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:	David I Spivak, Tristan Giesa, Elizabeth Wood, Markus J Buehler
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2011
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/452b0363df254c55b8e69a83e2ff18a1
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spelling	oai:doaj.org-article:452b0363df254c55b8e69a83e2ff18a12021-11-04T06:09:05ZCategory theoretic analysis of hierarchical protein materials and social networks.1932-620310.1371/journal.pone.0023911https://doaj.org/article/452b0363df254c55b8e69a83e2ff18a12011-01-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/pmid/21931622/pdf/?tool=EBIhttps://doaj.org/toc/1932-6203Materials 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.David I SpivakTristan GiesaElizabeth WoodMarkus J BuehlerPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 6, Iss 9, p e23911 (2011)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q David I Spivak Tristan Giesa Elizabeth Wood Markus J Buehler Category theoretic analysis of hierarchical protein materials and social networks.
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.
format	article
author	David I Spivak Tristan Giesa Elizabeth Wood Markus J Buehler
author_facet	David I Spivak Tristan Giesa Elizabeth Wood Markus J Buehler
author_sort	David I Spivak
title	Category theoretic analysis of hierarchical protein materials and social networks.
title_short	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_sort	category theoretic analysis of hierarchical protein materials and social networks.
publisher	Public Library of Science (PLoS)
publishDate	2011
url	https://doaj.org/article/452b0363df254c55b8e69a83e2ff18a1
work_keys_str_mv	AT davidispivak categorytheoreticanalysisofhierarchicalproteinmaterialsandsocialnetworks AT tristangiesa categorytheoreticanalysisofhierarchicalproteinmaterialsandsocialnetworks AT elizabethwood categorytheoreticanalysisofhierarchicalproteinmaterialsandsocialnetworks AT markusjbuehler categorytheoreticanalysisofhierarchicalproteinmaterialsandsocialnetworks
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Category theoretic analysis of hierarchical protein materials and social networks.

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