Understanding Health and Disease with Multidimensional Single-Cell Methods

Current efforts in the biomedical sciences and related interdisciplinary fields are focused on gaining a molecular understanding of health and disease, which is a problem of daunting complexity that spans many orders of magnitude in characteristic length scales, from small molecules that regulate cell function to cell ensembles that form tissues and organs working together as an organism. In order to uncover the molecular nature of the emergent properties of a cell, it is essential to measure multiple cell components simultaneously in the same cell. In turn, cell heterogeneity requires multiple cells to be measured in order to understand health and disease in the organism. This review summarizes current efforts towards a data-driven framework that leverages single-cell technologies to build robust signatures of healthy and diseased phenotypes. While some approaches focus on multicolor flow cytometry data and other methods are designed to analyze high-content image-based screens, we emphasize the so-called Supercell/SVM paradigm (recently developed by the authors of this review and collaborators) as a unified framework that captures mesoscopic-scale emergence to build reliable phenotypes. Beyond their specific contributions to basic and translational biomedical research, these efforts illustrate, from a larger perspective, the powerful synergy that might be achieved from bringing together methods and ideas from statistical physics, data mining, and mathematics to solve the most pressing problems currently facing the life sciences.Comment: 25 pages, 7 figures; revised version with minor changes. To appear in J. Phys.: Cond. Mat

A Microstructural View of Burrowing with RoboClam

RoboClam is a burrowing technology inspired by Ensis directus, the Atlantic razor clam. Atlantic razor clams should only be strong enough to dig a few centimeters into the soil, yet they burrow to over 70 cm. The animal uses a clever trick to achieve this: by contracting its body, it agitates and locally fluidizes the soil, reducing the drag and energetic cost of burrowing. RoboClam technology, which is based on the digging mechanics of razor clams, may be valuable for subsea applications that could benefit from efficient burrowing, such as anchoring, mine detonation, and cable laying. We directly visualize the movement of soil grains during the contraction of RoboClam, using a novel index-matching technique along with particle tracking. We show that the size of the failure zone around contracting RoboClam, can be theoretically predicted from the substrate and pore fluid properties, provided that the timescale of contraction is sufficiently large. We also show that the nonaffine motions of the grains are a small fraction of the motion within the fluidized zone, affirming the relevance of a continuum model for this system, even though the grain size is comparable to the size of RoboClam

Multiple Permitting and Bounded Turing Reducibilities

We look at various properties of the computably enumerable (c.e.) not totally ω-c.e. Turing degrees. In particular, we are interested in the variant of multiple permitting given by those degrees. We define a property of left-c.e. sets called universal similarity property which can be viewed as a universal or uniform version of the property of array noncomputable c.e. sets of agreeing with any c.e. set on some component of a very strong array. Using a multiple permitting argument, we prove that the Turing degrees of the left-c.e. sets with the universal similarity property coincide with the c.e. not totally ω-c.e. degrees. We further introduce and look at various notions of socalled universal array noncomputability and show that c.e. sets with those properties can be found exactly in the c.e. not totally ω-c.e. Turing degrees and that they guarantee a special type of multiple permitting called uniform multiple permitting. We apply these properties of the c.e. not totally ω-c.e. degrees to give alternative proofs of well-known results on those degrees as well as to prove new results. E.g., we show that a c.e. Turing degree contains a left-c.e. set which is not cl-reducible to any complex left-c.e. set if and only if it is not totally ω-c.e. Furthermore, we prove that the nondistributive finite lattice S7 can be embedded into the c.e. Turing degrees precisely below any c.e. not totally ω-c.e. degree. We further look at the question of join preservation for bounded Turing reducibilities r and r′ such that r is stronger than r′. We say that join preservation holds for two reducibilities r and r′ if every join in the c.e. r-degrees is also a join in the c.e. r′-degrees. We consider the class of monotone admissible (uniformly) bounded Turing reducibilities, i.e., the reflexive and transitive Turing reducibilities with use bounded by a function that is contained in a (uniformly computable) family of strictly increasing computable functions. This class contains for example identity bounded Turing (ibT-) and computable Lipschitz (cl-) reducibility. Our main result of Chapter 3 is that join preservation fails for cl and any strictly weaker monotone admissible uniformly bounded Turing reducibility. We also look at the dual question of meet preservation and show that for all monotone admissible bounded Turing reducibilities r and r′ such that r is stronger than r′, meet preservation holds. Finally, we completely solve the question of join and meet preservation in the classical reducibilities 1, m, tt, wtt and T