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Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks

Materials in biology span all the scales from Angstroms to meters and typically consist of complex hierarchical assemblies of simple building blocks. Here we describe an application of category theory to describe structural and resulting functional properties of biological protein materials by devel...

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Autores principales: Spivak, David I., Giesa, Tristan, Wood, Elizabeth, Buehler, Markus J.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Public Library of Science 2011
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3169555/
https://www.ncbi.nlm.nih.gov/pubmed/21931622
http://dx.doi.org/10.1371/journal.pone.0023911
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author Spivak, David I.
Giesa, Tristan
Wood, Elizabeth
Buehler, Markus J.
author_facet Spivak, David I.
Giesa, Tristan
Wood, Elizabeth
Buehler, Markus J.
author_sort Spivak, David I.
collection PubMed
description Materials in biology span all the scales from Angstroms to meters and typically consist of complex hierarchical assemblies of simple building blocks. Here we describe an application of category theory to describe structural and resulting functional properties of biological protein materials by developing so-called ologs. An olog is like a “concept web” or “semantic network” except that it follows a rigorous mathematical formulation based on category theory. This key difference ensures that an olog is unambiguous, highly adaptable to evolution and change, and suitable for sharing concepts with other olog. We consider simple cases of beta-helical and amyloid-like protein filaments subjected to axial extension and develop an olog representation of their structural and resulting mechanical properties. We also construct a representation of a social network in which people send text-messages to their nearest neighbors and act as a team to perform a task. We show that the olog for the protein and the olog for the social network feature identical category-theoretic representations, and we proceed to precisely explicate the analogy or isomorphism between them. The examples presented here demonstrate that the intrinsic nature of a complex system, which in particular includes a precise relationship between structure and function at different hierarchical levels, can be effectively represented by an olog. This, in turn, allows for comparative studies between disparate materials or fields of application, and results in novel approaches to derive functionality in the design of de novo hierarchical systems. We discuss opportunities and challenges associated with the description of complex biological materials by using ologs as a powerful tool for analysis and design in the context of materiomics, and we present the potential impact of this approach for engineering, life sciences, and medicine.
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spelling pubmed-31695552011-09-19 Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks Spivak, David I. Giesa, Tristan Wood, Elizabeth Buehler, Markus J. PLoS One Research Article Materials in biology span all the scales from Angstroms to meters and typically consist of complex hierarchical assemblies of simple building blocks. Here we describe an application of category theory to describe structural and resulting functional properties of biological protein materials by developing so-called ologs. An olog is like a “concept web” or “semantic network” except that it follows a rigorous mathematical formulation based on category theory. This key difference ensures that an olog is unambiguous, highly adaptable to evolution and change, and suitable for sharing concepts with other olog. We consider simple cases of beta-helical and amyloid-like protein filaments subjected to axial extension and develop an olog representation of their structural and resulting mechanical properties. We also construct a representation of a social network in which people send text-messages to their nearest neighbors and act as a team to perform a task. We show that the olog for the protein and the olog for the social network feature identical category-theoretic representations, and we proceed to precisely explicate the analogy or isomorphism between them. The examples presented here demonstrate that the intrinsic nature of a complex system, which in particular includes a precise relationship between structure and function at different hierarchical levels, can be effectively represented by an olog. This, in turn, allows for comparative studies between disparate materials or fields of application, and results in novel approaches to derive functionality in the design of de novo hierarchical systems. We discuss opportunities and challenges associated with the description of complex biological materials by using ologs as a powerful tool for analysis and design in the context of materiomics, and we present the potential impact of this approach for engineering, life sciences, and medicine. Public Library of Science 2011-09-08 /pmc/articles/PMC3169555/ /pubmed/21931622 http://dx.doi.org/10.1371/journal.pone.0023911 Text en Spivak et al. http://creativecommons.org/licenses/by/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.
spellingShingle Research Article
Spivak, David I.
Giesa, Tristan
Wood, Elizabeth
Buehler, Markus J.
Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks
title Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks
title_full Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks
title_fullStr Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks
title_full_unstemmed Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks
title_short Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks
title_sort category theoretic analysis of hierarchical protein materials and social networks
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3169555/
https://www.ncbi.nlm.nih.gov/pubmed/21931622
http://dx.doi.org/10.1371/journal.pone.0023911
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