Very short-term plasticity in hippocampal synapses

Hippocampal pyramidal neurons often fire in bursts of action potentials with short interspike intervals (2–10 msec). These high-frequency bursts may play a critical role in the functional behavior of hippocampal neurons, but synaptic plasticity at such short times has not been carefully studied. To study synaptic modulation at very short time intervals, we applied pairs of stimuli with interpulse intervals ranging from 7 to 50 msec to CA1 synapses isolated by the method of minimal stimulation in hippocampal slices. We have identified three components of short-term paired-pulse modulation, including (i) a form of synaptic depression manifested after a prior exocytotic event, (ii) a form of synaptic depression that does not depend on a prior exocytotic event and that we postulate is based on inactivation of presynaptic N-type Ca2+ channels, and (iii) a dependence of paired-pulse facilitation on the exocytotic history of the synapse.

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

TROSY in triple-resonance experiments: New perspectives for sequential NMR assignment of large proteins

The NMR assignment of 13C, 15N-labeled proteins with the use of triple resonance experiments is limited to molecular weights below ∼25,000 Daltons, mainly because of low sensitivity due to rapid transverse nuclear spin relaxation during the evolution and recording periods. For experiments that exclusively correlate the amide proton (1HN), the amide nitrogen (15N), and 13C atoms, this size limit has been previously extended by additional labeling with deuterium (2H). The present paper shows that the implementation of transverse relaxation-optimized spectroscopy ([15N,1H]-TROSY) into triple resonance experiments results in several-fold improved sensitivity for 2H/13C/15N-labeled proteins and approximately twofold sensitivity gain for 13C/15N-labeled proteins. Pulse schemes and spectra recorded with deuterated and protonated proteins are presented for the [15N, 1H]-TROSY-HNCA and [15N, 1H]-TROSY-HNCO experiments. A theoretical analysis of the HNCA experiment shows that the primary TROSY effect is on the transverse relaxation of 15N, which is only little affected by deuteration, and predicts sensitivity enhancements that are in close agreement with the experimental data.