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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| Format: | Article |
| Language: | en_US |
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Public Library of Science
2012
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| Online Access: | http://hdl.handle.net/1721.1/69110 https://orcid.org/0000-0002-4173-9659 https://orcid.org/0000-0002-6601-9199 |
| _version_ | 1826216611530407936 |
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| author | Giesa, Tristan Wood, Elizabeth Spivak, David I Buehler, Markus J |
| author2 | Massachusetts Institute of Technology. Center for Materials Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Center for Materials Science and Engineering Giesa, Tristan Wood, Elizabeth Spivak, David I Buehler, Markus J |
| author_sort | Giesa, Tristan |
| collection | MIT |
| 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. |
| first_indexed | 2024-09-23T16:49:54Z |
| format | Article |
| id | mit-1721.1/69110 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:49:54Z |
| publishDate | 2012 |
| publisher | Public Library of Science |
| record_format | dspace |
| spelling | mit-1721.1/691102022-09-29T21:49:38Z Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks Giesa, Tristan Wood, Elizabeth Spivak, David I Buehler, Markus J Massachusetts Institute of Technology. Center for Materials Science and Engineering Massachusetts Institute of Technology. Center for Computational Engineering Massachusetts Institute of Technology. Department of Civil and Environmental Engineering Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Laboratory for Atomistic and Molecular Mechanics Beuhler, Markus Jochen Spivak, David I. Giesa, Tristan Wood, Elizabeth Buehler, Markus J. 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. Presidential Early Career Award for Scientists and Engineers (N000141010562) United States. Army Research Office. Multidisciplinary University Research Initiative (W911NF0910541) United States. Office of Naval Research (grant N000141010841) Massachusetts Institute of Technology. Dept. of Mathematics Studienstiftung des deutschen Volkes Clark Barwick Jacob Lurie 2012-02-15T17:50:22Z 2012-02-15T17:50:22Z 2011-09 2011-07 Article http://purl.org/eprint/type/JournalArticle 1932-6203 http://hdl.handle.net/1721.1/69110 Spivak, David I. et al. “Category Theoretic Analysis of Hierarchical Protein Materials and Social Networks.” Ed. Laurent Kreplak. PLoS ONE 6.9 (2011): e23911. Web. 15 Feb. 2012. https://orcid.org/0000-0002-4173-9659 https://orcid.org/0000-0002-6601-9199 en_US http://dx.doi.org/10.1371/journal.pone.0023911 PLoS ONE Creative Commons Attribution http://creativecommons.org/licenses/by/2.5/ application/pdf Public Library of Science PLoS |
| spellingShingle | Giesa, Tristan Wood, Elizabeth Spivak, David I 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 |
| url | http://hdl.handle.net/1721.1/69110 https://orcid.org/0000-0002-4173-9659 https://orcid.org/0000-0002-6601-9199 |
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