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.

Characterization of the transposition pattern of the Ac element in Arabidopsis thaliana using endonuclease I-SceI

We have investigated physical distances and directions of transposition of the maize transposable element Ac in Arabidopsis thaliana. We prepared a transferred DNA (T-DNA) construct that carried a non-autonomous derivative of Ac with a site for cleavage by endonuclease I-SceI (designated dAc-I-RS element). Another cleavage site was also introduced into the T-DNA region outside dAc-I-RS. Three transgenic Arabidopsis plants were generated, each of which had a single copy of the T-DNA at a different chromosomal location. These transgenic plants were crossed with the Arabidopsis that carried the gene for Ac transposase and progeny in which dAc-I-RS had been transposed were isolated. After digestion of the genomic DNA of these progeny with endonuclease I-SceI, sizes of segment of DNA were determined by pulse-field gel electrophoresis. We also performed linkage analysis for the transposed elements and sites of mutations near the elements. Our results showed that 50% of all transposition events had occurred within 1,700 kb on the same chromosome, with 35% within 200 kb, and that the elements transposed in both directions on the chromosome with roughly equal probability. The data thus indicate that the Ac–Ds system is most useful for tagging of genes that are present within 200 kb of the chromosomal site of Ac in Arabidopsis. In addition, determination of the precise localization of the transposed dAc-I-RS element should definitely assist in map-based cloning of genes around insertion sites.

Crystal structure of the Holliday junction migration motor protein RuvB from Thermus thermophilus HB8

We report here the crystal structure of the RuvB motor protein from Thermus thermophilus HB8, which drives branch migration of the Holliday junction during homologous recombination. RuvB has a crescent-like architecture consisting of three consecutive domains, the first two of which are involved in ATP binding and hydrolysis. DNA is likely to interact with a large basic cleft, which encompasses the ATP-binding pocket and domain boundaries, whereas the junction-recognition protein RuvA may bind a flexible β-hairpin protruding from the N-terminal domain. The structures of two subunits, related by a noncrystallographic pseudo-2-fold axis, imply that conformational changes of motor protein coupled with ATP hydrolysis may reflect motility essential for its translocation around double-stranded DNA.

The role of surface loops (residues 204-216 and 627-646) in the motor function of the myosin head.

A characteristic feature of all myosins is the presence of two sequences which despite considerable variations in length and composition can be aligned with loops 1 (residues 204-216) and 2 (residues 627-646) in the chicken myosin-head heavy chain sequence. Recently, an intriguing hypothesis has been put forth suggesting that diverse performances of myosin motors are achieved through variations in the sequences of loops 1 and 2 [Spudich, J. (1994) Nature (London) 372, 515-518]. Here, we report on the study of the effects of tryptic digestion of these loops on the motor and enzymatic functions of myosin. Tryptic digestions of myosin, which produced heavy meromyosin (HMM) with different percentages of molecules cleaved at both loop 1 and loop 2, resulted in the consistent decrease in the sliding velocity of actin filaments over HMM in the in vitro motility assays, did not affect the Vmax, and increased the Km values for actin-activated ATPase of HMM. Selective cleavage of loop 2 on HMM decreased its affinity for actin but did not change the sliding velocity of actin in the in vitro motility assays. The cleavage of loop 1 and HMM decreased the mean sliding velocity of actin in such assays by almost 50% but did not alter its affinity for HMM. To test for a possible kinetic determinant of the change in motility, 1-N6-ethenoadenosine diphosphate (epsilon-ADP) release from cleaved and uncleaved myosin subfragment 1 (S1) was examined. Tryptic digestion of loop 1 slightly accelerated the release of epsilon-ADP from S1 but did not affect the rate of epsilon-ADP release from acto-S1 complex. Overall, the results of this work support the hypothesis that loop 1 can modulate the motor function of myosin and suggest that such modulation involves a mechanism other than regulation of ADP release from myosin.