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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.


Related in: MedlinePlus

Estimation of the amount of noise in the experimentally observed trichome pattern. (A–C) A hexagon pattern with increasing amount of noise, controlled by the parameter ε (A: ε=0.1, B: ε=0.3, C: ε=0.5). (D) Difference between the local irregularity as measured by the distance between neighbors, the angle between pairs of adjacent neighbors, and the anisotropy of the neighbors distribution of the observed trichome and a noisy hexagonal pattern. The minimum shows that trichomes resemble a hexagonal pattern with a noise level of 0.44. Reproduced with permission from Greese et al. (2012) © The Institution of Engineering and Technology.
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Figure 2: Estimation of the amount of noise in the experimentally observed trichome pattern. (A–C) A hexagon pattern with increasing amount of noise, controlled by the parameter ε (A: ε=0.1, B: ε=0.3, C: ε=0.5). (D) Difference between the local irregularity as measured by the distance between neighbors, the angle between pairs of adjacent neighbors, and the anisotropy of the neighbors distribution of the observed trichome and a noisy hexagonal pattern. The minimum shows that trichomes resemble a hexagonal pattern with a noise level of 0.44. Reproduced with permission from Greese et al. (2012) © The Institution of Engineering and Technology.

Mentions: Other studies have used various related tessellation-based measures to characterize spatial point patterns (Boots, 1986; Marcelpoil and Usson, 1992; Duyckaerts et al., 1994; Croxdale, 2000; Schaap and van de Weygaert, 2000; Chiu, 2003), mostly focusing on the area of the Voronoi polygons or Delaunay triangles. Depending on whether one wants to detect differences in point density or measure spatial arrangement independent of point density, different measurements are appropriate. In order to estimate the overall amount of noise present in the observed trichome pattern, one can compare the values of the neighborhood measures obtained from experiments with the corresponding values for hexagonal point patterns with increasing noise level. Figures 2A–C show hexagon patterns for an increasing amount of irregularity (see text box for details). Aggregating the differences between the experimentally obtained values and the values for a noisy hexagonal point pattern into an objective function allows for estimation of the noise level which best reflects the noise in trichome patterning (Figure 2D, see Shapiro et al., 1985; Kinney et al., 2001 for similar calibration methods). This approach shows that trichomes show about 44% noise in relation to hexagonal patterns (see text box Figure 2 or Greese et al., 2012 for details), which is considerable for a tightly regulated patterning system. What does this mean for the patterning process? As it appears the patterning mechanism is important, as contrasted to a purely random process, to achieve a more or less homogeneous trichome density. The exact spatial distribution seems to be of less importance.


Quantification of variability in trichome patterns.

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

Estimation of the amount of noise in the experimentally observed trichome pattern. (A–C) A hexagon pattern with increasing amount of noise, controlled by the parameter ε (A: ε=0.1, B: ε=0.3, C: ε=0.5). (D) Difference between the local irregularity as measured by the distance between neighbors, the angle between pairs of adjacent neighbors, and the anisotropy of the neighbors distribution of the observed trichome and a noisy hexagonal pattern. The minimum shows that trichomes resemble a hexagonal pattern with a noise level of 0.44. 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 2: Estimation of the amount of noise in the experimentally observed trichome pattern. (A–C) A hexagon pattern with increasing amount of noise, controlled by the parameter ε (A: ε=0.1, B: ε=0.3, C: ε=0.5). (D) Difference between the local irregularity as measured by the distance between neighbors, the angle between pairs of adjacent neighbors, and the anisotropy of the neighbors distribution of the observed trichome and a noisy hexagonal pattern. The minimum shows that trichomes resemble a hexagonal pattern with a noise level of 0.44. Reproduced with permission from Greese et al. (2012) © The Institution of Engineering and Technology.
Mentions: Other studies have used various related tessellation-based measures to characterize spatial point patterns (Boots, 1986; Marcelpoil and Usson, 1992; Duyckaerts et al., 1994; Croxdale, 2000; Schaap and van de Weygaert, 2000; Chiu, 2003), mostly focusing on the area of the Voronoi polygons or Delaunay triangles. Depending on whether one wants to detect differences in point density or measure spatial arrangement independent of point density, different measurements are appropriate. In order to estimate the overall amount of noise present in the observed trichome pattern, one can compare the values of the neighborhood measures obtained from experiments with the corresponding values for hexagonal point patterns with increasing noise level. Figures 2A–C show hexagon patterns for an increasing amount of irregularity (see text box for details). Aggregating the differences between the experimentally obtained values and the values for a noisy hexagonal point pattern into an objective function allows for estimation of the noise level which best reflects the noise in trichome patterning (Figure 2D, see Shapiro et al., 1985; Kinney et al., 2001 for similar calibration methods). This approach shows that trichomes show about 44% noise in relation to hexagonal patterns (see text box Figure 2 or Greese et al., 2012 for details), which is considerable for a tightly regulated patterning system. What does this mean for the patterning process? As it appears the patterning mechanism is important, as contrasted to a purely random process, to achieve a more or less homogeneous trichome density. The exact spatial distribution seems to be of less importance.

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