A Kinetic Model for Semidilute Bacterial Suspensions

Suspensions of self-propelled microscopic particles, such as swimming bacteria, exhibit collective motion leading to remarkable experimentally observable macroscopic properties. Rigorous mathematical analysis of this emergent behavior can provide significant insight into the mechanisms behind these experimental observations; however, there are many theoretical questions remaining unanswered. In this paper, we study a coupled PDE/ODE system first introduced in the physics literature and used to investigate numerically the effective viscosity of a bacterial suspension. We then examine the kinetic theory associated with the coupled system, which is designed to capture the long-time behavior of a Stokesian suspension of point force dipoles (infinitesimal spheroids representing self-propelled particles) with Lennard-Jones--type repulsion. A planar shear background flow is imposed on the suspension through the novel use of Lees--Edwards quasi-periodic boundary conditions applied to a representative volume. We show the existence and uniqueness of solutions for all time to the equations of motion for particle configurations---dipole orientations and relative positions. This result follows from first establishing the regularity of the solution to the fluid equations. The existence and uniqueness result allows us to define the Liouville equation for the probability density of configurations. We show that this probability density defines the average bulk stress in the suspension underlying the definition of many macroscopic quantities of interest, in particular the effective viscosity. These effective properties are determined by microscopic interactions highlighting the multiscale nature of this work

A Kinetic Model for Semidilute Bacterial Suspensions

Suspensions of self-propelled microscopic particles, such as swimming bacteria, exhibit collective motion leading to remarkable experimentally observable macroscopic properties. Rigorous mathematical analysis of this emergent behavior can provide significant insight into the mechanisms behind these experimental observations; however, there are many theoretical questions remaining unanswered. In this paper, we study a coupled PDE/ODE system first introduced in the physics literature and used to investigate numerically the effective viscosity of a bacterial suspension. We then examine the kinetic theory associated with the coupled system, which is designed to capture the long-time behavior of a Stokesian suspension of point force dipoles (infinitesimal spheroids representing self-propelled particles) with Lennard-Jones--type repulsion. A planar shear background flow is imposed on the suspension through the novel use of Lees--Edwards quasi-periodic boundary conditions applied to a representative volume. We show the existence and uniqueness of solutions for all time to the equations of motion for particle configurations---dipole orientations and relative positions. This result follows from first establishing the regularity of the solution to the fluid equations. The existence and uniqueness result allows us to define the Liouville equation for the probability density of configurations. We show that this probability density defines the average bulk stress in the suspension underlying the definition of many macroscopic quantities of interest, in particular the effective viscosity. These effective properties are determined by microscopic interactions highlighting the multiscale nature of this work

Viscosity of Bacterial Suspensions: Hydrodynamic Interactions and Self-induced Noise

The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further increases of the concentration yield an increase of the viscosity. We derive an explicit asymptotic formula for the effective viscosity in terms of known physical parameters and show that hydrodynamic interactions are manifested as self-induced noise in the absence of any explicit stochasticity in the system

Viscosity of Bacterial Suspensions: Hydrodynamic Interactions and Self-induced Noise

The viscosity of a suspension of swimming bacteria is investigated analytically and numerically. We propose a simple model that allows for efficient computation for a large number of bacteria. Our calculations show that long-range hydrodynamic interactions, intrinsic to self-locomoting objects in a viscous fluid, result in a dramatic reduction of the effective viscosity. In agreement with experiments on suspensions of Bacillus subtilis, we show that the viscosity reduction is related to the onset of large-scale collective motion due to interactions between the swimmers. The simulations reveal that the viscosity reduction occurs only for relatively low concentrations of swimmers: Further increases of the concentration yield an increase of the viscosity. We derive an explicit asymptotic formula for the effective viscosity in terms of known physical parameters and show that hydrodynamic interactions are manifested as self-induced noise in the absence of any explicit stochasticity in the system

Effective Viscosity of Dilute Bacterial Suspensions: A Two-Dimensional Model

Suspensions of self-propelled particles are studied in the framework of two-dimensional (2D) Stokesean hydrodynamics. A formula is obtained for the effective viscosity of such suspensions in the limit of small concentrations. This formula includes the two terms that are found in the 2D version of Einstein's classical result for passive suspensions. To this, the main result of the paper is added, an additional term due to self-propulsion which depends on the physical and geometric properties of the active suspension. This term explains the experimental observation of a decrease in effective viscosity in active suspensions.Comment: 15 pages, 3 figures, submitted to Physical Biolog

The Contribution of Accessory Toxins of Vibrio cholerae O1 El Tor to the Proinflammatory Response in a Murine Pulmonary Cholera Model

The contribution of accessory toxins to the acute inflammatory response to Vibrio cholerae was assessed in a murine pulmonary model. Intranasal administration of an El Tor O1 V. cholerae strain deleted of cholera toxin genes (ctxAB) caused diffuse pneumonia characterized by infiltration of PMNs, tissue damage, and hemorrhage. By contrast, the ctxAB mutant with an additional deletion in the actin-cross-linking repeats-in-toxin (RTX) toxin gene (rtxA) caused a less severe pathology and decreased serum levels of proinflammatory molecules interleukin (IL)-6 and murine macrophage inflammatory protein (MIP)-2. These data suggest that the RTX toxin contributes to the severity of acute inflammatory responses. Deletions within the genes for either hemagglutinin/protease (hapA) or hemolysin (hlyA) did not significantly affect virulence in this model. Compound deletion of ctxAB, hlyA, hapA, and rtxA created strain KFV101, which colonized the lung but induced pulmonary disease with limited inflammation and significantly reduced serum titers of IL-6 and MIP-2. 100% of mice inoculated with KFV101 survive, compared with 20% of mice inoculated with the ctxAB mutant. Thus, the reduced virulence of KFV101 makes it a prototype for multi-toxin deleted vaccine strains that could be used for protection against V. cholerae without the adverse effects of the accessory cholera toxins

A community-based approach to trials of aerobic exercise in aging and Alzheimer’s disease

The benefits of exercise for aging have received considerable attention in both the popular and academic press. The putative benefits of exercise for maximizing cognitive function and supporting brain health have great potential for combating Alzheimer’s disease (AD). Aerobic exercise offers a low-cost, low-risk intervention that is widely available and may have disease modifying effects. Demonstrating aerobic exercise alters the AD process would have enormous public health implications. The purpose of this paper is to a report the protocol of a current, community-based pilot study of aerobic exercise for AD to guide future investigation. This manuscript provides 1) an overview of possible benefits of exercise in those with dementia, 2) a rationale and recommendations for implementation of a community-based approach, 3) recommendation for implementation of similar study protocols, 4) unique challenges in conducting an exercise trial in AD

Linkage analyses in Caribbean Hispanic families identify novel loci associated with familial late-onset Alzheimer's disease

INTRODUCTION: We performed linkage analyses in Caribbean Hispanic families with multiple late-onset Alzheimer's disease (LOAD) cases to identify regions that may contain disease causative variants. METHODS: We selected 67 LOAD families to perform genome-wide linkage scan. Analysis of the linked regions was repeated using the entire sample of 282 families. Validated chromosomal regions were analyzed using joint linkage and association. RESULTS: We identified 26 regions linked to LOAD (HLOD ≥3.6). We validated 13 of the regions (HLOD ≥2.5) using the entire family sample. The strongest signal was at 11q12.3 (rs2232932: HLODmax = 4.7, Pjoint = 6.6 × 10(-6)), a locus located ∼2 Mb upstream of the membrane-spanning 4A gene cluster. We additionally identified a locus at 7p14.3 (rs10255835: HLODmax = 4.9, Pjoint = 1.2 × 10(-5)), a region harboring genes associated with the nervous system (GARS, GHRHR, and NEUROD6). DISCUSSION: Future sequencing efforts should focus on these regions because they may harbor familial LOAD causative mutations