Configurational thermostats for molecular systems

A new method of thermostatting non-equilibrium molecular dynamics (NEMD) simulations is described. The thermostat is based on a recently developed, entirely configurational expression for the temperature. To demonstrate this method, thermostatted NEMD simulations are performed on WCA atoms, linear, freely jointed Lennard-Jones 8-mer chains and a united-atom model of n-decane under a constant applied strain rate. The results of simulations thermostatted kinetically (the standard method) and configurationally are compared. As expected, both types of thermostat yield identical system properties for low strain rates. For higher strain rates, both thermostats yield the same qualitative dependence of system properties on applied strain rate. The great advantage of the configurational thermostat is that no a priori knowledge of the streaming velocity is required. For molecular systems and atomic systems in most flow geometries, the analytical form for the atomic streaming velocity is not known. This makes the implementation of standard kinetic thermostats highly problematic.     

Entropy, thermostats, and chaotic hypothesis

The chaotic hypothesis is proposed as a basic for a general theory of nonequilibrium stationary states.     

Finite thermostats in classical and quantum nonequilibrium

Models for studying systems in stationary states but out of equilibrium have often empirical nature and very often break the fundamental time reversal symmetry. Here, a formal interpretation will be discussed of the widespread idea that, in any event, the particular friction model choice should not matter physically. The proposal is, quite generally, that for the same physical system a time reversible model should be possible. Examples about the Navier–Stokes equations are given.     

Discretization errors in molecular dynamics simulations with deterministic and stochastic thermostats

We investigate the influence of numerical discretization errors on computed averages in a molecular dynamics simulation of TIP4P liquid water at 300 K coupled to different deterministic (Nosé–Hoover and Nosé–Poincaré) and stochastic (Langevin) thermostats. We propose a couple of simple practical approaches to estimating such errors and taking them into account when computing the averages. We show that it is possible to obtain accurate measurements of various system quantities using step sizes of up to 70% of the stability threshold of the integrator, which for the system of TIP4P liquid water at 300 K corresponds to the step size of about 7 fs.     

Correction: New stiff matter solutions are really not stiff

Four new solutions in general relativity have recently been derived as representing static spherically symmetric stiff matter,=p. It is pointed out that the equation of state is, in fact,+p=0. It is further shown that two of the solutions are physically reasonable, turning out to represent the vacuum, one of them with a term.     

Coarse-graining stiff bonds

The method of constraints in molecular dynamics is useful because it avoids the resolution of high frequency motions with very small time steps. However, the price to pay is that both the dynamics and the statistics of a constrained system differ from those of the unconstrained one. Instead of using constraints, we propose to dispose of high frequency motions by a coarse-graining procedure in which fast variables are eliminated. These fast variables are thus modeled as friction and thermal fluctuations. We illustrate the methodology with a simple model case, a diatomic molecule in a monoatomic solvent, in which the bond between the atoms of a diatomic molecule is stiff. Although the example is very simple and does not display the interesting effects of “wrong” statistics of the constrained system (i.e. the well-known issue connected to the Fixman potential), it is well suited to give the proof of concept of the whole procedure.     

Material selection for acoustic radiators that are light and stiff

The headmass is a key element in tonpilz transducer design. As an acoustic radiator, a successful headmass must be built from a material that is both light and stiff. To assess the suitability of ceramics for this application, the authors used the mechanical properties of candidate materials to perform a theoretical comparison based on the flexural behavior of square plates. Although not a comprehensive metric for identifying the best headmass materials, the headmass flexure may be usefully employed as a first-level selection criteria. A software routine based on thin plate and thick plate theory was created to evaluate the flexural behavior in candidate materials.     

Backbone-only restraints for fast determination of the protein fold: the role of paramagnetism-based restraints. Cytochrome b562 as an example

CH(alpha) residual dipolar couplings (Deltardc's) were measured for the oxidized cytochrome b562 from Escherichia coli as a result of its partial self-orientation in high magnetic fields due to the anisotropy of the overall magnetic susceptibility tensor. Both the low spin iron (III) heme and the four-helix bundle fold contribute to the magnetic anisotropy tensor. CH(alpha) Deltardc's, which span a larger range than the analogous NH values (already available in the literature) sample large space variations at variance with NH Deltardc's, which are largely isooriented within alpha helices. The whole structure is now significantly refined with the chemical shift index and CH(alpha) Deltardc's. The latter are particularly useful also in defining the molecular magnetic anisotropy parameters. It is shown here that the backbone folding can be conveniently and accurately determined using backbone restraints only, which include NOEs, hydrogen bonds, residual dipolar couplings, pseudocontact shifts, and chemical shift index. All these restraints are easily and quickly determined from the backbone assignment. The calculated backbone structure is comparable to that obtained by using also side chain restraint. Furthermore, the structure obtained with backbone only restraints is, in its whole, very similar to that obtained with the complete set of restraints. The paramagnetism based restraints are shown to be absolutely relevant, especially for Deltardc's.     

Twist and writhe dynamics of stiff polymers

I consider the dynamics of a stiff filament, in particular the coupling of twist and bend via writhe. The time dependence of the writhe of a filament of length L is ([Wr(t) - Wr(0)]2) > approximately Lt(1/4). Simulations, on a simple model of a stiff polymer, are used to confirm scaling arguments. Fuller's theorem, and its relation with geometric phases, is reconsidered for open filaments.     

Protein–protein docking with interface residue restraints

The prediction of protein–protein complex structures is crucial for fundamental understanding of celluar processes and drug design. Despite significant progresses in the field, the accuracy of ab initio docking without using any experimental restraints remains relatively low. With the rapid advancement of structural biology, more and more information about binding can be derived from experimental data such as NMR experiments or chemical cross-linking. In addition, information about the residue contacts between proteins may also be derived from their sequences by using evolutionary analysis or deep learning. Here, we propose an efficient approach to incorporate interface residue restraints into protein–protein docking, which is named as HDOCKsite. Extensive evaluations on the protein–protein docking benchmark 4.0 showed that HDOCKsite significantly improved the docking performance and obtained a much higher success rate in binding mode predictions than original ab initio docking.     

Elasticity of stiff polymer networks

We study the elasticity of a two-dimensional random network of rigid rods ("Mikado model"). The essential features incorporated into the model are the anisotropic elasticity of the rods and the random geometry of the network. We show that there are three distinct scaling regimes, characterized by two distinct length scales on the elastic backbone. In addition to a critical rigidity percolation region and a homogeneously elastic regime we find a novel intermediate scaling regime, where the elasticity is dominated by bending deformations.     

Numerical strategies for filtering partially observed stiff stochastic differential equations

In this paper, we present a fast numerical strategy for filtering stochastic differential equations with multiscale features. This method is designed such that it does not violate the practical linear observability condition and, more importantly, it does not require the computationally expensive cross correlation statistics between multiscale variables that are typically needed in standard filtering approach. The proposed filtering algorithm comprises of a “macro-filter” that borrows ideas from the Heterogeneous Multiscale Methods and a “micro-filter” that reinitializes the fast microscopic variables to statistically reflect the unbiased slow macroscopic estimate obtained from the macro-filter and macroscopic observations at asynchronous times. We will show that the proposed micro-filter is equivalent to solving an inverse problem for parameterizing differential equations. Numerically, we will show that this microscopic reinitialization is an important novel feature for accurate filtered solutions, especially when the microscopic dynamics is not mixing at all.     

Experimental consequences and constraints for magninos

A stable weakly interacting massive particle can simultaneously solve both the solar neutrino and missing mass problems. In a previous paper we have identified this particle with a neutral lepton with mass of order 4–10 GeV and an anomalous magnetic moment of order 10⁻² (in natural units). We call this new particle a “magnino”. In one scenario, the magnino is the neutral component of an electroweak doublet. Its charged partner must have a mass only a few GeV heavier. In this paper we discuss the experimental consequences of the magnino, its charged partner and associated Higgs.     

Propagation and relaxation of tension in stiff polymers

We present a unified theory for the longitudinal dynamic response of a stiff polymer in solution to various external perturbations (mechanical excitations, hydrodynamic flows, electrical fields, temperature quenches, etc.) that can be represented as sudden changes of ambient/boundary conditions. The theory relies on a comprehensive analysis of the nonequilibrium propagation and relaxation of backbone stresses in a wormlike chain. We recover and substantially extend previous results based on heuristic arguments. New experimental implications are pointed out.     

Crumpling of a stiff tethered membrane

A first-principles numerical model for crumpling of a stiff tethered membrane is introduced. This model displays wrinkles, ridge formation, ridge collapse, and initiation of stiffness divergence. The amplitude and wavelength of the wrinkles and the scaling exponent of the stiffness divergence are consistent with both theory and experiment. Close to the stiffness divergence further buckling is hindered by the nonzero thickness of the membrane, and its elastic behavior becomes similar to that of dry granular media. No change in the distribution of contact forces can be observed at the crossover, implying that the network of ridges is then simultaneously a granular force-chain network.