Contagion risks and security investment in directed networks.

We develop a model for contagion risks and optimal security investment in a directed network of interconnected agents with heterogeneous degrees, loss functions, and security profiles. Our model generalizes several contagion models in the literature, particularly the independent cascade model and the linear threshold model. We state various limit theorems on the final size of infected agents in the case of random networks with given vertex degrees for finite and infinite-variance degree distributions. The results allow us to derive a resilience condition for the network in response to the infection of a large group of agents and quantify how contagion amplifies small shocks to the network. We show that when the degree distribution has infinite variance and highly correlated in- and out-degrees, even when agents have high thresholds, a sub-linear fraction of initially infected agents is enough to trigger the infection of a positive fraction of nodes. We also demonstrate how these results are sensitive to vertex and edge percolation (intervention). We then study the asymptotic Nash equilibrium and socially optimal security investment. In the asymptotic limit, agents' risk depends on all other agents' investments through an aggregate quantity that we call network vulnerability. The limit theorems enable us to capture the impact of one class of agents' decisions on the overall network vulnerability. Based on our results, the vulnerability is semi-analytic, allowing for a tractable Nash equilibrium. We provide sufficient conditions for investment in equilibrium to be monotone in network vulnerability. When investment is monotone, we demonstrate that the (asymptotic) Nash equilibrium is unique. In the specific example of two types of core-periphery agents, we illustrate the strong effect of cost heterogeneity on network vulnerability and the non-monotonous investment as a function of costs.

A DNA methylation atlas of normal human cell types.

DNA methylation is a fundamental epigenetic mark that governs gene expression and chromatin organization, thus providing a window into cellular identity and developmental processes1. Current datasets typically include only a fraction of methylation sites and are often based either on cell lines that underwent massive changes in culture or on tissues containing unspecified mixtures of cells2-5. Here we describe a human methylome atlas, based on deep whole-genome bisulfite sequencing, allowing fragment-level analysis across thousands of unique markers for 39 cell types sorted from 205 healthy tissue samples. Replicates of the same cell type are more than 99.5% identical, demonstrating the robustness of cell identity programmes to environmental perturbation. Unsupervised clustering of the atlas recapitulates key elements of tissue ontogeny and identifies methylation patterns retained since embryonic development. Loci uniquely unmethylated in an individual cell type often reside in transcriptional enhancers and contain DNA binding sites for tissue-specific transcriptional regulators. Uniquely hypermethylated loci are rare and are enriched for CpG islands, Polycomb targets and CTCF binding sites, suggesting a new role in shaping cell-type-specific chromatin looping. The atlas provides an essential resource for study of gene regulation and disease-associated genetic variants, and a wealth of potential tissue-specific biomarkers for use in liquid biopsies.

Evaluation of cell-free DNA approaches for multi-cancer early detection.

In the Circulating Cell-free Genome Atlas (NCT02889978) substudy 1, we evaluate several approaches for a circulating cell-free DNA (cfDNA)-based multi-cancer early detection (MCED) test by defining clinical limit of detection (LOD) based on circulating tumor allele fraction (cTAF), enabling performance comparisons. Among 10 machine-learning classifiers trained on the same samples and independently validated, when evaluated at 98% specificity, those using whole-genome (WG) methylation, single nucleotide variants with paired white blood cell background removal, and combined scores from classifiers evaluated in this study show the highest cancer signal detection sensitivities. Compared with clinical stage and tumor type, cTAF is a more significant predictor of classifier performance and may more closely reflect tumor biology. Clinical LODs mirror relative sensitivities for all approaches. The WG methylation feature best predicts cancer signal origin. WG methylation is the most promising technology for MCED and informs development of a targeted methylation MCED test.

Universal lung epithelium DNA methylation markers for detection of lung damage in liquid biopsies.

BACKGROUND: Circulating biomarkers for lung damage are lacking. Lung epithelium-specific DNA methylation patterns can potentially report the presence of lung-derived cell-free DNA (cfDNA) in blood, as an indication of lung cell death. METHODS: We sorted human lung alveolar and bronchial epithelial cells from surgical specimens, and obtained their methylomes using whole-genome bisulfite sequencing. We developed a PCR sequencing assay determining the methylation status of 17 loci with lung-specific methylation patterns, and used it to assess lung-derived cfDNA in the plasma of healthy volunteers and patients with lung disease. RESULTS: Loci that are uniquely unmethylated in alveolar or bronchial epithelial cells are enriched for enhancers controlling lung-specific genes. Methylation markers extracted from these methylomes revealed that normal lung cell turnover probably releases cfDNA into the air spaces, rather than to blood. People with advanced lung cancer show a massive elevation of lung cfDNA concentration in blood. Among individuals undergoing bronchoscopy, lung-derived cfDNA is observed in the plasma of those later diagnosed with lung cancer, and to a lesser extent in those diagnosed with other lung diseases. Lung cfDNA is also elevated in patients with acute exacerbation of COPD compared with patients with stable disease, and is associated with future exacerbation and mortality in these patients. CONCLUSIONS: Universal cfDNA methylation markers of normal lung epithelium allow for mutation-independent, sensitive and specific detection of lung-derived cfDNA, reporting on ongoing lung injury. Such markers can find broad utility in the study of normal and pathologic human lung dynamics.

Epidemic Spreading and Equilibrium Social Distancing in Heterogeneous Networks.

We study a multi-type SIR epidemic process within a heterogeneous population that interacts through a network. We base social contact on a random graph with given vertex degrees, and we give limit theorems on the fraction of infected individuals. For given social distancing individual strategies, we establish the epidemic reproduction number R 0 , which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper, we study the equilibrium of the social distancing game. Individuals choose their social distancing level according to an anticipated global infection rate, which must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of an equilibrium. In the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal.

Inertial microfluidic physics.

Microfluidics has experienced massive growth in the past two decades, and especially with advances in rapid prototyping researchers have explored a multitude of channel structures, fluid and particle mixtures, and integration with electrical and optical systems towards solving problems in healthcare, biological and chemical analysis, materials synthesis, and other emerging areas that can benefit from the scale, automation, or the unique physics of these systems. Inertial microfluidics, which relies on the unconventional use of fluid inertia in microfluidic platforms, is one of the emerging fields that make use of unique physical phenomena that are accessible in microscale patterned channels. Channel shapes that focus, concentrate, order, separate, transfer, and mix particles and fluids have been demonstrated, however physical underpinnings guiding these channel designs have been limited and much of the development has been based on experimentally-derived intuition. Here we aim to provide a deeper understanding of mechanisms and underlying physics in these systems which can lead to more effective and reliable designs with less iteration. To place the inertial effects into context we also discuss related fluid-induced forces present in particulate flows including forces due to non-Newtonian fluids, particle asymmetry, and particle deformability. We then highlight the inverse situation and describe the effect of the suspended particles acting on the fluid in a channel flow. Finally, we discuss the importance of structured channels, i.e. channels with boundary conditions that vary in the streamwise direction, and their potential as a means to achieve unprecedented three-dimensional control over fluid and particles in microchannels. Ultimately, we hope that an improved fundamental and quantitative understanding of inertial fluid dynamic effects can lead to unprecedented capabilities to program fluid and particle flow towards automation of biomedicine, materials synthesis, and chemical process control.

Microstructure-induced helical vortices allow single-stream and long-term inertial focusing.

Fluid inertia has been used to position microparticles in confined channels because it leads to precise and predictable particle migration across streamlines in a high-throughput manner. To focus particles, typically two inertial effects have been employed: inertial migration of particles in combination with geometry-induced secondary flows. Still, the strong scaling of inertial effects with fluid velocity or channel flow rate have made it challenging to design inertial focusing systems for single-stream focusing using large-scale microchannels. Use of large-scale microchannels (≥100 µm) reduces clogging over long durations and could be suitable for non-single-use flow cells in cytometry systems. Here, we show that microstructure-induced helical vortices yield single-stream focusing of microparticles with continuous and robust operation. Numerical and experimental results demonstrate how structures contribute to improve focusing in these larger channels, through controllable cross-stream particle migration, aided by locally-tuned secondary flows from sequential obstacles that act to bring particles closer to a single focusing equilibrium position. The large-scale inertial focuser developed here can be operated in a high-throughput manner with a maximum throughput of approximately 13,000 particles per s.

Engineering fluid flow using sequenced microstructures.

Controlling the shape of fluid streams is important across scales: from industrial processing to control of biomolecular interactions. Previous approaches to control fluid streams have focused mainly on creating chaotic flows to enhance mixing. Here we develop an approach to apply order using sequences of fluid transformations rather than enhancing chaos. We investigate the inertial flow deformations around a library of single cylindrical pillars within a microfluidic channel and assemble these net fluid transformations to engineer fluid streams. As these transformations provide a deterministic mapping of fluid elements from upstream to downstream of a pillar, we can sequentially arrange pillars to apply the associated nested maps and, therefore, create complex fluid structures without additional numerical simulation. To show the range of capabilities, we present sequences that sculpt the cross-sectional shape of a stream into complex geometries, move and split a fluid stream, perform solution exchange and achieve particle separation. A general strategy to engineer fluid streams into a broad class of defined configurations in which the complexity of the nonlinear equations of fluid motion are abstracted from the user is a first step to programming streams of any desired shape, which would be useful for biological, chemical and materials automation.

Intrinsic particle-induced lateral transport in microchannels.

In microfluidic systems at low Reynolds number, the flow field around a particle is assumed to maintain fore-aft symmetry, with fluid diverted by the presence of a particle, returning to its original streamline downstream. This current model considers particles as passive components of the system. However, we demonstrate that at finite Reynolds number, when inertia is taken into consideration, particles are not passive elements in the flow but significantly disturb and modify it. In response to the flow field, particles translate downstream while rotating. The combined effect of the flow of fluid around particles, particle rotation, channel confinement (i.e., particle dimensions approaching those of the channel), and finite fluid inertia creates a net recirculating flow perpendicular to the primary flow direction within straight channels that resembles the well-known Dean flow in curved channels. Significantly, the particle generating this flow remains laterally fixed as it translates downstream and only the fluid is laterally transferred. Therefore, as the particles remain inertially focused, operations can be performed around the particles in a way that is compatible with downstream assays such as flow cytometry. We apply this particle-induced transfer to perform fluid switching and mixing around rigid microparticles as well as deformable cells. This transport phenomenon, requiring only a simple channel geometry with no external forces to operate, offers a practical approach for fluid transfer at high flow rates with a wide range of applications, including sample preparation, flow reaction, and heat transfer.

Dynamic self-assembly and control of microfluidic particle crystals.

Engineered two-phase microfluidic systems have recently shown promise for computation, encryption, and biological processing. For many of these systems, complex control of dispersed-phase frequency and switching is enabled by nonlinearities associated with interfacial stresses. Introducing nonlinearity associated with fluid inertia has recently been identified as an easy to implement strategy to control two-phase (solid-liquid) microscale flows. By taking advantage of inertial effects we demonstrate controllable self-assembling particle systems, uncover dynamics suggesting a unique mechanism of dynamic self-assembly, and establish a framework for engineering microfluidic structures with the possibility of spatial frequency filtering. Focusing on the dynamics of the particle-particle interactions reveals a mechanism for the dynamic self-assembly process; inertial lift forces and a parabolic flow field act together to stabilize interparticle spacings that otherwise would diverge to infinity due to viscous disturbance flows. The interplay of the repulsive viscous interaction and inertial lift also allow us to design and implement microfluidic structures that irreversibly change interparticle spacing, similar to a low-pass filter. Although often not considered at the microscale, nonlinearity due to inertia can provide a platform for high-throughput passive control of particle positions in all directions, which will be useful for applications in flow cytometry, tissue engineering, and metamaterial synthesis.

Label-free cell separation and sorting in microfluidic systems.

Cell separation and sorting are essential steps in cell biology research and in many diagnostic and therapeutic methods. Recently, there has been interest in methods which avoid the use of biochemical labels; numerous intrinsic biomarkers have been explored to identify cells including size, electrical polarizability, and hydrodynamic properties. This review highlights microfluidic techniques used for label-free discrimination and fractionation of cell populations. Microfluidic systems have been adopted to precisely handle single cells and interface with other tools for biochemical analysis. We analyzed many of these techniques, detailing their mode of separation, while concentrating on recent developments and evaluating their prospects for application. Furthermore, this was done from a perspective where inertial effects are considered important and general performance metrics were proposed which would ease comparison of reported technologies. Lastly, we assess the current state of these technologies and suggest directions which may make them more accessible.