The transition to synchronization of networked systems.

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which corresponds to a specific clustered state. The network's nodes involved in each of the clusters can be identified, and the value of the coupling strength at which the events are taking place can be approximately ascertained. Finally, we present large-scale simulations which show the accuracy of the approximation made, and of our predictions in describing the synchronization transition of both synthetic and real-world large size networks, and we even report that the observed sequence of clusters is preserved in heterogeneous networks made of slightly non-identical systems.

Multidisciplinary ecosystem to study lifecourse determinants and prevention of early-onset burdensome multimorbidity (MELD-B) - protocol for a research collaboration.

Background: Most people living with multiple long-term condition multimorbidity (MLTC-M) are under 65 (defined as 'early onset'). Earlier and greater accrual of long-term conditions (LTCs) may be influenced by the timing and nature of exposure to key risk factors, wider determinants or other LTCs at different life stages. We have established a research collaboration titled 'MELD-B' to understand how wider determinants, sentinel conditions (the first LTC in the lifecourse) and LTC accrual sequence affect risk of early-onset, burdensome MLTC-M, and to inform prevention interventions. Aim: Our aim is to identify critical periods in the lifecourse for prevention of early-onset, burdensome MLTC-M, identified through the analysis of birth cohorts and electronic health records, including artificial intelligence (AI)-enhanced analyses. Design: We will develop deeper understanding of 'burdensomeness' and 'complexity' through a qualitative evidence synthesis and a consensus study. Using safe data environments for analyses across large, representative routine healthcare datasets and birth cohorts, we will apply AI methods to identify early-onset, burdensome MLTC-M clusters and sentinel conditions, develop semi-supervised learning to match individuals across datasets, identify determinants of burdensome clusters, and model trajectories of LTC and burden accrual. We will characterise early-life (under 18 years) risk factors for early-onset, burdensome MLTC-M and sentinel conditions. Finally, using AI and causal inference modelling, we will model potential 'preventable moments', defined as time periods in the life course where there is an opportunity for intervention on risk factors and early determinants to prevent the development of MLTC-M. Patient and public involvement is integrated throughout.

An information-theoretic approach to single cell sequencing analysis.

BACKGROUND: Single-cell sequencing (sc-Seq) experiments are producing increasingly large data sets. However, large data sets do not necessarily contain large amounts of information. RESULTS: Here, we formally quantify the information obtained from a sc-Seq experiment and show that it corresponds to an intuitive notion of gene expression heterogeneity. We demonstrate a natural relation between our notion of heterogeneity and that of cell type, decomposing heterogeneity into that component attributable to differential expression between cell types (inter-cluster heterogeneity) and that remaining (intra-cluster heterogeneity). We test our definition of heterogeneity as the objective function of a clustering algorithm, and show that it is a useful descriptor for gene expression patterns associated with different cell types. CONCLUSIONS: Thus, our definition of gene heterogeneity leads to a biologically meaningful notion of cell type, as groups of cells that are statistically equivalent with respect to their patterns of gene expression. Our measure of heterogeneity, and its decomposition into inter- and intra-cluster, is non-parametric, intrinsic, unbiased, and requires no additional assumptions about expression patterns. Based on this theory, we develop an efficient method for the automatic unsupervised clustering of cells from sc-Seq data, and provide an R package implementation.

Stratification of asthma by lipidomic profiling of induced sputum supernatant.

BACKGROUND: Asthma is a chronic respiratory disease with significant heterogeneity in its clinical presentation and pathobiology. There is need for improved understanding of respiratory lipid metabolism in asthma patients and its relation to observable clinical features. OBJECTIVE: We performed a comprehensive, prospective, cross-sectional analysis of the lipid composition of induced sputum supernatant obtained from asthma patients with a range of disease severities, as well as from healthy controls. METHODS: Induced sputum supernatant was collected from 211 adults with asthma and 41 healthy individuals enrolled onto the U-BIOPRED (Unbiased Biomarkers for the Prediction of Respiratory Disease Outcomes) study. Sputum lipidomes were characterized by semiquantitative shotgun mass spectrometry and clustered using topologic data analysis to identify lipid phenotypes. RESULTS: Shotgun lipidomics of induced sputum supernatant revealed a spectrum of 9 molecular phenotypes, highlighting not just significant differences between the sputum lipidomes of asthma patients and healthy controls, but also within the asthma patient population. Matching clinical, pathobiologic, proteomic, and transcriptomic data helped inform the underlying disease processes. Sputum lipid phenotypes with higher levels of nonendogenous, cell-derived lipids were associated with significantly worse asthma severity, worse lung function, and elevated granulocyte counts. CONCLUSION: We propose a novel mechanism of increased lipid loading in the epithelial lining fluid of asthma patients resulting from the secretion of extracellular vesicles by granulocytic inflammatory cells, which could reduce the ability of pulmonary surfactant to lower surface tension in asthmatic small airways, as well as compromise its role as an immune regulator.

Persistent homology analysis distinguishes pathological bone microstructure in non-linear microscopy images.

We present a topological method for the detection and quantification of bone microstructure from non-linear microscopy images. Specifically, we analyse second harmonic generation (SHG) and two photon excited autofluorescence (TPaF) images of bone tissue which capture the distribution of matrix (fibrillar collagen) structure and autofluorescent molecules, respectively. Using persistent homology statistics with a signed Euclidean distance transform filtration on binary patches of images, we are able to quantify the number, size, distribution, and crowding of holes within and across samples imaged at the microscale. We apply our methodology to a previously characterized murine model of skeletal pathology whereby vascular endothelial growth factor expression was deleted in osteocalcin-expressing cells (OcnVEGFKO) presenting increased cortical porosity, compared to wild type (WT) littermate controls. We show significant differences in topological statistics between the OcnVEGFKO and WT groups and, when classifying the males, or females respectively, into OcnVEGFKO or WT groups, we obtain high prediction accuracies of 98.7% (74.2%) and 77.8% (65.8%) respectively for SHG (TPaF) images. The persistence statistics that we use are fully interpretable, can highlight regions of abnormality within an image and identify features at different spatial scales.

Geometry and symmetry in biochemical reaction systems.

Complex systems of intracellular biochemical reactions have a central role in regulating cell identities and functions. Biochemical reaction systems are typically studied using the language and tools of graph theory. However, graph representations only describe pairwise interactions between molecular species and so are not well suited to modelling complex sets of reactions that may involve numerous reactants and/or products. Here, we make use of a recently developed hypergraph theory of chemical reactions that naturally allows for higher-order interactions to explore the geometry and quantify functional redundancy in biochemical reactions systems. Our results constitute a general theory of automorphisms for oriented hypergraphs and describe the effect of automorphism group structure on hypergraph Laplacian spectra.

Universal principles of lineage architecture and stem cell identity in renewing tissues.

Adult tissues in multicellular organisms typically contain a variety of stem, progenitor and differentiated cell types arranged in a lineage hierarchy that regulates healthy tissue turnover. Lineage hierarchies in disparate tissues often exhibit common features, yet the general principles regulating their architecture are not known. Here, we provide a formal framework for understanding the relationship between cell molecular 'states' and cell 'types', based on the topology of admissible cell state trajectories. We show that a self-renewing cell type - if defined as suggested by this framework - must reside at the top of any homeostatic renewing lineage hierarchy, and only there. This architecture arises as a natural consequence of homeostasis, and indeed is the only possible way that lineage architectures can be constructed to support homeostasis in renewing tissues. Furthermore, under suitable feedback regulation, for example from the stem cell niche, we show that the property of 'stemness' is entirely determined by the cell environment, in accordance with the notion that stem cell identities are contextual and not determined by hard-wired, cell-intrinsic characteristics. This article has an associated 'The people behind the papers' interview.

Stability and steady state of complex cooperative systems: a diakoptic approach.

Cooperative dynamics are common in ecology and population dynamics. However, their commonly high degree of complexity with a large number of coupled degrees of freedom renders them difficult to analyse. Here, we present a graph-theoretical criterion, via a diakoptic approach (divide-and-conquer) to determine a cooperative system's stability by decomposing the system's dependence graph into its strongly connected components (SCCs). In particular, we show that a linear cooperative system is Lyapunov stable if the SCCs of the associated dependence graph all have non-positive dominant eigenvalues, and if no SCCs which have dominant eigenvalue zero are connected by a path.

Noise-processing by signaling networks.

Signaling networks mediate environmental information to the cell nucleus. To perform this task effectively they must be able to integrate multiple stimuli and distinguish persistent signals from transient environmental fluctuations. However, the ways in which signaling networks process environmental noise are not well understood. Here we outline a mathematical framework that relates a network's structure to its capacity to process noise, and use this framework to dissect the noise-processing ability of signaling networks. We find that complex networks that are dense in directed paths are poor noise processors, while those that are sparse and strongly directional process noise well. These results suggest that while cross-talk between signaling pathways may increase the ability of signaling networks to integrate multiple stimuli, too much cross-talk may compromise the ability of the network to distinguish signal from noise. To illustrate these general results we consider the structure of the signalling network that maintains pluripotency in mouse embryonic stem cells, and find an incoherent feedforward loop structure involving Stat3, Tfcp2l1, Esrrb, Klf2 and Klf4 is particularly important for noise-processing. Taken together these results suggest that noise-processing is an important function of signaling networks and they may be structured in part to optimize this task.

Dimensionality reduction and spectral properties of multilayer networks.

Network representations are useful for describing the structure of a large variety of complex systems. Although most studies of real-world networks suppose that nodes are connected by only a single type of edge, most natural and engineered systems include multiple subsystems and layers of connectivity. This new paradigm has attracted a great deal of attention and one fundamental challenge is to characterize multilayer networks both structurally and dynamically. One way to address this question is to study the spectral properties of such networks. Here we apply the framework of graph quotients, which occurs naturally in this context, and the associated eigenvalue interlacing results to the adjacency and Laplacian matrices of undirected multilayer networks. Specifically, we describe relationships between the eigenvalue spectra of multilayer networks and their two most natural quotients, the network of layers and the aggregate network, and show the dynamical implications of working with either of the two simplified representations. Our work thus contributes in particular to the study of dynamical processes whose critical properties are determined by the spectral properties of the underlying network.

Microdynamics and criticality of adaptive regulatory networks.

We present a model of adaptive regulatory networks consisting of a simple biologically motivated rewiring procedure coupled to an elementary stability criterion. The resulting networks exhibit a characteristic stationary heavy-tailed degree distribution, show complex structural microdynamics, and self-organize to a dynamically critical state. We show analytically that the observed criticality results from the formation and breaking of transient feedback loops during the adaptive process.

Spectral characteristics of network redundancy.

Many real-world complex networks contain a significant amount of structural redundancy, in which multiple vertices play identical topological roles. Such redundancy arises naturally from the simple growth processes which form and shape many real-world systems. Since structurally redundant elements may be permuted without altering network structure, redundancy may be formally investigated by examining network automorphism (symmetry) groups. Here, we use a group-theoretic approach to give a complete description of spectral signatures of redundancy in undirected networks. In particular, we describe how a network's automorphism group may be used to directly associate specific eigenvalues and eigenvectors with specific network motifs.