Essential dynamics of proteins

Analysis of extended molecular dynamics (MD) simulations of lysozyme in vacuo and in aqueous solution reveals that it is possible to separate the configurational space into two subspaces: (1) an “essential” subspace containing only a few degrees of freedom in which anharmonic motion occurs that comprises most of the positional fluctuations; and (2) the remaining space in which the motion has a narrow Gaussian distribution and which can be considered as “physically constrained.” If overall translation and rotation are eliminated, the two spaces can be constructed by a simple linear transformation in Cartesian coordinate space, which remains valid over several hundred picoseconds. The transformation follows from the covariance matrix of the positional deviations. The essential degrees of freedom seem to describe motions which are relevant for the function of the protein, while the physically constrained subspace merely describes irrelevant local fluctuations. The near-constraint behavior of the latter subspace allows the separation of equations of motion and promises the possibility of investigating independently the essential space and performing dynamic simulations only in this reduced space. © 1993 Wiley-Liss, Inc.     

Perturbation analysis of 6DoF flight dynamics and passive dynamic stability of hovering fruit fly Drosophila melanogaster

Insects exhibit exquisite control of their flapping flight, capable of performing precise stability and steering maneuverability. Here we develop an integrated computational model to investigate flight dynamics of insect hovering based on coupling the equations of 6 degree of freedom (6DoF) motion with the Navier-Stokes (NS) equations. Unsteady aerodynamics is resolved by using a biology-inspired dynamic flight simulator that integrates models of realistic wing-body morphology and kinematics, and a NS solver. We further develop a dynamic model to solve the rigid body equations of 6DoF motion by using a 4th-order Runge-Kutta method. In this model, instantaneous forces and moments based on the NS-solutions are represented in terms of Fourier series. With this model, we perform a systematic simulation-based analysis on the passive dynamic stability of a hovering fruit fly, Drosophila melanogaster, with a specific focus on responses of state variables to six one-directional perturbation conditions during latency period. Our results reveal that the flight dynamics of fruit fly hovering does not have a straightforward dynamic stability in a conventional sense that perturbations damp out in a manner of monotonous convergence. However, it is found to exist a transient interval containing an initial converging response observed for all the six perturbation variables and a terminal instability that at least one state variable subsequently tends to diverge after several wing beat cycles. Furthermore, our results illustrate that a fruit fly does have sufficient time to apply some active mediation to sustain a steady hovering before losing body attitudes.     

A numerical method for simulating the dynamics of human walking

This paper presents a general method for simulating the movement of the lower extremity during human walking. It is based upon two separate algorithms: one for single support (an open kinematic chain), and the other for the double support phase (a closed-loop linkage). Central to each of these is the recursive Newton-Euler inverse dynamics algorithm, applicable, as given, to any serial, spatial linkage.

For the unconstrained single support model, the Newton-Euler scheme is applied directly to numerically generate the equations of motion. In the case of double support, however, the kinematic constraint equations are used to first eliminate the redundant degrees of freedom, and then solve for the unknown ground reactions under the constrained limb.

The attractiveness of the method is that it offers a compact alternative to manually deriving the equations defining a mathematical model for human gait.     

Investigation of the influence of external factors on the conformational dynamics of rhodopsin-like receptors by means of molecular dynamics simulation

Abstract

The study reports about the influence of binding of orthosteric ligands on the conformational dynamics of β-2-adrenoreceptor. Using molecular dynamics (MD) simulation, we found that there was a little fraction of active states of the receptor in its apo (ligand-free) ensemble. Analysis of MD trajectories indicated that such spontaneous activation of the receptor is accompanied by the motion in intracellular part of its alpha-helices. Thus, receptor’s constitutive activity directly results from its conformational dynamics. On the other hand, the binding of a full agonist resulted in a significant shift of the initial equilibrium towards its active state. Finally, the binding of the inverse agonist stabilized the receptor in its inactive state. It is likely that the binding of inverse agonists might be a universal way of constitutive activity inhibition in vivo. Our results indicate that ligand binding redistribute pre-existing conformational degrees of freedom (in accordance to the Monod–Wyman–Changeux Model) of the receptor rather than cause induced fit in it. Therefore, the ensemble of biologically relevant receptor conformations is encoded in its spatial structure, and individual conformations from that ensemble might be used by the cell in conformity with the physiological behavior.     

Ad hoc continuum-atomistic thermostat for modeling heat flow in molecular dynamics simulations

An ad hoc thermostating procedure that couples a molecular dynamics (MD) simulation and a numerical solution to the continuum heat flow equation is presented. The method allows experimental thermal transport properties to be modeled without explicitly including electronic degrees of freedom in a MD simulation. The method is demonstrated using two examples, heat flow from a constant temperature silver surface into a single crystal bulk, and a tip sliding along a silver surface. For the former it is shown that frictional forces based on the Hoover thermostat applied locally to grid regions of the simulation are needed for effective feedback between the atomistic and continuum equations. For fast tip sliding the thermostat results in less surface heating, and higher frictional and normal forces compared to the same simulation without the thermostat.     

A structure-based simulation approach for electron paramagnetic resonance spectra using molecular and stochastic dynamics simulations

Electron paramagnetic resonance (EPR) spectroscopy using site-directed spin-labeling is an appropriate technique to analyze the structure and dynamics of flexible protein regions as well as protein-protein interactions under native conditions. The analysis of a set of protein mutants with consecutive spin-label positions leads to the identification of secondary and tertiary structure elements. In the first place, continuous-wave EPR spectra reflect the motional freedom of the spin-label specifically linked to a desired site within the protein. EPR spectra calculations based on molecular dynamics (MD) and stochastic dynamics simulations facilitate verification or refinement of predicted computer-aided models of local protein conformations. The presented spectra simulation algorithm implies a specialized in vacuo MD simulation at 600 K with additional restrictions to sample the entire accessible space of the bound spin-label without large temporal effort. It is shown that the distribution of spin-label orientations obtained from such MD simulations at 600 K agrees well with the extrapolated motion behavior during a long timescale MD at 300 K with explicit water. The following potential-dependent stochastic dynamics simulation combines the MD data about the site-specific orientation probabilities of the spin-label with a realistic rotational diffusion coefficient yielding a set of trajectories, each more than 700 ns long, essential to calculate the EPR spectrum. Analyses of a structural model of the loop between helices E and F of bacteriorhodopsin are illustrated to demonstrate the applicability and potentials of the reported simulation approach. Furthermore, effects on the motional freedom of bound spin-labels induced by solubilization of bacteriorhodopsin with Triton X-100 are examined.     

A mezoscopic model of nucleic acids. Part 2. An effective potential energy function for DNA

In this study we present an effective Potential of Mean Force (PMF) designed for Lagrangian and Quaternion Molecular Dynamics (LQMD) of DNA. The DNA model is built from pseudoatoms as well as rigid and pseudo-elastic bodies described by a limited number of selected Cartesian and internal degrees of freedom. Phosphate groups, deoxyribose rings and nucleic acid bases are represented by pseudoparticles, some of them with internal degrees of freedom. PMF is defined as the sum of effective bonded and long-range potentials. The potentials were fitted to numerical free energy surfaces. Over 50 free energy surfaces, each depending on a conformational variable (pseudobond length, angle or dihedral angle) and the pseudorotation phase of the nearest neighbour deoxribose ring, were computed. The numerical free energy surfaces were obtained from probability distributions derived from a 1.5 ns conventional, microscopic MD simulation of the d(GpC)9 double helical DNA molecule. An umbrella sampling method was used to simulate transitions between the A and B DNA forms, and PMF reproduces these transitions.     

Modeling of control and learning in a stepping motion

In a previous study (Beuter et al. 1986) the authors modeled a stepping motion using a three-body linkage with four degrees of freedom. Stepping was simulated by using three task parameters (i.e., step height, length, and duration) and sinusoidal joint angular velocity profiles. The results supported the concept of a hierarchical control structure with open-loop control during normal operation. In this study we refine the dynamic model and improve the simulation technique by incorporating the dynamics of the leg after landing, adding a foot segment to the model, and preprogramming the complete step motion using cycloids. The equations of the forces and torques developed on the ground by the foot during the landing phase are derived using the Lagrangian method. Simulation results are compared to experimental data collected on a subject stepping four times over an obstacle using a Selspot motion analysis system. A hierarchical control model that incorporates a learning process is proposed. The model allows an efficient combination of open and closed loop control strategies and involves hardwired movement segments. We also test the hypothesis of cycloidal velocity profiles in the joint programs against experimental data using a novel curve-fitting procedure based on analytical rather than numerical differentiation. The results suggest multiob-jective optimization of the joint's motion. The control and learning model proposed here will help the understanding of the mechanisms responsible for assembling selected movement segments into goaldirected movement sequences in humans.     

Characteristic domain motion in the ribosome recycling factor revealed by 15N NMR relaxation experiments and molecular dynamics simulations

The backbone dynamics of ribosome recycling factor (RRF) from Escherichia coli in water were characterized by (15)N NMR relaxation analysis and molecular dynamics (MD) simulation. RRF is composed of two domains connected by a joint region that consists of two peptide chains, such that the overall structure seems to mimic that of tRNA. MD trajectories indicated that the relative orientation of domains varies on the nanosecond time scale. We analyzed the observed (15)N T(1), T(2), and NOE using an extended model-free spectral density function in which the domain motions with a nanosecond time scale were considered. At 30 degrees C, the order parameters of slow motion () were determined to be approximately 0.9 for domain I and 0.7 for domain II, respectively. These values indicate that domain I is nearly fixed on the molecular diffusion frame, and domain II is wobbling in a cone for which the semi-angle is about 30 degrees.     

A continuum-atomistic method for incorporating Joule heating into classical molecular dynamics simulations

A hybrid atomistic-continuum method is presented for incorporating Joule heating into large-scale molecular dynamics (MD) simulations. When coupled to a continuum thermostat, the method allows resistive heating and heat transport in metals to be modeled without explicitly including electronic degrees of freedom. Atomic kinetic energies in a MD simulation are coupled via an ad hoc feedback loop to continuum current and heat transfer equations that are solved numerically on a finite difference grid (FDG). For resistive heating, the resistance in each region of the FDG is calculated from the experimental resistivity, atomic density, and average kinetic energy in the MD simulation. A network of resistors is established from which the potential at every FDG region is calculated given an applied voltage. The potential differences and the resistance between connected FDG regions are used to calculate the current between the two points and the heat generated from that current. This information is then added back into the atomic simulation. The method is demonstrated by simulating Joule heating and melting, along with associated changes in current, of single and bundles of metal nanowires, as well as a “pinched” wire under applied strain.     

Interaction against different environmental dynamics during a leg extension task is controlled by temporal rather than amplitude scaling of muscular activity

Force exertion against different mechanical environments can affect motor control strategies in order to account for the altered environmental dynamics and to maintain the ability to produce force. Here, we investigated the change of muscular activity of selected muscles of the lower extremities while the participants interacted with an external mechanical device of variable stability. Twenty-five healthy participants exerted force against the device by performing a unilateral ballistic leg extension task under 1 or 3 degrees of freedom (DoF). Directional force data and electromyographic responses from four leg muscles (TA, VM, GM, PL) were recorded. Muscle responses to the altered experimental conditions were analyzed by calculating time to peak electrical activity (TTP), peak electrical activity (PEA), slope of EMG-signal and muscle activity. It was found that neuromuscular system adjustments to the task are expressed mainly by temporal (TTP) rather than amplitude (PEA) scaling of muscular activity. This change was specific for the investigated muscles. Moreover, a selective increase of muscle activity occurred while increasing external DoF. This scheme was accompanied by a significant reduction of applicable force against the device in the unstable 3 DoF condition. The findings suggest that orchestration of movement control is linked to environmental dynamics also affecting the ability to produce force under dynamic conditions. The adjustments of the neuromuscular system are rather temporal in nature being consistent with the impulse timing hypothesis of motor control.     

Drug resistance of enteric bacteria. V. High frequency of transduction of R factors with bacteriophage epsilon

Kameda, Mitsuo (Gunma University, Maebashi, Japan), Kenji Harada, Mitsue Suzuki, and Susumu Mitsuhashi. Drug resistance of enteric bacteria. V. High frequency of transduction of R factors with bacteriophage epsilon. J. Bacteriol. 90:1174-1181. 1965.-In the transduction of R factors with phage epsilon(15), a lysate capable of transducing the markers for (TC) or (CM.SM.SA) resistance at high frequency was obtained. The transducing agent is a defective element called epsilon(15)dR(23) which lacks certain functions of phage epsilon(15). After lysogenization with normal epsilon(15) phage and ultraviolet (UV) induction, strains carrying the epsilon(15)dR(23) element produce lysates which have a high frequency of transduction (HFT) on group E(1)Salmonella. Lytic lysates prepared on phage epsilon(15) sensitive strain with the epsilon(15)dR(23) element have a low frequency of transduction (LFT). Lytic growth of phage epsilon(34) on an epsilon(15)dR(23) strain or UV induction of an epsilon(34) lysogenic strain containing epsilon(15)dR(23) results in LFT lysates on group E(2)Salmonella. On UV induction, group E(2)Salmonella (epsilon(15) lysogens) with the epsilon(15)dR(23) element give lysates which are HFT on group E(1)Salmonella but are LFT when tested on group E(2)Salmonella. In all instances, the production of drug-resistant transductants requires infection of the cell with only a single epsilon(15)dR(23) element. It appears that the resistance region of the R factor has replaced that portion of phage genome which is essential for vegetative replication and superinfection immunity. The epsilon(15)dR(23) element does not contain the genetic determinants of the R factor responsible for transmissibility, inhibition of F mating, and interference between two R factors.     

Multibreath tracer species dynamics in the lung

By studying the behavior of various tracer species in the lungs, one can assess many important characteristics which distinguish normal and abnormal function. Quantitative evaluation of function depends on the use of an appropriate model in conjunction with experimental data. A multi-compartment model is derived from mass balances to describe dynamic as well as (breath-averaged) steady-state transport processes between the environment and pulmonary capillary blood. The breathing cycle is divided into three time periods (inspiration, expiration, and pause) so that the model equations are discrete in time. No other model of tracer species transport in the lungs deals simultaneously with species dynamics, variable breathing pattern, distribution inhomogeneities, and non-equilibrium between alveolar gas and capillary blood. Models currently in the literature are shown to be special cases of the model presented here.     

Spectral EMG changes in vastus medialis muscle following short range of motion isokinetic training.

This study was aimed at exploring the carryover effect of short range of motion (RoM) isokinetic conditioning on vastus medialis (VM) motor unit recruitment (MUR) across the full RoM. Fifty-five women were randomly assigned to one of four groups: G1 (n = 14) and G2 (n = 14) trained concentrically at 30 and 90 degrees /s, respectively whereas G3 (n = 13) and G4 (n = 14) trained similarly but using the eccentric mode. All 4 groups trained within 30-60 degrees of knee flexion. The training protocol consisted of 4 sets of 10 maximal repetitions, 3 times a week for 6 weeks. sEMG was recorded from the VM for analysis of mean frequency of the EMG power spectrum prior to the training period and 2 days after its termination. The EMG assessments took place during dynamic contractions within 3 angular RoM's: 85-60 degrees (R1), 60-30 degrees (R2) and 30-5 degrees (R3). In addition MUR was evaluated during isometric contractions at 10 degrees , 45 degrees and 80 degrees . Significant increases were observed in the MUR at R1, R2, and R3 during dynamic contractions as well as in all 3 angles during isometric contractions. These findings applied equally regardless of the mode of contraction and motion speed during training. The fact that MUR increased significantly within untrained RoM's may point out to the potential benefits of short RoM conditioning, particularly in those cases where, during specific phases of rehabilitation, a wider RoM may be contraindicative.     

Molecular dynamics simulation of the docking of substrates to proteins

A simple method is described to perform docking of subtrates to proteins or probes to receptor molecules by a modification of molecular dynamics simulations. The method consists of a separation of the center-of-mass motion of the substrate from its internal and rotational motions, and a separate coupling to different thermal baths for both types of motion of the substrate and for the motion of the receptor. Thus the temperatures and the time constants of coupling to the baths can be arbitrarily varied for these three types of motion, allowing either a frozen or a flexible receptor and allowing control of search rate without disturbance of internal structure. In addition, an extra repulsive term between substrate and protein was applied to smooth the interaction. The method was applied to a model substrate docking onto a model surface, and to the docking of phosphocholine onto immunoglobulin McPC603, in both cases with a frozen receptor. Using transrational temperatures of the substrate in the range of 1300–1700 K and room temperature for the internal degrees of freedom of the substrate, an efficient nontrapping exploratory search (“helicopter view”) is obtained, which visits the correct binding sites. Low energy conformations can then be further investigated by separate search or by dynamic simulated annealing. In both cases the correct minima were identified. The possibility to work with flexible receptors is discussed. © 1994 Wiley-Liss, Inc.     

Dissipative Irreversibility from Nosé's Reversible Mechanics

Abstract

Nose's Hamiltonian mechanics makes possible the efficient simulation of irreversible flows of mass, momentum and energy. Such flows illustrate the paradox that reversible microscopic equations of motion underlie the irreversible behavior described by the second law of thermodynamics. This generic behavior of molecular many-body systems is illustrated here for the simplest possible system, with only one degree of freedom: a one-body Frenkel-Kontorova model for isothermal electronic conduction. This model system, described by Nosé-Hoover Hamiltonian dynamics, exhibits several interesting features: (1) deterministic and reversible equations of motion; (2) Lyapunov instability, with phase-space offsets increasing exponentially with time; (3) limit cycles; (4) dissipative conversion of work (potential energy) into heat (kinetic energy): and (5) phase-space contraction, a characteristic feature of steady irreversible flows. The model is particularly instructive in illustrating and explaining a paradox associated with steady-state statistical mechanics: the Gibbs entropy of a nonequilibrium steady state decreases continuously to minus infinity.