Insights into enzyme catalysis from QM/MM modelling: transition state stabilization in chorismate mutase

Chorismate mutase provides an important test of theories of enzyme catalysis, and of modelling methods. The Claisen rearrangement of chorismate to prephenate in the enzyme has been modelled here by a combined quantum mechanics/molecular mechanics (QM/MM) method. Several pathways have been calculated. The sensitivity of the results to details of model preparation and pathway calculation is tested, and the results are compared in detail to previous similar studies and experiments. The potential energy barrier for the enzyme reaction is estimated at 24.5—31.6 kcal mol^?1 (AMl/CHARMM), and 2.7—11.9 kcal mol^?1 with corrections (e.g. B3LYP/6-31 + G(d)). In agreement with previous studies, the present analysis of the calculated paths provides unequivocal evidence of significant transition state stabilization by the enzyme, indicating that this is central to catalysis by the enzyme. The active site is exquisitely complementary to the transition state, stabilizing it more than the substrate, so reducing the barrier to reaction. A number of similar pathways for reaction exist in the protein, as expected. Small structural differences give rise to differences in energetic contributions. Major electrostatic contributions to transition state stabilization come in all cases from Arg90, Arg7, one or two water molecules, and Glu78 (Glu78 destabilizes the transition state less than the substrate), while Arg63 contributes significantly in one model.     

偶氮苯的光化学顺反异构化反应及其在光强测定中的应用

本文叙述了用偶氮苯露光计测定光强的原理。本方法也同样可用于测定A<﹦>B型光化学异构化反应的量子产率,设计了专用的计算机程序来处理在光强和量子产率的测定中的各种有关数据。     

SEM Modeling with Singular Moment Matrices Part II: ML-Estimation of Sampled Stochastic Differential Equations

Linear stochastic differential equations are expressed as an exact discrete model (EDM) and estimated with structural equation models (SEMs) and the Kalman filter (KF) algorithm. The oversampling approach is introduced in order to formulate the EDM on a time grid which is finer than the sampling intervals. This leads to a simple computation of the nonlinear parameter functionals of the EDM. For small discretization intervals, the functionals can be linearized, and standard software permitting only linear parameter restrictions can be used. However, in this case the SEM approach must handle large matrices leading to degraded performance and possible numerical problems. The methods are compared using coupled linear random oscillators with time-varying parameters and irregular sampling times.     

SEM Modeling with Singular Moment Matrices Part I: ML-Estimation of Time Series

A structural equation model (SEM) with deterministic intercepts is introduced. The Gaussian likelihood function does not contain determinants of sample moment matrices and is thus well-defined for only one statistical unit. The SEM is applied to the dynamic state space model and compared with the Kalman filter (KF) approach. The likelihood of both methods are shown to be equivalent, but for long time series numerical problems occur in the SEM approach, which are traced to the inversion of the latent state covariance matrix. Both approaches are compared on several aspects. The SEM approach is now open for idiographic (N = 1) analysis and estimation of panel data with correlated units.     

The Hoyle state in nuclear lattice effective field theory

We review the calculation of the Hoyle state of ¹²C in nuclear lattice effective field theory (NLEFT) and its anthropic implications in the nucleosynthesis of ¹²C and ¹⁶O in red giant stars. We also analyse the extension of NLEFT to the regime of medium-mass nuclei, with emphasis on the determination of the ground-state energies of the α nuclei ¹⁶O, ²⁰Ne, ²⁴Mg, and ²⁸Si by Euclidean time projection. Finally, we discuss recent NLEFT results for the spectrum, electromagnetic properties, and α-cluster structure of ¹⁶O.     

Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels

In this paper we investigate the attainable order of (global)convergence of collocation approximations in certain polynomialspline spaces for solution of Volterra integrodifferential equationswith weakly singular kernels. While the use of quasi-uniformmeshes leads, due to the nonsmooth nature of these solutions,to convergence of order less than one, regardless of the degreeof the approximating spline function, collocation on suitablygraded meshes will be shown to yield optimal convergence rates.