Pulse radiolysis studies of ortho-quinone chemistry relevant to melanogenesis.

The contributions of pulse radiolysis towards characterisation of unstable ortho-quinones relevant to melanogenesis are reviewed. The quinones discussed include dopaquinone, the precursor of both eumelanogenesis and phaeomelanogenesis, and 5-S-cysteinyldopaquinone, an early component of the phaeomelanogenic pathway. Redox exchange between dopaquinone and 5-S-cysteinyldopa is shown to be a determinant of the balance between eumelanogenesis and phaeomelanogenesis. Ortho-quinones resulting from the oxidation of tertiary N,N-dialkylcatecholamines cyclise to redox-inactive betaines which fail to autoactivate tyrosinase. This is consistent with the dopa detected during melanogenesis catalysed by tyrosinase being formed indirectly by a combination of dopaquinone intramolecular reductive addition to form leucodopachrome (cyclodopa), followed by redox exchange between remaining dopaquinone and leucodopachrome. Rapid tautomerism of the ortho-quinone of 4-cyanomethylcatechol to a redox-inactive quinomethane likewise inhibits tyrosinase autoactivation. The incorporation of trihydric phenol moieties in melanin is modelled by the reactions of several ortho-quinones with phloroglucinol, which itself is not directly oxidised by tyrosinase due to the meta-positioning of the hydroxyl groups. The importance of a susceptibility towards nucleophilic attack as well as a propensity to undergo redox-exchange, in the chemistry of melanogenic ortho-quinones, is emphasised.     

Enhancing and Enacting Curricular Progressions in Elementary Mathematics

In this study, we examined how curricular resources supported three expert teachers in their enactment of progressions. Using a video-stimulated interview process, we documented the multiple types of progressions identified, described, and enacted by the teachers. Results indicate that the teachers used four different types of progressions—mathematical concepts, instructional activities, number choices, and student solutions—and that the progressions were embedded within each other. This study contributes to the field’s understanding of the ways in which expert teachers make use of curriculum- and research-based progressions in their teaching practices.     

Higher-Order Kinetic Term for Controlling Photon Mass in Off-Shell Electrodynamics

In relativistic classical and quantum mechanics with Poincaré-invariant parameter, particle worldlines are traced out by the evolution of spacetime events. The formulation of a covariant canonical framework for the evolving events leads to a dynamical theory in which mass conservation is demoted from a priori constraint to the status of conserved Noether current for a certain class of interactions. In pre-Maxwell electrodynamics—the local gauge theory associated with this framework —events induce five local off-shell fields, which mediate interactions between instantaneous events, not between the worldlines which represent entire particle histories. The fifth field, required to compensate for dependence of gauge transformations on the evolution parameter, enables the exchange of mass between particles and fields. In the equilibrium limit, these pre-Maxwell fields are pushed onto the zero-mass shell, but during interactions there is no mechanism regulating the mass that photons may acquire, even when event trajectories evolve far into the spacelike region. This feature of the off-shell formalism requires the application of some ad hoc mechanism for controlling the photon mass in two opposite physical domains: the low energy motion of a charged event in classical Coulomb scattering, and the renormalization of off-shell quantum electrodynamics. In this paper, we discuss a nonlocal, higher derivative correction to the photon kinetic term, which provides regulation of the photon mass in a manner which preserves the gauge invariance and Poincaré covariance of the original theory. We demonstrate that the inclusion of this term is equivalent to an earlier solution to the classical Coulomb problem, and that the resulting quantum field theory is renormalized.