A simple coarse-grained model for interacting protein complex

ABSTRACT

We present a simple coarse-grained model in which each amino acid residue is represented by one coarse-grained particle for interacting protein complex. In order to determine the coarse-grained potential function of the interaction between amino acid residues, free energy profile as a function of the distance between amino acid side chains is investigated by using all-atom molecular dynamics simulations with thermodynamic integration method. The Langevin dynamics simulation with Gō-like model and our coarse-grained model reproduces homotetramer complex structure of GCN4-pLI and shows that interaction between hydrophobic amino acid residues promote the association of GCN4-pLI monomers.     

Thermal evolution of hole dynamics in the large-dimensional model

The dynamics of a single hole in the t - J model is solved exactly for all temperature, T, in the limit of large spatial dimensions, , using the Feenberg renormalized perturbation series. We focus in particular on single-particle spectra, together with optical and static hole conductivities. Explicit results are illustrated for a Bethe lattice, and exemplify the continuous thermal evolution of the underlying string picture from the T =0 string-pinned limit through to the paramagnetic phase. Quenched site-disorder is also readily incorporated, exact results thereby being obtained for the interplay between disorder and thermally-induced hole dynamics. Received 16 September 1998     

A coarse-grained model of the effective interaction for charged amino acid residues and its application to formation of GCN4-pLI tetramer

ABSTRACT

We present a simple coarse-grained model of the effective interaction for charged amino acid residues, such as Glu and Lys, in a water solvent. The free-energy profile as a function of the distance between two charged amino acid side-chain analogues in an explicit water solvent is calculated with all-atom molecular dynamics simulation and thermodynamic integration method. The calculated free-energy profile is applied to the coarse-grained potential of the effective interaction between two amino acid residues. The Langevin dynamics simulations with our coarse-grained potential are performed for association of a small protein complex, GCN4-pLI tetramer. The tetramer conformation reproduced by our coarse-grained model is similar to the X-ray crystallographic structure. We show that the effective interaction between charged amino acid residues stabilises association and orientation of protein complex. We also investigate the association pathways of GCN4-pLI tetramer.     

Theory and simulation of coupled grain boundary migration and grain rotation in low angle grain boundaries

Abstract

Microstructure evolution due to coupled grain boundary migration and grain rotation in low angle grain boundaries is studied through a combination of molecular dynamics and phase field modeling. We have performed two dimensional molecular dynamics simulations on a bicrystal with a circular grain embedded in a larger grain. Both size and orientation of the embedded grain are observed to evolve with time. The shrinking embedded grain is observed to have two regimes: constant dislocation density on the grain boundary followed by constant rate of increase in dislocation density. Based on these observations from the molecular dynamics simulations, a theoretical formulation of the kinetics of coupled grain rotation is developed. The grain rotation rate is derived for the two regimes of constant dislocation density and constant rate of change of dislocation density on the grain boundary during evolution. The theoretical calculation of the grain rotation rate shows strong dependence on the grain size and compares very well with the molecular dynamics simulations. A multi-order parameter based phase field model with coupled grain rotation is developed using the theoretical formulation to model polycrystalline microstructure evolution.     

Theoretical study on interaction of cytochrome f and plastocyanin complex by a simple coarse-grained model with molecular crowding effect

ABSTRACT

We present a simple coarse-grained model with the molecular crowding effect in solvent to investigate the structure and dynamics of protein complexes including association and/or dissociation processes and investigate some physical properties such as the structure and the reaction rate from the viewpoint of the hydrophobic intermolecular interactions of protein complex. In the present coarse-grained model, a function depending upon the density of hydrophobic amino acid residues in a binding area of the complex is introduced, and the function involves the molecular crowding effect for the intermolecular interactions of hydrophobic amino acid residues between proteins. We propose a hydrophobic intermolecular potential energy between proteins by using the density-dependent function. The present coarse-grained model is applied to the complex of cytochrome f and plastocyanin by using the Langevin dynamics simulation to investigate some physical properties such as the complex structure, the electron transfer reaction rate constant from plastocyanin to cytochrome f and so on. We find that for proceeding the electron transfer reaction, the distance between metals in their active sites is necessary within about 18 Å. We discuss some typical complex structures formed in the present simulation in relation to the molecular crowding effect on hydrophobic interactions.     

Cellular automata approach for the dynamics of HIV infection under antiretroviral therapies: The role of the virus diffusion

We study a cellular automata model to test the timing of antiretroviral therapy strategies for the dynamics of infection with human immunodeficiency virus (HIV). We focus on the role of virus diffusion when its population is included in previous cellular automata model that describes the dynamics of the lymphocytes cells population during infection. This inclusion allows us to consider the spread of infection by the virus-cell interaction, beyond that which occurs by cell–cell contagion. The results show an acceleration of the infectious process in the absence of treatment, but show better efficiency in reducing the risk of the onset of AIDS when combined antiretroviral therapies are used even with drugs of low effectiveness. Comparison of results with clinical data supports the conclusions of this study.     

Computational study of cold ions trapped in a double-well potential

We report a rigorous computational treatment of quantum dynamics of cold ions in a double-well trap using the time-dependent Schrödinger equation. Our method employs a numerically accurate approach that avoids approximations, such as assumption of weak coupling between the wells; normal mode nature of vibrations; or harmonic approximation for energy spectrum of the double-well system. Our goal is to reproduce, from first principles, the process of energy swaps between the wells observed in the experiments at NIST [Nature 471, 196 (2011)] and Innsbruck [Nature 471, 200 (2011)]. The model parameters and the initial conditions are carefully chosen to mimic experimental conditions. We obtain accurate energies and wave functions of the system numerically, and study the evolution of motional wave packets to provide new insight. This model reproduces experimental results obtained by NIST and Innsbruck in detail. We explain the energy transfer in terms of wave packet dynamics in the asymmetric potential energy well. We also show that, for a localised initial wave packet, this phenomenon can be interpreted using the terms of classical dynamics, such as trajectory of motion governed by the well-known simple principle: the angle of reflection equals the angle of incidence.     

Invariant Sets and Explicit Solutions to a Third-Order Model for the Shearless Stratified Turbulent Flow

Abstract

We study dynamics of the shearless stratified turbulent flows. Using the method of differential constraints we find a class of explicit solutions to the problem under consideration and establish that the differential constraint obtained coincides with the well-known Zeman–Lumley model for stratified flows.     

Ferromagnetic modes in spin glasses and dilute ferromagnets

We generalize the theories for the dynamics of spin glasses of Halperin and Saslow, and Dzyaloshinskii and Volovik to include additional partial ferromagnetic order. We find that the sixfold degenerate antiferromagnetic spin wave modes obtained in both theories split into two longitudinal and 2×2 transverse modes with different dispersion. In a certain range of wave vectorsq one obtains antiferromagnetic, ferromagnetic, andq-independent modes. The damping of these modes is calculated for a phenomelogical hydrodynamic model and their implications for the specific heat and electrical resistivity are discussed.     

Squeezed states and quantum chaos

We examine the dynamics of a wave packet that initially corresponds to a coherent state in the model of a quantum rotator excited by a periodic sequence of kicks. This model is the main model of quantum chaos and allows for a transition from regular behavior to chaotic in the classical limit. By doing a numerical experiment we study the generation of squeezed states in quasiclassical conditions and in a time interval when quantum-classical correspondence is well-defined. We find that the degree of squeezing depends on the degree of local instability in the system and increases with the Chirikov classical stochasticity parameter. We also discuss the dependence of the degree of squeezing on the initial width of the packet, the problem of stability and observability of squeezed states in the transition to quantum chaos, and the dynamics of disintegration of wave packets in quantum chaos. Zh. éksp. Teor. Fiz. 113, 111–127 (January 1998)     

A molecular dynamics investigation of dynamical heterogeneity in supercooled water

We investigate the presence of dynamical heterogeneity in supercooled water with molecular dynamics simulations using the new water model proposed by Mahoney and Jorgensen [M.W. Mahoney, W.L. Jorgensen J. Chem. Phys. 112, 8910 (2000)]. Prompted by recent theoretical results [J.P. Garrahan, D. Chandler, Phys. Rev. Lett. 89, 35704 (2002)] we study the dynamical aggregation of the least and the most mobile molecules. We find dynamical heterogeneity in supercooled water and string-like dynamics for the most mobile molecules. We also find the dynamical aggregation of the least mobile molecules. The two kinds of dynamical aggregation appear however to be very different. Characteristic times are different and evolve differently. String-like motions appear only for the most mobile molecules, a result predicted by the facilitation theory. The aggregation of the least mobile molecules is more organized than the bulk while the opposite is observed for the most mobile molecules.     

A mathematical model for transmission dynamics of HIV/AIDS with effect of weak CD4+ T cells

A mathematical model is proposed for the dynamics of HIV/AIDS with incorporation of weak CD4⁺ T cells. The model considers three different categories of cells: uninfected CD4⁺ T cells, infected CD4⁺ T cells, and virus. The anticipated model helps to illustrate the many of mystifying features of HIV infection more clearly. This model demonstrates two steady states: an infection-free equilibrium state, in which there is no virus, and an infection equilibrium state, in which virus and infected T cells are present. We have also calculated the local stability of the infection-free equilibrium and infection equilibrium for the model when the valuable reproduction number is less than and greater than one. With the help of Lyapunov's second method and the geometric approach, we are defining the novel conditions for the global stability of infection-free equilibrium state and infection equilibrium state. This study, which knocks off-balance the system, is articulated by a small variation of the parameters conceded by the system from one stable state to an unstable state. The dynamics of this new steady state are calculated both numerically and via the stability analysis.     

Quantum Fields, Cosmological Constant and Symmetry Doubling

We explore how energy-parity, a protective symmetry for the cosmological constant [Kaplan and Sundrum, 2005], arises naturally in the classical phase space dynamics of matter.We derive and generalize the Liouville operator of electrodynamics, incorporating a “varying alpha” and diffusion.In this model, a one-parameter deformation connects classical ensemble and quantum field theory. PACS:03.65.Ta, 03.70+k, 05.20.-y     

Ising model with competing “uncle–nephew” interactions

ABSTRACT

We consider the Ising model on the semi-infinite Cayley tree of second order with competing interactions up to the third-nearest-neighbors with spins belonging to the different branches of the tree and for this model investigate the problem of phase transition.     

Solitons and Deformed Lattices I

Abstract

We study a model describing some aspects of the dynamics of biopolymers. The models involve either one or two finite chains with a number N of sites that represent the “units” of a biophysical system. The mechanical degrees of freedom of these chains are coupled to the internal degrees of freedom through position dependent excitation transfer functions. We reconsider the case of the one chain model discussed by Mingaleev et al. and present new results concerning the soliton sector of this model. We also give new (preliminary) results in the two chain model in which case we have introduced an interaction potential inspired by the Morse potential.     

Formation of argon cluster with proton seeding

ABSTRACT

We employ force-field molecular dynamics simulations to investigate the kinetics of nucleation to new liquid or solid phases in a dense gas of particles, seeded with ions. We use precise atomic pair interactions, with physically correct long-range behaviour, between argon atoms and protons. Time dependence of molecular cluster formation is analysed at different proton concentration, temperature and argon gas density. The modified phase transitions with proton seeding of the argon gas are identified and analysed. The seeding of the gas enhances the formation of nano-size atomic clusters and their aggregation. The strong attraction between protons and bath gas atoms stabilises large nano-clusters and the critical temperature for evaporation. An analytical model is proposed to describe the stability of argon-proton droplets and is compared with the molecular dynamics simulations.     

Entanglement, Hubbard Model, and Symmetries

Entangled quantum states are an important component of quantum computing techniques such as quantum error-correction, dense coding, and quantum teleportation. We use the requirements for a state in the Hilbert space C ² C ² to be entangled to find when states evolving under the two-point Hubbard model become entangled. We also investigate the connection of entanglement and discrete symmetries of the two-point Hubbard model. Furthermore we discuss the inclusion of phonon coupling.     

Replicator Dynamics and Mathematical Description of Multi-Agent Interaction in Complex Systems

Abstract

We consider the general properties of the replicator dynamical system from the standpoint of its evolution and stability. Vector field analysis as well as spectral properties of such system has been studied. A Lyaponuv function for the investigation of the evolution of the system has been proposed. The generalization of replicator dynamics to the case of multi-agent systems is introduced. We propose a new mathematical model to describe the multi-agent interaction in complex system.     

Fracture of a biopolymer gel as a viscoplastic disentanglement process

We present an extensive experimental study of mode-I, steady, slow crack dynamics in gelatin gels. Taking advantage of the sensitivity of the elastic stiffness to gel composition and history we confirm and extend the model for fracture of physical hydrogels which we proposed in a previous paper (Nature Mater. 5, 552 (2006)), which attributes decohesion to the viscoplastic pull-out of the network-constituting chains. So, we propose that, in contrast with chemically cross-linked ones, reversible gels fracture without chain scission.