Teoria efetiva de campos e geometria de moléculas longas
The goal of this thesis is to construct an effective description of the dynamics of curves in three dimensions applicable in the context of protein physics. The model is intended to reproduce a variety of geometric characteristics observed in real proteins, assuming that proteins can be approxima...
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| Formato: | doctoralThesis |
| Idioma: | pt_BR |
| Publicado em: |
Brasil
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| Endereço do item: | https://repositorio.ufrn.br/jspui/handle/123456789/28781 |
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| Resumo: | The goal of this thesis is to construct an effective description of the dynamics of curves
in three dimensions applicable in the context of protein physics. The model is intended
to reproduce a variety of geometric characteristics observed in real proteins, assuming
that proteins can be approximated by long continuous curves. The degrees of freedom in
the effective description are parameterized by the curvature and torsion functions. The
minimal necessary model is constructed in terms of an energy functional depending on
four phenomenological parameters. We discuss static configurations of the effective model,
which appear in two different classes: minima of the effective potential and soliton-like
configurations interpolating between pairs of minima. In proteins such classes correspond to
most common secondary structures (alpha-helices and beta-strands) and motifs connecting
those structures (loops, turns, hairpins etc.) In order to obtain the values for the parameters,
the solutions of the model are compared with real protein structures extracted from the
Protein Data Bank. A very specific relation between the curvature and torsion predicted
by the model allows us to universally fix three of the parameters of the model. We show
that the fourth parameter is not universal. It controls the characteristic size of the motifs
connecting alpha-helices and beta-strands and may be used to explain the absence of
beta-strands in some proteins and their abundance in the others. In the most appealing
scenario the model features “stable” alpha-helices and “metastable” beta-strands. We study
the classical and quantum stability of the metastable configurations. We derive estimates
for the temperatures of classical phase transitions and show that quantum transitions are
suppressed. We also discuss how realistic discrete proteins “stabilize” beta strands and
hairpin-like motifs. |
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