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Quantification of variability in trichome patterns.

Greese B, Hülskamp M, Fleck C - Front Plant Sci (2014)

Bottom Line: One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication.To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns.Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.

View Article: PubMed Central - PubMed

Affiliation: Computational Biology and Biological Physics, Faculty for Theoretical Physics and Astronomy, Lund University Lund, Sweden.

ABSTRACT
While pattern formation is studied in various areas of biology, little is known about the noise leading to variations between individual realizations of the pattern. One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication. These processes are potentially variable due to, e.g., the abundance of cell components or environmental conditions. To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns. Here, we review recent approaches toward characterization of noise on trichome initiation. We present methods for the quantification of spatial patterns, which are the basis for data-driven mathematical modeling and enable the analysis of noise from different sources. Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.

No MeSH data available.


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Spatial variability in trichome patterns and influence of different sources of noise. (A,B) Effect of the reduced activator mobility (k15). (A) Immobile activator (k15 = 0). This situation resembles the trichome patterning system as the activating complex of GL1 and GL3 is cell autonomous. The disorder from the random initial conditions remain in the final pattern. (B) With increasing activator mobility (k15 = 0.075) the peaks widen and the pattern becomes more regular. (C) Effect of noisy initial conditions on simulated trichome patterns with mobile activator. The plot shows the normalized mean variation coefficient of the neighbor distances (squares) and angles (triangles) as well as the normalized mean anisotropy (circles). All measures decrease for increasing activator mobility, thereby illustrating less variability. (D) Effect of random spatially inhomogeneous parameters on the simulated trichome pattern with mobile activator. The plot shows the mean relative neighbor measures (distances lower group, angles middle group, anisotropy upper group) for three selected model parameters that are represented by line styles. (C,D) All measures are normalized to the values of a random point pattern, i.e., zero denotes a perfectly regular and one a completely random point pattern. Reproduced with permission from Greese et al. (2012) © The Institution of Engineering and Technology.
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Figure 3: Spatial variability in trichome patterns and influence of different sources of noise. (A,B) Effect of the reduced activator mobility (k15). (A) Immobile activator (k15 = 0). This situation resembles the trichome patterning system as the activating complex of GL1 and GL3 is cell autonomous. The disorder from the random initial conditions remain in the final pattern. (B) With increasing activator mobility (k15 = 0.075) the peaks widen and the pattern becomes more regular. (C) Effect of noisy initial conditions on simulated trichome patterns with mobile activator. The plot shows the normalized mean variation coefficient of the neighbor distances (squares) and angles (triangles) as well as the normalized mean anisotropy (circles). All measures decrease for increasing activator mobility, thereby illustrating less variability. (D) Effect of random spatially inhomogeneous parameters on the simulated trichome pattern with mobile activator. The plot shows the mean relative neighbor measures (distances lower group, angles middle group, anisotropy upper group) for three selected model parameters that are represented by line styles. (C,D) All measures are normalized to the values of a random point pattern, i.e., zero denotes a perfectly regular and one a completely random point pattern. Reproduced with permission from Greese et al. (2012) © The Institution of Engineering and Technology.

Mentions: The trichome initiation process resembles an activator-inhibitor system with an immobile activator (Gierer and Meinhardt, 1972; Meinhardt and Gierer, 1974; Koch and Meinhardt, 1994). If both, the activator and the inhibitor, are mobile, the resulting pattern depends only weakly on the initial conditions (Maini et al., 1997; Page et al., 2005). In a fast initial phase the early activator peaks are formed. These are usually not very pronounced. On a longer time-scale the activator peaks align and grow. Biologically, only the peaks at the later stage lead to an observable result, unless it becomes feasible to track the protein content in single cells in a tissue. The mobility of the activator allows the activator peaks to move slightly for optimal alignment (Holloway and Harrison, 1995; Ward and Wei, 2002). However, in the singular limit of vanishing activator mobility the optimal alignment of the peaks is impaired, and noise from the initial conditions remains in the final pattern. This can be seen in Figures 3A,B, where we show examples of simulation results for increasing mobility of the activator (see Figure 3, text box for further explanation). In Figure 3C the local irregularity of the simulated trichome pattern is plotted against the mobility of the activator (which is a complex consisting of GL1 and GL3 in case of the simulated trichome system). The pattern becomes more irregular with decreasing activator mobility, which is a known effect in reaction-diffusion systems (Holloway and Harrison, 1995). In other words, the cell autonomy of the activator in trichome patterning restricts the degree of regularity (see Greese et al., 2012 for details).


Quantification of variability in trichome patterns.

Greese B, Hülskamp M, Fleck C - Front Plant Sci (2014)

Spatial variability in trichome patterns and influence of different sources of noise. (A,B) Effect of the reduced activator mobility (k15). (A) Immobile activator (k15 = 0). This situation resembles the trichome patterning system as the activating complex of GL1 and GL3 is cell autonomous. The disorder from the random initial conditions remain in the final pattern. (B) With increasing activator mobility (k15 = 0.075) the peaks widen and the pattern becomes more regular. (C) Effect of noisy initial conditions on simulated trichome patterns with mobile activator. The plot shows the normalized mean variation coefficient of the neighbor distances (squares) and angles (triangles) as well as the normalized mean anisotropy (circles). All measures decrease for increasing activator mobility, thereby illustrating less variability. (D) Effect of random spatially inhomogeneous parameters on the simulated trichome pattern with mobile activator. The plot shows the mean relative neighbor measures (distances lower group, angles middle group, anisotropy upper group) for three selected model parameters that are represented by line styles. (C,D) All measures are normalized to the values of a random point pattern, i.e., zero denotes a perfectly regular and one a completely random point pattern. Reproduced with permission from Greese et al. (2012) © The Institution of Engineering and Technology.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4230044&req=5

Figure 3: Spatial variability in trichome patterns and influence of different sources of noise. (A,B) Effect of the reduced activator mobility (k15). (A) Immobile activator (k15 = 0). This situation resembles the trichome patterning system as the activating complex of GL1 and GL3 is cell autonomous. The disorder from the random initial conditions remain in the final pattern. (B) With increasing activator mobility (k15 = 0.075) the peaks widen and the pattern becomes more regular. (C) Effect of noisy initial conditions on simulated trichome patterns with mobile activator. The plot shows the normalized mean variation coefficient of the neighbor distances (squares) and angles (triangles) as well as the normalized mean anisotropy (circles). All measures decrease for increasing activator mobility, thereby illustrating less variability. (D) Effect of random spatially inhomogeneous parameters on the simulated trichome pattern with mobile activator. The plot shows the mean relative neighbor measures (distances lower group, angles middle group, anisotropy upper group) for three selected model parameters that are represented by line styles. (C,D) All measures are normalized to the values of a random point pattern, i.e., zero denotes a perfectly regular and one a completely random point pattern. Reproduced with permission from Greese et al. (2012) © The Institution of Engineering and Technology.
Mentions: The trichome initiation process resembles an activator-inhibitor system with an immobile activator (Gierer and Meinhardt, 1972; Meinhardt and Gierer, 1974; Koch and Meinhardt, 1994). If both, the activator and the inhibitor, are mobile, the resulting pattern depends only weakly on the initial conditions (Maini et al., 1997; Page et al., 2005). In a fast initial phase the early activator peaks are formed. These are usually not very pronounced. On a longer time-scale the activator peaks align and grow. Biologically, only the peaks at the later stage lead to an observable result, unless it becomes feasible to track the protein content in single cells in a tissue. The mobility of the activator allows the activator peaks to move slightly for optimal alignment (Holloway and Harrison, 1995; Ward and Wei, 2002). However, in the singular limit of vanishing activator mobility the optimal alignment of the peaks is impaired, and noise from the initial conditions remains in the final pattern. This can be seen in Figures 3A,B, where we show examples of simulation results for increasing mobility of the activator (see Figure 3, text box for further explanation). In Figure 3C the local irregularity of the simulated trichome pattern is plotted against the mobility of the activator (which is a complex consisting of GL1 and GL3 in case of the simulated trichome system). The pattern becomes more irregular with decreasing activator mobility, which is a known effect in reaction-diffusion systems (Holloway and Harrison, 1995). In other words, the cell autonomy of the activator in trichome patterning restricts the degree of regularity (see Greese et al., 2012 for details).

Bottom Line: One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication.To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns.Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.

View Article: PubMed Central - PubMed

Affiliation: Computational Biology and Biological Physics, Faculty for Theoretical Physics and Astronomy, Lund University Lund, Sweden.

ABSTRACT
While pattern formation is studied in various areas of biology, little is known about the noise leading to variations between individual realizations of the pattern. One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication. These processes are potentially variable due to, e.g., the abundance of cell components or environmental conditions. To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns. Here, we review recent approaches toward characterization of noise on trichome initiation. We present methods for the quantification of spatial patterns, which are the basis for data-driven mathematical modeling and enable the analysis of noise from different sources. Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.

No MeSH data available.


Related in: MedlinePlus