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Congruent qualitative behaviour of complete and reconstructed phase-space trajectories from biomolecular dynamics simulation

Caves, L.S.D. and Verma, C.S. (2002) Congruent qualitative behaviour of complete and reconstructed phase-space trajectories from biomolecular dynamics simulation. Proteins - Structure Function and Genetics, 47 (1). pp. 25-30. ISSN 0887-3585

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Abstract

Central to the study of a complex dynamical system is knowledge of its phase space behavior. Experimentally, it is rarely possible to record a system's (multidimensional) phase space variables. Rather, the system is observed via one (or few) scalar-valued signal(s) of emission or response. In dynamical systems analysis, the multidimensional phase space of a system can be reconstructed by manipulation of a one-dimensional signal. The trick is in the construction of a (higher-dimensional) space through the use of a time lag (or delay) on the signal time series. The trajectory in this embedding space can then be examined using phase portraits generated in selected subspaces. By contrast, in computer simulation, one has an embarrassment of riches: direct access to the complete multidimensional phase space variables, at arbitrary time resolution and precision. Here, the problem is one of reducing the dimensionality to make analysis tractable. This can be achieved through linear or nonlinear projection of the trajectory into subspaces containing high information content. This study considers trajectories of the small protein crambin from molecular dynamics simulations. The phase space behavior is examined using principal component analysis on the Cartesian coordinate covariance matrix of 138 dimensions. In addition, the phase space is reconstructed from a one dimensional signal, representing the radius of gyration of the structure along the trajectory. Comparison of low-dimensional phase portraits obtained from the two methods shows that the complete phase space distribution is well represented by the reconstruction. The study suggests that it may be possible to develop a deeper connection between the experimental and simulated dynamics of biomolecules via phase space reconstruction using data emerging from recent advances in single-molecule time-resolved biophysical techniques.

Item Type: Article
Institution: The University of York
Academic Units: The University of York > Chemistry (York)
Depositing User: York RAE Import
Date Deposited: 19 Feb 2009 11:31
Last Modified: 19 Feb 2009 11:31
Published Version: http://dx.doi.org/10.1002/prot.10063
Status: Published
Publisher: John Wiley & Sons, Ltd
Refereed: Yes
Identification Number: 10.1002/prot.10063
URI: http://eprints.whiterose.ac.uk/id/eprint/7362

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