More efficient Brownian dynamics algorithms

We examine the relative efficiencies of three- algorithms for performing Brownian Dynamics simulations without many-body hydrodynamics. We compare the conventional Brownian Dynamics algorithm of Ermak (CBD), Smart Monte Carlo (SMC) which incorporates Boltzmann sampling into essentially a CBD procedure, and the Stochastic Runge Kutta (SRK) method. We show, using the repulsive potential φ(r) = ε(σ/r) ⁿ , where n = 36 and 72, that the SRK algorithm gives the most accurate short-time dynamics for the mean-square displacements. The SRK algorithm static and dynamical properties converge better with a reducing time step to the exact values, than those generated by the CBD algorithm; giving efficiency gains typically of a factor of 3–4. Both CBD and SMC have the incorrect sign for the first correction term to the mean square displacement in a time step, whereas the SRK algorithm gives essentially the exact solution to order Δt ², where Δt is the simulation time step. In fact, these correction terms are almost equal and opposite in sign. Expressions for these terms were derived in terms of the average interaction energy per particle. The force, shear and bulk stress autocorrelation functions were calculated. The average energy per particle and time correlation functions at short time have values in excess of the exact values, while the corresponding quantities for SRK are below this. This difference in behaviour can be traced back to the extent of compliance of the particle trajectories with the exact expansion of the Smoluchowski equation. The accuracy, at a given value of the time step, of the stochastic algorithms can significantly depend on the form of the interaction potential between particles. It is also demonstrated that the long time limits of various correlation functions are fairly insensitive to a particular scheme (SRK or CBD) used in the simulations. All the correlation functions have a stretched exponential region at intermediate to long times, and the values of the exponents on density and force law steepness have been determined.     

Acylation versus sulfonylation in the inhibition of elastase by 3-oxo-beta-sultams

beta-Sultams are the sulfonyl analogues of beta-lactams, and 3-oxo-beta-sultams are both beta-lactams and beta-sultams and, therefore, susceptible to nucleophilic attack at either the acyl or the sulfonyl center. They are novel inactivators of serine enzymes. The second-order rate constant for the inactivation of elastase at pH 6 by N-benzyl-4,4-dimethyl-3-oxo-beta-sultam is 768 M-1 s-1, which is 103-fold greater than that with N-benzoyl beta-sultam. However, in contrast to N-acyl beta-sultams, which sulfonylate the active site serine residue to form a sulfonate ester, 3-oxo-beta-sultams inhibit the enzyme by acylation followed by slow deacylation to regenerate the active enzyme.     

Solid-state NMR spectroscopic methods in chemistry

Over the last decades, NMR spectroscopy has grown into an indispensable tool for chemical analysis, structure determination, and the study of dynamics in organic, inorganic, and biological systems. It is commonly used for a wide range of applications from the characterization of synthetic products to the study of molecular structures of systems such as catalysts, polymers, and proteins. Although most NMR experiments are performed on liquid-state samples, solid-state NMR is rapidly emerging as a powerful method for the study of solid samples and materials. This Review outlines some of the developments of solid-state NMR spectroscopy, including techniques such as cross-polarization, magic-angle spinning, multiple-pulse sequences, homo- and heteronuclear decoupling and recoupling techniques, multiple-quantum spectroscopy, and dynamic angle spinning, as well as their applications to structure determination. Modern solid-state NMR spectroscopic techniques not only produce spectra with a resolution close to that of liquid-state spectra, but also capitalize on anisotropic interactions, which are often unavailable for liquid samples. With this background, the future of solid-state NMR spectroscopy in chemistry appears to be promising, indeed.     

Remarks on the theory of rods

A rod theory, defined as a curve at every point of which is attached a rotation vector, is shown to be a special constrained case of a rod theory in which two deformable directors are attached to each point of a curve.

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Zusammenfassung Eine Theorie von Stäben, die als Kurve bezeichnet wird, an jedem Punkt deren ein Rotationsvektor angebracht ist, wird als besonderer Zwangsfall einer Theorie von Stäben dargestellt, in der zwei verformbare Direktoren an jeden Punkt einer Kurve angebracht werden.

     

The effect of fibre length on the overall moduli of composite materials

An application of the self-consistent method (s.c.m.) is given to the problem of determining overall moduli for short fibre reinforced composites. It is assumed that the fibres can be considered to be spheroids. For fully-aligned fibres, the numerical results are presented in graphical form and show the dependence of the compliances on aspect ratio and volume fraction. It is shown that an aspect ratio of 100 is essentially infinite. By making use of some (albeit tentative) ideas on how to handle the misalignment of fibres the s.c.m. results are shown to compare favourably with experiment.     

A General Method for Constrained Analysis of Fluorescence Anisotropy Decay: Application of the Steady-State Anisotropy

Time-resolved fluorescence anisotropy is an invaluable method for investigating the internal and rotational dynamics of biomolecules. The range of rotational motions detectable by anisotropy decay is limited by the fluorescence lifetime; typically, a depolarizing motion may be resolved if the associated correlation time is between 0.1 and 10 times the intensity decay lifetime. To extend that range and to improve the recovery of anisotropy decay parameters, a general analytical method has been developed. This procedure utilizes a modification of Lagrange multiplier methods to constrain the values of the iterated kinetic parameters during nonlinear least-squares analysis of anisotropy decay data. The form of the constraint equation is derived from the classic relationship between the decay parameters and the steady-state anisotropy, which can be simply and accurately measured. Application of the constraint to analyses of synthetic data sets increased the accuracy of recovery by decreasing the uncertainty in the iterated parameters. The constraint also enabled the accurate recovery of correlation times that were a factor of 30 greater than the fluorescence lifetime, although it did not improve recovery of correlation times that were much shorter than the lifetime. Using this technique, it should now be possible to characterize the dynamics of larger macromolecules and assemblies than those that can currently be studied by fluorescence anisotropy decay.