Potent and selective structure-based dibenzofuran inhibitors of transthyretin amyloidogenesis: kinetic stabilization of the native state

Transthyretin (TTR) amyloidogenesis requires rate-limiting tetramer dissociation and partial monomer denaturation to produce a misassembly competent species. This process has been followed by turbidity to identify transthyretin amyloidogenesis inhibitors including dibenzofuran-4,6-dicarboxylic acid (1). An X-ray cocrystal structure of TTR.1(2) reveals that it only utilizes the outer portion of the two thyroxine binding pockets to bind to and inhibit TTR amyloidogenesis. Herein, structure-based design was employed to append aryl substituents at C1 of the dibenzofuran ring to complement the unused inner portion of the thyroxine binding pockets. Twenty-eight amyloidogenesis inhibitors of increased potency and dramatically increased plasma TTR binding selectivity resulted. These function by imposing kinetic stabilization on the native tetrameric structure of TTR, creating a barrier that is insurmountable under physiological conditions. Since kinetic stabilization of the TTR native state by interallelic trans suppression is known to ameliorate disease, there is reason to be optimistic that the dibenzofuran-based inhibitors will do the same. Preventing the onset of amyloidogenesis is the most conservative strategy to intervene clinically, as it remains unclear which of the TTR misassembly intermediates results in toxicity. The exceptional binding selectivity enables these inhibitors to occupy the thyroxine binding site(s) in a complex biological fluid such as blood plasma, required for inhibition of amyloidogenesis in humans. It is now established that the dibenzofuran-based amyloidogenesis inhibitors have high selectivity, affinity, and efficacy and are thus excellent candidates for further pharmacologic evaluation.     

Limiting distributions of the number of pure strategy Nash equilibria in n-person games

We study the number of pure strategy Nash equilibria in a “random” n-person non-cooperative game in which all players have a countable number of strategies. We consider both the cases where all players have strictly and weakly ordinal preferences over their outcomes. For both cases, we show that the distribution of the number of pure strategy Nash equilibria approaches the Poisson distribution with mean 1 as the numbers of strategies of two or more players go to infinity. We also find, for each case, the distribution of the number of pure strategy Nash equilibria when the number of strategies of one player goes to infinity, while those of the other players remain finite.     

Fibre sizing using Fraunhofer diffraction

The light scattering pattern from absorbing cylinders is shown to be adequately described by Fraunhofer diffraction for cylinders with diameter greater than 8 μm for light of wavelength 632.8 nm. This permits the use of a simple inversion procedure based on a Fourier transform of the scattering pattern to obtain the size distribution of fibre widths. For fibres of diameter less than 8 μm the same inversion procedure may be used when an electron micrograph of the fibres becomes the scattering object. The maximum resolution of this inversion procedure is shown to be proportional to the largest angle scanned and its performance with experimental data is illustrated.     

Function-space quasi-Newton algorithms for optimal control problems with bounded controls and singular arcs

Two existing function-space quasi-Newton algorithms, the Davidon algorithm and the projected gradient algorithm, are modified so that they may handle directly control-variable inequality constraints. A third quasi-Newton-type algorithm, developed by Broyden, is extended to optimal control problems. The Broyden algorithm is further modified so that it may handle directly control-variable inequality constraints. From a computational viewpoint, dyadic operator implementation of quasi-Newton methods is shown to be superior to the integral kernel representation. The quasi-Newton methods, along with the steepest descent method and two conjugate gradient algorithms, are simulated on three relatively simple (yet representative) bounded control problems, two of which possess singular subarcs. Overall, the Broyden algorithm was found to be superior. The most notable result of the simulations was the clear superiority of the Broyden and Davidon algorithms in producing a sharp singular control subarc.This research was supported by the National Science Foundation under Grant Nos. GK-30115 and ENG 74-21618 and by the National Aeronautics and Space Administration under Contract No. NAS 9-12872.     

Average boundary conditions in Cauchy problems

We consider the general Cauchy problem with initial data in a Hilbert space and with a formal dissipative linear generator. A complete parametrization is known of the (abstract) boundary conditions which make this problem well set. We exhibit a distinguished subset $\text{B}$_E of the set $\text{B}$ of boundary conditions and demonstrate explicitly that the evolution associated with each B in $\text{B}$ can be represented as a (time independent) average over the evolutions associated with B′ in $\text{B}$_E. Applications are discussed to Schrödinger equations in bounded regions or with singular potentials.     

Periodically poled lithium niobate monolithic nanosecond optical parametric oscillators and generators

We fabricated and characterized periodically poled lithium niobate monolithic optical parametric oscillators (OPO's) and generators. The compact monolithic devices were trivial to align and operate and provided widely tunable, nearly diffraction-limited, stable output pulses. Low thresholds and high conversion efficiencies were obtained when the devices were pumped with 3.5-ns 1.064-mum pulses. In addition, the monolithic OPO devices exhibited broad tuning by crystal rotation through noncollinear phase matching. The bandwidth-broadening effects exhibited in the noncollinear phase-matching geometry were measured and explained.     

Dynamic supercoiling bifurcations of growing elastic filaments

Certain bacteria form filamentous colonies when the cells fail to separate after dividing. In Bacillus subtilis, Bacillus thermus, and Cyanobacteria, the filaments can wrap into complex supercoiled structures as the cells grow. The structures may be solenoids or plectonemes, with or without branches in the latter case. Any microscopic theory of these morphological instabilities must address the nature of pattern selection in the presence of growth, for growth renders the problem nonautonomous and the bifurcations dynamic. To gain insight into these phenomena, we formulate a general theory for growing elastic filaments with bending and twisting resistance in a viscous medium, and study an illustrative model problem: a growing filament with preferred twist, closed into a loop. Growth depletes the twist, inducing a twist strain. The closure of the loop prevents the filament from unwinding back to the preferred twist; instead, twist relaxation is accomplished by the formation of supercoils. Growth also produces viscous stresses on the filament which even in the absence of twist produce buckling instabilities. Our linear stability analysis and numerical studies reveal two dynamic regimes. For small intrinsic twist the instability is akin to Euler buckling, leading to solenoidal structures, while for large twist it is like the classic writhing of a twisted filament, producing plectonemic windings. This model may apply to situations in which supercoils form only, or more readily, when axial rotation of filaments is blocked. Applications to specific biological systems are proposed.     

The general relativistic hydrogen atom

The general relativistic Dirac equation is formulated in an arbitrary curved space-time using differential forms. These equations are applied to spherically symmetric systems with arbitrary charge and mass. For the case of a black hole (with event horizon) it is shown that the Dirac Hamiltonian is self-adjoint, has essential spectrum the whole real line and no bound states. Although rigorous results are obtained only for a spherically symmetric system, it is argued that, in the presence of any event horizon there will be no bound states. The case of a naked singularity is investigated with the results that the Dirac Hamiltonian is not self-adjoint. The self-adjoint extensions preserving angular momentum are studied and their spectrum is found to consist of an essential spectrum corresponding to that of a free electron plus eigenvalues in the gap (–mc ², +mc ²). It is shown that, for certain boundary conditions, neutrino bound states exist.Supported in part by the National Science Foundation     

The application of homodyne spectroscopy to the study of low-frequency microturbulence in the TEXT tokamak

Summary The wave propagation direction of microturbulence in a tokamak plasma has been accurately measured by application of a new homodyne spectroscopy technique. This method has been used in conjunction with a collective far-infrared laser scattering experiment on TEXT. The low-frequency density fluctuations are observed to propagate primarily in the electron diamagnetic drift direction, however, the broadband spectra also possess an appreciable level of fluctuations traveling in the ion drift direction. Application of the homodyne spectroscopy technique represents an inexpensive and easily implemented alternative to the more technically demanding heterodyne schemes available in the far-infrared.