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Internet Electronic Journal of Molecular Design - IEJMD, ISSN 1538-6414, CODEN IEJMAT
| ABSTRACT - Internet Electron. J. Mol. Des. July 2004, Volume 3, Number 7, 412-425 |
Which is the Dynamics of Stretched Biomolecular Chains?
Vincenzo Villani
Internet Electron. J. Mol. Des. 2004, 3, 412-425
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Abstract:
The pulled chain-ends problem, where external forces are applied
at both ends of a linear chain, is of general interest in the
behavior of macromolecules in rubber networks, during the
elastic deformation process. The present work approaches the
biopolymer elasticity and the non-linearity of its dynamics. In
particular, the constrained dynamics of an elastic repeat motif of
Elastin, the rubber protein of vertebrates, interesting also as a
biomaterial in medicine, is considered. Four models with
external forces for the hydrated Elastin flexible sequence
Gly-Leu-Gly-Gly have been developed. The free molecule represents
the chain in the relaxed state of the elastomeric network
(unperturbed model) in fact, on microscopic length scales
individual chains move essentially freely as in a polymer
solution. The forced ones model the chain in the elastin strained
states (stretched models). The applied constrains take implicitly
into account the effect transmitted down to both the ends inside
the stressed polymer network. In such a way the attention is
focused to the internal changes induced in the stretched chain. In
this framework the Elastin oligopeptide Ac-Gly-Leu-Gly-Gly-NMe
has been modeled in aqueous solution by nearly 8 ns of
MD on parallel computers. The chain dynamics was carefully
analyzed in terms of probability density distributions, time
correlation functions, fast Fourier transforms, Hurst critical
exponent, according to the classical theory of the rubber
elasticity. The end-to-end distance and the gyration radius
describing conformational motions, the mass-center
displacement describing translational motions and the
configurational 3N-dimensional vector Rq, whose components
are the Cartesian coordinates of chain atoms, describing the
global displacement of the peptide was considered. In all cases
an anomalous diffusion with H < 1/2, typical of the fractional
Brownian motions of Self-Organized Criticality in poor-solvent
solution, has been observed. The global mobility of unstrained or
strained chains is similar, although due to strongly different
effects. In fact, in the unperturbed system the motion is
equidistributed among all internal degree-of-freedom, in contrast,
on stretching, the symmetry breaking of the internal motions is
observed and the dynamics concentrates in the few slower
collective modes with large fluctuations of the mass-center. This
behavior typical of nonlinear complex systems is at the basis of
the self-organized dynamics. The proposed mechanism of
Chaos-Symmetry-Breaking, in agreement with the previous mechanism
of Transition-to-Chaos would be at the basis of the entropic drop
and retractile force of the rubber elasticity. As expected, the
entropy change in the proposed mechanism is proportional to the
density of the cross-links and models the dynamics of
constrained chains in the non-ideal rubber.
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