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.     

A PRESSURE-BASED EULER SCHEME FOR TRANSONIC INTERNAL AND EXTERNAL FLOW SIMULATION

SUMMARY

The development of a pressure-based Euler scheme, based on a collocated grid arrangement and solving for Cartesian mass flux components is described. An implicit numerical dissipation model, which includes second and fourth difference terms expressed in pressure, is demonstrated. A smoothing function, which includes a two-level filter, is used to adjust the second order-dissipation. The successful calculations for the inviscid transonic aerodynamic flow around airfoil NACA0012 are presented. The transonic quasi-one-dimensional flow calculation in a converging-diverging nozzle is chosen as an example of an internal flow simulation.     

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.     

Local spin II

Equations are discussed for computing, from ah initio wavefunctions, average values of quantities like S_A. S_B which appear in the Heisenberg model Hamiltonian of magnetism. These equations are based on projection operators onto local regions of space. They result in local spin operators S_A which obey the definition of angular momentum operators and commute with each other. These averages are evaluated for UHF and CI wavefunctions for a few examples of closed and open shell molecules. The calculations are compared with the assumptions made in the Noodleman method for evaluating the parameters in the Heisenberg Hamiltonian and with various definitions of bond order.     

Shock Tube Measurements of Ignition Delay Times for the Butanol Isomers Using the Constrained‐Reaction‐Volume Strategy

Ignition delay times of sec‐, iso‐, and tert‐butanol were measured behind reflected shock waves using both conventional operation and a new constrained‐reaction‐volume (CRV) strategy. This CRV filling method constrains the volume of reactive gases, thereby producing near‐constant‐pressure test conditions for reflected shock measurements. The initial reflected shock conditions cover temperatures ranging from 828 to 1095 K, pressures near 20 atm and an equivalence ratio of 1.0 in air mixtures. Additional data were also collected at 30 atm and at φ = 0.5 for iso‐butanol/O₂/N₂ mixtures. At 20 atm and φ = 1.0, the ignition delay time increases for the isomers in the following order: n‐butanol, iso‐butanol and sec‐butanol, and tert‐butanol. Modeling of all collected data using the Vasu and Sarathy (Energy Fuel 2013, 27, 7072–7080) mechanism showed overall good agreement with the experimental data.     

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.     

Travelling waves in a reaction-diffusion system modelling fungal mycelia

We discuss travelling-wave solutions of a system of coupledreaction—diffusion equations used by the authors to describethe macroscopic behaviour of fungal mycelia. Such systems havebeen used in a multitude of applications; and, in particular,Merkin and Needham (1990, Proc. R. Soc. Lond. A 430, 315–45)have studied a certain formulation as a model for generic isothermalchemical reactions. We show that an alternative analysis providesmore complete results in ascertaining the conditions under whichtravelling-wave solutions exist and that it allows a wider rangeof parameter values to be considered; this is essential to theapplication considered in the present case. Numerical investigationsof travelling-wave solutions and the related initial-value problemare included to motivate and extend the analysis.