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27
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Introduction
E. Panagiotou
Department of Mathematics, University of Tennessee at Chattanooga.
Assistant Professor.
Research in Applied Topology and Molecular Simulation
Publications
Publications (27)
Measuring the entanglement complexity of collections of open curves in 3-space has been an intractable , yet pressing mathematical problem, relevant to a plethora of physical systems, such as in polymers and biopolymers. In this manuscript, we give a novel definition of the Jones polynomial that generalizes the classic Jones polynomial to collectio...
Proteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in applied knot theory allow to characterize the topological characteristics of proteins (knotted or n...
Biopolymers, like chromatin, are often confined in small volumes. Confinement has a great effect on polymer conformations, including polymer entanglement. Polymer chains and other filamentous structures can be represented by polygonal curves in 3-space. In this manuscript, we examine the topological complexity of polygonal chains in 3-space and in...
Proteins fold in 3-dimensional conformations which are important for their function. Characterizing the global conformation of proteins rigorously and separating secondary structure effects from topological effects is a challenge. New developments in Applied Knot Theory allow to characterize the topological characteristics of proteins (knotted or n...
In this article, we define Vassiliev measures of complexity for open curves in 3-space. These are related to the coefficients of the enhanced Jones polynomial of open curves in 3-space. These Vassiliev measures are continuous functions of the curve coordinates; as the ends of the curve tend to coincide, they converge to the corresponding Vassiliev...
Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topologi...
In this manuscript we define Vassiliev measures of complexity for open curves in 3-space. These are related to the coefficients of the enhanced Jones polynomial of open curves in 3-space. These Vassiliev measures are continuous functions of the curve coordinates and as the ends of the curve tend to coincide, they converge to the corresponding Vassi...
The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its spike protein. Understanding protein rearrangement and identifying specific residues where mutations affect protein rearrangement has attracted a lot of attention for drug development. We use a mathematical method introdu...
Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topologi...
In this manuscript, we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket polynomial of curves in 3-space and show that it has real coefficients and is a continuous function of the curve coordinates. This is used to define the Jones polynomial in...
In this manuscript we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket polynomial of curves in 3-space and show that it has real coefficients and is a continuous function of the chain coordinates. This is used to define the Jones polynomial in...
Bottlebrushes are an emerging class of polymers, characterized by a high density of side chains grafted to a linear backbone that offer promise in creating materials with unusual combinations of mechanical, chemical, and optoelectronic properties. Understanding the role of molecular architecture in the organization and assembly of bottlebrushes is...
In this manuscript we review recent results that show how measures of topological entanglement can be used to provide information relevant to dynamics and mechanics of polymers. We use Molecular Dynamics simulations of coarse-grained models of polymer melts and solutions of linear chains in different settings. We apply the writhe to give estimates...
Focusing on a small set of proteins that i) fold in a concerted, all-or-none fashion and ii) do not contain knots or slipknots, we show that the Gauss linking integral, the torsion and the number of sequence-distant contacts provide information regarding the folding rate. Our results suggest that the global topology/geometry of the proteins shifts...
We study the linking matrix, a measure of entanglement for a collection of closed or open chains in 3-space based on the Gauss linking number. Periodic boundary conditions (PBC) are often used in the simulation of physical systems of filaments. To measure entanglement of closed or open chains in systems employing PBC we use the periodic linking mat...
We draw on mathematical results from topology to develop quantitative methods for polymeric materials to characterize the relationship between polymer chain entanglement and bulk viscoelastic responses. We generalize the mathematical notion of the Linking Number and Writhe to be applicable to open (linear) chains. We show how our results can be use...
The strength of entanglement present in a tubular structure consisting of short filaments is assessed using a periodic boundary condition model by employing the magnitude of the eigenvalues of the periodic linking matrix associated to the filamental structure. The effects of tube radius and of the alignment of the filaments on the strength of entan...
Olympic systems are collections of small ring polymers whose aggregate properties are largely characterized by the extent (or absence) of topological linking in contrast with the topological entanglement arising from physical movement constraints associated with excluded volume contacts or arising from chemical bonds. First, discussed by de Gennes,...
Periodic Boundary Conditions (PBC) are often used for the simulation of complex physical systems. Using the Gauss linking number, we define the periodic linking number as a measure of entanglement for two oriented curves in a system employing PBC. In the case of closed chains in PBC, the periodic linking number is an integer topological invariant t...
We employ a primitive path (PP) algorithm and the Gauss linking integral to study the degree of entanglement and knotting characteristics of linear polymer model chains in a melt under the action of a constant pulling force applied to selected chain ends. Our results for the amount of entanglement, the linking number, the average crossing number, t...
Using the Gauss linking integral we define a new measure of entanglement for a collection of closed or open chains, the linking matrix. For a system employing periodic boundary conditions (PBC) we use the periodic linking number and the periodic self- linking number to define the periodic linking matrix. We discuss its properties with respect to th...
We propose a method to estimate N_{e}, the entanglement length, that incorporates both local and global topological characteristics of chains in a melt under equilibrium conditions. This estimate uses the writhe of the chains, the writhe of the primitive paths, and the number of kinks in the chains in a melt. An advantage of this method is that it...
We define the local periodic linking number, LK, between two oriented closed
or open chains in a system with three-dimensional periodic boundary conditions.
The properties of LK indicate that it is an appropriate measure of entanglement
between a collection of chains in a periodic system. Using this measure of
linking to assess the extent of entang...
Random walks and polygons are used to model polymers. In this paper we consider the extension of writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. We show that the mean squared l...