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.

Photosystem II Cyclic Heterogeneity and Photoactivation in the Diazotrophic, Unicellular Cyanobacterium Cyanothece Species ATCC 511421

The unicellular, diazotrophic cyanobacterium Cyanothece sp. ATCC 51142 demonstrated important modifications to photosystem II (PSII) centers when grown under light/dark N2-fixing conditions. The properties of PSII were studied throughout the diurnal cycle using O2-flash-yield and pulse-amplitude-modulated fluorescence techniques. Nonphotochemical quenching (qN) of PSII increased during N2 fixation and persisted after treatments known to induce transitions to state 1. The qN was high in cells grown in the dark, and then disappeared progressively during the first 4 h of light growth. The photoactivation probability, ε, demonstrated interesting oscillations, with peaks near 3 h of darkness and 4 and 10 h of light. Experiments and calculations of the S-state distribution indicated that PSII displays a high level of heterogeneity, especially as the cells prepare for N2 fixation. We conclude that the oxidizing side of PSII is strongly affected during the period before and after the peak of nitrogenase activity; changes include a lowered capacity for O2 evolution, altered dark stability of PSII centers, and substantial changes in qN.

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.

Voltage dependence of the pattern and frequency of discrete Ca2+ release events after brief repriming in frog skeletal muscle

Applying a brief repolarizing pre-pulse to a depolarized frog skeletal muscle fiber restores a small fraction of the transverse tubule membrane voltage sensors from the inactivated state. During a subsequent depolarizing test pulse we detected brief, highly localized elevations of myoplasmic Ca2+ concentration (Ca2+ “sparks”) initiated by restored voltage sensors in individual triads at all test pulse voltages. The latency histogram of these events gives the gating pattern of the sarcoplasmic reticulum (SR) calcium release channels controlled by the restored voltage sensors. Both event frequency and clustering of events near the start of the test pulse increase with test pulse depolarization. The macroscopic SR calcium release waveform, obtained from the spark latency histogram and the estimated open time of the channel or channels underlying a spark, exhibits an early peak and rapid marked decline during large depolarizations. For smaller depolarizations, the release waveform exhibits a smaller peak and a slower decline. However, the mean use time and mean amplitude of the individual sparks are quite similar at all test depolarizations and at all times during a given depolarization, indicating that the channel open times and conductances underlying sparks are essentially independent of voltage. Thus, the voltage dependence of SR Ca2+ release is due to changes in the frequency and pattern of occurrence of individual, voltage-independent, discrete release events.