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.cell division | computer modeling | live imaging | Arabidopsis T he 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...