A 3D Motile Rod-Shaped Monotrichous Bacterial Model

Electrodeformation of Vesicles Suspended in a Liquid Medium

Deformation of flexible vesicles suspended in a fluid medium due to an applied electric field can provide valuable insight into deformation dynamics at a very small scale. In an electric field, the response of the vesicle membrane is strongly influenced by the conductivity of surrounding fluid, vesicle size and shape, and the magnitude of applied field. We studied the electrodeformation of vesicles immersed in a fluid media under a DC electric field. An immersed interface method is used to solve the electric field over the domain with conductive or non-conductive vesicles while an immersed boundary method is employed to solve fluid flow, fluid-solid interaction, membrane mechanics and vesicle deformation. Initial force analysis on the membrane surface reveals almost linear influence of vesicle size, but the vesicle size does not affect the long-term deformation which is consistent with experimental evidence. Highly nonlinear effect of the applied field as well as the conductivity ratios inside and outside of the vesicle are observed. Results also point towards an early linear deformation regime followed by an equilibrium stage for the membranes. Modeling results suggest that electrodeforming vesicles can create unique external flows for different conductivity ratios. Moreover, significant influence of the initial aspect ratio of the vesicle on the force distribution is observed across a range of conductivity ratios.

Hybrid finite difference/finite element immersed boundary method

The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach.

Modeling polymorphic transformation of rotating bacterial flagella in a viscous fluid

The helical flagella that are attached to the cell body of bacteria such as Escherichia coli and Salmonella typhimurium allow the cell to swim in a fluid environment. These flagella are capable of polymorphic transformation in that they take on various helical shapes that differ in helical pitch, radius, and chirality. We present a mathematical model of a single flagellum described by Kirchhoff rod theory that is immersed in a fluid governed by Stokes equations. We perform numerical simulations to demonstrate two mechanisms by which polymorphic transformation can occur, as observed in experiments. First, we consider a flagellar filament attached to a rotary motor in which transformations are triggered by a reversal of the direction of motor rotation [L. Turner et al., J. Bacteriol. 182, 2793 (2000)10.1128/JB.182.10.2793-2801.2000]. We then consider a filament that is fixed on one end and immersed in an external fluid flow [H. Hotani, J. Mol. Biol. 156, 791 (1982)10.1016/0022-2836(82)90142-5]. The detailed dynamics of the helical flagellum interacting with a viscous fluid is discussed and comparisons with experimental and theoretical results are provided.

Swimming behavior of Pseudomonas aeruginosa studied by holographic 3D tracking

Holographic 3D tracking was applied to record and analyze the swimming behavior of Pseudomonas aeruginosa. The obtained trajectories allow to qualitatively and quantitatively analyze the free swimming behavior of the bacterium. This can be classified into five distinct swimming patterns. In addition to the previously reported smooth and oscillatory swimming motions, three additional patterns are distinguished. We show that Pseudomonas aeruginosa performs helical movements which were so far only described for larger microorganisms. Occurrence of the swimming patterns was determined and transitions between the patterns were analyzed.

Modeling and simulation of dielectrophoretic particle-particle interactions and assembly

Electric field induced particle-particle interactions and assembly are of great interest due to their useful applications in micro devices. The behavior of particles becomes more complex if multiple particles interact with each other at the same time. In this paper, we present a numerical study of two dimensional DC dielectrophoresis based particle-particle interactions and assembly for multiple particles using a hybrid immersed interface-immersed boundary method. The immersed interface method is employed to capture the physics of electrostatics in a fluid media with suspended particles. Particle interaction based dielectrophoretic forces are obtained using Maxwell's stress tensor without any boundary or volume integration. This electrostatic force distribution mimics the actual physics of the immersed particles in a fluid media. The corresponding particle response and hydrodynamic interactions are captured through the immersed boundary method by solving the transient Navier-Stokes equations. The interaction and assembly of multiple electrically similar and dissimilar particles are studied for various initial positions and orientations. Numerical results show that in a fluid media, similar particles form a chain parallel to the applied electric field, whereas dissimilar particles form a chain perpendicular to the applied electric field. Irrespective of initial position and orientation, particles first align themselves parallel or perpendicular to the electric field depending on the similarity or dissimilarity of particles. The acceleration and deceleration of particles are also observed and analyzed at different phases of the assembly process. This comprehensive study can be used to explain the multiple particle interaction and assembly phenomena observed in experiments.

Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models.