Functions of the two glutamate transporters GLAST and GLT-1 in the retina

In the retina, the glutamate transporter GLAST is expressed in Müller cells, whereas the glutamate transporter GLT-1 is found only in cones and various types of bipolar cells. To investigate the functional role of this differential distribution of glutamate transporters, we have analyzed GLAST and GLT-1 mutant mice. In GLAST-deficient mice, the electroretinogram b-wave and oscillatory potentials are reduced and retinal damage after ischemia is exacerbated, whereas GLT-1-deficient mice show almost normal electroretinograms and mild increased retinal damage after ischemia. These results demonstrate that GLAST is required for normal signal transmission between photoreceptors and bipolar cells and that both GLAST and GLT-1 play a neuroprotective role during ischemia in the retina.

Advances in random matrix theory, zeta functions, and sphere packing

Over four hundred years ago, Sir Walter Raleigh asked his mathematical assistant to find formulas for the number of cannonballs in regularly stacked piles. These investigations aroused the curiosity of the astronomer Johannes Kepler and led to a problem that has gone centuries without a solution: why is the familiar cannonball stack the most efficient arrangement possible? Here we discuss the solution that Hales found in 1998. Almost every part of the 282-page proof relies on long computer verifications. Random matrix theory was developed by physicists to describe the spectra of complex nuclei. In particular, the statistical fluctuations of the eigenvalues (“the energy levels”) follow certain universal laws based on symmetry types. We describe these and then discuss the remarkable appearance of these laws for zeros of the Riemann zeta function (which is the generating function for prime numbers and is the last special function from the last century that is not understood today.) Explaining this phenomenon is a central problem. These topics are distinct, so we present them separately with their own introductory remarks.