Langevin dynamics for rigid bodies of arbitrary shape

We present an algorithm for carrying out Langevin dynamics simulations on complex rigid bodies by incorporating the hydrodynamic resistance tensors for arbitrary shapes into an advanced rotational integration scheme. The integrator gives quantitative agreement with both analytic and approximate hydrodynamic theories for a number of model rigid bodies and works well at reproducing the solute dynamical properties (diffusion constants and orientational relaxation times) obtained from explicitly solvated simulations.     

Theory of anharmonicity in the lattice dynamics of crystals of rigid molecules

The use of the rigid-molecule approximation in the theory of lattice dynamics of molecular crystals leads to higher-order kinetic energy terms when anharmonic effects are allowed for. The conventional theory of lattice dynamics is extended to take account of these terms.     

Implementation of a molecular dynamics approach with rigid fragments to simulation of chemical reactions in biomolecular systems

We describe a new implementation of the molecular dynamics method aimed at simulation of the properties of biomolecular systems in which chemical reactions are possible. The quantum mechanical/molecular mechanical method based on the effective fragment potential theory is used for calculating the energies and forces along trajectories. Due to specific features of the effective fragment theory, the behavior of the molecular mechanical subsystem is described by rigid body dynamics. The method has been applied to simulation of proton transfer along the chain of water molecules inside the gramicidin channel.     

Protein dynamics tightly connected to the dynamics of surrounding and internal water molecules.

Proteins are key components of biological cells. For example, enzymes catalyze biochemical reactions, membrane transporters are responsible for uptake and release of critical and superfluous components from the cell environment, and structural proteins are responsible for the stability of the cell wall and cytoskeleton. Many of the diverse protein functions involve dynamic transitions ranging from small local atomic displacements up to large allosteric conformational changes. In any conformation, proteins are in contact with the universal solvent medium of cells, water. Water not only surrounds proteins but is often an integral part of proteins and also is involved in key mechanistic steps. This Minireview discusses recent experimental and theoretical results on the role of water for protein dynamics and function.     

Langevin dynamics in constant pressure extended systems

The advantages of performing Langevin dynamics in extended systems are discussed. A simple Langevin dynamics scheme for producing the canonical ensemble is reviewed, and is then extended to the Hoover ensemble. We show that the resulting equations of motion generate the isobaric-isothermal ensemble. The Parrinello-Rahman ensemble is then discussed and we show that despite the presence of intrinsic probability gradients in this system, a Langevin dynamics approach samples the extended phase space in the correct fashion. The implementation of these methods in the ab initio plane wave density functional theory code CASTEP [M. D. Segall, P. L. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clarke, and M. C. Payne, J. Phys.: Condens. Matter 14, 2717 (2003)] is demonstrated.     

Time reversible and symplectic integrators for molecular dynamics simulations of rigid molecules

Molecular dynamics integrators are presented for translational and rotational motion of rigid molecules in microcanonical, canonical, and isothermal-isobaric ensembles. The integrators are all time reversible and are also, in some approaches, symplectic for the microcanonical ensembles. They are developed utilizing the quaternion representation on the basis of the Trotter factorization scheme using a Hamiltonian formalism. The structure is similar to that of the velocity Verlet algorithm. Comparison is made with standard integrators in terms of stability and it is found that a larger time step is stable with the new integrators. The canonical and isothermal-isobaric molecular dynamics simulations are defined by using a chain thermostat approach according to generalized Nosé-Hoover and Andersen methods.     

Internal dynamics in complexes of water with organic molecules. Details of the internal motions in tert-butylalcohol-water

The peculiar propensity of water to have a high internal dynamic activity in its molecular complexes with organic molecules is described in this paper. Often, the corresponding large amplitude motions are reflected in the tunnelling splittings of the rotational transitions which, in turn, provide information for the determination of the potential energy surfaces and of the noncovalent interactions of water with a variety of atoms and/or functional groups. A classification of this kind of molecular complexes is given, also in relation to the tunnelling features of the rotational spectra. As a specific example, the rotational spectrum of tert-butylalcohol-water, investigated by Fourier transform microwave spectroscopy, is reported. Details are given of the large amplitude motions which take place in the adduct, the internal rotation of the hydroxyl group and the oscillations of the water molecule, by interpreting the experimental data with a flexible model.     

Dynamic bond constraints in protein Langevin dynamics

Bond constraint algorithms for molecular dynamics typically take, as the target constraint lengths, the values of the equilibrium bond lengths defined in the potential. In Langevin form, the equations of motion are temperature dependent, which gives the average value for the individual bond lengths a temperature dependence. In addition to this, locally constant force fields can shift the local equilibrium bond lengths. To restore the average bond lengths in constrained integration to their unconstrained values, we suggest changing the constraint length used by popular constraint methods such as RATTLE [H. C. Andersen, J. Comput. Phys. 52, 23 (1983)] at each step. This allows us to more accurately capture the equilibrium bond length changes (with respect to the potential) due to the local equilibration and temperature effects. In addition, the approximations to the unconstrained nonbonded energies are closer using the dynamic constraint method than a traditional fixed constraint algorithm. The mechanism for finding the new constrained lengths involves one extra calculation of the bonded components of the force, and therefore adds O(N) time to the constraint algorithm. Since most molecular dynamics calculations are dominated by the O(N2) nonbonded forces, this new method does not take significantly more time than a fixed constraint algorithm.     

Networks of rigid molecules

Networks of rigid molecules do not fit into the paradigm of classical theories of rubber elasticity. Some experimental properties of rigid polyamide networks are summarised, and the basis for a theoretical understanding of such systems is discussed and elaborated in terms of the properties such as the existence of several conformational states and twist of such network elements.     

Design of quasisymplectic propagators for Langevin dynamics

A vector field splitting approach is discussed for the systematic derivation of numerical propagators for deterministic dynamics. Based on the formalism, a class of numerical integrators for Langevin dynamics are presented for single and multiple time step algorithms.     

Accelerating the convergence of path integral dynamics with a generalized Langevin equation

The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.     

Langevin dynamics simulation of polymer-assisted virus-like assembly

Starting from a coarse grained representation of the building units of the minute virus of mice and a flexible polyelectrolyte molecule, we have explored the mechanism of assembly into icosahedral structures with the help of Langevin dynamics simulations and the parallel tempering technique. Regular icosahedra with appropriate symmetry form only in a narrow range of temperature and polymer length. Within this region of parameters where successful assembly would proceed, we have systematically investigated the growth kinetics. The assembly of icosahedra is found to follow the classical nucleation and growth mechanism in the absence of the polymer, with the three regimes of nucleation, linear growth, and slowing down in the later stage. The calculated average nucleation time obeys the laws expected from the classical nucleation theory. The linear growth rate is found to obey the laws of secondary nucleation as in the case of lamellar growth in polymer crystallization. The same mechanism is seen in the simulations of the assembly of icosahedra in the presence of the polymer as well. The polymer reduces the nucleation barrier significantly by enhancing the local concentration of subunits via adsorbing them on their backbone. The details of growth in the presence of the polymer are also found to be consistent with the classical nucleation theory, despite the smallness of the assembled structures.     

Long-time overdamped Langevin dynamics of molecular chains

We present a novel algorithm of constrained, overdamped dynamics to study the long-time properties of peptides, proteins, and related molecules. The constraints are applied to an all-atom model of the molecule by projecting out all components of the nonbonding interactions which tend to alter fixed bond lengths and angles. Because the overdamped dynamical equations are first order in time, the constraints are satisfied by inversion of a banded matrix at each timestep, which is computationally efficient. Thermal effects are included through a Langevin noise term in the equation of motion. Because high-frequency components of the motion have been eliminated, the timestep of the algorithm is determined by the nonbonding forces, which are two to three orders of magnitude weaker than the bonding forces. Using polyalanine as a test example, we demonstrate that trajectories simulating a microsecond of motion can be run about 10³ times faster than an equivalent molecular dynamics simulation. © 1994 by John Wiley & Sons, Inc.     

Improved configuration space sampling: Langevin dynamics with alternative mobility

We present a new and efficient method for determining optimal configurations of a large number (N) of interacting particles. We use a coarse-grained stochastic Langevin equation in the overdamped limit to describe the dynamics of this system and replace the standard mobility by an effective space dependent inverse Hessian correlation matrix. Due to the analogy of the drift term in the Langevin equation and the update scheme in Newton's method, we expect accelerated dynamics or improved convergence in the convex part of the potential energy surface Phi. The stochastic noise term, however, is not only essential for proper thermodynamic sampling but also allows the system to access transition states in the concave parts of Phi. We employ a Broyden-Fletcher-Goldfarb-Shannon method for updating the local mobility matrix. Quantitative analysis for one and two dimensional systems shows that the new method is indeed more efficient than standard methods with constant effective friction. Due to the construction, our effective mobility adapts high values/low friction in configurations which are less optimal and low values/high friction in configurations that are more optimal.     

Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow

The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution of the model. The extensions of DNA molecules for different Weissenberg numbers are analyzed. Comparison with the experimental results available in the literature is carried out to estimate the contribution of the effect of internal viscosity.     

Langevin dynamics simulations of macromolecules on parallel computers

A parallel algorithm is developed that allows efficient Langevin-dynamics simulations of macromolecular coils, which is the usual structure of synthetic polymers in solution and in bulk. Contrary to usual so-called spatial decomposition algorithms, we map the one-dimensional topology of the chain molecule on the parallel computer. The speedup of the algorithm is measured on different multi-processor systems. The reliability of the parallel calculations is shown by comparison with sequential simulations.     

Liquid crystal molecules with an enyne rigid core

New mesogens are always a source of interest, especially when they possess a non‐conventional architecture. In this article are presented the synthesis and polymorphism of a series of compounds possessing a 1,4‐diaryl‐1‐buten‐3‐yne moiety as the rigid core with an alkoxy chain on each side. Such a core is termed an enyne core. The alkoxy chain is lengthened on each side of the enyne core according to two different fashions: symmetrically and asymmetrically. In this way a rich polymorphism is achieved in some compounds. At lower chain length, the compounds exhibit smectic H and nematic phases where cybotactic groups are observed in X‐ray diffraction patterns. As the alkoxy chains extend, smectic C and smectic F phases appear. The non‐cylindrical shape of these compounds involves a molecular packing that is preserved throughout the polymorphism. A comparison between symmetric and asymmetric compounds, from X‐ray diffraction pattern analysis of their smectic H phases, reveals a parallel molecular stacking. It also discloses the importance of the moiety that is lengthened since different polymorphisms are obtained.     

Liquid crystal molecules with an enyne rigid core

New mesogens are always a source of interest, especially when they possess a non-conventional architecture. In this article are presented the synthesis and polymorphism of a series of compounds possessing a 1,4-diaryl-1-buten-3-yne moiety as the rigid core with an alkoxy chain on each side. Such a core is termed an enyne core. The alkoxy chain is lengthened on each side of the enyne core according to two different fashions: symmetrically and asymmetrically. In this way a rich polymorphism is achieved in some compounds. At lower chain length, the compounds exhibit smectic H and nematic phases where cybotactic groups are observed in X-ray diffraction patterns. As the alkoxy chains extend, smectic C and smectic F phases appear. The non-cylindrical shape of these compounds involves a molecular packing that is preserved throughout the polymorphism. A comparison between symmetric and asymmetric compounds, from X-ray diffraction pattern analysis of their smectic H phases, reveals a parallel molecular stacking. It also discloses the importance of the moiety that is lengthened since different polymorphisms are obtained.