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.

A conventional myosin motor drives neurite outgrowth

Neuritic outgrowth is a striking example of directed motility, powered through the actions of molecular motors. Members of the myosin superfamily of actin-associated motors have been implicated in this complex process. Although conventional myosin II is known to be present in neurons, where it is localized at the leading edge of growth cones and in the cell cortex close to the plasma membrane, its functional involvement in growth cone motility has remained unproven. Here, we show that antisense oligodeoxyribonucleotides, complementary to a specific isoform of conventional myosin (myosin IIB), attenuate filopodial extension whereas sense and scrambled control oligodeoxyribonucleotides have no effect. Attenuation is shown to be reversible, neurite outgrowth being restored after cessation of the antisense regimen. Myosin IIB mRNA was present during active neurite extension, but levels were minimal in phenotypically rounded cells before neurite outgrowth and message levels decreased during antisense treatment. By contrast, the myosin IIA isoform is shown to be expressed constitutively both before and during neurite outgrowth and throughout exposure to myosin IIB antisense oligodeoxyribonucleotides. These results provide direct evidence that a conventional two-headed myosin is required for growth cone motility and is responsible, at least in part, for driving neuritic process outgrowth.

Responses of the phototransduction cascade to dim light.

The biochemistry of visual excitation is kinetically explored by measuring the activity of the cGMP phosphodiesterase (PDE) at light levels that activate only a few tens of rhodopsin molecules per rod. At 23 degrees C and in the presence of ATP, the pulse of PDE activity lasts 4 s (full width at half maximum). Complementing the rod outer segments (ROS) with rhodopsin kinase (RK) and arrestin or its splice variant p44 does not significantly shorten the pulse. But when the ROS are washed, the duration of the signal doubles. Adding either arrestin or p44 back to washed ROS approximately restores the pulse width to its initial value, with p44 being 10 times more efficient than arrestin. This supports the idea that, in vivo, capping of phosphorylated R* is mostly done by p44. When myristoylated (14:0) recoverin is added to unwashed ROS, the pulse duration and amplitude increase by about 50% if the free calcium is 500 nM. This effect increases further if the calcium is raised to 1 microM. Whenever R* deactivation is changed--when RK is exogenously enriched or when ATP is omitted from the buffer--there is no impact on the rising slope of the PDE pulse but only on its amplitude and duration. We explain this effect as due to the unequal competition between transducin and RK for R*. The kinetic model issued from this idea fits the data well, and its prediction that enrichment with transducin should lengthen the PDE pulse is successfully validated.