A combinatorial approach to knot recognition

This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in a compact, accessible manner, and to show how to use it for computational purposes. In particular, we address how to determine colorability of a knot, and propose to use SAT solving to search for colorings. The computational complexity of the problem, both in theory and in our implementation, is discussed. In the last part, we explain how coloring can be utilized in knot recognition

Fast Room-Temperature Detection of Terahertz Quantum Cascade Lasers with Graphene-Loaded Bow-Tie Plasmonic Antenna Arrays

We present a fast room-temperature terahertz detector based on interdigitated bow-tie antennas contacting graphene. Highly efficient photodetection was achieved by using two metals with different work functions as the arms of a bow-tie antenna contacting graphene. Arrays of the bow-ties were fabricated in order to enhance the responsivity and coupling of the incoming light to the detector, realizing an efficient imaging system. The device has been characterized and tested with a terahertz quantum cascade laser emitting in single frequency around 2 THz, yielding a responsivity of ∼34 μA/W and a noise-equivalent power of ∼1.5 × 10$^{-7}$ W/Hz$^{1/2}$.R.D., Y.R., and H.E.B. acknowledge financial support from the Engineering and Physical Sciences Research Council (Grant No. EP/J017671/1, Coherent Terahertz Systems). S.H. acknowledges funding from EPSRC (Grant No. EP/K016636/1, GRAPHTED). H.L. and J.A.Z. acknowledge financial support from the EPSRC (Grant No. EP/L019922/1). J.A.A.-W. acknowledges a Research Fellowship from Churchill College, Cambridge. H.J.J. thanks the Royal Commission for the Exhibition of 1851 for her Research Fellowship.This is the final version of the article. It first appeared from American Chemical Society via https://doi.org/10.1021/acsphotonics.6b0040

Exponential Random Graph Modeling for Complex Brain Networks

Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However, the literature on their use in biological networks (especially brain networks) has remained sparse. Descriptive models based on a specific feature of the graph (clustering coefficient, degree distribution, etc.) have dominated connectivity research in neuroscience. Corresponding generative models have been developed to reproduce one of these features. However, the complexity inherent in whole-brain network data necessitates the development and use of tools that allow the systematic exploration of several features simultaneously and how they interact to form the global network architecture. ERGMs provide a statistically principled approach to the assessment of how a set of interacting local brain network features gives rise to the global structure. We illustrate the utility of ERGMs for modeling, analyzing, and simulating complex whole-brain networks with network data from normal subjects. We also provide a foundation for the selection of important local features through the implementation and assessment of three selection approaches: a traditional p-value based backward selection approach, an information criterion approach (AIC), and a graphical goodness of fit (GOF) approach. The graphical GOF approach serves as the best method given the scientific interest in being able to capture and reproduce the structure of fitted brain networks

Highly Parallel Translation of DNA Sequences into Small Molecules

A large body of in vitro evolution work establishes the utility of biopolymer libraries comprising 1010 to 1015 distinct molecules for the discovery of nanomolar-affinity ligands to proteins.[1], [2], [3], [4], [5] Small-molecule libraries of comparable complexity will likely provide nanomolar-affinity small-molecule ligands.[6], [7] Unlike biopolymers, small molecules can offer the advantages of cell permeability, low immunogenicity, metabolic stability, rapid diffusion and inexpensive mass production. It is thought that such desirable in vivo behavior is correlated with the physical properties of small molecules, specifically a limited number of hydrogen bond donors and acceptors, a defined range of hydrophobicity, and most importantly, molecular weights less than 500 Daltons.[8] Creating a collection of 1010 to 1015 small molecules that meet these criteria requires the use of hundreds to thousands of diversity elements per step in a combinatorial synthesis of three to five steps. With this goal in mind, we have reported a set of mesofluidic devices that enable DNA-programmed combinatorial chemistry in a highly parallel 384-well plate format. Here, we demonstrate that these devices can translate DNA genes encoding 384 diversity elements per coding position into corresponding small-molecule gene products. This robust and efficient procedure yields small molecule-DNA conjugates suitable for in vitro evolution experiments

The Circadian Clock Protein Timeless Regulates Phagocytosis of Bacteria in Drosophila

Survival of bacterial infection is the result of complex host-pathogen interactions. An often-overlooked aspect of these interactions is the circadian state of the host. Previously, we demonstrated that Drosophila mutants lacking the circadian regulatory proteins Timeless (Tim) and Period (Per) are sensitive to infection by S. pneumoniae. Sensitivity to infection can be mediated either by changes in resistance (control of microbial load) or tolerance (endurance of the pathogenic effects of infection). Here we show that Tim regulates resistance against both S. pneumoniae and S. marcescens. We set out to characterize and identify the underlying mechanism of resistance that is circadian-regulated. Using S. pneumoniae, we found that resistance oscillates daily in adult wild-type flies and that these oscillations are absent in Tim mutants. Drosophila have at least three main resistance mechanisms to kill high levels of bacteria in their hemolymph: melanization, antimicrobial peptides, and phagocytosis. We found that melanization is not circadian-regulated. We further found that basal levels of AMP gene expression exhibit time-of-day oscillations but that these are Tim-independent; moreover, infection-induced AMP gene expression is not circadian-regulated. We then show that phagocytosis is circadian-regulated. Wild-type flies exhibit up-regulated phagocytic activity at night; Tim mutants have normal phagocytic activity during the day but lack this night-time peak. Tim appears to regulate an upstream event in phagocytosis, such as bacterial recognition or activation of phagocytic hemocytes. Interestingly, inhibition of phagocytosis in wild type flies results in survival kinetics similar to Tim mutants after infection with S. pneumoniae. Taken together, these results suggest that loss of circadian oscillation of a specific immune function (phagocytosis) can have significant effects on long-term survival of infection

Human Papillomavirus Type 16 Entry: Retrograde Cell Surface Transport along Actin-Rich Protrusions

The lateral mobility of individual, incoming human papillomavirus type 16 pseudoviruses (PsV) bound to live HeLa cells was studied by single particle tracking using fluorescence video microscopy. The trajectories were computationally analyzed in terms of diffusion rate and mode of motion as described by the moment scaling spectrum. Four distinct modes of mobility were seen: confined movement in small zones (30–60 nm in diameter), confined movement with a slow drift, fast random motion with transient confinement, and linear, directed movement for long distances. The directed movement was most prominent on actin-rich cell protrusions such as filopodia or retraction fibres, where the rate was similar to that measured for actin retrograde flow. It was, moreover, sensitive to perturbants of actin retrograde flow such as cytochalasin D, jasplakinolide, and blebbistatin. We found that transport along actin protrusions significantly enhanced HPV-16 infection in sparse tissue culture, cells suggesting a role for in vivo infection of basal keratinocytes during wound healing

Coaching Models of School-Based Prevention and Promotion Programmes: A Qualitative Exploration of UK Teachers' Perceptions

There has been increased interest in recent years regarding the utility of imported universal prevention and promotion (P&P) programmes in UK schools, many of which have a coaching model attached. However, there have been relatively few studies exploring the cultural transferability and social validity of these models, even though evidence suggests that these factors are important to the successful implementation of the programmes, and thus the achievement of the intended outcomes. The aim of the current study was to explore the coaching practices that teachers report experiencing, and to further understanding of the perceived benefts of these coaching practices to teachers. The sample consisted of 33 teachers implementing one of two universal, school-based P&P programmes, Good Behavior Game and Promoting Alternative Thinking Strategies as part of large-scale, randomised controlled trials. Qualitative, semi-structured interviews were conducted, and data were analysed thematically utilising a hybrid approach. Teachers typically reported engaging in six distinct practices with their coaches. While the majority of these practices were in line with coaching literature, there were some discrepancies between intended coaching practices and teachers’ reports. The coaching practices were generally perceived to be acceptable to teachers. Two unanticipated practices, validation and motivation, appeared to be of particular value to teachers, although these are not currently a prominent feature in existing coaching models. The fndings provide implications for improving the development of socially valid coaching models for UK schools

Multilevel Selection in Models of Prebiotic Evolution II: A Direct Comparison of Compartmentalization and Spatial Self-Organization

Multilevel selection has been indicated as an essential factor for the evolution of complexity in interacting RNA-like replicator systems. There are two types of multilevel selection mechanisms: implicit and explicit. For implicit multilevel selection, spatial self-organization of replicator populations has been suggested, which leads to higher level selection among emergent mesoscopic spatial patterns (traveling waves). For explicit multilevel selection, compartmentalization of replicators by vesicles has been suggested, which leads to higher level evolutionary dynamics among explicitly imposed mesoscopic entities (protocells). Historically, these mechanisms have been given separate consideration for the interests on its own. Here, we make a direct comparison between spatial self-organization and compartmentalization in simulated RNA-like replicator systems. Firstly, we show that both mechanisms achieve the macroscopic stability of a replicator system through the evolutionary dynamics on mesoscopic entities that counteract that of microscopic entities. Secondly, we show that a striking difference exists between the two mechanisms regarding their possible influence on the long-term evolutionary dynamics, which happens under an emergent trade-off situation arising from the multilevel selection. The difference is explained in terms of the difference in the stability between self-organized mesoscopic entities and externally imposed mesoscopic entities. Thirdly, we show that a sharp transition happens in the long-term evolutionary dynamics of the compartmentalized system as a function of replicator mutation rate. Fourthly, the results imply that spatial self-organization can allow the evolution of stable folding in parasitic replicators without any specific functionality in the folding itself. Finally, the results are discussed in relation to the experimental synthesis of chemical Darwinian systems and to the multilevel selection theory of evolutionary biology in general. To conclude, novel evolutionary directions can emerge through interactions between the evolutionary dynamics on multiple levels of organization. Different multilevel selection mechanisms can produce a difference in the long-term evolutionary trend of identical microscopic entities

A combinatorial extracellular matrix platform identifies cell-extracellular matrix interactions that correlate with metastasis

Extracellular matrix interactions have essential roles in normal physiology and many pathological processes. Although the importance of extracellular matrix interactions in metastasis is well documented, systematic approaches to identify their roles in distinct stages of tumorigenesis have not been described. Here we report a novel-screening platform capable of measuring phenotypic responses to combinations of extracellular matrix molecules. Using a genetic mouse model of lung adenocarcinoma, we measure the extracellular matrix-dependent adhesion of tumour-derived cells. Hierarchical clustering of the adhesion profiles differentiates metastatic cell lines from primary tumour lines. Furthermore, we uncovered that metastatic cells selectively associate with fibronectin when in combination with galectin-3, galectin-8 or laminin. We show that these molecules correlate with human disease and that their interactions are mediated in part by α3β1 integrin. Thus, our platform allowed us to interrogate interactions between metastatic cells and their microenvironments, and identified extracellular matrix and integrin interactions that could serve as therapeutic targets.National Institutes of Health (U.S.) (Grant K99-CA151968)National Institutes of Health (U.S.). Ruth L. Kirschstein National Research Service AwardStand Up To Cancer (SU2C/AACR)David H. Koch Institute for Integrative Cancer Research at MIT (CTC Project)Harvard Stem Cell Institute (SG-0046-08-00)National Cancer Center (Postdoctoral Fellowship)National Cancer Institute (U.S.) (U54CA126515)National Cancer Institute (U.S.) (U54CA112967)Howard Hughes Medical InstituteMassachusetts Institute of Technology. Ludwig Center for Molecular Oncolog