Chemically mediated mechanical expansion of the pollen tube cell wall.

Morphogenesis of plant cells is tantamount to the shaping of the stiff cell wall that surrounds them. To this end, these cells integrate two concomitant processes: 1), deposition of new material into the existing wall, and 2), mechanical deformation of this material by the turgor pressure. However, due to uncertainty regarding the mechanisms that coordinate these processes, existing models typically adopt a limiting case in which either one or the other dictates morphogenesis. In this report, we formulate a simple mechanism in pollen tubes by which deposition causes turnover of cell wall cross-links, thereby facilitating mechanical deformation. Accordingly, deposition and mechanics are coupled and are both integral aspects of the morphogenetic process. Among the key experimental qualifications of this model are: its ability to precisely reproduce the morphologies of pollen tubes; its prediction of the growth oscillations exhibited by rapidly growing pollen tubes; and its prediction of the observed phase relationships between variables such as wall thickness, cell morphology, and growth rate within oscillatory cells. In short, the model captures the rich phenomenology of pollen tube morphogenesis and has implications for other plant cell types.

The mechanics of explosive dispersal and self-burial in the seeds of the filaree, Erodium cicutarium (Geraniaceae).

The filaree (Erodium cicutarium), a small, flowering plant related to geraniums, possesses a unique seed dispersal mechanism: the plant can fling its seeds up to half a meter away; and the seeds can bury themselves by drilling into the ground, twisting and untwisting in response to changes in humidity. These feats are accomplished using awns, helical bristles of dead but hygroscopically active tissue attached to the seeds. Here, we describe the kinematics of explosive dispersal and self-burial based on detailed high-speed and time-lapse videos. We use these observations to develop a simple mechanical model that accounts for the coiling behavior of the awn and allows comparison of the strain energy stored in the awn with the kinetic energy at launch. The model is used to examine tradeoffs between dispersal distance and reliability of the dispersal mechanism. The mechanical model may help in understanding the invasive potential of this species and provides a framework for examining other evolutionary tradeoffs in seed dispersal mechanisms among the Geraniaceae.

Analytic formulas for discrete stochastic models of cell populations with both differentiation and de-differentiation.

Cell differentiation often appears to be a stochastic process particularly in the hemopoietic system. One of the earliest stochastic models for the growth of stem cell populations was proposed by Till et al. in 1964. In this model there are just two cell types: stem cells and specialized cells. At each time step there is a fixed probability that a stem cell differentiates into a specialized cell and a fixed probability that it undergoes mitosis to produce two stem cells. Even though this model is conceptually simple the myriad of possible outcomes has made it difficult to analyse. We present original closed-form expressions for the probability functions and a fast algorithm for computing them. Renewed interest in stem cells has raised questions about the effect de-differentiation has on stem cell populations. We have extended the stochastic model to include de-differentiation and show that even a small amount of de-differentiation can have a large effect on stem cell population growth.

Finding the center of a phyllotactic pattern.

The calculation of divergence angles between primordia in a plant apex depends on the point used as the center of the apex. In mathematically ideal phyllotactic patterns, the center is well defined but there has not been a precise definition for the center of naturally occurring phyllotactic patterns. A few techniques have been proposed for estimating the location of the center but without a precise definition for the center the accuracy of these methods cannot be known. This paper provides a precise definition that can be used as the center of a phyllotactic pattern and a numerical method which can accurately find it. These tools will make it easier to compare theory against experiment in phyllotaxis.