Martin Tchernookov

Mechanistic insights from a quantitative analysis of pollen tube guidance

BackgroundPlant biologists have long speculated about the mechanisms that guide pollen tubes to ovules. Although there is now evidence that ovules emit a diffusible attractant, little is known about how this attractant mediates interactions between the pollen tube and the ovules.ResultsWe employ a semi-in vitro assay, in which ovules dissected from Arabidopsis thaliana are arranged around a cut style on artificial medium, to elucidate how ovules release the attractant and how pollen tubes respond to it. Analysis of microscopy images of the semi-in vitro system shows that pollen tubes are more attracted to ovules that are incubated on the medium for longer times before pollen tubes emerge from the cut style. The responses of tubes are consistent with their sensing a gradient of an attractant at 100-150 μm, farther than previously reported. Our microscopy images also show that pollen tubes slow their growth near the micropyles of functional ovules with a spatial range that depends on ovule incubation time.ConclusionsWe propose a stochastic model that captures these dynamics. In the model, a pollen tube senses a difference in the fraction of receptors bound to an attractant and changes its direction of growth in response; the attractant is continuously released from ovules and spreads isotropically on the medium. The model suggests that the observed slowing greatly enhances the ability of pollen tubes to successfully target ovules. The relation of the results to guidance in vivo is discussed.

A list-based algorithm for evaluation of large deviation functions

As the analog of the free energy for dynamical trajectories, the large deviation function plays a central role in the statistical mechanics of systems far from equilibrium. Here, we identify numerical issues that can arise when the model of interest evolves according to a continuous-time dynamics. This analysis motivates the introduction of an algorithm in which a list of previously visited states is used to resample the distribution of interest. We discuss the convergence properties of our algorithm in detail and demonstrate its application to the single-site zero-range process and the many-site totally asymmetric exclusion process.

Critical behavior of a model for catalyzed autoamplification

We examine the critical behavior of a model of catalyzed autoamplification inspired by a common motif in genetic networks. Similar to models in the directed percolation (DP) universality class, a phase transition between an absorbing state with no copies of the autoamplifying species A and an active state with a finite amount of A occurs at the point at which production and removal of A are balanced. A suitable coordinate transformation shows that this model corresponds to one with three fields, one of which relaxes exponentially, one of which displays critical behavior, and one of which has purely diffusive dynamics but exerts an influence on the critical field. Using stochastic simulations that account for discrete molecular copy numbers in one, two, and three dimensions, we show that this model has exponents that are distinct from previously studied reaction-diffusion systems, including the few with more than one field (unidirectionally coupled DP processes and the diffusive epidemic process). Thus the requirement of a catalyst changes the fundamental physics of autoamplification. Estimates for the exponents of the diffusive epidemic process in two dimensions are also presented.