Search

Over the last ten years, isogenic tagging (IT) has revolutionised the study of bacterial infection dynamics in laboratory animal models. However, quantitative analysis of IT data has been hindered by the piecemeal development of relevant statistical models. The most promising approach relies on stochastic Markovian models of bacterial population dynamics within and among organs. Here we present an efficient numerical method to fit such stochastic dynamic models to in vivo experimental IT data. A common approach to statistical inference with stochastic dynamic models relies on producing large numbers of simulations, but this remains a slow and inefficient method for all but simple problems, especially when tracking bacteria in multiple locations simultaneously. Instead, we derive and solve the systems of ordinary differential equations for the two lower-order moments of the stochastic variables (mean, variance and covariance). For any given model structure, and assuming linear dynamic rates, we demonstrate how the model parameters can be efficiently and accurately estimated by divergence minimisation. We then apply our method to an experimental dataset and compare the estimates and goodness-of-fit to those obtained by maximum likelihood estimation. While both sets of parameter estimates had overlapping confidence regions, the new method produced lower values for the division and death rates of bacteria: these improved the goodness-of-fit at the second time point at the expense of that of the first time point. This flexible framework can easily be applied to a range of experimental systems. Its computational efficiency paves the way for model comparison and optimal experimental design.

Intravenous inoculation of Salmonella enterica serovar Typhimurium into mice is a prime experimental model of invasive salmonellosis. The use of wild-type isogenic tagged strains (WITS) in this system has revealed that bacteria undergo independent bottlenecks in the liver and spleen before establishing a systemic infection. We recently showed that those bacteria that survived the bottleneck exhibited enhanced growth when transferred to naive mice. In this study, we set out to disentangle the components of this in vivo adaptation by inoculating mice with WITS grown either in vitro or in vivo. We developed an original method to estimate the replication and killing rates of bacteria from experimental data, which involved solving the probability-generating function of a non-homogeneous birth-death-immigration process. This revealed a low initial mortality in bacteria obtained from a donor animal. Next, an analysis of WITS distributions in the livers and spleens of recipient animals indicated that in vivo-passaged bacteria started spreading between organs earlier than in vitro-grown bacteria. These results further our understanding of the influence of passage in a host on the fitness and virulence of Salmonella enterica and represent an advance in the power of investigation on the patterns and mechanisms of host-pathogen interactions.

Salmonella enterica infections are a significant global health issue, and development of vaccines against these bacteria requires an improved understanding of how vaccination affects the growth and spread of the bacteria within the host. We have combined in vivo tracking of molecularly tagged bacterial subpopulations with mathematical modelling to gain a novel insight into how different classes of vaccines and branches of the immune response protect against secondary Salmonella enterica infections of the mouse. We have found that a live Salmonella vaccine significantly reduced bacteraemia during a secondary challenge and restrained inter-organ spread of the bacteria in the systemic organs. Further, fitting mechanistic models to the data indicated that live vaccine immunisation enhanced both the bacterial killing in the very early stages of the infection and bacteriostatic control over the first day post-challenge. T-cell immunity induced by this vaccine is not necessary for the enhanced bacteriostasis but is required for subsequent bactericidal clearance of Salmonella in the blood and tissues. Conversely, a non-living vaccine while able to enhance initial blood clearance and killing of virulent secondary challenge bacteria, was unable to alter the subsequent bacterial growth rate in the systemic organs, did not prevent the resurgence of extensive bacteraemia and failed to control the spread of the bacteria in the body.

Understanding the evolution of a complex genetic algorithm is a non-trivial problem, however, genetic-algorithm visualization is in its infancy. This paper reviews some of the current approaches and presents a new visualization approach based on Sammon mapping. Sammon mapping is a nonlinear mapping of a set of vectors in p-dimensional space to a set in r-dimensional space, where r < p. The mapping attempts to preserve in r-space the Euclidean inter-vector distances present in p-space. We demonstrate that a Sammon mapping to 2-space of binary chromosomes present in a higher-dimensional allele space during the execution of a genetic algorithm can indicate the presence of multiple solutions. Shortfalls of this approach are discussed along with possible solutions.

Understanding the evolution of a complex genetic algorithm is a non-trivial problem, however, genetic-algorithm visualization is in its infancy. This paper reviews some of the current approaches and presents a new visualization approach based on Sammon mapping. Sammon mapping is a nonlinear mapping of a set of vectors in p-dimensional space to a set in r-dimensional space, where r < p. The mapping attempts to preserve in r-space the Euclidean inter-vector distances present in p-space. We demonstrate that a Sammon mapping to 2-space of binary chromosomes present in a higher-dimensional allele space during the execution of a genetic algorithm can indicate the presence of multiple solutions. Shortfalls of this approach are discussed along with possible solutions.