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.     

A chemical potential equalization model for treating polarization in molecular mechanical force fields

Molecular mechanical force fields are widely used in molecular simulation studies due to their simplicity and efficiency. Although accurate enough for many purposes, force fields are approximations and neglect several effects that are important at an atomic level. Probably the most significant of these, that is not taken into account by the majority of force fields, is the ability of the charge distribution of a molecule to polarize in response to changes in its environment. There are several ways of including polarization effects in force fields but, in this paper, we investigate a relatively new approach, called the chemical potential equalization model, which is based upon the principle of electronegativity equalization and which is a generalization of the class of fluctuating charge models. We detail the principles behind the model and of our implementation of it and then present parametrizations of the model for the molecules, methane and water, and the chloride anion. Gas- and solution-phase calculations to test the parametrizations indicate that the model gives results that are in good agreement with experiment and that compare well to those obtained with non-polarizable force fields and other polarizable models.     

A LOCAL MESH REFINEMENT ALGORITHM APPLIED TO TURBULENT FLOW

This paper presents a local mesh refinement procedure based on a discretization over internal interfaces where the averaging is performed on the coarse side. It is implemented in a multigrid environment but can optionally be used without it. The discretization for the convective terms in the velocity and the temperature equation is the QUICK scheme, while the HYBRID-UPWIND scheme is used in the turbulence equations. The turbulence model used is a two-layer k–ϵ model. We have applied this formulation on a backward-facing step at Re=800 and on a three-dimensional turbulent ventilated enclosure, where we have resolved a geometrically complex inlet consisting of 84 nozzles. In both cases the concept of local mesh refinements was found to be an efficient and accurate solution strategy. © 1997 by John Wiley & Sons, Ltd.     

From Molecule to Cluster to Bulk: Water OH Vibrations in Different Surroundings

Vibrational spectra for the O—H stretching motion of HDO molecules in different surroundings have been calculated by quantum mechanical ab initio methods and compared with experimental spectra. The free water molecule, water chains, and ion–water clusters are discussed. Solvent effects on OH vibrations in liquid water have been calculated as well as “in-crystal” OH frequencies in some ice and ionic crystalline hydrate structures. The importance of nonadditivity effects, electron correlation (at the mp 2 level), and long-range interactions for the total frequency downshift is demonstrated. It is shown that the inclusion of these effects, in conjunction with a variational quantum mechanical treatment of the anharmonic vibrational stretching motion (force constants up to the fourth order), yields vibrational frequencies in quantitative agreement with experiment for a wide range of aqueous systems.     

FORECASTING TREE SIZE DISTRIBUTION BY NUMERICAL APPROXIMATION OF THE FORWARD KOLMOGOROV EQUATION

ABSTRACT. Forest management planning of uneven‐aged stands involves forecasting of the tree size distribution. The temporal development of the size distribution in a forest stand may be described by the forward Kolmogorov equation. The objective of this study is to illustrate that numerical approximation of the solution to the equation provides a reasonably accurate way of forecasting future tree size distribution, especially for stands with non‐normal size distribution. Furthermore, a method for the practical application is devised. The analyses compare observed and forecasted tree size distributions for two forest stands, 1) an unthinned stand of Sitka spruce (Picea sitchensis (Bong.) Carr.), and 2) an uneven‐aged stand of beech (Fagus sylvatica L.) managed under the selection system. The analyses show that the size distribution in the uneven‐aged stand may be forecasted correctly for a 20 25 year period, while for the even‐aged stand the method seems to fail after 10 to 15 years.     

Finite-Element Methods for a Strongly Damped Wave Equation

Error estimates of optimal order are proved for semidiscreteand completely discrete finite-element methods for a linearwave equation with strong damping, arising in viscoelastic theory.It is demonstrated that the exact solution may be interpretedin terms of an analytic semigroup, and as a result that, althoughthe solution has essentially the spatial regularity of its initialdata, it is infinitely differentiable in time for t>0. Theestimates for the spatially discrete method are derived by energyarguments. Rational approximation of analytic semigroups isdiscussed in a general setting, by means of spectral representation,and the results are used to analyse the completely discreteschemes. Both smooth (and compatible) and less smooth data areconsidered.     

Effects of drying and pressing on the pore structure in the cellulose fibre wall studied by 1H and 2H NMR relaxation

A 1H and 2H NMR relaxation method was used to investigate the influence of drying and pressing on the pore size and pore size distribution in the cellulose fibre wall. The investigation was made in the moisture interval in which cellulose fibres normally shrink, i.e. from a moisture ratio of about 1.5 g water/g fibre to dry fibres. When the moisture content of a fibre sample was decreased by drying or pressing, the pores decreased in size and the pore size distribution became narrower. It was found that there were only small differences at a given moisture content between the pore size distributions of samples prepared by drying and by pressing. The results also indicate that the pore shrinkage in cellulose fibres during pressing or drying is a process in which the cell wall pores of a wet cellulose fibre successively shrink as the moisture content decreases. It was observed that, at low moisture contents, pressing and drying resulted in different 1H NMR spin-lattice relaxation profiles. This is discussed in terms of morphology differences in the fibre matrix. The mobility of the protons in the solid phase influences the liquid 1H NMR spin-lattice relaxation in heterogeneous systems through magnetization transfer. We have also studied the effects of hornification in recycled pulps     

Cluster modelling of O(1s) core excitons at the (100) surface of alkaline-earth oxides

Calculations have been performed on the O(1s) X-ray absorption spectra of the O^2- ion in the series of alkaline-earth oxides MgO, CaO, SrO. The static exchange approach has been used to calculate the near-edge X-ray absorption fine structure (NEXAFS) spectra for a range of cluster models (up to 50 atoms), representing both the (100) surface and the bulk of the different lattices. The clusters have been embedded in a proper representation of both the surrounding crystal ions and the Madelung potential generated by the infinite crystal. In the surface clusters discrete levels lying around 1.5 eV below the calculated ionization potential were found and characterized. This surface state has been studied further by performing complete active space self-consistent field (CASSCF) calculations in which the polarization of the crystal ions has been taken into account by means of a core polarization potential (CPP) method as well as the Mott-Littleton approach. After inclusion of this potential, the calculated ionization potentials show good agreement with XPS measurements.     

AN INDICATOR FOR ECOSYSTEM EXTERNALITIES IN FISHING

Ecosystem externalities arise when one use of an ecosystem affects its other uses through the production functions of the ecosystem. We use simulations with a size‐spectrum ecosystem model to investigate the ecosystem externality created by fishing of multiple species. The model is based upon general ecological principles and is calibrated to the North Sea. Two fleets are considered: a “forage fish” fleet targeting species that mature at small sizes and a “large fish” fleet targeting large piscivorous species. Based on the marginal analysis of the present value of the rent, we develop a benefit indicator that explicitly divides the consequences of fishing into internal and external benefits. This analysis demonstrates that the forage fish fleet has a notable economic impact on the large fish fleet, but the reverse is not true. The impact can be either negative or positive, which entails that for optimal economic exploitation, the forage fishery has to be adjusted according to the large fish fishery. With the present large fish fishery in the North Sea, the two fisheries are well adjusted; however, the present combined exploitation level is too high to achieve optimal economic rents.