Helicobacter pylori is a bacterium which infects the human stomach, where it is known to cause ulcers and stomach cancer. It has a helical cell body and swims using rotating flagellar filaments. I will discuss two of our recent projects involving this interesting bacterium. In order to colonize the stomach epithelium, it must swim through the gastric mucus. For a long time the helical shape of the cell body was thought to play a role in allowing it to corkscrew through the mucus gel, recent work showed that in fact H. pylori actively creates a heterogeneous complex medium as it swims through gastric mucus by generating ammonia that locally neutralizes the acidic gastric environment, turning nearby gel into a fluid pocket. Using simple physical models, we estimate the size of the fluid pocket by analyzing the coupled swimming and diffusion of ammonia, and show it is likely much larger than the bacterium. What is the role, then, of H. pylori's helical shape? Through imaging of swimming H. pylori and numerical modeling, we investigate how much advantage the helical shape can provide for swimming through Newtonian fluids. We find that it increases swimming speed by at most 15% relative to rod-shaped cells.

As observed by Poiseuille in 1836, a flexible object nearby a wall acquires lift as it deforms in the local shear, causing lateral movement away from the wall. This purely viscous effect is known as wall-induced migration. If the fluid layer that initially separates the object from the wall if very narrow, as is the case when a cell first enters the blood stream, it is challenging to resolve this phenomenon using grid-based methods, such as finite differences or finite volumes. I will describe a lubricated immersed boundary method that uses a subgrid model to resolve these lubrication layers and is able to capture wall-induced migration more accurately than the classical immersed boundary method. I will also discuss attempts to incorporate wall-induced migration into a complex fluid model.

Aligned suspensions of semi-flexible fibers play an integral role in many systems, including cell mitosis, the formation of microtubule asters, and hairy walls in both biological and micro-fluidic devices. We derive a continuum model for these suspensions based on local slender body theory, and use this model to investigate a variety of simple problems, including the rheology of these suspensions, buckling instabilities and the generation of streaming flows due to transport along the microtubules, and their use as valves (or flow rectifiers) in micro-fluidic applications.

Solids are typically simulated using a Lagrangian approach with a grid that moves with the material, whereas fluids are typically simulated using an Eulerian approach with a fixed spatial grid. In this talk, a fully Eulerian method for simulating solids will be presented, based on introducing a reference map variable to model finite-deformation constitutive relations. This allows for fluid-structure interactions and multiphase materials to be simulated using a single fixed grid, simplifying the coupling between phases. The technique is well-suited to a variety of problems in biomechanics, and it will be applied to a recent experimental study to investigate the role of mechanical interactions in tumor growth.

Some biological fluids, e.g. biofilms, are also growing. As such the realities of physical materials are important to function. In particular, function is often constrained by transport of soluble quantities, such as substrates and signals, into or out of the material. However, the combination of transport with reaction can lead to spatial heterogeneity and length scale formation within their structure, even without direct biological control. Examples include formation of active layers, formation of “external” structure (like fingering), and formation of “internal” structure (like lumps). Conversely, such pattern formation can impact function, particularly through transport but also through mechanics. Examples include formation of microenvironments and impacts on community level transport efficiency. Relatively simple mathematical models of biofilms, coupling growth with transport, will be used to illustrate the importance of physics in form and function of growing fluids.

The spontaneous emergence of large-scale coherent motions and patterns is a striking feature of many active soft matter systems and often results from long-ranged hydrodynamic interactions driven by internal active forces. In the first part of my talk, I will focus on bacterial suspensions, where hydrodynamic instabilities are known to arise due to the force dipoles exerted by motile microorganisms which couple to their orientations through the flows they generate. Using both models and simulations, I will analyze the interplay between these instabilities and geometrical confinement, where an apparent transition to superfluidity can be harnessed to drive unidirectional streaming flows. The second part of the talk will address the seemingly very different – yet perhaps related – case of chromosomal dynamics inside the nucleus during cell interphase, where experiments recently revealed coherent motion on large length and time scales. A model of chromatin dynamics as a confined polymer chain acted upon by molecular enzymes exerting force dipoles will be discussed, where hydrodynamic interactions emerge once again as a potential mechanism for coherent motions and large-scale self-organization.

Biogels are complex polymeric networks whose proper function is important to many physiological processes. For example, the proper function of mucus gel is important for airway clearance, reproduction, digestion, gastric protection, and disease protection and its failure is involved in cystic fibrosis, gastric ulcers, and reproductive dysfunction. Fibrin clots are crucial for prevention of bleeding after injury but inappropriate formation of clots is implicated in hearts attacks and strokes. There are three phases of biogel dynamics that are important to their biological function. These are their formation (i.e., blood clotting), degradation (clot dissolution), and swelling/deswelling kinetics (during mucin secretion/exocytosis, for example). The purpose of this talk is to describe recent advances in the study of the dynamics of fibrin clot formation. In particular, I will derive and discuss features of a new partial differential equation model that describes the growth of fibrin clots as a polymerization/gelation reaction. The solution of this PDE model gives insight into the branching structure of clots that are formed under various physiological conditions.

The gastric mucus layer is widely recognized to serve a protective function, shielding your stomach wall from the extremely low pH and digestive enzymes present in the stomach lumen. Often described as a "diffusion barrier," the mucus is believed to hinder the transport of small diffusive species from the stomach interior (lumen), to the wall (mucosa). However, there is no consensus on the mechanism by which the mucus layer hinders lumen-to-wall transport while allowing acid and enzymes secreted from the mucosa unimpeded transport to the lumen. Using physical principles, we develop a mathematical description of electro-diffusion within a two-phase gel, and use it to test physiological hypotheses that are beyond current experimental techniques. Furthermore, we explore what regulatory mechanisms are necessary to segregate an acidic stomach interior from a neutral stomach wall.

A genome is a complete copy of the entire set of genetic material that makeup a specific organism. Progress in live-cell microscopy had made clear that the genome is far from being a static information warehouse. Rather, it is a mechanically active entity that is constantly altering its shape. Chromosome motion can be described from polymer physics principles. Considering the organization of these long macromolecules and their constant exposure to random forces, understanding the mechanisms that alter their behavior requires integrating cell biology with physical principles that govern fluctuating chains. This talk focuses in applications of polymer theory to the studies of nuclear organization and function in yeast cells. In particular, we will show how cross-linking dynamics drive the formation of the nucleolus and how this organization resembles phase transitions observed in some hydrogel systems.

During early vertebrate embryogenesis, neural crest cells (NCCs) migrate in clusters from the neural tube to various target locations over long distances. Their collective migration is tightly regulated by environmental signals and intercellular interactions. Strikingly, NCC clusters are capable of spontaneously developing a persistent migration down migratory corridors in the absence of chemoattractants. To understand this phenomenon, we built a vertex-dynamics model that predicts the key modes of cell interactions—contact inhibition of locomotion (CIL) and co-attraction (COA)—through the modulation of Rho GTPase biochemistry. Using such a signaling-based model, as opposed to implementing hard-coded simulation rules, we find that CIL and COA conspire to suppress Rac1 activity, leading to the persistence of polarization (POP) of clustering cells and thus the spontaneous directional migration in the absence of chemical gradients.

We study edge fluctuations of a flat colloidal membrane comprised of a monolayer of aligned filamentous viruses. Experiments reveal that a peak in the spectrum of the in-plane edge fluctuations arises for sufficiently strong virus chirality. Accounting for internal liquid crystalline degrees of freedom by the length, curvature, and geodesic torsion of the edge, we calculate the spectrum of the edge fluctuations. The theory quantitatively describes the experimental data, demonstrating that chirality couples in-plane and out-of-plane edge fluctuations to produce the peak.

In this talk, I will discuss two related problems involving soft material particles in confined flows. The first involves the flow of vesicles and vesicle trains in capillary and square channel flows. We will develop a Bretherton-inspired theory for highly confined vesicles using lubrication and parallel flow theory to predict the mobility and extra pressure drop necessary to create flow in channels and tubes. This will be complemented with numerical simulations of vesicle flows throughout the entire range of confinement and comparison to new and existing experiments. In the second problem, we will develop a Boltzmann collision theory for predicting migration of RBCs (away from walls) at various hematocrits in the pressure-driven flow through channels. We will compare these predictions again to large scale suspension simulations of such flows, particularly examining the cross stream concentration distribution and the formation of the so-called Fahraeus Lindqvist layer. We shall focus on the differences between such theories in Couette flow and Poiseuille flow, as well as what physics is necessary to get quantitative agreement with the large scale simulations. In the last part of the talk, we will extend this theory to include rigid particle (e.g. platelet) margination into the FL layer in the RBC flow including adherence to the walls via a two-step kinetic process.

Micro-organisms can swim in a variety of environments, interacting with chemicals and other proteins in the fluid. Some of these extra proteins or cells may act as friction, possibly preventing or enhancing forward progression of swimmers. The homogenized fluid flow is assumed to be governed by the incompressible Brinkman equation, where a friction term with a resistance parameter represents a sparse array of obstacles. Representing the swimmers with a centerline approximation, we employ regularized fundamental solutions to investigate swimming speeds, trajectories, and interactions of swimmers. Although attraction of two swimmers is more efficient in the Stokes regime, we find that attraction does not occur for larger resistance.

Many microorganisms evolve in media that contain (bio)-polymers and/or solids; examples include cervical mucus, intestinal fluid, wet soil, and tissues. These so-called complex fluids often exhibit non-Newtonian rheological behavior such as shear-thinning viscosity and elasticity. In this talk, I will discuss recent experiments on the effects of fluid elasticity on the swimming behavior of microorganisms. Two main microorganisms are used, the green algae C. reinhardtii (a puller-type swimmer) and the bacterium E. coli (a pusher-type swimmer). For the case of pullers (C. reinhardtii), we find that fluid elasticity hinders the cell’s overall swimming speed but leads to an increase in the cell’s flagellum beating frequency. The beating kinematics and flagellum waveforms are also significantly modified by fluid elasticity. For the case of pushers (E. coli), the presence of even small amount of polymers in the medium suppresses the bacteria run-and-tumble mechanism. The bacteria spend more time in ballistic mode and swim faster as well. Single molecule experiments using fluorescently labeled DNA show that the flow fields generated by E. coli are able to stretch initially coiled polymer molecules and thus induce elastic stresses in fluid. These results demonstrate the intimate link between swimming kinematics and fluid rheology and that one can control the spreading and motility of microorganisms by tuning fluid properties.

Many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus, wet soil, and tissues. Yet the effects of fluid elasticity on microorganism motility are still poorly understood, partly because, in experiments the swimmer strokes (or gait) depend on the properties of the fluid medium, which obfuscates the mechanisms responsible for observed behavioral changes. In this study, we use experimental data on the gaits of Chlamydomonas reinhardtti swimming in Newtonian and viscoelastic fluids as inputs to numerical simulations that decouple the swimmer gait and fluid type. In viscoelastic fluids, cells employing Newtonian gaits swim faster, but cells with viscoelastic gaits are more efficient. Cells with Newtonian gaits generate larger fluid stresses and require more power to swim in a viscoelastic fluid, suggesting that the viscoelastic gait is an adaptation to power limitations. Generally, elastic stress accumulates at distal tips of flagella, which provides both forward and backward speed enhancements from an effective ``elastic inertia''. These findings can be explained by examining the orientation of the flagellar tip relative to the direction of motion, and we demonstrate that long thin objects in viscoelastic fluids accumulate more elastic stresses at tips when moving tangent to the swimming direction, compared to the normal direction. This stress/orientation relationship is reversed from viscous fluid theory. The importance of tip effects and orientation on the development of elastic stresses and the role of elastic inertia reshapes our understanding of how flagellated swimmers and cilia interact with viscoelastic fluid environments.

The role of passive body dynamics on the kinematics of swimming micro-organisms in complex fluids is investigated. Asymptotic analysis of small amplitude motions of a finite-length undulatory swimmer in a Stokes-Oldroyd-B fluid is used to predict shape changes that result as body elasticity and fluid elasticity are varied. Results from the analysis are compared with numerical simulations, and the numerically simulated shape changes agree with the analysis at both small and large amplitudes, even for strongly elastic flows. We compute a stroke-induced swimming speed that accounts for the shape changes, but not additional effects of fluid elasticity. Elastic-induced shape changes lead to larger amplitude strokes for sufficiently soft swimmers in a viscoelastic fluid, and these stroke boosts can lead to swimming speed-ups. However, for the strokes we examine, we find that additional effects of fluid elasticity generically result in a slow-down. Our high amplitude strokes in strongly elastic flows lead to a qualitatively different regime in which highly concentrated elastic stresses accumulate near swimmer bodies and dramatic slow-downs are seen.

Liquid crystals (LCs) are anisotropic, viscoelastic fluids that can be used to direct colloids into organized assemblies with unusual optical, mechanical, and electrical properties. In past studies, the colloids have been sufficiently rigid that their individual shapes and properties have not been strongly coupled to elastic stresses imposed by the LCs. We will discuss how soft colloids (micrometer-sized shells) behave in LCs. We reveal a sharing of strain between the LC and shells, resulting in formation of spindle-like shells and other complex shapes. These results hint at previously unidentified designs of reconfigurable soft materials with applications in sensing and biology. Numerical approaches to solving this complex fluid-structure interaction problem and related efforts relevant to biolocomotion will also be discussed.

We present a two-phase model of platelet aggregation in coronary-artery-sized blood vessels. The model tracks the number densities of three platelet populations, as well as the concentration of a platelet activating chemical. Bound platelets in a thrombus move in a velocity field different from that of the bulk fluid. Stresses produced by the elastic bonds act on the bound platelet material. Movement of the bound platelet material and that of the background fluid are coupled through an interphase drag and an incompressibility constraint. Computational results from the two-phase model indicate that through complicated fluid-structure interactions, the platelet thrombus can develop significant spatial inhomogeneities and that the amount of intraclot flow may greatly affect the growth, density, and stability of a thrombus.

Many biological fluids, like mucus or cytoplasm, have prominent viscoelastic properties. As a result, immersed and passive particles exhibit subdiffusive behavior, which is to say the variance of the particle displacement grows sublinearly with time. Passive microrheology, which records displacement of such particles and extract mechanical properties of the fluid environment, is premised on the idea that statistics of particles trajectories can reveal fundamental information about the fluid environment. We probe this hypothesis on two fronts. First, we present a Landau-Lifshitz-Navier-Stokes model of a passive particle advected in a viscoelastic fluid and show how the mean square displacement and first step auto-correlation in the increment process are related to those of the fluid's modes. Second, we address the uncertainty in reconstructing loss and storage moduli which characterize the elastic and viscous properties of the fluid from simulated data as an inverse problem.

We present a new method for sampling stochastic displacements in Brownian Dynamics (BD) simulations of colloidal scale particles. The method relies on a new formulation for Ewald summation of the Rotne-Prager-Yamakawa (RPY) tensor, which guarantees that the real-space and wave-space contributions to the tensor are independently symmetric and positive-definite for all possible particle configurations. Brownian displacements are drawn from a superposition of two independent samples: a wave-space (far-field or long-ranged) contribution, computed using techniques from fluctuating hydrodynamics and non-uniform Fast Fourier Transforms; and a real-space (near-field or short-ranged) correction, computed using a Krylov subspace method. The combined computational complexity of drawing these two independent samples scales linearly with the number of particles. The proposed method circumvents the super-linear scaling exhibited by all known iterative sampling methods applied directly to the RPY tensor that results from the power law growth of the condition number of tensor with the number of particles. Calculations for hard sphere dispersions and colloidal gels are illustrated and used to explore the role of microstructure on performance of the algorithm. In practice, the logarithmic part of the predicted scaling is not observed and the algorithm scales linearly for up to 4 million particles, obtaining speed ups of over an order of magnitude over existing iterative methods, and making the cost of computing Brownian displacements comparable the cost of computing deterministic displacements in BD simulations. A high-performance implementation employing non-uniform fast Fourier transforms implemented on graphics processing units and integrated with the software package HOOMD-blue is used for benchmarking.

Active particles are self-driven objects, biological or otherwise, which convert stored or ambient energy into systematic motion. The motion of small active particles in Newtonian fluids has received considerable attention, with interest ranging from phoretic propulsion to biological locomotion, whereas studies on active bodies immersed in complex fluids are comparatively scarce. A simple model for an active particle considers a sphere with an axisymmetric distribution of slip-velocities on its surface, known as the squirmer model. This model has been helpful in developing insights into the dynamics of both biological swimmers, like Volvox and Opalina, and synthetic self-propelling colloids. In this talk we present a theory for an active squirmer-type particle in a complex fluid, and then discuss the effects of viscoelasticity and shear-thinning rheology in the context of biological locomotion and the propulsion of colloidal Janus particles.

We discuss our recent advances in developing meshfree methods based on radial basis functions (RBFs) for numerically solving biologically relevant partial differential equations (PDEs) on surfaces. The primary advantages of these methods are 1) they only require a set of nodes on the surface of interest and the corresponding normal vectors; 2) they can give high orders of accuracy; and 3) they algorithmically accessible. Commonly perceived disadvantages are that these methods are computationally expensive and not well suited for advection-dominated problems. A goal of this talk will be to demonstrate how to overcome these issues.

We present a robust and scalable meshfree framework for solving partial differential equations on irregular domains and surfaces motivated by biological applications. First, we present O(N) methods for generating node sets on irregular domains and surfaces based on meshfree parametric geometric models based on spectrally-accurate Radial Basis Function (RBF) interpolation. Then, we demonstrate the solution of some model problems using high-order RBF-based finite difference (RBF-FD) methods. This talk summarizes joint work with Grady Wright, Aaron Fogelson, Mike Kirby and others.

Cell Mitosis is a fundamental process in eukaryotic cell reproduction, during which parent cell’s nucleus first dissembles leading to DNA and chromosome replication, then chromosomes migrate to new locations within the parent cell to form offspring nuclei which triggers cytokinesis leading to the formation of two offspring cells eventually. In this presentation, we develop a full 3D multiphase hydrodynamic model to study the fundamental mitotic mechanism in cytokinesis, the final stage of mitosis. The model describes the cortical layer, a cytoplasmic layer next to the cell membrane rich in F-actins and myosins, as an active liquid crystal system and integrate the extra cellular matrix material and the nucleus into a multiphase complex fluid mixture. With the novel active matter model built in the system, our 3D simulations show very good qualitative agreement with the experimental obtained images. The hydrodynamic model together with the GPU based numerical solver provides an effective tool for studying cell mitosis theoretically and computationally.

Blood is a suspension of objects of various shapes, sizes and mechanical properties, whose distribution during flow is important in many contexts. Red blood cells tend to migrate toward the center of a blood vessel, leaving a cell-free layer at the vessel wall, while white blood cells and platelets are preferentially found near the walls, a phenomenon called margination that is critical for the physiological responses of inflammation and hemostasis. Additionally, drug delivery particles in the bloodstream also undergo margination – the influence of these phenomena on the efficacy of such particles is unknown. In this talk a mechanistic theory is developed to describe segregation in blood and other confined multicomponent suspensions. It incorporates the two key phenomena arising in these systems at low Reynolds number: hydrodynamic pair collisions and wall-induced migration. The theory predicts that the cell-free layer thickness follows a master curve relating it in a specific way to confinement ratio and volume fraction. Results from experiments and detailed simulations with different parameters (flexibility of different components in the suspension, viscosity ratio, confinement, among others) collapse onto the same curve. In simple shear flow, several regimes of segregation arise, depending on the value of a "margination parameter" M. Most importantly, there is a critical value of M below which a sharp "drainage transition" occurs: one component is completely depleted from the bulk flow to the vicinity of the walls. Direct simulations also exhibit this transition as the size or flexibility ratio of the components changes. Results are presented for both Couette and plane Poiseuille flow. Experiments performed in the laboratory of Wilbur Lam indicate the physiological and clinical importance of these observations.