Subknots in ideal knots, random knots, and knotted proteins
نویسندگان
چکیده
We introduce disk matrices which encode the knotting of all subchains in circular knot configurations. The disk matrices allow us to dissect circular knots into their subknots, i.e. knot types formed by subchains of the global knot. The identification of subknots is based on the study of linear chains in which a knot type is associated to the chain by means of a spatially robust closure protocol. We characterize the sets of observed subknot types in global knots taking energy-minimized shapes such as KnotPlot configurations and ideal geometric configurations. We compare the sets of observed subknots to knot types obtained by changing crossings in the classical prime knot diagrams. Building upon this analysis, we study the sets of subknots in random configurations of corresponding knot types. In many of the knot types we analyzed, the sets of subknots from the ideal geometric configurations are found in each of the hundreds of random configurations of the same global knot type. We also compare the sets of subknots observed in open protein knots with the subknots observed in the ideal configurations of the corresponding knot type. This comparison enables us to explain the specific dispositions of subknots in the analyzed protein knots.
منابع مشابه
Knots, Slipknots, and Ephemeral Knots in Random Walks and Equilateral Polygons
The probability that a random walk or polygon in the 3-space or in the simple cubic lattice contains a knot goes to one at the length goes to infinity. Here, we prove that this is also true for slipknots consisting of unknotted portions, called the slipknot, that contain a smaller knotted portion, called the ephemeral knot. As is the case with knots, we prove that any topological knot type occu...
متن کاملKnots and Swelling in Protein Folding
Abstract Proteins can sometimes be knotted, and for many reasons the study of knotted proteins is rapidly becoming very important. For example, it has been proposed that a knot increases the stability of a protein. Knots may also alter enzymatic activities and enhance binding. Moreover, knotted proteins may even have some substantial biomedical significance in relation to illnesses such as Park...
متن کاملSedimentation of macroscopic rigid knots and its relation to gel electrophoretic mobility of DNA knots
We address the general question of the extent to which the hydrodynamic behaviour of microscopic freely fluctuating objects can be reproduced by macrosopic rigid objects. In particular, we compare the sedimentation speeds of knotted DNA molecules undergoing gel electrophoresis to the sedimentation speeds of rigid stereolithographic models of ideal knots in both water and silicon oil. We find th...
متن کاملExperimental detection of knotted conformations in denatured proteins.
Structures that contain a knot formed by the path of the polypeptide backbone represent some of the most complex topologies observed in proteins. How or why these topological knots arise remains unclear. By developing a method to experimentally trap and detect knots in nonnative polypeptide chains, we find that two knotted methyltransferases, YibK and YbeA, can exist in a trefoil-knot conformat...
متن کاملTight knots in proteins: can they block the mitochondrial pores?
Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process since the diameter of the pore is smaller than the size of maximally tightened knot. In the present article, I briefly review the experimental and numerical studies of tight knots in proteins, with a particular emphasis on...
متن کامل