Experience-dependent, asymmetric expansion of hippocampal place fields

Theories of sequence learning based on temporally asymmetric, Hebbian long-term potentiation predict that during route learning the spatial firing distributions of hippocampal neurons should enlarge in a direction opposite to the animal’s movement. On a route AB, increased synaptic drive from cells representing A would cause cells representing B to fire earlier and more robustly. These effects appeared within a few laps in rats running on closed tracks. This provides indirect evidence for Hebbian synaptic plasticity and a functional explanation for why place cells become directionally selective during route following, namely, to preserve the synaptic asymmetry necessary to encode the sequence direction.

Monitoring the GAP catalyzed H-Ras GTPase reaction at atomic resolution in real time

The molecular reaction mechanism of the GTPase-activating protein (GAP)-catalyzed GTP hydrolysis by Ras was investigated by time resolved Fourier transform infrared (FTIR) difference spectroscopy using caged GTP (P3-1-(2-nitro)phenylethyl guanosine 5′-O-triphosphate) as photolabile trigger. This approach provides the complete GTPase reaction pathway with time resolution of milliseconds at the atomic level. Up to now, one structural model of the GAP⋅Ras⋅GDP⋅AlFx transition state analog is known, which represents a “snap shot” along the reaction-pathway. As now revealed, binding of GAP to Ras⋅GTP shifts negative charge from the γ to β phosphate. Such a shift was already identified by FTIR in GTP because of Ras binding and is now shown to be enhanced by GAP binding. Because the charge distribution of the GAP⋅Ras⋅GTP complex thus resembles a more dissociative-like transition state and is more like that in GDP, the activation free energy is reduced. An intermediate is observed on the reaction pathway that appears when the bond between β and γ phosphate is cleaved. In the intermediate, the released Pi is strongly bound to the protein and surprisingly shows bands typical of those seen for phosphorylated enzyme intermediates. All these results provide a mechanistic picture that is different from the intrinsic GTPase reaction of Ras. FTIR analysis reveals the release of Pi from the protein complex as the rate-limiting step for the GAP-catalyzed reaction. The approach presented allows the study not only of single proteins but of protein–protein interactions without intrinsic chromophores, in the non-crystalline state, in real time at the atomic level.

Ergodic theorems along sequences and Hardy fields.

Let a(x) be a real function with a regular growth as x --> infinity. [The precise technical assumption is that a(x) belongs to a Hardy field.] We establish sufficient growth conditions on a(x) so that the sequence ([a(n)])(infinity)(n=1) is a good averaging sequence in L2 for the pointwise ergodic theorem. A sequence (an) of positive integers is a good averaging sequence in L2 for the pointwise ergodic theorem if in any dynamical system (Omega, Sigma, m, T) for f [symbol, see text] in L2(Omega) the averages [equation, see text] converge for almost every omicron in. Our result implies that sequences like ([ndelta]), where delta > 1 and not an integer, ([n log n]), and ([n2/log n]) are good averaging sequences for L2. In fact, all the sequences we examine will turn out to be good averaging for Lp, p > 1; and even for L log L. We will also establish necessary and sufficient growth conditions on a(x) so that the sequence ([a(n)]) is good averaging for mean convergence. Note that for some a(x) (e.g., a(x) = log2 x), ([a(n)]) may be good for mean convergence without being good for pointwise convergence.