Circuit topology of linear polymers: a statistical mechanical treatment

Mashaghi, Alireza; Ramezanpour, Abolfazl

doi:10.1039/c5ra08106h

Cited by 14 publications

(23 citation statements)

References 21 publications

(55 reference statements)

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“…In Ref. [25] we used local topological data to reconstruct such an energy function. There, we observed that appropriate forms of two-contact interactions are enough to describe simple structural orders like modules and sectors.…”

Section: Discussionmentioning

confidence: 99%

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Distance measures and evolution of polymer chains in their topological space

Mashaghi

Ramezanpour

2015

Soft Matter

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Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology. For folded linear biomolecules, arrangement of intramolecular contacts is identified as a key topological property, termed as circuit topology. Distance measures are proposed as reaction coordinates to represent progress along a pathway from initial topology to final topology.Certain topological classes are shown to be more accessible from a random topology. We study dynamic stability and pathway degeneracy associated with a topological reaction and found that off-pathways might seriously hamper evolution to desired topologies. Finally we present an algorithm for estimating the number of intermediate topologies visited during a topological reaction.The results of this study are relevant to, among others, structural studies of RNA and proteins, analysis of topologically associated domains in chromosomes, and molecular evolution.

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Section: Discussionmentioning

confidence: 99%

“…We observed that such energy functions could be useful in the study of complex link configurations in the presence of structural modules and sectors [25].…”

Section: A Distance Of Two Matrix Configurationsmentioning

confidence: 99%

Distance measures and evolution of polymer chains in their topological space

Mashaghi

Ramezanpour

2015

Soft Matter

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“…Biological circuit topology is a mathematical approach that describes the relationships between intramolecular contacts within a folded molecule [13][14][15][16][17][18][19][20]. In this framework, pairwise relations between contacts can be defined using the logic rules of set theory [13,14].…”

Section: Introductionmentioning

confidence: 99%

A Circuit Topology Approach to Categorizing Changes in Biomolecular Structure

et al. 2020

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The biological world is composed of folded linear molecules of bewildering topological complexity and diversity. The topology of folded biomolecules such as proteins and ribonucleic acids is often subject to change during biological processes. Despite intense research, we lack a solid mathematical framework that summarizes these operations in a principled manner. Circuit topology, which formalizes the arrangements of intramolecular contacts, serves as a general mathematical framework to analyze the topological characteristics of folded linear molecules. In this work, we translate familiar molecular operations in biology, such as duplication, permutation, and elimination of contacts, into the language of circuit topology. We show that for such operations there are corresponding matrix representations as well as basic rules that serve as a foundation for understanding these operations within the context of a coherent algebraic framework. We present several biological examples and provide a simple computational framework for creating and analyzing the circuit diagrams of proteins and nucleic acids. We expect our study and future developments in this direction to facilitate a deeper understanding of natural molecular processes and to provide guidance to engineers for generating complex polymeric materials.

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“…1). The arrangement of the contacts has been shown to be a determinant of the folding rates and unfolding pathways of biomolecules, [14] and has important implications for bimolecular evolution and molecular engineering [15,16].…”

Section: Introductionmentioning

confidence: 99%

Topology sorting and characterization of folded polymers using nano-pores

Nikoofard

Mashaghi

2016

Nanoscale

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Here we report on the translocation of folded polymers through nano-pores using molecular dynamic simulations. Two cases are studied: one in which a folded molecule unfolds upon passage and one in which the folding remains intact as the molecule passes through the nano-pore. The topology of a folded polymer chain is defined as the arrangement of the intramolecular contacts, known as circuit topology. In the case where intramolecular contacts remain intact, we show that the dynamics of passage through a nano-pore varies for molecules with differing topologies: a phenomenon that can be exploited to enrich certain topologies in mixtures. We find that the nano-pore allows reading of the topology for short chains. Moreover, when the passage is coupled with unfolding, the nano-pore enables discrimination between pure states, i.e., states in which the majority of contacts are arranged identically. In this case, as we show here, it is also possible to read the positions of the contact sites along a chain. Our results demonstrate the applicability of nano-pore technology to characterize and sort molecules based on their topology.

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Circuit topology of linear polymers: a statistical mechanical treatment

Cited by 14 publications

References 21 publications

Distance measures and evolution of polymer chains in their topological space

Distance measures and evolution of polymer chains in their topological space

A Circuit Topology Approach to Categorizing Changes in Biomolecular Structure

Topology sorting and characterization of folded polymers using nano-pores

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