The dynamics and statistics of knots in biopolymers
Date issued
Authors
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
License
Abstract
Knots have a plethora of applications in our daily life from fishing to securing surgical sutures. Even within the microscopic scale, various polymeric systems have a great capability to become entangled and knotted. As a notable instance, knots and links can either appear spontaneously or by the aid of chaperones during entanglement in biopolymers such as DNA and proteins. Despite the fact that
knotted proteins are rare, they feature different type of topologies. They span from simple trefoil knot, up to the most complex protein knot, the Stevedore. Knotting ability of polypeptide chain complicates the conundrum of protein folding, that already was a difficult problem by itself. The sequence of amino acids is the most remarkable feature of the polypeptide chains, that establishes a set of interactions and govern the protein to fold into the knotted native state. We tackle the puzzle
of knotted protein folding by introducing a structure based coarse-grained model. We show that the nontrivial structure of the knotted protein can be encoded as a set of specific local interaction along the polypeptide chain that maximizes the folding probability. In contrast to proteins, knots in sufficiently long DNA and RNA filaments are frequent and diverse with a much smaller degree of sequence dependency. The presence of topological constraints in DNA and RNA strands give rise to a rich variety of structural and dynamical features. We show that the knotting probability of a dsDNA, can be increased by introducing, along its sequence, two adhesive regions. We show that entanglement pattern in links and knots, play a key role in conformational properties of chains. In particular, we demonstrate that a double knotted semi-flexible polymer chain under strong stretching possesses a free energy minimum when the two knots are intertwined, and that the free energy of the
intertwined state is deepening when the relative chirality of the knots is opposite. Additionally, we show that the braid of DNA rings with identical/non-identical crossing pattern, enforces negative/positive and weak/strong correlation between the entangled rings.