Ephrin-dependent growth and pruning of hippocampal axons

Neuronal connections are arranged topographically such that the spatial organization of neurons is preserved by their termini in the targets. During the development of topographic projections, axons initially explore areas much wider than the final targets, and mistargeted axons are pruned later. The molecules regulating these processes are not known. We report here that the ligands of the Eph family tyrosine kinase receptors may regulate both the initial outgrowth and the subsequent pruning of axons. In the presence of ephrins, the outgrowth and branching of the receptor-positive hippocampal axons are enhanced. However, these axons are induced later to degenerate. These observations suggest that the ephrins and their receptors may regulate topographic map formation by stimulating axonal arborization and by pruning mistargeted axons.

Odor space and olfactory processing: Collective algorithms and neural implementation

Several basic olfactory tasks must be solved by highly olfactory animals, including background suppression, multiple object separation, mixture separation, and source identification. The large number N of classes of olfactory receptor cells—hundreds or thousands—permits the use of computational strategies and algorithms that would not be effective in a stimulus space of low dimension. A model of the patterns of olfactory receptor responses, based on the broad distribution of olfactory thresholds, is constructed. Representing one odor from the viewpoint of another then allows a common description of the most important basic problems and shows how to solve them when N is large. One possible biological implementation of these algorithms uses action potential timing and adaptation as the “hardware” features that are responsible for effective neural computation.

Abnormal dendritic spines in fragile X knockout mice: Maturation and pruning deficits

Fragile X syndrome arises from blocked expression of the fragile X mental retardation protein (FMRP). Golgi-impregnated mature cerebral cortex from fragile X patients exhibits long, thin, tortuous postsynaptic spines resembling spines observed during normal early neocortical development. Here we describe dendritic spines in Golgi-impregnated cerebral cortex of transgenic fragile X gene (Fmr1) knockout mice that lack expression of the protein. Dendritic spines on apical dendrites of layer V pyramidal cells in occipital cortex of fragile X knockout mice were longer than those in wild-type mice and were often thin and tortuous, paralleling the human syndrome and suggesting that FMRP expression is required for normal spine morphological development. Moreover, spine density along the apical dendrite was greater in the knockout mice, which may reflect impaired developmental organizational processes of synapse stabilization and elimination or pruning.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.