Dynamik and diffusion of gradient copolymers
Final Report Abstract
The problem of search optimization often becomes crucial for living beings as well as for mindless molecular-level searchers such as proteins. These problems are intrinsically intertwined with the field of first-passage phenomena. In this project we have concentrated on studying the search and first-passage problems involving anomalous diffusion: foraging of animals, search over polymers and copolymer translocation. In order to achieve the goals of the project we have developed models based on fractional diffusion equations and confirmed the results with Monte-Carlo simulations. We proposed a new definition of search efficiency and argued in favor of its use for a wide class of search problems. For all search and dynamical problems which we have studied, we confirmed our hypothesis that the presence of a bias essentially affects the search efficiency and, hence, the optimization of search strategy. Both for animal foraging and search over a polymer the existence of bias towards a target considerably improves both the efficiency and reliability of the search. Contrary to the common belief in the community we showed that Lévy flights do not always present an optimal search strategy of a blind random searcher. Brownian motion outperforms Lévy flights in cases when searcher starts in the vicinity of the target or drifted towards it. In the cases of relatively unfavorable initial conditions (such as bias from the target or large distance from it) Lévy flights perform better. Study of translocation of gradient polymers motivated us to consider influence of piece-wise linear potentials onto first-passage time properties. We found a surprising effect of first-passage time enhancement due to potential barriers. We have shown that the same effect can be observed for gradient copolymers. Thus, we proved that polymer translocation properties can be strongly affected by a sequence of gradient copolymer.
Publications
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J. Stat. Mech., L03001 (2012)
V. V. Palyulin and R. Metzler
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J. Phys. A Math. Theor. 47 032002 (2014)
V. V. Palyulin and R. Metzler
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Proc. Natl. Acad. Sci. USA, 111, 2931 (2014)
V. V. Palyulin, A.V. Chechkin and R. Metzler
