Normal mode

About: Normal mode is a research topic. Over the lifetime, 15642 publications have been published within this topic receiving 353226 citations. The topic is also known as: Characteristic vibration, normal mode.

Collective motions in proteins: a covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations.

Abstract: A method is described for identifying collective motions in proteins from molecular dynamics trajectories or normal mode simulations. The method makes use of the covariances of atomic positional fluctuations. It is illustrated by an analysis of the bovine pancreatic trypsin inhibitor. Comparison of the covariance and cross-correlation matrices shows that the relative motions have many similar features in the different simulations. Many regions of the protein, especially regions of secondary structure, move in a correlated manner. Anharmonic effects, which are included in the molecular dynamics simulations but not in the normal analysis, are of some importance in determining the larger scale collective motions, but not the more local fluctuations. Comparisons of molecular dynamics simulations in the present and absence of solvent indicate that the environment is of significance for the long-range motions.

The Optimal Growth of Tropical Sea Surface Temperature Anomalies

Abstract: It is argued from SST observations for the period 1950–90 that the tropical Indo-Pacific ocean-atmosphere system may be described as a stable linear dynamical system driven by spatially coherent Gaussian white noise. Evidence is presented that the predictable component of SST anomaly growth is associated with the constructive interference of several damped normal modes after an optimal initial structure is set up by the white noise forcing. In particular, El Nino–Southern Oscillation (ENSO) growth is associated with an interplay of at least three damped normal modes, with periods longer than two years and decay times of 4 to 8 months, rather than the manifestation of a single unstable mode whose growth is arrested by nonlinearities. Interestingly, the relevant modes are not the three least damped modes of the system. Rather, mode selection, and the establishment of the optimal initial structure from which growth occurs, are controlled by the stochastic forcing. Experiments conducted with an empir...

Harmonic dynamics of proteins: normal modes and fluctuations in bovine pancreatic trypsin inhibitor.

Abstract: A normal mode analysis making use of an empirical potential function including local and nonlocal (nonbonded) interactions is performed for the bovine pancreatic trypsin inhibitor in the full conformational space of the molecule (1,740 degrees of freedom); that is, all bond lengths and angles, as well as dihedral angles, are included for the 580-atom system consisting of all heavy atoms and polar hydrogens. The heavy-atom frequency spectrum shows a dense distribution between 3 and 1,800 cm-1, with 350 modes below 216 cm-1. Most of the low-frequency modes, of which many have significant anharmonic character, are found to be delocalized over the protein. The root-mean-square amplitudes of the atomic fluctuations are calculated at 300 K from the normal modes and compared with those obtained from a solution molecular dynamics simulation based on the same potential function; very good agreement is obtained for the variation in the main-chain fluctuations as a function of residue number, though larger differences occur for the side chains. The fluctuations are generally, though not always, dominated by frequencies below 30 cm-1, in accord with the results of the dynamics simulation. The vibrational contributions to the thermodynamic properties of the protein are calculated as a function of temperature; the effects of perturbations on the spectrum, suggested for ligand or substrate binding, are examined. The analysis demonstrates that, in spite of the anharmonic contributions to the potential, a normal mode description can provide useful results concerning the internal motions of proteins.

Black-hole normal modes: A WKB approach. I. Foundations and application of a higher-order WKB analysis of potential-barrier scattering.

Abstract: We present a semianalytic technique for determining the complex normal-mode frequencies of black holes. The method makes use of the WKB approximation, carried to third order beyond the eikonal approximation. Mathematically, the problem is similar to studying one-dimensional quantum-mechanical scattering near the peak of a potential barrier, and determining the scattering resonances. Under such conditions, a modification of the usual WKB approach must be used. We obtain the connection formulas that relate the amplitudes of incident, reflected, and transmitted waves, to the third WKB order. By imposing the normal-mode (resonance) boundary condition of a zero incident amplitude with nonzero transmitted and reflected amplitudes, we find a simple formula that determines the real and imaginary parts of the normal-mode frequency of perturbation (or of the quantum-mechanical energy of the resonance) in terms of the derivatives (up to and including sixth order) of the barrier function evaluated at the peak, and in terms of the quantity (n+(1/2)), where n is an integer and labels the fundamental mode (resonance), first overtone, and so on. This higher-order approach may find uses in barrier-tunneling problems in atomic and nuclear physics.