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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

Quantification of trichome patterns. (A) Neighborhood measures for trichomes (black dots) on a single leaf. The left panel shows the Voronoi diagram (light red lines) and the modified Delaunay triangulation (light green lines) as well as the Voronoi polygon (dark red line) and the contiguous Voronoi polygon (dark green line) for a selected trichome. The right panel shows a magnification of one trichome (in the center) with its six neighbors and the neighbor distances and angles (blue lines and arcs). The anisotropy is related to the ratio of the principal axes of the ellipse (red lines). Reproduced with permisson from Greese et al. (2012) © The Institution of Engineering and Technology. (B) Construction of an autocorrelogram for a simple pattern containing three points. Three copies of the original pattern are superimposed such that each time one point lies in the origin of the coordinate system. (C) Truncated autocorrelogram for a data set with real trichome data. (D) Additionally rotated autocorrelogram. (E) Further reduced autocorrelogram where the mean and the standard deviation of the neighbor distances and angles are highlighted.
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Figure 1: Quantification of trichome patterns. (A) Neighborhood measures for trichomes (black dots) on a single leaf. The left panel shows the Voronoi diagram (light red lines) and the modified Delaunay triangulation (light green lines) as well as the Voronoi polygon (dark red line) and the contiguous Voronoi polygon (dark green line) for a selected trichome. The right panel shows a magnification of one trichome (in the center) with its six neighbors and the neighbor distances and angles (blue lines and arcs). The anisotropy is related to the ratio of the principal axes of the ellipse (red lines). Reproduced with permisson from Greese et al. (2012) © The Institution of Engineering and Technology. (B) Construction of an autocorrelogram for a simple pattern containing three points. Three copies of the original pattern are superimposed such that each time one point lies in the origin of the coordinate system. (C) Truncated autocorrelogram for a data set with real trichome data. (D) Additionally rotated autocorrelogram. (E) Further reduced autocorrelogram where the mean and the standard deviation of the neighbor distances and angles are highlighted.

Mentions: A suitable characterization of spatial trichome patterns is built on a tessellation (see Box 1) of the trichome positions, which splits the domain of the leaf into polygons that do not overlap or intersect, i.e., together they exactly cover the domain. A commonly used tessellation is the Voronoi diagram (Okabe et al., 2000), in which each point is assigned a polygon that contains that part of the domain that is closer to its defining point than to any other point (Figure 1A, left). Hence, the Voronoi diagram can be interpreted as an assignment of an influence area around each trichome that results from the inhibitory signal. Notably, the inverse of its area can be taken as a local density at its defining point (Duyckaerts et al., 1994). When pairs of trichomes whose Voronoi polygons share a common edge are connected by a straight line, the result is a Delaunay triangulation of the leaf (Figure 1A, left). The agglomerate of all triangles involving a selected trichome is called the contiguous Voronoi polygon, and it can also be used to calculate local density (Schaap and van de Weygaert, 2000). Various modifications have been proposed to adapt Delaunay triangulations to specific biological systems, resulting in different neighborhood graphs (Jaromczyk and Toussaint, 1992; Raymond et al., 1993). Pairs of neighbors can be defined by the edges present in the modified triangulation, such that each trichome is assigned a set of (mostly six) neighbors (Figure 1A, right) (Greese et al., 2012). Similar definitions of neighbors on graphs have been used elsewhere (Shapiro et al., 1985; Tanemura et al., 1991; Raymond et al., 1993; Duyckaerts et al., 1994; Eglen and Willshaw, 2002). For trichomes, the neighborhood concept has been used to restrict commonly used tessellation-based methods to the local scale that is important for developmental patterning systems (Greese, 2011; Greese et al., 2012).


Quantification of variability in trichome patterns.

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

Quantification of trichome patterns. (A) Neighborhood measures for trichomes (black dots) on a single leaf. The left panel shows the Voronoi diagram (light red lines) and the modified Delaunay triangulation (light green lines) as well as the Voronoi polygon (dark red line) and the contiguous Voronoi polygon (dark green line) for a selected trichome. The right panel shows a magnification of one trichome (in the center) with its six neighbors and the neighbor distances and angles (blue lines and arcs). The anisotropy is related to the ratio of the principal axes of the ellipse (red lines). Reproduced with permisson from Greese et al. (2012) © The Institution of Engineering and Technology. (B) Construction of an autocorrelogram for a simple pattern containing three points. Three copies of the original pattern are superimposed such that each time one point lies in the origin of the coordinate system. (C) Truncated autocorrelogram for a data set with real trichome data. (D) Additionally rotated autocorrelogram. (E) Further reduced autocorrelogram where the mean and the standard deviation of the neighbor distances and angles are highlighted.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Quantification of trichome patterns. (A) Neighborhood measures for trichomes (black dots) on a single leaf. The left panel shows the Voronoi diagram (light red lines) and the modified Delaunay triangulation (light green lines) as well as the Voronoi polygon (dark red line) and the contiguous Voronoi polygon (dark green line) for a selected trichome. The right panel shows a magnification of one trichome (in the center) with its six neighbors and the neighbor distances and angles (blue lines and arcs). The anisotropy is related to the ratio of the principal axes of the ellipse (red lines). Reproduced with permisson from Greese et al. (2012) © The Institution of Engineering and Technology. (B) Construction of an autocorrelogram for a simple pattern containing three points. Three copies of the original pattern are superimposed such that each time one point lies in the origin of the coordinate system. (C) Truncated autocorrelogram for a data set with real trichome data. (D) Additionally rotated autocorrelogram. (E) Further reduced autocorrelogram where the mean and the standard deviation of the neighbor distances and angles are highlighted.
Mentions: A suitable characterization of spatial trichome patterns is built on a tessellation (see Box 1) of the trichome positions, which splits the domain of the leaf into polygons that do not overlap or intersect, i.e., together they exactly cover the domain. A commonly used tessellation is the Voronoi diagram (Okabe et al., 2000), in which each point is assigned a polygon that contains that part of the domain that is closer to its defining point than to any other point (Figure 1A, left). Hence, the Voronoi diagram can be interpreted as an assignment of an influence area around each trichome that results from the inhibitory signal. Notably, the inverse of its area can be taken as a local density at its defining point (Duyckaerts et al., 1994). When pairs of trichomes whose Voronoi polygons share a common edge are connected by a straight line, the result is a Delaunay triangulation of the leaf (Figure 1A, left). The agglomerate of all triangles involving a selected trichome is called the contiguous Voronoi polygon, and it can also be used to calculate local density (Schaap and van de Weygaert, 2000). Various modifications have been proposed to adapt Delaunay triangulations to specific biological systems, resulting in different neighborhood graphs (Jaromczyk and Toussaint, 1992; Raymond et al., 1993). Pairs of neighbors can be defined by the edges present in the modified triangulation, such that each trichome is assigned a set of (mostly six) neighbors (Figure 1A, right) (Greese et al., 2012). Similar definitions of neighbors on graphs have been used elsewhere (Shapiro et al., 1985; Tanemura et al., 1991; Raymond et al., 1993; Duyckaerts et al., 1994; Eglen and Willshaw, 2002). For trichomes, the neighborhood concept has been used to restrict commonly used tessellation-based methods to the local scale that is important for developmental patterning systems (Greese, 2011; Greese et al., 2012).

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