Christophe Golé

The Possible and the Actual in Phyllotaxis: Bridging the Gap between Empirical Observations and Iterative Models

This article presents new methods for the geometrical analysis of phyllotactic patterns and their comparison with patterns produced by simple, discrete dynamical systems. We introduce the concept of ontogenetic graph as a parsimonious and mechanistically relevant representation of a pattern. The ontogenetic graph is extracted from the local geometry of the pattern and does not impose large-scale regularity on it as for the divergence angle and other classical descriptors. We exemplify our approach by analyzing the phyllotaxis of two asteraceae inflorescences in the light of a hard disk model. The simulated patterns offer a very good match to the observed patterns for over 150 iterations of the model.

Ghost circles for twist maps

Abstract Completely ordered invariant circles are found for the gradient of the energy flow in the state space, containing the critical sets corresponding to the Birkhoff orbits of all rotation number. In particular, these ghost circles contain the Aubry-Mather sets and map-invariant circles as completely critical sets when these exist. We give a criterion for a sequence of rational ghost circles to converge to a completely critical one.

Kif11 dependent cell cycle progression in radial glial cells is required for proper neurogenesis in the zebrafish neural tube

Radial glia serve as the resident neural stem cells in the embryonic vertebrate nervous system, and their proliferation must be tightly regulated to generate the correct number of neuronal and glial cell progeny in the neural tube. During a forward genetic screen, we recently identified a zebrafish mutant in the kif11 loci that displayed a significant increase in radial glial cell bodies at the ventricular zone of the spinal cord. Kif11, also known as Eg5, is a kinesin-related, plus-end directed motor protein responsible for stabilizing and separating the bipolar mitotic spindle. We show here that Gfap+ radial glial cells express kif11 in the ventricular zone and floor plate. Loss of Kif11 by mutation or pharmacological inhibition with S-trityl-L-cysteine (STLC) results in monoastral spindle formation in radial glial cells, which is characteristic of mitotic arrest. We show that M-phase radial glia accumulate over time at the ventricular zone in kif11 mutants and STLC treated embryos. Mathematical modeling of the radial glial accumulation in kif11 mutants not only confirmed an ~226× delay in mitotic exit (likely a mitotic arrest), but also predicted two modes of increased cell death. These modeling predictions were supported by an increase in the apoptosis marker, anti-activated Caspase-3, which was also found to be inversely proportional to a decrease in cell proliferation. In addition, treatment with STLC at different stages of neural development uncovered two critical periods that most significantly require Kif11 function for stem cell progression through mitosis. We also show that loss of Kif11 function causes specific reductions in oligodendroglia and secondary interneurons and motorneurons, suggesting these later born populations require proper radial glia division. Despite these alterations to cell cycle dynamics, survival, and neurogenesis, we document unchanged cell densities within the neural tube in kif11 mutants, suggesting that a mechanism of compensatory regulation may exist to maintain overall proportions in the neural tube. We propose a model in which Kif11 normally functions during mitotic spindle formation to facilitate the progression of radial glia through mitosis, which leads to the maturation of progeny into specific secondary neuronal and glial lineages in the developing neural tube.

Symplectic Twist Maps and the Theorem of Conley-Zehnder for General Cotangent Bundles

We announce the existence and multiplicity of periodic orbits for time dependent Hamiltonian systems on cotangent bundle of arbitrary compact manifolds. We discretize the variational problem by decomposing the time 1 map into a product of symplectic twist maps.

Suspension of Symplectic Twist Maps by Hamiltonians

We extend some results of Moser [17], Bialy and Polterovitch [1], on the suspension of symplectic twist maps by Hamiltonian flows.