells to n = T + 2 cells. Also plotted are the number of events per time step and the CV in the pattern spacing. With stripe alignment there is no change in the CV of the pattern spacing. (d) A comparison of the final pattern state achieved after 10 000 steps with different amounts of signal noise. The figures show the mean values obtained after 10 simulations at a signal range of two cells and a threshold, T = 9. Optimized patterns are achieved with noise levels in the range 0.001 < Nt <0.01. Similar results (data not shown) were obtained when spatial noise was used instead of (or in addition to) temporal noise. NB: Standard errors (95% confidence intervals) in the mean values plotted in (c,d) were less than 1% (left-hand y-axis) and less than 0.01 (right-hand y-axis) and so were not visible on this scale.
Mentions: To further investigate the dynamics of this process, we carried out simulations at different lattice sizes and boundary types. Figure 6 shows the results of when noisy signalling was implemented with second neighbour shell communication and an inhibition threshold of nine signalling cells (see also electronic supplementary material, movie M2). In the smaller array with fixed boundaries (figure 6a), the stripes align themselves to the cell boundaries (at which there was no signal). In a large array with toroidal boundaries (figure 6b), regions of alignment emerge. This demonstrates that the tendency for stripes to locally align is an inherent property of the system that is not boundary dependent. However, in the smaller array, the fixed boundaries bias the orientation of this local effect. Note that when simulations were implemented in a large array with fixed boundaries (data not shown) stripes close to boundaries aligned with them; however, stripes in the central field aligned themselves in arbitrary directions within distinct regions (as in figure 6b). We think it probable that, based upon the scale of most biological patterns [3,40], boundary effects will be significant in most developmental systems (as in figure 6a).Figure 6.

Bottom Line: Here, we develop a general model of protrusion-based patterning to analyse the role of noise in this process.By analysing the effects of introducing thresholds required for signal detection in this model of lateral inhibition, our study shows how filopodia-mediated cell-cell communication can generate complex patterns of spots and stripes, which, in the presence of signalling noise, align themselves across a patterning field.Thus, intermittent protrusion-based signalling has the potential to yield robust self-organizing tissue-wide patterns without the need to invoke diffusion-mediated signalling.

View Article: PubMed Central - PubMed

Affiliation: CoMPLEX, University College London, London, UK. m.cohen@ucl.ac.uk

Show MeSH
Related in: MedlinePlus