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Category theoretic analysis of hierarchical protein materials and social networks.

ABSTRACT: 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.

SUBMITTER: Spivak DI

PROVIDER: S-EPMC3169555 | biostudies-literature | 2011

REPOSITORIES: biostudies-literature

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Category theoretic analysis of hierarchical protein materials and social networks.

Spivak David I DI Giesa Tristan T Wood Elizabeth E Buehler Markus J MJ

PloS one 20110908 9

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 ol ...[more]

PMID: 21931622

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Project description:Note: Data Use Restrictions: <ul> <li>The data must only be used for genetic research projects solely in the area of health-related social-network research.</li> </ul> This study compiles detailed information on family and social ties linked to participants in the offspring cohort of the Framingham Heart Study. The investigators took computerized information from self-report data used by the FHS for over 30 years to facilitate health exam scheduling. These tracking sheets asked participants to identify people close to them, which were assumed by the investigators to indicate a social tie. Individuals are listed as "egos" (if the ties are from their perspective) and/or "alters" (if they are linked as a friend or family members to one of the other participants). All egos were FHS offspring participants while alters could be FHS participants in any cohort or non-participants. This information was combined with internal FHS pedigree data on family ties to list family member alters (as well as the nature of their relationship). The resultant dataset therefore includes each ego-alter tie, the nature of their relationship and the start and end dates for their ties for each of seven waves for the offspring study. Due to privacy concerns, all exam dates for individuals are listed relative to the initial FHS exam date. The study investigators chose a random, confidential date, to which all initial exam dates are linked (by number of months from random date to initial exam date). With this information, researchers can have access to the temporal relationships among participants' exam dates while remaining unaware of the actual exam dates for individual participants. During each clinic exam cycle, the participants undergo a detailed examination including physical examination, medical history, laboratory testing, and electrocardiogram. Over the years, other tests (that may not be performed at every exam cycle) have included pulmonary function, lifestyle, physical function, cognitive function questionnaires, and various noninvasive cardiovascular tests including echocardiograms. This study involves phenotypic data from these exams including (when available) basic body measurements (height, weight, blood pressure), laboratory values (blood sugar levels, LDL levels), information on smoking and alcohol use, and tests of depression and cognitive functioning. Important links to apply for individual-level data <ol> <li><a href="http://dbgap.ncbi.nlm.nih.gov/aa/wga.cgi?view_pdf&stacc=phs000153.v3.p3" target="_blank">Data Use Certification Requirements (DUC)</a></li> <li><a href="GetPdf.cgi?id=phd001183.1" target="_blank">Instructions to Request Authorized Access</a></li> <li><a href="http://view.ncbi.nlm.nih.gov/dbgap-controlled" target="_blank">Apply here for controlled access to individual level data</a></li> <li><a href="GetPdf.cgi?id=phd000317" target="_blank">Participant Protection Policy FAQ</a></li> </ol> In 1948, researchers recruited men and women from the town of Framingham, Massachusetts, beginning the first round of extensive physical examinations and lifestyle interviews that would later be analyzed for common patterns related to CVD development. Initially, the Framingham Heart Study enrolled 5,209 men and women from the Framingham area who were between the ages of 28 and 62 years. Beginning in 1971, the Framingham Heart Study enrolled 5,124 men and women, who were either offspring of the original cohort or spouses of those offspring. In 2002, 4,095 third generation participants (men and women) were enrolled.

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Category theoretic analysis of hierarchical protein materials and social networks.

Publications

Category theoretic analysis of hierarchical protein materials and social networks.

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