Compressive stress triggers fibroblasts spreading over cancer cells to generate carcinoma in situ organization.

At the early stage of tumor progression, fibroblasts are located at the outer edges of the tumor, forming an encasing layer around it. In this work, we have developed a 3D in vitro model where fibroblasts' layout resembles the structure seen in carcinoma in situ. We use a microfluidic encapsulation technology to co-culture fibroblasts and cancer cells within hollow, permeable, and elastic alginate shells. We find that in the absence of spatial constraint, fibroblasts and cancer cells do not mix but segregate into distinct aggregates composed of individual cell types. However, upon confinement, fibroblasts enwrap cancer cell spheroid. Using a combination of biophysical methods and live imaging, we find that buildup of compressive stress is required to induce fibroblasts spreading over the aggregates of tumor cells. We propose that compressive stress generated by the tumor growth might be a mechanism that prompts fibroblasts to form a capsule around the tumor.

From disks to channels: dynamics of active nematics confined to an annulus.

Confinement can be used to systematically tame turbulent dynamics occurring in active fluids. Although periodic channels are the simplest geometries to study confinement numerically, the corresponding experimental realizations require closed racetracks. Here, we computationally study 2D active nematics confined to such a geometry-an annulus. By systematically varying the annulus inner radius and channel width, we bridge the behaviors observed in the previously studied asymptotic limits of the annulus geometry: a disk and an infinite channel. We identify new steady-state behaviors, which reveal the influence of boundary curvature and its interplay with confinement. We also show that, below a threshold inner radius, the dynamics are insensitive to the presence of the inner hole. We explain this insensitivity through a simple scaling analysis. Our work sheds further light on design principles for using confinement to control the dynamics of active nematics.

IDENTIFIABILITY OF INFECTION MODEL PARAMETERS EARLY IN AN EPIDEMIC.

It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series I(t) during the entire epidemic, the parameters can be successfully estimated. In this article we observe that estimation will fail in practice if only infected case data during the early part of the epidemic (prepeak) is available. This fact can be explained using a well-known phenomenon called dynamical compensation. We use this concept to derive an unidentifiability manifold in the parameter space of SEIR that consists of parameters indistinguishable from I(t) early in the epidemic. Thus, identifiability depends on the extent of the system trajectory that is available for observation. Although the existence of the unidentifiability manifold obstructs the ability to exactly determine the parameters, we suggest that it may be useful for uncertainty quantification purposes. A variant of SEIR recently proposed for COVID-19 modeling is also analyzed, and an analogous unidentifiability surface is derived.

Self-mixing in microtubule-kinesin active fluid from nonuniform to uniform distribution of activity.

Active fluids have applications in micromixing, but little is known about the mixing kinematics of systems with spatiotemporally-varying activity. To investigate, UV-activated caged ATP is used to activate controlled regions of microtubule-kinesin active fluid and the mixing process is observed with fluorescent tracers and molecular dyes. At low Péclet numbers (diffusive transport), the active-inactive interface progresses toward the inactive area in a diffusion-like manner that is described by a simple model combining diffusion with Michaelis-Menten kinetics. At high Péclet numbers (convective transport), the active-inactive interface progresses in a superdiffusion-like manner that is qualitatively captured by an active-fluid hydrodynamic model coupled to ATP transport. Results show that active fluid mixing involves complex coupling between distribution of active stress and active transport of ATP and reduces mixing time for suspended components with decreased impact of initial component distribution. This work will inform application of active fluids to promote micromixing in microfluidic devices.

Pattern formation in a four-ring reaction-diffusion network with heterogeneity.

In networks of nonlinear oscillators, symmetries place hard constraints on the system that can be exploited to predict universal dynamical features and steady states, providing a rare generic organizing principle for far-from-equilibrium systems. However, the robustness of this class of theories to symmetry-disrupting imperfections is untested in free-running (i.e., non-computer-controlled) systems. Here, we develop a model experimental reaction-diffusion network of chemical oscillators to test applications of the theory of dynamical systems with symmeries in the context of self-organizing systems relevant to biology and soft robotics. The network is a ring of four microreactors containing the oscillatory Belousov-Zhabotinsky reaction coupled to nearest neighbors via diffusion. Assuming homogeneity across the oscillators, theory predicts four categories of stable spatiotemporal phase-locked periodic states and four categories of invariant manifolds that guide and structure transitions between phase-locked states. In our experiments, we observed that three of the four phase-locked states were displaced from their idealized positions and, in the ensemble of measurements, appeared as clusters of different shapes and sizes, and that one of the predicted states was absent. We also observed the predicted symmetry-derived synchronous clustered transients that occur when the dynamical trajectories coincide with invariant manifolds. Quantitative agreement between experiment and numerical simulations is found by accounting for the small amount of experimentally determined heterogeneity in intrinsic frequency. We further elucidate how different patterns of heterogeneity impact each attractor differently through a bifurcation analysis. We show that examining bifurcations along invariant manifolds provides a general framework for developing intuition about how chemical-specific dynamics interact with topology in the presence of heterogeneity that can be applied to other oscillators in other topologies.

Exact Coherent Structures and Phase Space Geometry of Preturbulent 2D Active Nematic Channel Flow.

Confined active nematics exhibit rich dynamical behavior, including spontaneous flows, periodic defect dynamics, and chaotic "active turbulence." Here, we study these phenomena using the framework of exact coherent structures, which has been successful in characterizing the routes to high Reynolds number turbulence of passive fluids. Exact coherent structures are stationary, periodic, quasiperiodic, or traveling wave solutions of the hydrodynamic equations that, together with their invariant manifolds, serve as an organizing template of the dynamics. We compute the dominant exact coherent structures and connecting orbits in a preturbulent active nematic channel flow, which enables a fully nonlinear but highly reduced-order description in terms of a directed graph. Using this reduced representation, we compute instantaneous perturbations that switch the system between disparate spatiotemporal states occupying distant regions of the infinite-dimensional phase space. Our results lay the groundwork for a systematic means of understanding and controlling active nematic flows in the moderate- to high-activity regime.

Multiscale Microtubule Dynamics in Active Nematics.

In microtubule-based active nematics, motor-driven extensile motion of microtubule bundles powers chaotic large-scale dynamics. We quantify the interfilament sliding motion both in isolated bundles and in a dense active nematic. The extension speed of an isolated microtubule pair is comparable to the molecular motor stepping speed. In contrast, the net extension in dense 2D active nematics is significantly slower; the interfilament sliding speeds are widely distributed about the average and the filaments exhibit both contractile and extensile relative motion. These measurements highlight the challenge of connecting the extension rate of isolated bundles to the multimotor and multifilament interactions present in a dense 2D active nematic. They also provide quantitative data that is essential for building multiscale models.

Pan-African evolution of within- and between-country COVID-19 dynamics.

The coronavirus disease 2019 (COVID-19) pandemic is heterogeneous throughout Africa and threatening millions of lives. Surveillance and short-term modeling forecasts are critical to provide timely information for decisions on control strategies. We created a strategy that helps predict the country-level case occurrences based on cases within or external to a country throughout the entire African continent, parameterized by socioeconomic and geoeconomic variations and the lagged effects of social policy and meteorological history. We observed the effect of the Human Development Index, containment policies, testing capacity, specific humidity, temperature, and landlocked status of countries on the local within-country and external between-country transmission. One-week forecasts of case numbers from the model were driven by the quality of the reported data. Seeking equitable behavioral and social interventions, balanced with coordinated country-specific strategies in infection suppression, should be a continental priority to control the COVID-19 pandemic in Africa.

Partition, Reaction, and Diffusion Coefficients of Bromine in Elastomeric Polydimethylsiloxane.

Experiments and models were used to determine the extent to which aqueous bromine permeated into, and reacted with, the elastomer polydimethylsiloxane (PDMS). Thin films of PDMS were immersed in bromine water, and the absorbance of bromine in the aqueous phase was measured as a function of time. Kinetics were studied as a function of mass and thickness of the immersed PDMS films. We attribute the decrease of bromine in solution to permeation into PDMS, followed by a combination of diffusion, reversible binding, and an irreversible reaction with PDMS. In order to decouple the irreversible reaction from the reversible processes, kinetics were also studied for bromine-passivated PDMS films. Fits of the models to a variety of experiments yielded the partition coefficient of bromine between the water and PDMS phases, the diffusion constant of bromine in PDMS, the irreversible reaction constant between bromine and PDMS, the molar concentration of the reactive sites within PDMS, and the on and off rates of reversible binding of bromine to PDMS. Developing a quantitative reaction-diffusion model accounting for the transport of bromine through PDMS is necessary for the design of microfluidic devices fabricated using PDMS, which are used in experimental studies of the nonlinear dynamics of reaction-diffusion networks containing Belousov-Zhabotinsky chemical oscillators.

A Generalized Unscented Transformation for Probability Distributions.

The unscented transform uses a weighted set of samples called sigma points to propagate the means and covariances of nonlinear transformations of random variables. However, unscented transforms developed using either the Gaussian assumption or a minimum set of sigma points typically fall short when the random variable is not Gaussian distributed and the nonlinearities are substantial. In this paper, we develop the generalized unscented transform (GenUT), which uses 2n+1 sigma points to accurately capture up to the diagonal components of the skewness and kurtosis tensors of most probability distributions. Constraints can be analytically enforced on the sigma points while guaranteeing at least second-order accuracy. The GenUT uses the same number of sigma points as the original unscented transform while also being applicable to non-Gaussian distributions, including the assimilation of observations in the modeling of infectious diseases such as coronavirus (SARS-CoV-2) causing COVID-19.

Machine learning forecasting of active nematics.

Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.

Optimal Control of Active Nematics.

In this work we present the first systematic framework to sculpt active nematic systems, using optimal control theory and a hydrodynamic model of active nematics. We demonstrate the use of two different control fields, (i) applied vorticity and (ii) activity strength, to shape the dynamics of an extensile active nematic that is confined to a disk. In the absence of control inputs, the system exhibits two attractors, clockwise and counterclockwise circulating states characterized by two co-rotating topological +1/2 defects. We specifically seek spatiotemporal inputs that switch the system from one attractor to the other; we also examine phase-shifting perturbations. We identify control inputs by optimizing a penalty functional with three contributions: total control effort, spatial gradients in the control, and deviations from the desired trajectory. This work demonstrates that optimal control theory can be used to calculate nontrivial inputs capable of restructuring active nematics in a manner that is economical, smooth, and rapid, and therefore will serve as a guide to experimental efforts to control active matter.

Tracking and predicting the African COVID-19 pandemic.

The ongoing coronavirus disease 2019 (COVID-19) pandemic is heterogeneous throughout Africa and threatening millions of lives. Surveillance and short-term modeling forecasts are critical to provide timely information for decisions on control strategies. We use a model that explains the evolution of the COVID-19 pandemic over time in the entire African continent, parameterized by socioeconomic and geoeconomic variations and the lagged effects of social policy and meteorological history. We observed the effect of the human development index, containment policies, testing capacity, specific humidity, temperature and landlocked status of countries on the local within-country and external between-country transmission. One week forecasts of case numbers from the model were driven by the quality of the reported data. Seeking equitable behavioral and social interventions, balanced with coordinated country-specific strategies in infection suppression, should be a continental priority to control the COVID-19 pandemic in Africa.

Dynamics of Reaction-Diffusion Oscillators in Star and other Networks with Cyclic Symmetries Exhibiting Multiple Clusters.

We experimentally and theoretically investigate the dynamics of inhibitory coupled self-driven oscillators on a star network in which a single central hub node is connected to k peripheral arm nodes. The system consists of water-in-oil Belousov-Zhabotinsky ∼100 µm emulsion drops contained in storage wells etched in silicon wafers. We observed three dynamical attractors by varying the number of arms in the star graph and the coupling strength: (i) unlocked, uncorrelated phase shifts between all oscillators; (ii) locked, arm hubs synchronized in phase with a k-dependent phase shift between the arm and central hub; and (iii) center silent, a central hub stopped oscillating and the arm hubs oscillated without synchrony. We compare experiment to theory. For case (ii), we identified a logarithmic dependence of the phase shift on star degree, and were able to discriminate between contributions to the phase shift arising from star topology and oscillator chemistry.

Self-organized dynamics and the transition to turbulence of confined active nematics.

We study how confinement transforms the chaotic dynamics of bulk microtubule-based active nematics into regular spatiotemporal patterns. For weak confinements in disks, multiple continuously nucleating and annihilating topological defects self-organize into persistent circular flows of either handedness. Increasing confinement strength leads to the emergence of distinct dynamics, in which the slow periodic nucleation of topological defects at the boundary is superimposed onto a fast procession of a pair of defects. A defect pair migrates toward the confinement core over multiple rotation cycles, while the associated nematic director field evolves from a distinct double spiral toward a nearly circularly symmetric configuration. The collapse of the defect orbits is punctuated by another boundary-localized nucleation event, that sets up long-term doubly periodic dynamics. Comparing experimental data to a theoretical model of an active nematic reveals that theory captures the fast procession of a pair of [Formula: see text] defects, but not the slow spiral transformation nor the periodic nucleation of defect pairs. Theory also fails to predict the emergence of circular flows in the weak confinement regime. The developed confinement methods are generalized to more complex geometries, providing a robust microfluidic platform for rationally engineering 2D autonomous flows.

Insensitivity of active nematic liquid crystal dynamics to topological constraints.

Confining a liquid crystal imposes topological constraints on the orientational order, allowing global control of equilibrium systems by manipulation of anchoring boundary conditions. In this article, we investigate whether a similar strategy allows control of active liquid crystals. We study a hydrodynamic model of an extensile active nematic confined in containers, with different anchoring conditions that impose different net topological charges on the nematic director. We show that the dynamics are controlled by a complex interplay between topological defects in the director and their induced vortical flows. We find three distinct states by varying confinement and the strength of the active stress: A topologically minimal state, a circulating defect state, and a turbulent state. In contrast to equilibrium systems, we find that anchoring conditions are screened by the active flow, preserving system behavior across different topological constraints. This observation identifies a fundamental difference between active and equilibrium materials.

Engineering reaction-diffusion networks with properties of neural tissue.

We present an experimental system of networks of coupled non-linear chemical reactors, which we theoretically model within a reaction-diffusion framework. The networks consist of patterned arrays of diffusively coupled nanoliter-scale reactors containing the Belousov-Zhabotinsky (BZ) reaction. Microfluidic fabrication techniques are developed that provide the ability to vary the network topology and the reactor coupling strength and offer the freedom to choose whether an arbitrary reactor is inhibitory or excitatory coupled to its neighbor. This versatile experimental and theoretical framework can be used to create a wide variety of chemical networks. Here we design, construct and characterize chemical networks that achieve the complexity of central pattern generators (CPGs), which are found in the autonomic nervous system of a variety of organisms.

Controlling nanowire growth through electric field-induced deformation of the catalyst droplet.

Semiconductor nanowires with precisely controlled structure, and hence well-defined electronic and optical properties, can be grown by self-assembly using the vapour-liquid-solid process. The structure and chemical composition of the growing nanowire is typically determined by global parameters such as source gas pressure, gas composition and growth temperature. Here we describe a more local approach to the control of nanowire structure. We apply an electric field during growth to control nanowire diameter and growth direction. Growth experiments carried out while imaging within an in situ transmission electron microscope show that the electric field modifies growth by changing the shape, position and contact angle of the catalytic droplet. This droplet engineering can be used to modify nanowires into three dimensional structures, relevant to a range of applications, and also to measure the droplet surface tension, important for quantitative development of strategies to control nanowire growth.

Ellipsoidal particles encapsulated in droplets.

Using hydrodynamic focusing, we encapsulated polystyrene ellipsoidal particles in water droplets dispersed in an immiscible, continuous phase of light mineral oil. The axisymmetric shape of the drop partially encapsulating an elongated particle was computed as a function of the particle aspect ratio, droplet volume, and contact angle. When the droplet volume is within a certain range, pinned (partially engulfed) and fully engulfed equilibrium configurations coexist. Partial encapsulation may be preferred (has a lower free energy) even when the droplet's volume is sufficient to fully engulf the particle. The co-existence of multiple equilibrium states suggests possible hysteretic encapsulation behavior. We also estimate the axial capillary force exerted by the droplet on the particle as a function of volume and contact angle. The theoretical predictions are critically compared with experimental observations.

Model of ciliary clearance and the role of mucus rheology.

It has been observed that the transportability of mucus by cilial mats is dependent on the rheological properties of the mucus. Mucus is a non-Newtonian fluid that exhibits a plethora of phenomena such as stress relaxation, tensile stresses, shear thinning, and yielding behavior. These observations motivate the analysis in this paper that considers the first two attributes in order to construct a transport model. The model developed here assumes that the mucus is transported as a rigid body, the metachronal wave exhibits symplectic behavior, that the mucus is thin compared to the metachronal wavelength, and that the effects of individual cilia can be lumped together to impart an average strain to the mucus during contact. This strain invokes a stress in the mucus, whose non-Newtonian rheology creates tensile forces that persist into unsheared regions and allow the unsupported mucus to move as a rigid body whereas a Newtonian fluid would retrograde. This work focuses primarily on the Doi-Edwards model but results are generalized to the Jeffrey's and Maxwell fluids as well. The model predicts that there exists an optimal mucus rheology that maximizes the shear stress imparted to the mucus by the cilia for a given cilia motion. We propose that this is the rheology that the body strives for in order to minimize energy consumption. Predicted optimal rheologies are consistent with results from previous experimental studies when reasonable model parameters are chosen.