Dynamic transition

An important characteristic of biomolecular motion is that the different types of motion are interdependent and coupled to one another. For example, a large-scale dynamic transition cannot occur without involving several medium-scale motions, such as helix rearrangements. Medium-scale motions cannot occur without involving small-scale motions, such as side-chain movement. Finally, even side-chain motions cannot occur without the presence of the very fast atomic fluctuations, which can be viewed as the lubricant that enables the whole molecular construction to move. From the point of view of dynamic... 

A dynamic transition in the internal motions of proteins is seen with increasing temperamre [22]. The basic elements of this transition are reproduced by MD simulation [23]. As the temperature is increased, a transition from harmonic to anharmonic motion is seen, evidenced by a rapid increase in the atomic mean-square displacements. Comparison of simulation with quasielastic neutron scattering experiment has led to an interpretation of the dynamics involved in terms of rigid-body motions of the side chain atoms, in a way analogous to that shown above for the X-ray diffuse scattering [24]. 

With time-dependent computer simulation and visualization we can give the novices to QM a direct mind s eye view of many elementary processes. The simulations can include interactive modes where the students can apply forces and radiation to control and manipulate atoms and molecules. They can be posed challenges like trapping atoms in laser beams. These simulations are the inside story of real experiments that have been done, but without the complexity of macroscopic devices. The simulations should preferably be based on rigorous solutions of the time dependent Schrddinger equation, but they could also use proven approximate methods to broaden the range of phenomena to be made accessible to the students. Stationary states and the dynamical transitions between them can be presented as special cases of the full dynamics. All these experiences will create a sense of familiarity with the QM realm. The experiences will nurture accurate intuition that can then be made systematic by the formal axioms and concepts of QM. 

Figure 2. A schematic of the free energy density of an aperiodic lattice as a function of the effective Einstein oscillator force constant a (a is also an inverse square of the locahzation length used as input in the density functional of the liquid). Specifically, the curves shown characterize the system near the dynamical transition at Ta, when a secondary, metastable minimum in F a) begins to appear as the temperature is lowered. Taken from Ref. [47] with permission.

While this takes some account of operation under different conditions, it does not account for the dynamic transition from one state to another. Are these transitory states likely to have a significant influence on the optimality ... 

Grage SL, Afonin S, Ulrich AS (2010) Dynamic transitions of membrane-active peptides. Methods Mol Biol 618 183-207... 

Kirschner, D. A. and Blaurock, A. E. Organization, phylogenetic variations and dynamic transitions of myelin. In R. E. Martenson (ed.), Myelin biology and chemistry. Boca Raton, FL CRC Press, 1992, pp. 3-78. 

E. De Santis, G. Parisi and F. Ritort, On the static and dynamical transition in the mean-field... 

S S CONTENTS Preface, C. Allen Bush. Methods in Macromo-lecular Crystallography, Andrew J. Howard and Thomas L. Poulos. Circular Dichroism and Conformation of Unordered Polypeptides, Robert W. Woody. Luminescence Studies with Horse Liver Dehydrogenase Information on the Structure, Dynamics, Transitions and Interactions of this Enzyme, Maurice R. Eftink. Surface-Enhanced Resonance Raman Scattering (SERRS) Spectroscopy A Probe of Biomolecular Structure and Bonding at Surfaces, Therese M. Cotton, Jae-Ho Kim and Randall E. Holt. Three-Dimensional Conformations of Complex Carbohydrates, C. Allen Bush and Perse-veranda Cagas. Index. 

This relation determines a molecular weight M at which the mechanism of diffusion changes. To determine the dynamic transition point M, which separates the strongly entangled (M > M ) and weekly entangled (M < M ) systems, one considers the parameter B to be dependent on x and, taking equations (3.17) and (3.25) into account, finds a solution of the equation... 

Keywords QM/MM, molecular dynamics, transition state, drug metabolism, polymorphism,... 

In many investigations dynamic-mechanical properties have been determined not so much to correlate mechanical properties as to study the influence of polymer structure on thermo-mechanical behaviour. For this purpose, complex moduli are determined as a function of temperature at a constant frequency. In every transition region (see Chap. 2) there is a certain fall of the moduli, in many cases accompanied by a definite peak of the loss tangent (Fig. 13.22). These phenomena are called dynamic transitions. The spectrum of these damping peaks is a characteristic fingerprint of a polymer. Fig. 13.23 shows this for a series of polymers. 

Dynamic mechanical measurements, 407 Dynamic modulus, 451,508 Dynamic network of blobs, 279 Dynamic or absolute system of units, 53 Dynamic shear viscosity, 410 Dynamictensile viscosity, 410 Dynamic transitions, 418... 

Reat, V., Dunn, R., Ferrand, M., Finney, J.L., Daniel, R.M., and Smith, J.C. (2000) Solvent dependene of dynamic transition in protein solution, Proc. Natl. Acad. Sci. USA 97, 9961-9966. 

Lattice vibrations tend to destroy the correlation among Jahn-Teller centers. Thus, with increasing temperature, these centers may become independent of each other at a certain point, and their static Jahn-Teller effects convert to dynamic ones. At this point the crystal as a whole becomes more symmetric. This temperature-dependent static -O- dynamic transition is called a Jahn-Teller phase transition. Below the temperature of the phase transition, the cooperative Jahn-Teller effect governs the situation providing static distortion the overall structure of the crystal is of a lower symmetry. Above this temperature, the cooperation breaks down, the Jahn-Teller distortion becomes dynamic and the crystal itself becomes more symmetric. 

In order to understand the problem of finding TS with three or more DOFs, it is useful to address the question of dimensionalities, in configuration and phase space. In classical, Hamiltonian dynamics, transition states are grounded on the idea that certain surfaces (more precisely, certain manifolds) act as barriers in phase space. It is possible to devise barriers in phase space, since in phase space, in contrast to configuration space, two trajectories never cross [uniqueness of solutions of ODEs, see Eq. (4)]. In order to construct a barrier in phase space, the first step is to construct a manifold if that is made of a set of trajectories [8]. 

NMR spectroscopy probes transitions between nuclear spin states. The transition frequencies and relaxation times contain a wealth of information related to molecular structure and dynamics. Transition frequencies also reveal couplings between nuclear spins, and between electron and nuclear spins. The primary experimental observables in NMR are the chemical shift, which is related to the transition frequency, and the line width, which is related to the relaxation time. In paramagnetic systems, both of these parameters have the potential to be affected significantly by the unpaired electron, requiring special interpretation of data but also revealing information on the nature of the metal site. To make full use of NMR to study complex systems such as metallobiomolecules, it is important to understand the factors that influence observables in NMR. 

Changes in dynamic properties measured at temperatures between 200 and 273 K may not correlate well with the model discussed here, which is based on room temperature thermodynamic measurements. Perhaps this is not surprising, in view of the dependence of the dynamic transitions on both temperature and hydration level. 

There is a third possibility. There could be a purely dynamic transition at or near To, in which ergodicity is broken, but all thermodynamic variables remain continuous, so that no thermodynamic transition occurs. This would mean that below a critical temperature in the vicinity of Tg, the system is kinetically prevented from exploring all microstates that are thermodynamically allowed, but gets permanently locked into a finite subset of these... 

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