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Which is the Dynamics of Stretched Biomolecular Chains?

Author(s): Vincenzo Villani

Journal: Internet Electronic Journal of Molecular Design
ISSN 1538-6414

Volume: 3;
Issue: 7;
Start page: 412;
Date: 2004;
Original page

Keywords: molecular dynamics simulations | biomaterials | protein rubbers | time series nonlinear analysis | chaos | theory of rubber elasticity

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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