Nested sampling for Bayesian model comparison in the context of Salmonella disease dynamics.

Understanding the mechanisms underlying the observed dynamics of complex biological systems requires the statistical assessment and comparison of multiple alternative models. Although this has traditionally been done using maximum likelihood-based methods such as Akaike's Information Criterion (AIC), Bayesian methods have gained in popularity because they provide more informative output in the form of posterior probability distributions. However, comparison between multiple models in a Bayesian framework is made difficult by the computational cost of numerical integration over large parameter spaces. A new, efficient method for the computation of posterior probabilities has recently been proposed and applied to complex problems from the physical sciences. Here we demonstrate how nested sampling can be used for inference and model comparison in biological sciences. We present a reanalysis of data from experimental infection of mice with Salmonella enterica showing the distribution of bacteria in liver cells. In addition to confirming the main finding of the original analysis, which relied on AIC, our approach provides: (a) integration across the parameter space, (b) estimation of the posterior parameter distributions (with visualisations of parameter correlations), and (c) estimation of the posterior predictive distributions for goodness-of-fit assessments of the models. The goodness-of-fit results suggest that alternative mechanistic models and a relaxation of the quasi-stationary assumption should be considered.RD was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) (grant number BB/I002189/1). TJM was funded by the Biotechnology and Biological Sciences Research Council (BBSRC) (grant number BB/I012192/1). OR was funded by the Royal Society. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

The effects of vaccination and immunity on bacterial infection dynamics in vivo.

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.This work was supported by the Biotechnology and Biological Sciences Research Council [grant number BB/I002189/1].This is the published manuscript. It was originally published by PLOS One here: http://www.plospathogens.org/article/info%3Adoi%2F10.1371%2Fjournal.ppat.1004359

Dual role of splenic mononuclear and polymorphonuclear cells in the outcome of ciprofloxacin treatment of Salmonella enterica infections.

OBJECTIVES: To determine the immune cell populations associated with Salmonella enterica serovar Typhimurium before and after ciprofloxacin treatment using a murine model of systemic infection. The effect of depletion of immune cells associating with Salmonella on treatment outcome was also determined. METHODS: We infected mice with a Salmonella enterica serovar Typhimurium strain expressing GFP and used multicolour flow cytometry to identify splenic immune cell populations associating with GFP-positive Salmonella before and after treatment with ciprofloxacin. This was followed by depletion of different immune cell populations using antibodies and liposomes. RESULTS: Our results identified CD11b+CD11chi/lo (dendritic cells/macrophages) and Ly6G+CD11b+ (neutrophils) leucocytes as the main host cell populations that are associated with Salmonella after ciprofloxacin treatment. We therefore proceeded to test the effects of depletion of such populations during treatment. We show that depletion of Ly6G+CD11b+ populations resulted in an increase in the number of viable bacterial cells in the spleen at the end of ciprofloxacin treatment. Conversely, treatment with clodronate liposomes during antimicrobial treatment, which depleted the CD11b+CD11chi/lo populations, resulted in lower numbers of viable bacteria in the tissues. CONCLUSIONS: Our study identified host cells where Salmonella bacteria persist during ciprofloxacin treatment and revealed a dual and opposing effect of removal of Ly6G+CD11b+ and CD11b+CD11chi/lo host cells on the efficacy of antimicrobial treatment. This suggests a dichotomy in the role of these populations in clearance/persistence of Salmonella during antimicrobial treatment

A Semantic Hierarchy for Erasure Policies

We consider the problem of logical data erasure, contrasting with physical erasure in the same way that end-to-end information flow control contrasts with access control. We present a semantic hierarchy for erasure policies, using a possibilistic knowledge-based semantics to define policy satisfaction such that there is an intuitively clear upper bound on what information an erasure policy permits to be retained. Our hierarchy allows a rich class of erasure policies to be expressed, taking account of the power of the attacker, how much information may be retained, and under what conditions it may be retained. While our main aim is to specify erasure policies, the semantic framework allows quite general information-flow policies to be formulated for a variety of semantic notions of secrecy.Comment: 18 pages, ICISS 201

Within-host spatiotemporal dynamics of systemic Salmonella infection during and after antimicrobial treatment

$\textbf{Objectives:}$ We determined the interactions between efficacy of antibiotic treatment, pathogen growth rates and between-organ spread during systemic $\textit{Salmonella}$ infections. $\textbf{Methods:}$ We infected mice with isogenic molecularly tagged subpopulations of either a fast-growing WT or a slow-growing $\Delta$$\textit{aroC Salmonella}$ strain. We monitored viable bacterial numbers and fluctuations in the proportions of each bacterial subpopulation in spleen, liver, blood and mesenteric lymph nodes (MLNs) before, during and after the cessation of treatment with ampicillin and ciprofloxacin. $\textbf{Results:}$ Both antimicrobials induced a reduction in viable bacterial numbers in the spleen, liver and blood. This reduction was biphasic in infections with fast-growing bacteria, with a rapid initial reduction followed by a phase of lower effect. Conversely, a slow and gradual reduction of the bacterial load was seen in infections with the slow-growing strain, indicating a positive correlation between bacterial net growth rates and the efficacy of ampicillin and ciprofloxacin. The viable numbers of either bacterial strain remained constant in MLNs throughout the treatment with a relapse of the infection with WT bacteria occurring after cessation of the treatment. The frequency of each tagged bacterial subpopulation was similar in the spleen and liver, but different from that of the MLNs before, during and after treatment. $\textbf{Conclusions:}$ In $\textit{Salmonella}$ infections, bacterial growth rates correlate with treatment efficacy. MLNs are a site with a bacterial population structure different to those of the spleen and liver and where the total viable bacterial load remains largely unaffected by antimicrobials, but can resume growth after cessation of treatment.This work was supported by the Biotechnology and Biological Sciences Research Council (BBSRC) grant number BB/M000982/1 (http://www.bbsrc.ac.uk/research/grants/grants/AwardDetails.aspx?FundingReference=BB/M000982/1). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Quantification of the effects of antibodies on the extra- and intracellular dynamics of Salmonella enterica.

Antibodies are known to be essential in controlling Salmonella infection, but their exact role remains elusive. We recently developed an in vitro model to investigate the relative efficiency of four different human immunoglobulin G (IgG) subclasses in modulating the interaction of the bacteria with human phagocytes. Our results indicated that different IgG subclasses affect the efficacy of Salmonella uptake by human phagocytes. In this study, we aim to quantify the effects of IgG on intracellular dynamics of infection by combining distributions of bacterial numbers per phagocyte observed by fluorescence microscopy with a mathematical model that simulates the in vitro dynamics. We then use maximum likelihood to estimate the model parameters and compare them across IgG subclasses. The analysis reveals heterogeneity in the division rates of the bacteria, strongly suggesting that a subpopulation of intracellular Salmonella, while visible under the microscope, is not dividing. Clear differences in the observed distributions among the four IgG subclasses are best explained by variations in phagocytosis and intracellular dynamics. We propose and compare potential factors affecting the replication and death of bacteria within phagocytes, and we discuss these results in the light of recent findings on dormancy of Salmonella.This work was funded by grants from the Wellcome Trust and from the Medical Research Council to PM. O.R. is supported by the Royal Society through a University Research Fellowship. M.P. is supported by a studentship from the Wellcome Trust

Verifying Bounded Subset-Closed Hyperproperties

Hyperproperties are quickly becoming very popular in the context of systems security, due to their expressive power. They differ from classic trace properties since they are represented by sets of sets of executions instead of sets of executions. This allows us, for instance, to capture information flow security specifications, which cannot be expressed as trace properties, namely as predicates over single executions. In this work, we reason about how it is possible to move standard abstract interpretation-based static analysis methods, designed for trace properties, towards the verification of hyperproperties. In particular, we focus on the verification of bounded subset-closed hyperproperties which are easier to verify than generic hyperproperties. It turns out that a lot of interesting specifications (e.g., Non-Interference) lie in this category

Inferring within-host bottleneck size: A Bayesian approach.

Recent technical developments in microbiology have led to new discoveries on the within-host dynamics of bacterial infections in laboratory animals. In particular, they have highlighted the importance of stochastic bottlenecks at the onset of invasive disease. A number of approaches exist for bottleneck-size estimation with respect to within-host bacterial infections; however, some are more appropriate than others under certain circumstances. A Bayesian comparison of several approaches is made in terms of the availability of isogenic multitype bacteria (e.g., WITS), knowledge of post-bottleneck dynamics, and the suitability of dilution with monotype bacteria. A sampling approach to bottleneck-size estimation is also introduced. The results are summarised by a guiding flowchart, which we hope will promote the use of quantitative models in microbiology to refine the analysis of animal experiment data

Statically Analyzing Information Flows - An Abstract Interpretation-based Hyperanalysis for Non-Interference.

In the context of systems security, information flows play a central role. Unhandled information flows potentially leave the door open to very dangerous types of attacks, such as code injection or sen- sitive information leakage. Information flows verification is based on the definition of Non-Interference [8], which is known to be an hyperproperty [7], i.e., a property of sets of executions. The sound verification of hyperproperties is not trivial [3, 16]: It is not easy to adapt classic verification methods, used for trace properties, in order to deal with hyperproperties. In the present work, we design an abstract interpretation-based static analyzer soundly checking Non-Interference. In particular, we define an hyper abstract do- main, able to approximate the information flows occurring in the analyzed programs