Root apical meristems are composed of two zones in which either formative or proliferative cell divisions occur. Within the formative zone, autoreproductive initial cells (a-cells) occupy distinctive locations. By means of graph-L-systems, the behavior of one such type of a-cells has been investigated, with particular reference to root caps within the developing primordia of lateral roots of Lycopersicon esculentum cultivated in vitro. Here, the a-cells constitute the "protoderm initials", cells which are found also in the root cap of many angiosperm species. A set of cuboidal (i.e., six-sided) a-cells develops early in the ontogeny of a lateral-root primordium. Then, according to both anatomical observations and theoretical simulations obtained by the application of graph-L-systems, sequential production of descendents from each a-cell leads to the formation of a new autoreproductive cell (a), a cap columella initial (c), and two mother cells (e and f) whose respective descendents differentiate as root epidermis and cap flank cells. In this graph-L-system, there is specification of the location of sister cells with respect to the three orthogonal directions of a cuboidal. In the early stage of root cap formation, only a few rounds of these formative cell divisions by each a-cell and its four types of descendents are required to provide the basic set of cells necessary for full cap development. After the lateral root emerges from the parent root, there may be a temporary cessation of the formative divisions of the a-cells which give rise to columella initials. Columella production is then supported entirely by its own independent set of autoreproductive c-initials. At the same time, division of the autoreproductive protoderm initial cell is directed towards maintaining the cap flank and the epidermal cell files. The regulation of the types of formative division by the a-cell may be represented by means of a division counter which may be specific for a given species.
The primary root meristem of maize (Zea mays L.) contains longitudinal files of cells arranged in groups of familial descent (sisters, cousins, etc.). These groups, or packets, show ordered sequences of cell division which are transverse with respect to the apico-basal axis of the root. The sequences have been analysed in three zones of the meristem during the course of the first four cell generations following germination. In this period, the number of cells in the packets increases from one to 16. Theoretically, there are 48 possible division pathways that lead to the eight-cell stage, and nearly 2 x 10(6) that lead to the 16-cell stage. However, analysis shows that only a few of all the possible pathways are used in any particular zone of the root. This restriction of pathways results from inherited sequences of asymmetric cell divisions which lead to sister cells of unequal length. All possible division pathways can be generated by deterministic 'bootstrap' L-systems which assign different lifespans to sister cells of successive generations and hence specify their subsequent sequence of divisions. These systems simulate propagating patterns of cell divisions which agree with those actually found within the growing packets that comprise the root meristem. The patterns of division are specific to cells originating in various regions of the meristem of the germinating root. The importance of such systems is that they simulate patterns of cellular proliferation where there is ancestral dependency. They can therefore be applied in other growing and proliferating systems where this is suspected.
Topological developmental models with local (position of internodes) and global (branch lengths) characteristics are proposed to investigate the relationships between fundamental branching patterns of plants such as acrotony, mesotony, and basitony, including the coincidence of different patterns on the same plant. Modification of the basic acrotony during the development by means of, (1) the final expected main axis length results in either basitony or an extension of acrotony over a shortened main axis, (2) the final expected lateral branch length yields either lateral unlimited sympodial branching or the absence of proximal branches. Combinations of these schemes can have variable quantitative expressions on main and lateral axes.As applications, progressive morphological changes introduced by monotonic variations of parameter values give an insight into the relationships between determinate and indeterminate growth, using Lycopersicon as an example. -A theoretical framework is proposed as a possible aid for formalizing plant typology.
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