A neurotransmitter transporter encoded by the Drosophila inebriated gene

Behavioral and electrophysiological studies on mutants defective in the Drosophila inebriated (ine) gene demonstrated increased excitability of the motor neuron. In this paper, we describe the cloning and sequence analysis of ine. Mutations in ine were localized on cloned DNA by restriction mapping and restriction fragment length polymorphism (RFLP) mapping of ine mutants. DNA from the ine region was then used to isolate an ine cDNA. In situ hybridization of ine transcripts to developing embryos revealed expression of this gene in several cell types, including the posterior hindgut, Malpighian tubules, anal plate, garland cells, and a subset of cells in the central nervous system. The ine cDNA contains an open reading frame of 658 amino acids with a high degree of sequence similarity to members of the Na+/Cl−-dependent neurotransmitter transporter family. Members of this family catalyze the rapid reuptake of neurotransmitters released into the synapse and thereby play key roles in controlling neuronal function. We conclude that ine mutations cause increased excitability of the Drosophila motor neuron by causing the defective reuptake of the substrate neurotransmitter of the ine transporter and thus overstimulation of the motor neuron by this neurotransmitter. From this observation comes a unique opportunity to perform a genetic dissection of the regulation of excitability of the Drosophila motor neuron.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.