N. G. Cogan

Failure of antibiotic treatment in microbial populations

The tolerance of bacterial populations to biocidal or antibiotic treatment has been well documented in both biofilm and planktonic settings. However, there is still very little known about the mechanisms that produce this tolerance. Evidence that small, non-mutant subpopulations of bacteria are not affected by an antibiotic challenge has been accumulating and provides an attractive explanation for the failure of typical dosing protocols. Although a dosing challenge can kill the susceptible bacteria, the remaining persister cells can serve as a source of population regrowth. We give a condition for the failure of a periodic dosing protocol for a general chemostat model, which supports the simulations of an earlier, more specialized batch model. Our condition implies that the treatment protocol fails globally, in the sense that a mixed bacterial population will ultimately persist above a level that is independent of the initial composition of the population. We also give a sufficient condition for treatment success, at least for initial population compositions near the steady state of interest, corresponding to bacterial washout. Finally, we investigate how the speed at which the bacteria are wiped out depends on the duration of administration of the antibiotic. We find that this dependence is not necessarily monotone, implying that optimal dosing does not necessarily correspond to continuous administration of the antibiotic. Thus, genuine periodic protocols can be more advantageous in treating a wide variety of bacterial infections.

CHANNEL FORMATION IN GELS

We derive and give an analysis of a model of gel dynamics based on a two-phase description of the gel, where one phase consists of networked polymer and the second phase is the fluid solvent. It is found that for the gel to maintain an edge in a poor solvent, the function describing the osmotic pressure must be of a particular form. The model is used to study the behavior of a gel forced by a pressure gradient to move between two flat plates. The distribution of the network phase under these conditions is found to be nonuniform and dependent on the pressure gradient. There is a range of pressure gradients for which the network has regions of high and low volume fraction separated by a sharp boundary, indicative of a channel. We provide the bifurcation analysis of how these novel, singularly perturbed, channeled solutions occur.

Multiphase flow models of biogels from crawling cells to bacterial biofilms

This article reviews multiphase descriptions of the fluid mechanics of cytoplasm in crawling cells and growing bacterial biofilms. These two systems involve gels, which are mixtures composed of a polymer network permeated by water. The fluid mechanics of these systems is essential to their biological function and structure. Their mathematical descriptions must account for the mechanics of the polymer, the water, and the interaction between these two phases. This review focuses on multiphase flow models because this framework is natural for including the relative motion between the phases, the exchange of material between phases, and the additional stresses within the network that arise from nonspecific chemical interactions and the action of molecular motors. These models have been successful in accounting for how different forces are generated and transmitted to achieve cell motion and biofilm growth and they have demonstrated how emergent structures develop though the interactions of the two phases. A short description of multiphase flow models of tumor growth is included to highlight the flexibility of the model in describing diverse biological applications.

Effect of Periodic Disinfection on Persisters in a One-Dimensional Biofilm Model

It is well known that disinfection methods that successfully kill suspended bacterial populations often fail to eliminate bacterial biofilms. Recent efforts to understand biofilm survival have focused on the existence of small, but very tolerant, subsets of the bacterial population termed persisters. In this investigation, we analyze a mathematical model of disinfection that consists of a susceptible-persister population system embedded within a growing domain. This system is coupled to a reaction-diffusion system governing the antibiotic and nutrient.We analyze the effect of periodic and continuous dosing protocols on persisters in a one-dimensional biofilm model, using both analytic and numerical method. We provide sufficient conditions for the existence of steady-state solutions and show that these solutions may not be unique. Our results also indicate that the dosing ratio (the ratio of dosing time to period) plays an important role. For long periods, large dosing ratios are more effective than similar ratios for short periods. We also compare periodic to continuous dosing and find that the results also depend on the method of distributing the antibiotic within the dosing cycle.

Biofilms and infectious diseases: biology to mathematics and back again

There has been tremendous growth in biofilm research in the past three decades. This growth has been reflected in development of a wide variety of experimental, clinical, and theoretical techniques fostered by our increased knowledge. Keeping the theoretical developments abreast of the experimental advancements and ensuring that the theoretical results are disseminated to the experimental and clinical community is a major challenge. This manuscript provides an overview of recent developments in each scientific domain. More importantly, this manuscript aims to identify areas where the theory lags behind the experimental understanding (and vice versa). The major themes of the manuscript derive from discussions and presentations at a recent interdisciplinary workshop that brought together a variety of scientists whose underlying studies focus on biofilm processes.

Optimal Control Strategies for Disinfection of Bacterial Populations with Persister and Susceptible Dynamics

ABSTRACT It is increasingly clear that bacteria manage to evade killing by antibiotics and antimicrobials in a variety of ways, including mutation, phenotypic variations, and formation of biofilms. With recent advances in understanding the dynamics of the tolerance mechanisms, there have been subsequent advances in understanding how to manipulate the bacterial environments to eradicate the bacteria. This study focuses on using mathematical techniques to find the optimal disinfection strategy to eliminate the bacteria while managing the load of antibiotic that is applied. In this model, the bacterial population is separated into those that are tolerant to the antibiotic and those that are susceptible to disinfection. There are transitions between the two populations whose rates depend on the chemical environment. Our results extend previous mathematical studies to include more realistic methods of applying the disinfectant. The goal is to provide experimentally testable predictions that have been lacking in previous mathematical studies. In particular, we provide the optimal disinfection protocol under a variety of assumptions within the model that can be used to validate or invalidate our simplifying assumptions and the experimental hypotheses that we used to develop the model. We find that constant dosing is not the optimal method for disinfection. Rather, cycling between application and withdrawal of the antibiotic yields the fastest killing of the bacteria.

An Extension of the Boundary Integral Method Applied to Periodic Disinfection of a Dynamic Biofilm

Several tolerance mechanisms have been introduced to explain how bacterial biofilms are protected from disinfection. One mechanism describes the transition between two subpopulations of bacteria, one of which consumes nutrients, divides, and is susceptible to antimicrobial agents. The other subpopulation consists of dormant bacteria that are insensitive to treatments. It has been shown that the presence of this persister subpopulation can explain experimental observations of bacterial tolerance, at least in simplified domains. This investigation describes the development of a two-dimensional model of an established biofilm immersed in a flowing bulk fluid, where the biofilm influences the fluid dynamics and where the fluid flow can deform the biofilm. We introduce several extensions to this model, including the reaction between the biofilm and the antimicrobial agent, bacterial and exo-polymeric substance production, and persister dynamics. The model and numerical methods are based on the boundary integra...

Pattern Formation Exhibited by Biofilm Formation within Microfluidic Chambers

This article investigates the dynamics of an important bacterial pathogen, Xylella fastidiosa, within artificial plant xylem. The bacterium is the causative agent of a variety of diseases that strike fruit-bearing plants including Pierces disease of grapevine. Biofilm colonization within microfluidic chambers was visualized in a laboratory setting, showing robust, regular spatial patterning. We also develop a mathematical model, based on a multiphase approach that is able to capture the spacing of the pattern and points to the role of the exopolymeric substance as the main source of control of the pattern dynamics. We concentrate on estimating the attachment/detachment processes within the chamber because these are two mechanisms that have the potential to be engineered by applying various chemicals to prevent or treat the disease.

Modelling the interaction between the host immune response, bacterial dynamics and inflammatory damage in comparison with immunomodulation and vaccination experiments.

The immune system is a complex system of chemical and cellular interactions that responds quickly to queues that signal infection and then reverts to a basal level once the challenge is eliminated. Here, we present a general, four-component model of the immune systems response to a Staphylococcal aureus (S. aureus) infection, using ordinary differential equations. To incorporate both the infection and the immune system, we adopt the style of compartmenting the system to include bacterial dynamics, damage and inflammation to the host, and the host response. We incorporate interactions not previously represented including cross-talk between inflammation/damage and the infection and the suppression of the anti-inflammatory pathway in response to inflammation/damage. As a result, the most relevant equilibrium of the system, representing the health state, is an all-positive basal level. The model is able to capture eight different experimental outcomes for mice challenged with intratibial osteomyelitis due to S. aureus, primarily involving immunomodulation and vaccine therapies. For further validation and parameter exploration, we perform a parameter sensitivity analysis which suggests that the model is very stable with respect to variations in parameters, indicates potential immunomodulation strategies and provides a possible explanation for the difference in immune potential for different mouse strains.

Global sensitivity analysis used to interpret biological experimental results

Modeling host/pathogen interactions provides insight into immune defects that allow bacteria to overwhelm the host, mechanisms that allow vaccine strategies to be successful, and illusive interactions between immune components that govern the immune response to a challenge. However, even simplified models require a fairly high dimensional parameter space to be explored. Here we use global sensitivity analysis for parameters in a simple model for biofilm infections in mice. The results indicate which parameters are insignificant and are ‘frozen’ to yield a reduced model. The reduced model replicates the full model with high accuracy, using approximately half of the parameter space. We used the sensitivity to investigate the results of the combined biological and mathematical experiments for osteomyelitis. We are able to identify parts of the compartmentalized immune system that were responsible for each of the experimental outcomes. This model is one example for a technique that can be used generally.