Solution conformation by NMR and molecular modeling of three sulfide-free somatostatin octapeptide analogs compared to angiopeptin

Summary The conformation in dimethylsulfoxide of the somatostatin derivative angiopeptin and of three disulfide-free analogs was estimated by two-dimensional nuclear magnetic resonance spectroscopy at room temperature. The resulting 3D molecular graphics were compared and shown to reflect the observed differences in the inhibition of restenosis after rat aorta balloon injury by these octapeptide inhibitors. Angiopeptin and its active analog 2 displayed a relatively rigid conformation of the cyclic hexapeptide backbone due to the presence of two well-defined hydrogen bonds, further stabilized by a third hydrogen bond outside the ring. No such constraints were detected for the two biologically inactive analogs, which, compared to 2, had a two-atom longer or shorter hexapeptide ring. The well-defined structure of compound 2 may serve as an improved pharmacophore for this new class of drugs.     

Relaxation dynamics of 2,7- and 3,6-distyrylcarbazoles in solutions and in solid films: mechanism for efficient nonradiative deactivation in the 3,6-linked carbazole

We performed time-resolved spectral investigations of two distyrylcarbazole derivatives, 2,7- and 3,6-distyrylcarbazole (2,7-DPVTCz and 3,6-DPVTCz, respectively), in dilute toluene solution and in solid films mixed with poly(methyl methacrylate) (PMMA). The lifetime of 2,7-DPVTCz in its excited state in solution is approximately 100 times as great as that of 3,6-DPVTCz, consistent with their photophysical nature. The former shows intense emission, but the latter is nearly nonfluorescent in a free environment. Moreover, the lifetime of 3,6-DPVTCz in its excited state increased also approximately 100 times when the molecule was encapsulated in a 3,6-DPVTCz/PMMA solid film, indicating that intramolecular motion of the molecule significantly affects the observed relaxation dynamics in a confined environment. Calculations on the excited states indicate that an efficient intersystem crossing is activated upon twisting of the bridged C-C single bond in a free 3,6-linked carbazole; such efficient deactivation is impractical in 2,7-linked carbazole or for 3,6-linked carbazole in a PMMA matrix. Information obtained from experiments on femtosecond fluorescence enables us to distinguish crucial relaxation processes in the excited state for a profound understanding of the details of vibrational and electronic relaxations of 3,6-DPVTCz in solution.     

Phase sensitive demodulation in multiphoton microscopy.

Multiphoton laser scanning microscopy offers advantages in depth of penetration into intact samples over other optical sectioning techniques. To achieve these advantages it is necessary to detect the emitted light without spatial filtering. In this nondescanned (nonconfocal) approach, ambient room light can easily contaminate the signal, forcing experiments to be performed in absolute darkness. For multiphoton microscope systems employing mode-locked lasers, signal processing can be used to reduce such problems by taking advantage of the pulsed characteristics of such lasers. Specifically, by recovering fluorescence generated at the mode-locked frequency, interference from stray light and other ambient noise sources can be significantly reduced. This technology can be adapted to existing microscopes by inserting demodulation circuitry between the detector and data collection system. The improvement in signal-to-noise ratio afforded by this approach yields a more robust microscope system and opens the possibility of moving multiphoton microscopy from the research lab to more demanding settings, such as the clinic.     

Homoclinic orbits on compact hypersufaces in 293-1293-1293-1, of restricted contact type

Consider a smooth Hamiltonian system in ^2N , , the energy surface ={x/H(x)=H(0)} being compact, and 0 being a hyperbolic equilibrium. We assume, moreover, that {0} is of restricted contact type. These conditions are symplectically invariant. By a variational method, we prove the existence of an orbit homoclinic, i.e. non-constant and doubly asymptotic, to 0.     

Logarithmic correction to the probability of capture for dissipatively perturbed Hamiltonian systems

Hamiltonian systems are analyzed with a double homoclinic orbit connecting a saddle to itself. Competing centers exist. A small dissipative perturbation causes the stable and unstable manifolds of the saddle point to break apart. The stable manifolds of the saddle point are the boundaries of the basin of attraction for the competing attractors. With small dissipation, the boundaries of the basins of attraction are known to be tightly wound and spiral-like. Small changes in the initial condition can alter the equilibrium to which the solution is attracted. Near the unperturbed homoclinic orbit, the boundary of the basin of attraction consists of a large sequence of nearly homoclinic orbits surrounded by close approaches to the saddle point. The slow passage through an unperturbed homoclinic orbit (separatrix) is determined by the change in the value of the Hamiltonian from one saddle approach to the next. The probability of capture can be asymptotically approximated using this change in the Hamiltonian. The well-known leading-order change of the Hamiltonian from one saddle approach to the next is due to the effect of the perturbation on the homoclinic orbit. A logarithmic correction to this change of the Hamiltonian is shown to be due to the effect of the perturbation on the saddle point itself. It is shown that the probability of capture can be significantly altered from the well-known leading-order probability for Hamiltonian systems with double homoclinic orbits of the twisted type, an example of which is the Hamiltonian system corresponding to primary resonance. Numerical integration of the perturbed Hamiltonian system is used to verify the accuracy of the analytic formulas for the change in the Hamiltonian from one saddle approach to the next. (c) 1995 American Institute of Physics.     

Dispersion relations in string theory

We analyze the analytic continuation of the formally divergent one-loop amplitude for scattering of the gravitonmultiplet in the Type II superstring. In particular we obtain explicit double and single dispersion relations, formulas for all the successive branch cuts extending out to +, as well as for the decay rate of a massive string state of arbitrary mass2N into two string states of lower mass. We compare our results with the box diagram in a superposition of ³-like field theories. The stringy effects are traced to a convergence problem in this superposition.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98. No. 3, pp. 442–455, March, 1994.     

Results and estimates on pseudopowers

Let be a positive integer. We say looks like a power of 2 modulo a prime if there exists an integer such that . First, we provide a simple proof of the fact that a positive integer which looks like a power of modulo all but finitely many primes is in fact a power of . Next, we define an -pseudopower of the base to be a positive integer that is not a power of , but looks like a power of modulo all primes . Let denote the least such . We give an unconditional upper bound on , a conditional result (on ERH) that gives a lower bound, and a heuristic argument suggesting that is about for a certain constant . We compare our heuristic model with numerical data obtained by a sieve. Some results for bases other than are also given.

     

Weak decoherence and quantum trajectory graphs

Griffiths' quantum trajectories formalism is extended to describe weak decoherence. The decoherence conditions are shown to severely limit the complexity of histories composed of fine-grained events.