Effective viscosity of microswimmer suspensions

The measurement of a quantitative and macroscopic parameter to estimate the global motility of a large population of swimming biological cells is a challenge Experiments on the rheology of active suspensions have been performed. Effective viscosity of sheared suspensions of live unicellular motile micro-algae (\textit{Chlamydomonas Reinhardtii}) is far greater than for suspensions containing the same volume fraction of dead cells and suspensions show shear thinning behaviour. We relate these macroscopic measurements to the orientation of individual swimming cells under flow and discuss our results in the light of several existing models

A study of blow-ups in the Keller-Segel model of chemotaxis

We study the Keller-Segel model of chemotaxis and develop a composite particle-grid numerical method with adaptive time stepping which allows us to accurately resolve singular solutions. The numerical findings (in two dimensions) are then compared with analytical predictions regarding formation and interaction of singularities obtained via analysis of the stochastic differential equations associated with the Keller-Segel model

Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion

For a specific choice of the diffusion, the parabolic-elliptic Patlak-Keller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is a critical mass $M_c>0$ such that all the solutions with initial data of mass smaller or equal to $M_c$ exist globally while the solution blows up in finite time for a large class of initial data with mass greater than $M_c$. Unlike in space dimension 2, finite mass self-similar blowing-up solutions are shown to exist in space dimension $d?3$

Streaming instability of slime mold amoebae: An analytical model

During the aggregation of amoebae of the cellular slime mould Dictyostelium, the interaction of chemical waves of the signaling molecule cAMP with cAMP-directed cell movement causes the breakup of a uniform cell layer into branching patterns of cell streams. Recent numerical and experimental investigations emphasize the pivotal role of the cell-density dependence of the chemical wave speed for the occurrence of the streaming instability. A simple, analytically tractable, model of Dictyostelium aggregation is developed to test this idea. The interaction of cAMP waves with cAMP-directed cell movement is studied in the form of coupled dynamics of wave front geometries and cell density. Comparing the resulting explicit instability criterion and dispersion relation for cell streaming with the previous findings of model simulations and numerical stability analyses, a unifying interpretation of the streaming instability as a cAMP wave-driven chemotactic instability is proposed

Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations

We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated

Functional consequences of Kir2.1/Kir2.2 subunit heteromerization

Kir2 subunits form channels that underlie classical strongly inwardly rectifying potassium currents. While homomeric Kir2 channels display a number of distinct and physiologically important properties, the functional properties of heteromeric Kir2 assemblies, as well as the stoichiometries and the arrangements of Kir2 subunits in native channels, remain largely unknown. Therefore, we have implemented a concatemeric approach, whereby all four cloned Kir2 subunits were linked in tandem, in order to study the effects of Kir2.1 and Kir2.2 heteromerization on properties of the resulting channels. Kir2.2 subunits contributed stronger to single-channel conductance than Kir2.1 subunits, and channels containing two or more Kir2.2 subunits displayed conductances indistinguishable from that of a Kir2.2 homomeric channel. In contrast, single-channel kinetics was a more discriminating property. The open times were significantly shorter in Kir2.2 channels compared with Kir2.1 channels and decreased nearly proportionally to the number of Kir2.2 subunits in the heteromeric channel. Similarly, the sensitivity to block by barium also depended on the proportions of Kir2.1 to Kir2.2 subunits. Overall, the results showed that Kir2.1 and Kir2.2 subunits exert neither a dominant nor an anomalous effect on any of the properties of heteromeric channels. The data highlight opportunities and challenges of using differential properties of Kir2 channels in deciphering the subunit composition of native inwardly rectifying potassium currents

Analysis of stomatal and convective resistances to transpirational flow

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47839/1/484_2005_Article_BF01554062.pd

Quantitative techniques in 18FDG PET scanning in oncology

The clinical applications of 18F-fluoro-2-deoxyglucose (18FDG) positron emission tomography (PET) in oncology are becoming established. While simple static scanning techniques are used for the majority of routine clinical examinations, increasing use of PET in clinical trials to monitor treatment response with 18FDG and novel tracers reflecting different pharmacodynamic end points, often necessitates a more complex and quantitative analysis of radiopharmaceutical kinetics. A wide range of PET analysis techniques exist, ranging from simple visual analysis and semiquantitative methods to full dynamic studies with kinetic analysis. These methods are discussed, focusing particularly on the available methodologies that can be utilised in clinical trials