Cocaine: mechanism of inhibition of a muscle acetylcholine receptor studied by a laser-pulse photolysis technique.

Effects of cocaine on the muscle nicotinic acetylcholine receptor were investigated by using a chemical kinetic technique with a microsecond time resolution. This membrane-bound receptor regulates signal transmission between nerve and muscle cells, initiates muscle contraction, and is inhibited by cocaine, an abused drug. The inhibition mechanism is not well understood because of the lack of chemical kinetic techniques with the appropriate (microsecond) time resolution. Such a technique, utilizing laser-pulse photolysis, was recently developed; by using it the following results were obtained. (i) The apparent cocaine dissociation constant of the closed-channel receptor form is approximately 50 microM. High carbamoylcholine concentration and, therefore, increased concentrations of the open-channel receptor form, decrease receptor affinity for cocaine approximately 6-fold. (ii) The rate of the receptor reaction with cocaine is at least approximately 30-fold slower than the channel-opening rate, resulting in a cocaine-induced decrease in the concentration of open receptor channels without a concomitant decrease in the channel-opening or -closing rates. (iii) The channel-closing rate increases approximately 1.5-fold as the cocaine concentration is increased from 20 to 60 microM but then remains constant as the concentration is increased further. The results are consistent with a mechanism in which cocaine first binds rapidly to a regulatory site of the receptor, which can still form transmembrane channels. Subsequently, a slow step (t1/2 approximately 70 ms) leads to a receptor form that cannot form transmembrane channels, and acetylcholine receptor-mediated signal transmission is, therefore, blocked. Implications for the search for therapeutic agents that alleviate cocaine poisoning are mentioned.

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.