Optical rotatory dispersion and circular dichroism of cytochrome oxidase.
Optical rotatory dispersion of the oxidized and the reduced cytochrome oxidase has been measured from 196 to 550 nm. The experimental data have been analyzed in order to separate the extrinsic cotton effects from the rotations of the protein backbone. From the resolution, two cotton effects of similar sign are obtained in the Soret region. For the reduced enzyme, the cotton effect centered at 446.5 nm shows a molar amplitude of 192 k-degrees with a band width of 5.3 nm and rotational strength of 0.25 Debye magneton; the second cotton effect centered at 444 nm shows a molar amplitude of 45 k-degrees with a band width of 12.9 nm and rotational strength of 0.14 Debye magneton. Upon oxidation, the centers of these cotton effects shift to 432 and 423.7 nm. The amplitudes become 114 and 122 k-degrees with band widths of 6.1 and 11.2 nm and rotational strengths of 0.18 and 0.35 Debye magneton, respectively. In addition, a less defined third cotton effect centered at 376 nm appears with an amplitude of 28 k-degrees, band width of 18 nm, and rotational strength of – 0.15 Debye magneton. The circular dichroic curves constructed from the optical rotatory dispersion data by the Kronig-Kramers transform are in general agreement with the experimentally determined spectra. 
 
 
 
The backbone rotations are analyzed and expressed in the terms of Shechter-Blout's parameters. The effective helicity thus computed is 50% for the reduced and 44.5% for the oxidized form. 
 
 
 
The sources of the Soret cotton effects are discussed along with the possibilities of the components present (cytochromes a and a3 and copper), the intrinsic property of the Soret transition, possible splitting of the Soret band, interactions with the protein helix, and heme-heme and heme-copper couplings. The fact that the optical rotatory dispersion and circular dichroism behavior is dependent upon the oxidation state of cytochrome oxidase could arise either from an altered conformation of the protein backbone and/or from an altered interaction with the heme group. Regardless of the possibilities, the geometrical conformation of cytochrome oxidase and the electronic relation between the prosthetic group and the apoenzyme is dependent upon the oxidation state of the enzyme.
Studies on cytochrome oxidase. V. Factors affecting the optical rotatory dispersion of hematin a.
Abstract The optical rotatory dispersion (ORD) of the oxidized, reduced, and CO-reduced hematin a were affected by sodium chloride, pH of the medium, Emasol-1130, organic solvents, and pyridine in aqueous phosphate buffer. Increased concentration of NaCl transformed the ORD of hematin a from type I to type II; this effect paralleled the induced aggregation observed for NaCl. The ORD profile as a function of pH likewise indicated formation of larger aggregates as the pH was lowered. At pH 5.9, the ORD of all the three forms resembled that of type II. In the pH range of 8.5 to 11.5, the ORD of hematin a showed three isorotatory points: 431, 358, and 312 mµ; the dispersion curves for all the three forms did not vary significantly in this pH region. Organic solvents abolished the optical activity of hematin a. However, in the presence of a small amount of pyridine (0.01 to 0.75 m), heme a in aqueous medium not only showed a distinct hemochrome type spectrum with absorption maxima at 589 mµ and 442 mµ, but also exhibited anomalous optical rotations in both of the absorption regions. The Soret-Cotton effect exhibited a peak at 447.5 mµ and troughs at 425 and 480 mµ, respectively. The amplitude was 290,000 ± 30,000°. The corresponding circular dichroic spectrum showed a positive peak at 437.5 mµ and negative peaks at 410 and 460 mµ, respectively. The optical rotation under these conditions was still somewhat dependent on concentration; extrapolation to zero concentration gave a molar rotation of about 280,000°. Ultracentrifuge experiments did not detect any sedimenting species; i.e. the sedimentation coefficient was less than 0.8 S. Therefore, heme a existed in a much smaller aggregated form approaching the monomeric state. It is suggested that, under these conditions, the observed ORD in the presence of a limited amount of pyridine is a reflection of the stereochemistry and conformation of the molecule with heme-iron as the center of dissymmetry.
LYAPUNOV-BASED TRANSFER BETWEEN ELLIPTIC KEPLERIAN ORBITS
We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.