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 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 MathematicsStudienstiftung des deutschen VolkesClark BarwickJacob Luri

Global effects of land use on local terrestrial biodiversity

Human activities, especially conversion and degradation of habitats, are causing global biodiversity declines. How local ecological assemblages are responding is less clear--a concern given their importance for many ecosystem functions and services. We analysed a terrestrial assemblage database of unprecedented geographic and taxonomic coverage to quantify local biodiversity responses to land use and related changes. Here we show that in the worst-affected habitats, these pressures reduce within-sample species richness by an average of 76.5%, total abundance by 39.5% and rarefaction-based richness by 40.3%. We estimate that, globally, these pressures have already slightly reduced average within-sample richness (by 13.6%), total abundance (10.7%) and rarefaction-based richness (8.1%), with changes showing marked spatial variation. Rapid further losses are predicted under a business-as-usual land-use scenario; within-sample richness is projected to fall by a further 3.4% globally by 2100, with losses concentrated in biodiverse but economically poor countries. Strong mitigation can deliver much more positive biodiversity changes (up to a 1.9% average increase) that are less strongly related to countries' socioeconomic status