Basic ingredients of free energy calculations: A review

Methods to compute free energy differences between different states of a molecular system are reviewed with the aim of identifying their basic ingredients and their utility when applied in practice to biomolecular systems. A free energy calculation is comprised of three basic components: (i) a suitable model or Hamiltonian, (ii) a sampling protocol with which one can generate a representative ensemble of molecular configurations, and (iii) an estimator of the free energy difference itself. Alternative sampling protocols can be distinguished according to whether one or more states are to be sampled. In cases where only a single state is considered, six alternative techniques could be distinguished: (i) changing the dynamics, (ii) deforming the energy surface, (iii) extending the dimensionality, (iv) perturbing the forces, (v) reducing the number of degrees of freedom, and (vi) multi‐copy approaches. In cases where multiple states are to be sampled, the three primary techniques are staging, importance sampling, and adiabatic decoupling. Estimators of the free energy can be classified as global methods that either count the number of times a given state is sampled or use energy differences. Or, they can be classified as local methods that either make use of the force or are based on transition probabilities. Finally, this overview of the available techniques and how they can be best used in a practical context is aimed at helping the reader choose the most appropriate combination of approaches for the biomolecular system, Hamiltonian and free energy difference of interest. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Peculiarities of grid control over the current in a discharge with a cathode spot on the cesium liquid-metal cathode

We report on the results of successful implementation of full grid control in a cesium discharge with a cathode spot. The discharge is quenched by a negative grid pulse for a discharge current density up to 75 A/cm² in the grid plane for voltage switching up to 100 V in the pressure range 0.5–1.5 Pa for a voltage drop of 5–6 V in the discharge. It is shown that quenching is the break-off type. The discovered effect of “evacuation” of the heavy component (ions) from the grid-anode gap to the cathode region leads to an unusually long (hundreds of microseconds) time of stabilization of the steady state in the discharge under the experimental conditions.     

Molecular Dynamics Simulation of Ester‐Linked Hen Egg White Lysozyme Reveals the Effect of Missing Backbone Hydrogen Bond Donors on the Protein Structure

The three‐dimensional structure of a protein is stabilized by a number of different atomic interactions. One of these is hydrogen bonding. Its influence on the spatial structure of the hen egg white lysozyme is investigated by replacing peptide bonds (except those of the two proline residues) by ester bonds. Molecular dynamics simulations of native and ester‐linked lysozyme are compared with the native crystal structure and with NOE distance bounds derived from solution NMR experiments. The ester‐linked protein shows a slight compaction while losing its native structure. However, it does not unfold completely. The structure remains compact due to its hydrophobic core and a changed network of hydrogen bonds involving side chains.     

A New Algorithm for Solving the Word Problem in Braid Groups

One of the most interesting questions about a group is whether its word problem can be solved and how. The word problem in the braid group is of particular interest to topologists, algebraists, and geometers, and is the target of intensive current research. We look at the braid group from a topological point of view (rather than a geometric one). The braid group is defined by the action of diffeomorphisms on the fundamental group of a punctured disk. We exploit the topological definition in order to give a new approach for solving its word problem. Our algorithm, although not better in complexity, is faster in comparison with known algorithms for short braid words, and it is almost independent of the number of strings in the braids. Moreover, the algorithm is based on a new computer presentation of the elements of the fundamental group of a punctured disk. This presentation can be used also for other algorithms.     

μ+SR frequency shifts in the van‐Vleck paramagnet PrIn3

As part of an ongoing μ⁺SR study on cubic van‐Vleck paramagnets of the PrM₃ series ( M\ =\ In,Pb,Tl,Sn), in which the CEF level scheme varies systematically, we present preliminary static μ⁺SR results on a single crystal of PrIn₃. From the angular dependence and from the appearance of the μSR spectra, we could determine that stopped μ⁺ occupy octahedral sites of the (1/2, 0, 0) type, i.e. sites with 2 Pr and 4 In atoms as neighbors. The spectral frequency shifts can be accounted for by assigning to the Pr sites essentially unperturbed 4f dipole moment values, as derived from bulk magnetization measurements. The temperature dependence of the shifts scales to a good accuracy with the bulk susceptibility. It is concluded that unlike previous observations with PrNi₅, the local perturbations induced by an interstitial μ⁺ on the CEF levels of neighboring Pr in the PrIn₃ system are small compared with the unperturbed level splitting itself. This revised version was published online in July 2006 with corrections to the Cover Date.     

Direct Bioelectrocatalysis by NADP‐Reducing Hydrogenase from Pyrococcus furiosus

The direct bioelectrocatalysis by an NAD(P)‐reducing hydrogenase is reported for the first time. In contrast to previous attempts to involve similar enzymes in bioelectrocatalysis [1–4], which were in fact unsuccessful, in our report an effective electrocatalysis by Pyrococcus furiosus hydrogenase is convincingly shown by (i) achievement of the hydrogen equilibrium potential and (ii) a high current of hydrogen oxidation (0.3 mA cm^?2 at 100 mV overpotential and at 75 °C). The latter is just a few times lower compared to enzyme electrodes based on NAD(P)‐independent hydrogenases.