In silico analysis of antibiotic-induced Clostridium difficile infection: Remediation techniques and biological adaptations

Modeling the bacterial dynamics in the gut microbiota following an antibiotic‐induced perturbation

Recent studies have highlighted the importance of ecological interactions in dysbiosis of gut microbiota, but few focused on their role in antibiotic‐induced perturbations. We used the data from the CEREMI trial in which 22 healthy volunteers received a 3‐day course of ceftriaxone or cefotaxime antibiotics. Fecal samples were analyzed by 16S rRNA gene profiling, and the total bacterial counts were determined in each sample by flux cytometry. As the gut exposure to antibiotics could not be experimentally measured despite a marked impact on the gut microbiota, it was reconstructed using the counts of susceptible Escherichia coli. The dynamics of absolute counts of bacterial families were analyzed using a generalized Lotka–Volterra equations and nonlinear mixed effect modeling. Bacterial interactions were studied using a stepwise approach. Two negative and three positive interactions were identified. Introducing bacterial interactions in the modeling approach better fitted the data, and provided different estimates of antibiotic effects on each bacterial family than a simple model without interaction. The time to return to 95% of the baseline counts was significantly longer in ceftriaxone‐treated individuals than in cefotaxime‐treated subjects for two bacterial families: Akkermansiaceae (median [range]: 11.3 days [0; 180.0] vs. 4.2 days [0; 25.6], p = 0.027) and Tannerellaceae (13.7 days [6.1; 180.0] vs. 6.2 days [5.4; 17.3], p = 0.003). Taking bacterial interaction as well as individual antibiotic exposure profile into account improves the analysis of antibiotic‐induced dysbiosis.

A Computational Model of Bacterial Population Dynamics in Gastrointestinal Yersinia enterocolitica Infections in Mice

Simple Summary

Computational modeling of bacterial infection is an attractive way to simulate infection scenarios. In the long-term, such models could be used to identify factors that make individuals more susceptible to infection, or how interference with bacterial growth influences the course of bacterial infection. This study used different mouse infection models (immunocompetent, lacking a microbiota, and immunodeficient models) to develop a basic mathematical model of a Yersinia enterocolitica gastrointestinal infection. We showed that our model can reflect our findings derived from mouse infections, and we demonstrated how crucial the exact knowledge about parameters influencing the population dynamics is. Still, we think that computational models will be of great value in the future; however, to foster the development of more complex models, we propose the broad implementation of the interdisciplinary training of mathematicians and biologists.

Abstract

The complex interplay of a pathogen with its virulence and fitness factors, the host’s immune response, and the endogenous microbiome determine the course and outcome of gastrointestinal infection. The expansion of a pathogen within the gastrointestinal tract implies an increased risk of developing severe systemic infections, especially in dysbiotic or immunocompromised individuals. We developed a mechanistic computational model that calculates and simulates such scenarios, based on an ordinary differential equation system, to explain the bacterial population dynamics during gastrointestinal infection. For implementing the model and estimating its parameters, oral mouse infection experiments with the enteropathogen, Yersinia enterocolitica (Ye), were carried out. Our model accounts for specific pathogen characteristics and is intended to reflect scenarios where colonization resistance, mediated by the endogenous microbiome, is lacking, or where the immune response is partially impaired. Fitting our data from experimental mouse infections, we can justify our model setup and deduce cues for further model improvement. The model is freely available, in SBML format, from the BioModels Database under the accession number MODEL2002070001.

Mathematical-based microbiome analytics for clinical translation

Traditionally, human microbiology has been strongly built on the laboratory focused culture of microbes isolated from human specimens in patients with acute or chronic infection. These approaches primarily view human disease through the lens of a single species and its relevant clinical setting however such approaches fail to account for the surrounding environment and wide microbial diversity that exists in vivo. Given the emergence of next generation sequencing technologies and advancing bioinformatic pipelines, researchers now have unprecedented capabilities to characterise the human microbiome in terms of its taxonomy, function, antibiotic resistance and even bacteriophages. Despite this, an analysis of microbial communities has largely been restricted to ordination, ecological measures, and discriminant taxa analysis. This is predominantly due to a lack of suitable computational tools to facilitate microbiome analytics. In this review, we first evaluate the key concerns related to the inherent structure of microbiome datasets which include its compositionality and batch effects. We describe the available and emerging analytical techniques including integrative analysis, machine learning, microbial association networks, topological data analysis (TDA) and mathematical modelling. We also present how these methods may translate to clinical settings including tools for implementation. Mathematical based analytics for microbiome analysis represents a promising avenue for clinical translation across a range of acute and chronic disease states.

A MODEL ON BACTERIAL RESISTANCE CONSIDERING A GENERALIZED LAW OF MASS ACTION FOR PLASMID REPLICATION

Bacterial plasmids play a fundamental role in antibiotic resistance. However, a lack of knowledge about their biology is an obstacle in fully understanding the mechanisms and properties of plasmid-mediated resistance. This has motivated investigations of real systems in vitro to analyze the transfer and replication of plasmids. In this work, we address this issue with mathematical modeling. We formulate and perform a qualitative analysis of a nonlinear system of ordinary differential equations describing the competition dynamics between plasmids and sensitive and resistant bacteria. In addition, we estimated parameter values from empirical data. Our model predicts scenarios consistent with biological phenomena. The elimination or spread of infection depends on factors associated with bacterial reproduction and the transfer and replication of plasmids. From the estimated parameters, three bacterial growth experiments were analyzed in vitro. We determined the experiment with the highest bacterial growth rate and the highest rate of plasmid transfer. Moreover, numerical simulations were performed to predict bacterial growth.

Control of ecological outcomes through deliberate parameter changes in a model of the gut microbiome

The generalized Lotka-Volterra (gLV) equations are a mathematical proxy for ecological dynamics. We focus on a gLV model of the gut microbiome, in which the evolution of the gut microbial state is determined in part by pairwise interspecies interaction parameters that encode environmentally mediated resource competition between microbes. We develop an in silico method that controls the steady-state outcome of the system by adjusting these interaction parameters. This approach is confined to a bistable region of the gLV model. In this method, a dimensionality reduction technique called steady-state reduction (SSR) is first used to generate a two-dimensional (2D) gLV model that approximates the high-dimensional dynamics on the 2D subspace spanned by the two steady states. Then a bifurcation analysis of the 2D model analytically determines parameter modifications that drive an initial condition to a target steady state. This parameter modification of the reduced 2D model guides parameter modifications of the original high-dimensional model, resulting in a change of steady-state outcome in the high-dimensional model. This control method, called SSR-guided parameter change (SPARC), bypasses the computational challenge of directly determining parameter modifications in the original high-dimensional system. SPARC could guide the development of indirect bacteriotherapies, which seek to change microbial compositions by deliberately modifying gut environmental variables such as gut acidity or macronutrient availability.

Steady-state reduction of generalized Lotka-Volterra systems in the microbiome

The generalized Lotka-Volterra (gLV) equations, a classic model from theoretical ecology, describe the population dynamics of a set of interacting species. As the number of species in these systems grow in number, their dynamics become increasingly complex and intractable. We introduce steady-state reduction (SSR), a method that reduces a gLV system of many ecological species into two-dimensional subsystems that each obey gLV dynamics and whose basis vectors are steady states of the high-dimensional model. We apply this method to an experimentally-derived model of the gut microbiome in order to observe the transition between "healthy" and "diseased" microbial states. Specifically, we use SSR to investigate how fecal microbiota transplantation, a promising clinical treatment for dysbiosis, can revert a diseased microbial state to health.