Reversible signal transmission in an active mechanical metamaterial

Mechanical metamaterials are designed to enable unique functionalities, but are typically limited by an initial energy state and require an independent energy input to function repeatedly. Our study introduces a theoretical active mechanical metamaterial that incorporates a biological reaction mechanism to overcome this key limitation of passive metamaterials. Our material allows for reversible mechanical signal transmission, where energy is reintroduced by the biologically motivated reaction mechanism. By analysing a coarse grained continuous analogue of the discrete model, we find that signals can be propagated through the material by a travelling wave. Analysis of the continuum model provides the region of the parameter space that allows signal transmission, and reveals similarities with the well-known FitzHugh-Nagumo system. We also find explicit formulae that approximate the effect of the timescale of the reaction mechanism on the signal transmission speed, which is essential for controlling the material.Comment: 20 pages, 7 figure

Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from the complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, subset non-identifiable parameter spaces into identifiable parameter combinations that relate to individual data features, and overall provide additional biological insight from complex non-identifiable models

Isotopic fractionation of carbon during uptake by phytoplankton across the South Atlantic subtropical convergence

The stable isotopic composition of particulate organic carbon (δ13CPOC) in the surface waters of the global ocean can vary with the aqueous CO2 concentration ([CO2(aq)]) and affects the trophic transfer of carbon isotopes in the marine food web. Other factors such as cell size, growth rate and carbon concentrating mechanisms decouple this observed correlation. Here, the variability in δ13CPOC is investigated in surface waters across the south subtropical convergence (SSTC) in the Atlantic Ocean, to determine carbon isotope fractionation (ϵp) by phytoplankton and the contrasting mechanisms of carbon uptake in the subantarctic and subtropical water masses. Our results indicate that cell size is the primary determinant of δ13CPOC across the Atlantic SSTC in summer. Combining cell size estimates with CO2 concentrations, we can accurately estimate "p within the varying surface water masses in this region. We further utilize these results to investigate future changes in "p with increased anthropogenic carbon availability. Our results suggest that smaller cells, which are prevalent in the subtropical ocean, will respond less to increased [CO2(aq)] than the larger cells found south of the SSTC and in the wider Southern Ocean. In the subantarctic water masses, isotopic fractionation during carbon uptake will likely increase, both with increasing CO2 availability to the cell, but also if increased stratification leads to decreases in average community cell size. Coupled with decreasing δ13C of [CO2(aq)] due to anthropogenic CO2 emissions, this change in isotopic fractionation and lowering of δ13CPOC may propagate through the marine food web, with implications for the use of δ13CPOC as a tracer of dietary sources in the marine environment

Efficient inference and identifiability analysis for differential equation models with random parameters

Heterogeneity is a dominant factor in the behaviour of many biological processes. Despite this, it is common for mathematical and statistical analyses to ignore biological heterogeneity as a source of variability in experimental data. Therefore, methods for exploring the identifiability of models that explicitly incorporate heterogeneity through variability in model parameters are relatively underdeveloped. We develop a new likelihood-based framework, based on moment matching, for inference and identifiability analysis of differential equation models that capture biological heterogeneity through parameters that vary according to probability distributions. As our novel method is based on an approximate likelihood function, it is highly flexible; we demonstrate identifiability analysis using both a frequentist approach based on profile likelihood, and a Bayesian approach based on Markov-chain Monte Carlo. Through three case studies, we demonstrate our method by providing a didactic guide to inference and identifiability analysis of hyperparameters that relate to the statistical moments of model parameters from independent observed data. Our approach has a computational cost comparable to analysis of models that neglect heterogeneity, a significant improvement over many existing alternatives. We demonstrate how analysis of random parameter models can aid better understanding of the sources of heterogeneity from biological data.Comment: Minor changes to text. Additional results in supplementary material. Additional statistics regarding results given in main and supplementary materia

Ab Initio Structural Energetics of Beta-Si3N4 Surfaces

Motivated by recent electron microscopy studies on the Si3N4/rare-earth oxide interfaces, the atomic and electronic structures of bare beta-Si3N4 surfaces are investigated from first principles. The equilibrium shape of a Si3N4 crystal is found to have a hexagonal cross section and a faceted dome-like base in agreement with experimental observations. The large atomic relaxations on the prismatic planes are driven by the tendency of Si to saturate its dangling bonds, which gives rise to resonant-bond configurations or planar sp^2-type bonding. We predict three bare surfaces with lower energies than the open-ring (10-10) surface observed at the interface, which indicate that non-stoichiometry and the presence of the rare-earth oxide play crucial roles in determining the termination of the Si3N4 matrix grains.Comment: 4 Pages, 4 Figures, 1 tabl

Profile likelihood analysis for a stochastic model of diffusion in heterogeneous media

We compute profile likelihoods for a stochastic model of diffusive transport motivated by experimental observations of heat conduction in layered skin tissues. This process is modelled as a random walk in a layered one-dimensional material, where each layer has a distinct particle hopping rate. Particles are released at some location, and the duration of time taken for each particle to reach an absorbing boundary is recorded. To explore whether this data can be used to identify the hopping rates in each layer, we compute various profile likelihoods using two methods: first, an exact likelihood is evaluated using a relatively expensive Markov chain approach; and, second we form an approximate likelihood by assuming the distribution of exit times is given by a Gamma distribution whose first two moments match the expected moments from the continuum limit description of the stochastic model. Using the exact and approximate likelihoods we construct various profile likelihoods for a range of problems. In cases where parameter values are not identifiable, we make progress by re-interpreting those data with a reduced model with a smaller number of layers.Comment: 41 pages, 11 figure

Genome-wide association of white blood cell counts in Hispanic/Latino Americans: the Hispanic Community Health Study/Study of Latinos

Circulating white blood cell (WBC) counts (neutrophils, monocytes, lymphocytes, eosinophils, basophils) differ by ethnicity. The genetic factors underlying basal WBC traits in Hispanics/Latinos are unknown. We performed a genome-wide association study of total WBC and differential counts in a large, ethnically diverse US population sample of Hispanics/Latinos ascertained by the Hispanic Community Health Study and Study of Latinos (HCHS/SOL). We demonstrate that several previously known WBC-associated genetic loci (e.g. the African Duffy antigen receptor for chemokines null variant for neutrophil count) are generalizable to WBC traits in Hispanics/Latinos. We identified and replicated common and rare germ-line variants at FLT3 (a gene often somatically mutated in leukemia) associated with monocyte count. The common FLT3 variant rs76428106 has a large allele frequency differential between African and non-African populations. We also identified several novel genetic loci involving or regulating hematopoietic transcription factors (CEBPE-SLC7A7, CEBPA and CRBN-TRNT1) associated with basophil count. The minor allele of the CEBPE variant associated with lower basophil count has been previously associated with Amerindian ancestry and higher risk of acute lymphoblastic leukemia in Hispanics. Together, these data suggest that germline genetic variation affecting transcriptional and signaling pathways that underlie WBC development and lineage specification can contribute to inter-individual as well as ethnic differences in peripheral blood cell counts (normal hematopoiesis) in addition to susceptibility to leukemia (malignant hematopoiesis)

Reconstructing Druze population history

The Druze are an aggregate of communities in the Levant and Near East living almost exclusively in the mountains of Syria, Lebanon and Israel whose ~1000 year old religion formally opposes mixed marriages and conversions. Despite increasing interest in genetics of the population structure of the Druze, their population history remains unknown. We investigated the genetic relationships between Israeli Druze and both modern and ancient populations. We evaluated our findings in light of three hypotheses purporting to explain Druze history that posit Arabian, Persian or mixed Near Eastern-Levantine roots. The biogeographical analysis localised proto-Druze to the mountainous regions of southeastern Turkey, northern Iraq and southeast Syria and their descendants clustered along a trajectory between these two regions. The mixed Near Eastern-Middle Eastern localisation of the Druze, shown using both modern and ancient DNA data, is distinct from that of neighbouring Syrians, Palestinians and most of the Lebanese, who exhibit a high affinity to the Levant. Druze biogeographic affinity, migration patterns, time of emergence and genetic similarity to Near Eastern populations are highly suggestive of Armenian-Turkish ancestries for the proto-Druze

Inference of Population Structure using Dense Haplotype Data

The advent of genome-wide dense variation data provides an opportunity to investigate ancestry in unprecedented detail, but presents new statistical challenges. We propose a novel inference framework that aims to efficiently capture information on population structure provided by patterns of haplotype similarity. Each individual in a sample is considered in turn as a recipient, whose chromosomes are reconstructed using chunks of DNA donated by the other individuals. Results of this “chromosome painting” can be summarized as a “coancestry matrix,” which directly reveals key information about ancestral relationships among individuals. If markers are viewed as independent, we show that this matrix almost completely captures the information used by both standard Principal Components Analysis (PCA) and model-based approaches such as STRUCTURE in a unified manner. Furthermore, when markers are in linkage disequilibrium, the matrix combines information across successive markers to increase the ability to discern fine-scale population structure using PCA. In parallel, we have developed an efficient model-based approach to identify discrete populations using this matrix, which offers advantages over PCA in terms of interpretability and over existing clustering algorithms in terms of speed, number of separable populations, and sensitivity to subtle population structure. We analyse Human Genome Diversity Panel data for 938 individuals and 641,000 markers, and we identify 226 populations reflecting differences on continental, regional, local, and family scales. We present multiple lines of evidence that, while many methods capture similar information among strongly differentiated groups, more subtle population structure in human populations is consistently present at a much finer level than currently available geographic labels and is only captured by the haplotype-based approach. The software used for this article, ChromoPainter and fineSTRUCTURE, is available from http://www.paintmychromosomes.com/