Models of Microbial Dormancy in Biofilms and Planktonic Cultures

We present models of dormancy in a planktonic culture and in biofilm, and examine the relative advantage of short dormancy versus long dormancy times in each case. Simulations and analyses indicate that in planktonic batch cultures and in chemostats, live biomass is maximized by the fastest possible exit from dormancy. The lower limit of time to reawakening is thus perhaps governed by physiological, biochemical or other constraints within the cells. In biofilm we see that the slower waker has a defensive advantage over the fast waker due to a larger amount of dormant biomass, without an appreciable difference in total live biomass. Thus it would seem that typical laboratory culture conditions can be unrepresentative of the natural state. We discuss the computational methods developed for this work

A Multiscale Model of Biofilm as a Senescence-Structured Fluid

We derive a physiologically structured multiscale model for biofilm development. The model has components on two spatial scales, which induce different time scales into the problem. The macroscopic behavior of the system is modeled using growth-induced flow in a domain with a moving boundary. Cell-level processes are incorporated into the model using a so-called physiologically structured variable to represent cell senescence, which in turn affects cell division and mortality. We present computational results for our models which shed light on modeling the combined role senescence and the biofilm state play in the defense strategy of bacteria

Challenges in microbial ecology: building predictive understanding of community function and dynamics.

The importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth's soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited. Building predictive models that link MC composition to function is a key emerging challenge in microbial ecology. Here, we argue that addressing this challenge requires close coordination of experimental data collection and method development with mathematical model building. We discuss specific examples where model-experiment integration has already resulted in important insights into MC function and structure. We also highlight key research questions that still demand better integration of experiments and models. We argue that such integration is needed to achieve significant progress in our understanding of MC dynamics and function, and we make specific practical suggestions as to how this could be achieved

Mathematical Description of Microbial Biofilms

We describe microbial communities denoted biofilms and efforts to model some of their important aspects, including quorum sensing, growth, mechanics, and antimicrobial tolerance mechanisms

Removing the Stiffness of Curvature in Computing 3-D Filaments

In this paper, we present a new formulation for computing the motion of a curvature driven 3-D filament. This new numerical method has no high order time step stability constraints that are usually associated with curvature regularization. This result generalizes the previous work of Hou-Lowengrub-Shelley [7] for 2-D fluid interfaces with surface tension. Applications to 2-D vortex sheets, 3-D motion by curvature, the Kirchhoff rod model and nearly anti--parallel vortex filaments will be presented to demonstrate the robustness of the method. 1 Introduction In this paper, we present a new formulation for computing the motion of a curvature driven 3-D filament. This new numerical method has no high order time step stability constraints that are usually associated with curvature regularization. This result generalizes the previous work of Hou-Lowengrub-Shelley [7] for 2-D fluid interfaces with surface tension. Applications to 2-D vortex sheets, 3-D motion by curvature, the Kirchhoff rod ..

Remarks on Singularities, Dimension and Energy Dissipation for Ideal Hydrodynamics and MHD

For weak solutions of the incompressible Euler equations, there is energy conservation if the velocity is in the Besov space B 3 s with s greater than 1=3: B p s consists of functions that are Lip(s) (i.e., Holder continuous with exponent s) measured in the L p norm. Here this result is applied to a velocity field that is Lip(ff0 ) except on a set of co-dimension 1 on which it is Lip(ff1 ), with uniformity that will be made precise below. We show that the Frisch-Parisi multifractal formalism is valid (at least in one direction) for such a function, and that there is energy conservation if min ff (3ff + (ff)) ? 1. Analogous conservation results are derived for the equations of incompressible ideal MHD (i.e., zero viscosity and resistivity) for both energy and helicity . In addition, a necessary condition is derived for singularity development in ideal MHD generalizing the BealeKato -Majda condition for ideal hydrodynamics. [email protected]. Research supported in part by the..