The canonical ensemble via symplectic integrators using Nosé and Nosé-Poincaré chains

Simulations that sample from the canonical ensemble can be generated by the addition of a single degree of freedom, provided that the system is ergodic, as described by Nosé with subsequent modifications by Hoover to allow sampling in real time. Nosé-Hoover dynamics is not ergodic for small or stiff systems and the addition of auxiliary thermostats is needed to overcome this deficiency. Nosé-Hoover dynamics, like its derivatives, does not have a Hamiltonian structure, precluding the use of symplectic integrators which are noted for their long term stability and structure preservation. As an alternative to Nosé-Hoover, the Hamiltonian Nosé-Poincaré method was proposed by Bond, Laird, and Leimkuhler [J. Comput. Phys. 151, 114 (1999)], but the straightforward addition of thermostatting chains does not sample from the canonical ensemble. In this paper a method is proposed whereby additional thermostats can be applied to a Hamiltonian system while retaining sampling from the canonical ensemble. This technique has been used to construct thermostatting chains for the Nosé and Nosé-Poincaré methods.     

An Efficient Geometric Integrator for Thermostatted Anti-/Ferromagnetic Models

(Anti)-/ferromagnetic Heisenberg spin models arise from discretization of Landau–Lifshitz models in micromagnetic modelling. In many applications it is essential to study the behavior of the system at a fixed temperature. A formulation for thermostatted spin dynamics was given by Bulgac and Kusnetsov, which incorporates a complicated nonlinear dissipation/driving term while preserving spin length. It is essential to properly model this term in simulation, and simplified schemes give poor numerical performance, e.g., requiring an excessively small timestep for stable integration. In this paper we present an efficient, structure-preserving method for thermostatted spin dynamics.     

A temperature control technique for nonequilibrium molecular simulation

We describe a dynamical approach to thermal regulation in molecular dynamics. Temperature is moderated by a control law and an additional variable, as in Nose dynamics, but whose influence on the system decreases as the system approaches equilibrium. This device enables approximation of microcanonical averages and autocorrelation functions consistent with a given target temperature. Moreover, we demonstrate that the suggested technique is effective for the control of heat dissipation in a nonequilibrium setting, first by showing that the temperature control correctly regulates heat introduced by a rapid change to the system, and then by studying the slow relaxation of vibrational degrees of freedom (e.g., due to bonded atoms) in a solvent bath.     

Degradation and reconstruction of moenomycin A and derivatives: dissecting the function of the isoprenoid chain

Moenomycin A is the only known natural product that inhibits peptidoglycan biosynthesis by binding the bacterial transglycosylases. We describe a degradation/reconstruction route to manipulate the reducing end of moenomycin A. A comparison of the biological and enzyme inhibitory activity of moenomycin A and an analogue containing a nerol lipid in place of the natural C25 lipid chain provides insight into the role of the moenocinol unit. Our results show that a lipid chain having ten carbons in moenocinol is sufficient for enzyme inhibition, but a longer chain is required for biological acitivity, apparently because the molecule must partition into biological membranes to reach its target in bacterial cells.     

In vitro reconstitution of EryCIII activity for the preparation of unnatural macrolides

EryCIII is a desosaminyltransferase that converts an inactive macrolide precursor to a biologically active antibiotic. It may have potential for the synthesis of unnatural macrolides with useful biological activities. However, it has been difficult to reconstitute the activity of EryCIII in vitro. We report here that purified, inactive EryCIII can be converted to an active catalyst by the addition of another protein encoded in the same gene cluster, EryCII. The EryCII-treated protein retains activity even when EryCII is removed. We also show that AknT, an activator protein from an unrelated gene cluster, is capable of activating EryCIII. Although the mechanism of activation is not yet understood, we have concluded from these experiments that these antibiotic Gtf activator proteins do not function to deliver substrates to EryCIII and do not exert their effects by forming stable complexes with the Gtf during the glycosyltransfer reaction. We report that activated EryCIII is capable of utilizing an alternative sugar donor, so these results lay the groundwork for the production of novel macrolides.     

Differential inhibition of Staphylococcus aureus PBP2 by glycopeptide antibiotics

The glycopeptide antibiotics prevent maturation of the bacterial cell wall by binding to the terminal d-alanyl-d-alanine moiety of peptidoglycan precursors, thereby inhibiting the enzymes involved in the final stages of peptidoglycan synthesis. However, there are significant differences in the biological activity of particular glycopeptide derivatives that are not related to their affinity for d-Ala-d-Ala. We compare the ability of vancomycin and a set of clinically relevant glycopeptides to inhibit Staphylococcus aureus PBP2 (penicillin binding protein), the major transglycosylase in a clinically relevant pathogen, S. aureus. We report experiments suggesting that activity differences between glycopeptides against this organism reflect a combination of substrate binding and secondary interactions with key enzymes involved in peptidoglycan synthesis.     

A practical method for the stereoselective generation of beta-2-deoxy glycosyl phosphates

Beta-2-Deoxy sugar nucleotides are substrates used by a variety of glycosyltransferases (Gtfs). We have developed a chemical route to synthesize beta-2-deoxy sugar phosphates that starts from alpha-glycosyl chlorides. Our approach reliably provides access to a range of NDP beta-2-deoxy sugars essential for studying glycosyltransferases involved in the synthesis of biologically active natural products.     

Stochastic-dynamical thermostats for constraints and stiff restraints

A broad array of canonical sampling methods are available for molecular simulation based on stochastic-dynamical perturbation of Newtonian dynamics, including Langevin dynamics, Stochastic Velo- city Rescaling, and methods that combine Nosé-Hoover dynamics with stochastic perturbation. In this article we discuss several stochastic-dynamical thermostats in the setting of simulating systems with holonomic constraints. The approaches described are easily implemented and facilitate the recovery of correct canonical averages with minimal disturbance of the underlying dynamics. For the purpose of illustrating our results, we examine the numerical application of these methods to a simple atomic chain, where a Fixman term is required to correct the thermodynamic ensemble.     

Comparing the Efficiencies of Stochastic Isothermal Molecular Dynamics Methods

Molecular dynamics typically incorporates a stochastic-dynamical device, a “thermostat,” in order to drive the system to the Gibbs (canonical) distribution at a prescribed temperature. When molecular dynamics is used to compute time-dependent properties, such as autocorrelation functions or diffusion constants, at a given temperature, there is a conflict between the need for the thermostat to perturb the time evolution of the system as little as possible and the need to establish equilibrium rapidly. In this article we define a quantity called the “efficiency” of a thermostat which relates the perturbation introduced by the thermostat to the rate of convergence of average kinetic energy to its equilibrium value. We show how to estimate this quantity analytically, carrying out the analysis for several thermostats, including the Nosé-Hoover-Langevin thermostat due to Samoletov et al. (J. Stat. Phys. 128:1321–1336, 2007) and a generalization of the “stochastic velocity rescaling” method suggested by Bussi et al. (J. Chem. Phys. 126:014101, 2007). We find efficiency improvements (proportional to the number of degrees of freedom) for the new schemes compared to Langevin Dynamics. Numerical experiments are presented which precisely confirm our theoretical estimates.     

A Gentle Stochastic Thermostat for Molecular Dynamics

We discuss a dynamical technique for sampling the canonical measure in molecular dynamics. We present a method that generalizes a recently proposed scheme (Samoletov et al., J. Stat. Phys. 128:1321–1336, 2007), and which controls temperature by use of a device similar to that of Nosé dynamics, but adds random noise to improve ergodicity. In contrast to Langevin dynamics, where noise is added directly to each physical degree of freedom, the new scheme relies on an indirect coupling to a single Brownian particle. For a model with harmonic potentials, we show under a mild non-resonance assumption that we can recover the canonical distribution. In spite of its stochastic nature, experiments suggest that it introduces a relatively weak perturbative effect on the physical dynamics, as measured by perturbation of temporal autocorrelation functions. The kinetic energy is well controlled even in the early stages of a simulation.