Evolution of physics-based methodology for exploring the conformational energy landscape of proteins

The evolution of our physics-based computational methods for determining protein conformation without the introduction of secondary-structure predictions, homology modeling, threading, or fragment coupling is described. Initial use of a hard-sphere potential captured much of the structural properties of polypeptide chains, and subsequent more refined force fields, together with efficient methods of global optimization provide indications that progress is being made toward an understanding of the interresidue interactions that underlie protein folding.     

Reaction of 4‐benzylidene‐2‐methyl‐5‐oxazolone with amines,Part 2: Influence of substituents in para‐position in the phenyl ring and a substituent on amine nitrogen atom on the reaction kinetics

An influence of a structure of the amine (benzylamine, N‐methyl‐benzylamine, N‐isopropyl‐benzylamine, N‐methyl‐butylamine, N‐ethyl‐butylamine, sec‐butylamine, and tert‐butylamine) on a rate constant of the ring‐opening reaction of 4‐benzylidene‐2‐methyl‐5‐oxazolone (Ox) was studied. The good correlation between logarithm of the rate constants and Charton's steric substituent constant ν as well as good correlation with a form of the simple branching equation indicate that there is a steric effect because of substitution at C1 carbon atom of nucleophile which decreases the reaction rate. Additionally, an influence of a structure of the benzylidene moiety of Ox on a rate of the oxazolone ring‐opening reaction was studied. The substituents (? OH, ? OCH₃, ? N(CH₃)₂, ? Cl, ? NO₂) in para‐position of the phenyl ring of Ox substantially modified the rate of the reaction with benzylamine in acetonitrile. The rate of the Ox ring‐opening reaction decreased with increase of the electron‐donating properties of the substituent. A good correlation between the rate constants of the reaction of 4‐(4′‐substituted‐benzylidene)‐2‐methyl‐5‐oxazolones with benzylamine and the electron density at the reaction center (carbon C5 of the oxazolone ring), calculated using ab initio method, and the Hammett substituent constants, and CR equation were established. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 148–155, 2002; DOI 10.1002/kin.10039     

Essential dynamics/factor analysis for the interpretation of molecular dynamics trajectories

Subject of this work is the analysis of molecular dynamics (MD) trajectories of neurophysins I (NPI) and II (NPII) and their complexes with the neurophyseal nonapeptide hormones oxytocin (OT) and vasopresssin (VP), respectively, simulated in water. NPs serve in the neurosecretory granules as carrier proteins for the hormones before their release to the blood. The starting data consisted of two pairs of different trajectories for each of the (NPII/VP)2 and (NPI/OT)2 heterotetramers and two more trajectories for the NPII2 and NPI2 homodimers (six trajectories in total). Using essential dynamics which, to our judgement, is equivalent to factor analysis, we found that only about 10 degrees of freedom per trajectory are necessary and sufficient to describe in full the motions relevant for the function of the protein. This is consistent with these motions to explain about 90% of the total variance of the system. These principal degrees of freedom represent slow anharmonic motional modes, clearly pointing at distinguished mobility of the atoms involved in the protein's functionality.     

Fiber-assisted detection with photon number resolution

We report the development of a photon-number-resolving detector based on a fiber-optical setup and a pair of standard avalanche photodiodes. The detector is capable of resolving individual photon numbers and operates on the well-known principle by which a single-mode input state is split into a large number (eight) of output modes. We reconstruct the photon statistics of weak coherent input light from experimental data and show that there is a high probability of inferring the input photon number from a measurement of the number of detection events on a single run.     

Study of intrinsic localized vibrational modes in micromechanical oscillator arrays

Intrinsic localized modes (ILMs) have been observed in micromechanical cantilever arrays, and their creation, locking, interaction, and relaxation dynamics in the presence of a driver have been studied. The micromechanical array is fabricated in a 300 nm thick silicon-nitride film on a silicon substrate, and consists of up to 248 cantilevers of two alternating lengths. To observe the ILMs in this experimental system a line-shaped laser beam is focused on the 1D cantilever array, and the reflected beam is captured with a fast charge coupled device camera. The array is driven near its highest frequency mode with a piezoelectric transducer. Numerical simulations of the nonlinear Klein-Gordon lattice have been carried out to assist with the detailed interpretation of the experimental results. These include pinning and locking of the ILMs when the driver is on, collisions between ILMs, low frequency excitation modes of the locked ILMs and their relaxation behavior after the driver is turned off.     

Prediction of protein structure using a knowledge-based off-lattice united-residue force field and global optimization methods

A united-residue model of polypeptide chains developed in our laboratories with united side-chains and united peptide groups as interaction sites is presented. The model is designed to work in continuous space; hence efficient global-optimization methods can be applied. In this work, we adopted the distance-scaling method that is based on continuous deformation of the original rugged energy hypersurface to obtain a smoothed surface. The method has been applied successfully to predict the structures of simple motifs, such as the three-helix bundle structure of the 10-58 fragment of staphylococcal protein A in de novo folding simulations and more complicated motifs in inverse-folding simulations. Received: 24 April 1998 / Accepted: 4 August 1998 / Published online: 2 November 1998     

Endpoints of set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and strict contractions in uniform spaces

In this paper, we introduce the concepts of the set-valued dynamical systems of asymptotic contractions of Meir–Keeler type and set-valued dynamical systems of strict contractions in uniform spaces and we present a method which is useful for establishing conditions guaranteeing the existence and uniqueness of endpoints of these contractions and the convergence to these endpoints of all generalized sequences of iterations of these contractions. The result, concerning the investigations of problems of the set-valued asymptotic fixed point theory, include some well-known results of Meir and Keeler, Kirk and Suzuki concerning the asymptotic fixed point theory of single-valued maps in metric spaces. The result, concerning set-valued strict contractions (in which the contractive coefficient is not constant), is different from the result of Yuan concerning the existence of endpoints of Tarafdar–Vyborny generalized contractions (in which the contractive coefficient is constant) in bounded metric spaces and provides some examples of Tarafdar–Yuan topological contractions in compact uniform spaces. Definitions and results presented here are new for set-valued dynamical systems in uniform, locally convex and metric spaces and even for single-valued maps. Examples show a fundamental difference between our results and the well-known ones.     

New catalytic route to functionalized vinylboronates

Vinylsubstituted boronates i.e. vinyldioxaborolane and vinyldioxaborinane react regioselectively with olefins in the presence of RuHCl(CO)(PCy3)2 with the formation of functionalized vinylboron derivatives. The reaction opens a new catalytic route for preparation of organoboranes.     

On iterative convexity of diffeomorphism

Abstract

A function f is said to be iteratively convex if f possesses convex iterative roots of all orders. We give several constructions of iteratively convex diffeomorphisms and explain the phenomenon that the non-existence of convex iterative roots is a typical property of convex functions. We show also that a slight perturbation of iteratively convex functions causes loss of iterative convexity. However, every convex function can be approximate by iteratively convex functions.