Hermann B. Lück

A comprehensive model for acrotonic, mesotonic and basitonic branchings in plants

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.

Generation of 3-dimensional plant bodies by double wall map and stereomap systems

The seven described archetypes of development (Table 1) cover all developmental possibilities for systems with parity and a unique cell boundary length of 4, 5, or 6 (column (a)). The geometrical constraints given by the quantification of wall lengths according to the number of segments of which they are composed, lead in some cases to 3-dimensional plant bodies described by the cellular arrangement in their epidermis. All archetypes exhibit very common botanical features. Real organisms differ essentially from archetypical ones by non uniform lifespans of cells and finite mitotic activity of most cells. The relationship between maps respecting various lifespans and the corresponding archetype will be the object of a separate publication.

Double-wall Cellworks Systems for Plant Meristems

The development of the cellular pattern of plant meristems is simulated under rules specifying a constant positioning of division walls with respect to the previously introduced wall. The network, or cellwork, of the cell walls is, in analogy to real walls, represented by double-wall labeling.

Unconventional Leaves (An Application of Map ol-Systems to Biology)

Regularities of the positioning of cell division walls during the development of meristematic plant tissues may have morphogenetic consequences. A class of developmental constructions, double wall map generating OL-systems, was explored exhaustively and accounts for the number of concevable possibilities of wall insertions. The typology over theoretical organized cell layer configurations, which has been established in earlier works on the base of these systems, is completed here by an investigation on leaf-like structures.

Petri nets applied to experimental plant morphogenesis

Data from experiments on Erica × darleyensis and from related observations (Viemont and Beaujard, 1983) are taken for a critical analysis of the proposed model of morphogenetic phenomena. The criteria for judging the coherence of the constructions proposed in plant morphology are based on mathematical constructions deduced from Petri nets, especially elementary nets.

From Map Systems to Plant Morphogenesis

In a plant, growth is localized in some special, often distal areas, called meristems. Cell divisions and cell expansion contribute to the elongation of the axes, and also produce infinitely appendages such as leaves, stipules, and branches which are arranged in regular patterns. We want to give here a possible explanation for pattern inception in meristems on the basis of organized tissue growth.

Cellworks : An Application to Plant Morphogenesis

Cellwork-systems with double face labeling are used to investigate the division possibilities of autoreproductive tetrahedral cells. In plant morphogenesis, such cells, in apical position, are at the origin of the cell-rows which compose the shoots. The difference between 1, 2, or 3-rowed elementary theoretical shoots, with compact or tunica-like cell assemblage, can be traced back to specific orientations of the apical cells in their filiation.

Non‐Linear Patterns of Complex Ramification Schemes in Higher Plants (Proposition for an Insight)

Zusammenfassung Die Seitenzweige von Cupressus sempervirens L. sind auf vier Orthostichen in scheinbar mehr oder weniger zufalligen, voneinander unabhangigen Mustern angeordnet. Eine auf L-Systeme sich berufende mathematische Konstruktion gestattet die Definition eines Morphismus. Acht Parameter, Periodizitat der absoluten Wachstumsrate der zugrundeliegenden theoretischen Serien, die Variation dieser Raten in komplementaren Unterserien und eine Schwellenreaktion sind die Hauptargumente.