Molecular dynamics with the united-residue model of polypeptide chains. I. Lagrange equations of motion and tests of numerical stability in the microcanonical mode

The Lagrange formalism was implemented to derive the equations of motion for the physics-based united-residue (UNRES) force field developed in our laboratory. The C(alpha)...C(alpha) and C(alpha)...SC (SC denoting a side-chain center) virtual-bond vectors were chosen as variables. The velocity Verlet algorithm was adopted to integrate the equations of motion. Tests on the unblocked Ala(10) polypeptide showed that the algorithm is stable in short periods of time up to the time step of 1.467 fs; however, even with the shorter time step of 0.489 fs, some drift of the total energy occurs because of momentary jumps of the acceleration. These jumps are caused by numerical instability of the forces arising from the U(rot) component of UNRES that describes the energetics of side-chain-rotameric states. Test runs on the Gly(10) sequence (in which U(rot) is not present) and on the Ala(10) sequence with U(rot) replaced by a simple numerically stable harmonic potential confirmed this observation; oscillations of the total energy were observed only up to the time step of 7.335 fs, and some drift in the total energy or instability of the trajectories started to appear in long-time (2 ns and longer) trajectories only for the time step of 9.78 fs. These results demonstrate that the present U(rot) components (which are statistical potentials derived from the Protein Data Bank) must be replaced with more numerically stable functions; this work is under way in our laboratory. For the purpose of our present work, a nonsymplectic variable-time-step algorithm was introduced to reduce the energy drift for regular polypeptide sequences. The algorithm scales down the time step at a given point of a trajectory if the maximum change of acceleration exceeds a selected cutoff value. With this algorithm, the total energy is reasonably conserved up to a time step of 2.445 fs, as tested on the unblocked Ala(10) polypeptide. We also tried a symplectic multiple-time-step reversible RESPA algorithm and achieved satisfactory energy conservation for time steps up to 7.335 fs. However, at present, it appears that the reversible RESPA algorithm is several times more expensive than the variable-time-step algorithm because of the necessity to perform additional matrix multiplications. We also observed that, because Ala(10) folds and unfolds within picoseconds in the microcanonical mode, this suggests that the effective (event-based) time unit in UNRES dynamics is much larger than that of all-atom dynamics because of averaging over the fast-moving degrees of freedom in deriving the UNRES potential.     

Redoxindicatoren in der Spurenanalyse

Zusammenfassung Die Oxydation von Variaminblau in Gegenwart von Kupfer(II)-ionen und Cyaniden, Rhodaniden oder Jodiden wurde zur photometrischen Bestimmung der letztgenannten Ionen ausgenützt. Es gelingt noch Cyanidkonzentrationen von 0,03g CN^–/ml sicher zu erfassen. Rhodanid- und besonders Jodidionen müssen zur Bestimmung in größeren Konzentrationen zugegen sein.Bei den Versuchsarbeiten hat uns Frl. E.liwa Mithilfe geleistet. Wir sagen ihr dafür vielen Dank.Diese Arbeit ist ein Teil der Dissertation von Dipl.-Chem. F.Buhl.     

Approximating sequences for heteroclinic orbits

In this paper we construct two approximating sequences for heteroclinic solution to a scalar ODE. These sequences do not ‘intersect’ and bound a unique real solution from below and above, thus enabling us to estimate this solution with any accuracy.     

Synthesis and anti‐HIV activity of n‐(3‐amino‐3,4‐dihydro‐4‐oxopyrimidin‐2‐yl)‐4‐chloro‐2‐mercapto‐5‐methylbenzenesulfonamide derivatives

A series of N‐(3‐amino‐3,4‐dihydro‐4‐oxopyrimidin‐2‐yl)‐4‐chloro‐2‐mercapto‐5‐methylbenzenesulfonamide derivatives 10‐17 have been synthesized as potential anti‐HIV agents. The in vitro anti‐HIV‐1 activity of these compounds has been tested at the national Cancer Institute (Bethesda, MD), and the structure‐activity relationships are discussed. The selected N‐[3‐amino‐3,4‐dihydro‐6‐(tert‐butyl)‐4‐oxothieno[2,3‐e]pyrimidin‐2‐yl]‐4‐chloro‐2‐metcapto‐5‐methylbenzenesulfonamide ( 14 ) showed good anti‐HIV‐1 activity with 50% effective concentration (EC₅₀) value of 15 μM and weak cytotoxic effect (IC₅₀ = 106 μM).     

Pontryagin space structure in reproducing kernel Hilbert spaces over *-semigroups

The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of *-semigroups. It goes via the positive definite functions and related to them reproducing kernel Hilbert spaces. Our concern is in describing properties of elements of the semigroup which determine shift operators which serve as Pontryagin fundamental symmetries.