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.     

Stability of oscillatory two-phase Couette flow

The authors investigate the stability of two-phase Couette flowof different liquids bounded between plane parallel plates.One of the plates has a time-dependent velocity in its own plane,which is composed of a constant steady part and a time-harmoniccomponent. In the absence of time-harmonic modulations, theflow can be unstable to an interfacial instability if the viscositiesare different, and the more viscous fluid occupies the thinnerof the two layers. Using Floquet theory, it is shown analyticallyin the limit of long waves that time-periodic modulations inthe basic flow can have a significant influence on flow stability.In particular, flows which are otherwise unstable for extensiveranges of viscosity ratios can be stabilized completely by theinclusion of background modulations, a finding that can haveuseful consequences in many practical applications.     

Application of the density functional method to study phase transitions in an associating Lennard-Jones fluid adsorbed in energetically heterogeneous slit-Like pores

A density functional approach is used to study the adsorption of the four-bonding-site model associating Lennard-Jones fluid in slit-Like pores with energetically heterogeneous walls. The fluid-wall potential is qualitatively similar to that invoked by Röcken, P., Somoza, A., Tarazona, P., and Findenegg, G. H., 1999, J. chem. Phys., 108, 8089, i.e. it consists of a homogeneous part that varies in the direction perpendicular to the wall and a periodic part, varying also in one direction parallel to the wall. Both parts are modelled by Lennard-Jones 9,3-type functions. The structure of the adsorbed film is characterized by the local densities of all particles and the densities of the monomers. The phase diagrams are evaluated for several systems characterized by different corrugation of the adsorbing potential. The adsorbing field is strong enough to allow for the layering transition. As well as the formation of the so-called bridge phase that fills the pore space over the most energetic parts of the wall and of capillary condensation, the layering transition is observed within the first layer adjacent to the pore walls. If the adsorbing potential due to each pore wall is shifted in phase by π/2, the bridge phase is not formed.     

Molecular layering and local order in thin films of 1-alkyl-3-methylimidazolium ionic liquids using X-ray reflectivity

X-ray reflectivity measurements in air of thin films of 1-alkyl-3-methylimidazolium salts in the liquid, liquid crystalline and solid states supported on Si(111) are described. The films show Bragg features in both liquid crystalline and solid phases, but only after an initial annealing cycle. Kiessig fringes are observed only for the 1-octadecyl-3-methyl-imidazolium hexafluorophosphate films and, following analysis using Parratt32, a bi-layer model is proposed whereby the molecules are orientated with ionic groups at both salt-air and salt-silicon interfaces.     

A new observable to measure the top quark mass at hadron colliders

The $t\bar{t}+\mbox{1-jet} + X$ differential cross-section in proton?Cproton collisions at 7?TeV centre of mass energy is investigated with respect to its sensitivity to the top quark mass. The analysis includes higher order QCD corrections at NLO. The impact of the renormalization scale (?? _R), the factorization (?? _F) scale and of the choice of different proton??s PDF (parton distribution function) has been evaluated. In this study it is concluded that differential jet rates offer a promising option for alternative mass measurements of the top quark, with theoretical uncertainties below 1 GeV.     

ORGANIZED CRIMES AGAINST NATURE: ELEPHANTS IN SOUTHERN AFRICA

Poaching of elephants in Southern Africa is now dominated by international groups following a model of organized crime. This shift, from poaching conducted by small, local groups; with limited mobility, weapons, and technology, to individuals who organize, finance, equip, and transport well‐armed poaching units to previously scouted locations, has made the protection of elephants in Southern Africa much more difficult and dangerous. This paper develops a model of high‐tech criminal poaching. A poaching organization makes a decision on the number of “planned poaching expeditions.” If a poaching unit is intercepted the entire organization is destroyed, but is replaced by a new organization in the next year. The operating life of a poaching organization is a stochastic process, which in turn induces a stochastic evolution in the elephant population. Under plausible conditions, the number of planned poaching expeditions is highly sensitive to the probability of interception by anti‐poaching patrols, but is nonresponsive to reductions in the black‐market ivory price. Thereby it might be better to focus conservation efforts on increasing the probability of intercepting poaching units rather than trying to control black market ivory prices. A benchmark value of poaching expeditions is identified—above which elephants may slowly decline to extinction.     

Polynomial design for continuous-time control

The theory of polynomial design for multivariable continuous-timecontrol systems is developed. It is assumed that inputs arestationary stochastic, and a variation is applied to the controllerin order to find the transfer matrix of the latter which willminimize an appropriate H₂ norm.     

A Note on the Numerical Treatment of the k-epsilon Turbulence Model*

Numerical solution of the equations arising from the κ mdash; ε turbulence model has difficulties inherent to nonlinear convection-reaction-diffusion equations with strong reaction terms, resulting in that numerical schemes easily become unstable. We present a formulation that stresses on the robustness of the solution method, tackling common problems that produce instability. The main contribution concerns the loss of positivity of κ and ε, which is addressed by acting on the coefficients of the reaction and diffusion terms rather than on the turbulent variables themselves. In addition, a linearized implicit, non-iterative, treatment of the wall law is proposed.     

Structure and phase transitions in a network-forming associating Lennard-Jones fluid in a slit-like pore: a density functional approach

A study is reported of adsorption of an associating Lennard-Jones fluid with four associative sites per molecule in a slit-like pore. The density distribution of particles in the pore and thermodynamics properties are evaluated by using a density functional method. It is found that at low temperatures the fluid exhibits a set of layering transitions, followed by capillary condensation. Transitions are localized by analysing the grand canonical potential. The density profiles of particles and the distribution of unbound and differently bonded particles demonstrate changes in the structure of the fluid in the pore along the phase coexistence. The critical temperature is lower for a confined fluid, compared with the bulk counterpart. However, an increase in the energy of association increases the critical temperature. The envelope of the capillary condensation is narrower than the bulk liquid-vapour phase diagram. The dependence of the solvation force on the energy of association and on the bulk density is discussed.