Publications

We study bacterial diffusion in disordered porous media. Interactions with obstacles, at unknown locations, make this problem challenging. We approach it by abstracting the environment to cell states with memoryless transitions. With this, we derive an effective diffusivity that agrees well with simulations in explicit geometries. The diffusivity is non-monotonic, and we solve the optimal run length. We also find a rescaling that causes all of the theory and simulations to collapse. Our results indicate that a small set of microscopic features captures bacterial diffusion in disordered media.

This paper is associated with a poster winner of a 2022 American Physical Society's Division of Fluid Dynamics (DFD) Milton van Dyke Award for work presented at the DFD Gallery of Fluid Motion. The original poster is available online at the Gallery of Fluid Motion.

A growing list of diverse biological systems and their equally diverse functionalities provides realizations of a paradigm of emergent behavior. In each of these biological systems, pervasive ensembles of weak, short-lived, spatially local interactions act autonomously to convey functionalities at larger spatial and temporal scales. In this article, a range of diverse systems and functionalities are presented in a cursory manner with literature citations for further details. Then two systems and their properties are discussed in more detail: yeast chromosome biology and human respiratory mucus

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of noninteracting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function f (φ,Pe) of the obstacle area fraction φ and Péclet number Pe, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media (Peφ 1), and its extension to denser media is obtained using stochastic simulations. As we explain, the model is also easily generalized to describe dispersion in three dimensions.

The propulsion of mammalian spermatozoa relies on the spontaneous periodic oscillation of their flagella. These oscillations are driven internally by the coordinated action of ATP-powered dynein motors that exert sliding forces between microtubule doublets, resulting in bending waves that propagate along the flagellum and enable locomotion. We present an integrated chemomechanical model of a freely swimming spermatozoon that uses a sliding-control model of the axoneme capturing the two-way feedback between motor kinetics and elastic deformations while accounting for detailed fluid mechanics around the moving cell. We develop a robust computational framework that solves a boundary integral equation for the passive sperm head alongside the slender-body equation for the deforming flagellum described as a geometrically nonlinear internally actuated Euler-Bernoulli beam, and captures full hydrodynamic interactions. Nonlinear simulations are shown to produce spontaneous oscillations with realistic beating patterns and trajectories, which we analyze as a function of sperm number and motor activity. Our results indicate that the swimming velocity does not vary monotonically with dynein activity, but instead displays two maxima corresponding to distinct modes of swimming, each characterized by qualitatively different wave forms and trajectories. Our model also provides an estimate for the efficiency of swimming, which peaks at low sperm number.

When a founder cell and its progeny divide with incomplete cytokinesis, a network forms in which each intercellular bridge corresponds to a past mitotic event. Such networks are required for gamete production in many animals, and different species have evolved diverse final network topologies. Although mechanisms regulating network assembly have been identified in particular organisms, we lack a quantitative framework to understand network assembly and inter-species variability. Motivated by cell networks responsible for oocyte production in invertebrates, where the final topology is typically invariant within each species, we devised a mathematical model for generating cell networks, in which each node is an oscillator and, after a full cycle, the node produces a daughter to which it remains connected. These cell cycle oscillations are transient and coupled via diffusion over the edges of the network. By variation of three biologically motivated parameters, our model generates nearly all such networks currently reported across invertebrates. Furthermore, small parameter variations can rationalize cases of intra-species variation. Because cell networks outside of the ovary often form less deterministically, we propose model generalizations to account for sources of stochasticity.

In the early phases of growth, resurgent epidemic waves of SARS-CoV-2 incidence have been characterised by localised outbreaks. Therefore, understanding the geographic dispersion of emerging variants at the start of an outbreak is key for situational public health awareness. Using telecoms data, we derived mobility networks describing the movement patterns between local authorities in England, which we have used to inform the spatial structure of a Bayesian BYM2 model. Surge testing interventions can result in spatio-temporal sampling bias, and we account for this by extending the BYM2 model to include a random effect for each timepoint in a given area. Simulated-scenario modelling and real-world analyses of each variant that became dominant in England were conducted using our BYM2 model at local authority level in England. Simulated datasets were created using a stochastic metapopulation model, with the transmission rates between different areas parameterised using telecoms mobility data. Different scenarios were constructed to reproduce real-world spatial dispersion patterns that could prove challenging to inference, and we used these scenarios to understand the performance characteristics of the BYM2 model. The model performed better than unadjusted test positivity in all the simulation-scenarios, and in particular when sample sizes were small, or data was missing for geographical areas. Through the analyses of emerging variant transmission across England, we found a reduction in the early growth phase geographic clustering of later dominant variants as England became more interconnected from early 2022 and public health interventions were reduced. We have also shown the recent increased geographic spread and dominance of variants with similar mutations in the receptor binding domain, which may be indicative of convergent evolution of SARS-CoV-2 variants.

Large cells often rely on cytoplasmic flows for intracellular transport, maintaining homeostasis, and positioning cellular components. Understanding the mechanisms of these flows is essential for gaining insights into cell function, developmental processes, and evolutionary adaptability. Here, we focus on a class of self-organized cytoplasmic stirring mechanisms that result from fluid-structure interactions between cytoskeletal elements at the cell cortex. Drawing inspiration from streaming flows in late-stage fruit fly oocytes, we propose an analytically tractable active carpet theory. This model deciphers the origins and three-dimensional spatio-temporal organization of such flows. Through a combination of simulations and weakly nonlinear theory, we establish the pathway of the streaming flow to its global attractor: a cell-spanning vortical twister. Our study reveals the inherent symmetries of this emergent flow, its low-dimensional structure, and illustrates how complex fluid-structure interaction aligns with classical solutions in Stokes flow. This framework can be easily adapted to elucidate a broad spectrum of self-organized, cortex-driven intracellular flows.

High wall shear stress (WSS) is associated with risk of atherosclerotic plaque rupture, but there are numerous gaps in validating ultrasound-derived measurements of the parameter. Two major challenges are using simple models of stenosis and only evaluating WSS along a single 2D plane. To overcome these limitations, a novel simulation framework is herein demonstrated. The framework first models volumetric blood flow in actual stenosed human carotid artery geometries (using an immersed interface method (IIM) fluid structure interaction solver) and calculates the associated WSS. Then, the framework projects the modeled blood flow onto scatterers in Field II simulations of its ultrasonic interrogation. Volumetric ultrasound vector Doppler (VD) imaging using an elevationally swept L7-4 linear array was simulated in Field II, with variations in transmit sequences and flow conditions. In a ~55% stenosed human carotid artery under 600 mL/min flow, Bland-Altman analysis showed that a 3-angle plane wave (PW) transmit scheme estimated WSS with 0.04±0.64 Pa error (bias ± 95% CI) relative to the IIM ground truth, whereas transmitting with 5 angles increased accuracy, but decreased precision to -0.01±1.07 Pa, due to aliasing. These findings illustrate that the simulation framework enables direct comparison of data acquisition and processing methods for efficient development, validation, and refinement of WSS estimation methods in realistic clinical environments.

In the 0 + 1 -dimensional imaginary-time path integral formulation of quantum impurity problems, the retarded action encodes the hybridization of the impurity with the bath. In this article, we explore the computational power of representing the retarded action as matrix product state (RAMPS). We focus on the challenging Kondo regime of the single-impurity Anderson model, where nonperturbative strong-correlation effects arise at very low energy scales. We demonstrate that the RAMPS approach reliably reaches the Kondo regime for a range of interaction strengths U, with a numerical error scaling as a weak power law with inverse temperature. We investigate the convergence behavior of the method with respect to bond dimension and time discretization by analyzing the error of local observables in the full interacting problem and find polynomial scaling in both parameters. Our results suggest that the RAMPS approach offers an alternative avenue for exploring quantum impurity problems, thereby setting the stage for future advancements in the method's capability to address more complex quantum impurity scenarios. Overall, our study contributes to the development of efficient and accurate non-wave-function-based tensor-network methods for quantum impurity problems.