Analysis of cell division patterns in the Arabidopsis shoot apical meristem

The stereotypic pattern of cell shapes in the Arabidopsis shoot apical meristem (SAM) suggests that strict rules govern the placement of new walls during cell division. When a cell in the SAM divides, a new wall is built that connects existing walls and divides the cytoplasm of the daughter cells. Because features that are determined by the placement of new walls such as cell size, shape, and number of neighbors are highly regular, rules must exist for maintaining such order. Here we present a quantitative model of these rules that incorporates different observed features of cell division. Each feature is incorporated into a “potential function” that contributes a single term to a total analog of potential energy. New cell walls are predicted to occur at locations where the potential function is minimized. Quantitative terms that represent the well-known historical rules of plant cell division, such as those given by Hofmeister, Errera, and Sachs are developed and evaluated against observed cell divisions in the epidermal layer (L1) of Arabidopsis thaliana SAM. The method is general enough to allow additional terms for nongeometric properties such as internal concentration gradients and mechanical tensile forces.The Arabidopsis shoot apical meristem (SAM) is a structure at the tip of the shoot that is responsible for generating almost all of the above-ground tissue of the plant (1). Its epidermal and subepidermal cells are organized into layers with very few cells moving between layers (2, 3). When these cells expand they do so laterally, pushing other cells toward the periphery of the meristem. Division in these cells is anticlinal such that each layer remains one cell thick. The underlying mechanism determining the location of new cell walls is unknown but the qualitative properties of meristematic cell division are well documented (4–8). Perhaps the best known summary is Errera’s rule, derived following observations of soap bubble formation. In the modern interpretation, the plane of division corresponds to the shortest path that will halve the mother cell. Errera, in fact, wrote that the wall would be a surface “mit constanter mittlerer Krümmung (= Minimalfläche) [with constant mean curvature (= minimal area)]” (4). Because this does not specify a location for the new cell wall, more recent authors have added to this that the mother cell divides evenly (9, 10). With this modification, Errera’s rule is easily quantifiable.A second observation is Hofmeister’s rule: New cell walls usually form in a plane normal to the principal axis of cell elongation (5). This rule is more difficult to quantify, because the principal axis of cell elongation is often confused with the direction of growth. Cells are asymmetrical and hence a principal direction of cell elongation can easily be calculated (e.g., the principal axis of inertia or principal component of a segmentation). The assumption is often made that because the cell is more elongated in one direction that the primary growth of the cell has been along that direction, but this is not necessarily the case, because the elongation may be derived from a prior cell division. For example, if a symmetrical square divides into two rectangular cells, this does not mean that the two daughter cells have grown primarily along their longer axis. Quantification of cell growth direction is much more difficult: It requires the observation of matching points over time and varies with the internal and external tensile forces on the cell. It is not clear whether the instantaneous direction of cell growth or the longer-term average (e.g., as measured over a significant fraction of a cell generation) is more directly relevant to forming the division plane. Under compression, single cells tend to divide in a plane perpendicular to the principal axis of the stress tensor (11), which could indicate a mechanical basis for cell wall placement.Other observations are that new cell walls form in a plane perpendicular to existing cell walls (6), that cell walls tend to avoid four-way junctions (7), and that cell division planes tend to be staggered, like bricks in a wall (8). Because chemical signals can be induced by physical interactions such as mechanical stress and strain it is conceivable that these geometric indicators are merely emergent properties of the underlying physicochemical interaction processes that drives cell division. Although most of the geometric observations tend to be true most of the time, none of them is true all of the time, and it is not possible for all of them to be true at once. For example, the actual growth direction is rarely in alignment with the principal geometric axis of the cell, and hence the division cannot simultaneously satisfy shortest length and perpendicularity requirements. Such conflicting results can in principle be resolved by minimizing a sum of potential functions (12), and insight can often be gained into the underlying mechanisms by examining the results of the optimization. Additionally, recent work by Besson and Dumais (9) suggests that cell division in plants is inherently random. The new wall tends to find a global minimum length, but in situations where there are multiple similar local minima the global minimum is not necessarily chosen.Previously we looked at cell divisions in the shoot meristem using 2D maximum intensity projections (13). Some of the results from that work may have been biased owing to the inconsistent perspective on cells in the peripheral zone compared with the center created by projecting a 3D object into 2D space. Because the meristem is dome-shaped, when projecting the meristem from the top the cells in the center are viewed perpendicularly, whereas the cells toward the edges are viewed at an angle. This nonperpendicular viewing angle distorts the lengths of the cell walls and the angles at which the walls join each other. To rectify that problem the geometry of the cells must be examined in 3D. Here we expand on earlier work with more comprehensive 3D image processing techniques to analyze the division patterns in the local tangent plane. By using the image processing software MorphoGraphX (14) we were able to reconstruct the cell boundaries in the first layer of a growing SAM.Having a 3D model of the structure of the epidermal (L1) layer over time allowed us to generate a model composed of a set of functions, each incorporating a different feature from the observed cell divisions. The functions each contribute a single term to a greater potential function and new walls are predicted to form where the combined potential is reduced. This model also brought to light some of the shortcomings of previously proposed plant cell division rules. Additionally, these data allowed us to make the observations reported below of the dynamics of cell expansion and division in different regions of the SAM.