Distance measures and evolution of polymer chains in their topological space

Mashaghi, Alireza; Ramezanpour, Abolfazl

doi:10.1039/c5sm01482d

Cited by 13 publications

(21 citation statements)

References 41 publications

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“…With these restriction (d is ordered, S is ordered for d i = d j and no contacts between equal sites) S is said to be reduced. This gives uniqueness and the ordering is consistent with previously defined orders [20]. For the complete proof see Supplementary Information.…”

Section: Circuit Topologysupporting

confidence: 84%

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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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Section: Circuit Topologysupporting

confidence: 84%

“…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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“…6 Circuit topology has been recently proposed that formalizes the arrangement of intra-chain molecular contacts and allows for topology characterization of unknot folded chains, such as the majority of identified proteins (497% do not form knots). [7][8][9][10][11][12][13][14][15] How the molecules explore the topology landscape during folding and how the trajectory to the final topology is affected by external constraints are intriguing open questions. There are ubiquitous examples in nature and technology that macromolecules undergo drastic conformational changes under constraints, 16 including the translocation process of (bio)polymers through nanopores, [17][18][19][20][21] foldingunfolding transitions of globular proteins in shear flow [22][23][24] and constraining the chain ends by molecular chaperones and ribosomes.…”

Section: Introductionmentioning

confidence: 99%

Mapping a single-molecule folding process onto a topological space

Heidari

Satarifard

Mashaghi

2019

Phys. Chem. Chem. Phys.

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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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Distance measures and evolution of polymer chains in their topological space

Cited by 13 publications

References 41 publications

A Circuit Topology Approach to Categorizing Changes in Biomolecular Structure

A Circuit Topology Approach to Categorizing Changes in Biomolecular Structure

Mapping a single-molecule folding process onto a topological space

Topology sorting and characterization of folded polymers using nano-pores

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