Facing the challenges of multiscale modelling of bacterial and fungal pathogen-host interactions

Proof-of-concept for incorporating mechanistic insights from multi-omics analyses of polymyxin B in combination with chloramphenicol against Klebsiella pneumoniae

Carbapenemase-resistant Klebsiella pneumoniae (KP) resistant to multiple antibiotic classes necessitates optimized combination therapy. Our objective is to build a workflow leveraging omics and bacterial count data to identify antibiotic mechanisms that can be used to design and optimize combination regimens. For pharmacodynamic (PD) analysis, previously published static time-kill studies (J Antimicrob Chemother 70, 2015, 2589) were used with polymyxin B (PMB) and chloramphenicol (CHL) mono and combination therapy against three KP clinical isolates over 24 h. A mechanism-based model (MBM) was developed using time-kill data in S-ADAPT describing PMB-CHL PD activity against each isolate. Previously published results of PMB (1 mg/L continuous infusion) and CHL (C_max : 8 mg/L; bolus q6h) mono and combination regimens were evaluated using an in vitro one-compartment dynamic infection model against a KP clinical isolate (10⁸ CFU/ml inoculum) over 24 h to obtain bacterial samples for multi-omics analyses. The differentially expressed genes and metabolites in these bacterial samples served as input to develop a partial least squares regression (PLSR) in R that links PD responses with the multi-omics responses via a multi-omics pathway analysis. PMB efficacy was increased when combined with CHL, and the MBM described the observed PD well for all strains. The PLSR consisted of 29 omics inputs and predicted MBM PD response (R²  = 0.946). Our analysis found that CHL downregulated metabolites and genes pertinent to lipid A, hence limiting the emergence of PMB resistance. Our workflow linked insights from analysis of multi-omics data with MBM to identify biological mechanisms explaining observed PD activity in combination therapy.

MODELLING OF PATHOGENS IMPACT ON THE HUMAN DISEASE TRANSMISSION WITH OPTIMAL CONTROL STRATEGIES

This study concentrates on a nonlinear deterministic mathematical model for the impact of pathogens on human disease transmission with optimal control strategies. Both pathogen-free and coexistence equilibria are computed. The basic reproduction number R₀, which plays a vital role in mathematical epidemiology, was derived. The qualitative analysis of the model revealed the scenario for both pathogen-free and coexistence equilibria together with R₀. The local stability of the equilibria is established via the Jacobian matrix and Routh-Hurwitz criteria, while the global stability of the equilibria is proven by using an appropriate Lyapunov function. Also, the normalized sensitivity analysis has been performed to observe the impact of different parameters on R₀. The proposed model is extended into optimal control problem by incorporating three control variables, namely, preventive measure variable based on separation of susceptible from contacting the pathogens, integrated vector management based on chemical, biological control, ... etc. to kill pathogens and their carriers, and supporting infective medication variable based on the care of the infected individual in quarantine center. Optimal disease control analysis is examined using Pontryagin minimum principle. Numerical simulations are performed depending on analytical results and discussed quantitatively.

One model to rule them all? Modelling approaches across OneHealth for human, animal and plant epidemics

One hundred years after the 1918 influenza outbreak, are we ready for the next pandemic? This paper addresses the need to identify and develop collaborative, interdisciplinary and cross-sectoral approaches to modelling of infectious diseases including the fields of not only human and veterinary medicine, but also plant epidemiology. Firstly, the paper explains the concepts on which the most common epidemiological modelling approaches are based, namely the division of a host population into susceptible, infected and removed (SIR) classes and the proportionality of the infection rate to the size of the susceptible and infected populations. It then demonstrates how these simple concepts have been developed into a vast and successful modelling framework that has been used in predicting and controlling disease outbreaks for over 100 years. Secondly, it considers the compartmental models based on the SIR paradigm within the broader concept of a 'disease tetrahedron' (comprising host, pathogen, environment and man) and uses it to review the similarities and differences among the fields comprising the 'OneHealth' approach. Finally, the paper advocates interactions between all fields and explores the future challenges facing modellers. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Trends in mathematical modeling of host-pathogen interactions

Pathogenic microorganisms entail enormous problems for humans, livestock, and crop plants. A better understanding of the different infection strategies of the pathogens enables us to derive optimal treatments to mitigate infectious diseases or develop vaccinations preventing the occurrence of infections altogether. In this review, we highlight the current trends in mathematical modeling approaches and related methods used for understanding host-pathogen interactions. Since these interactions can be described on vastly different temporal and spatial scales as well as abstraction levels, a variety of computational and mathematical approaches are presented. Particular emphasis is placed on dynamic optimization, game theory, and spatial modeling, as they are attracting more and more interest in systems biology. Furthermore, these approaches are often combined to illuminate the complexities of the interactions between pathogens and their host. We also discuss the phenomena of molecular mimicry and crypsis as well as the interplay between defense and counter defense. As a conclusion, we provide an overview of method characteristics to assist non-experts in their decision for modeling approaches and interdisciplinary understanding.

High-Performance Agent-Based Modeling Applied to Vocal Fold Inflammation and Repair

Fast and accurate computational biology models offer the prospect of accelerating the development of personalized medicine. A tool capable of estimating treatment success can help prevent unnecessary and costly treatments and potential harmful side effects. A novel high-performance Agent-Based Model (ABM) was adopted to simulate and visualize multi-scale complex biological processes arising in vocal fold inflammation and repair. The computational scheme was designed to organize the 3D ABM sub-tasks to fully utilize the resources available on current heterogeneous platforms consisting of multi-core CPUs and many-core GPUs. Subtasks are further parallelized and convolution-based diffusion is used to enhance the performance of the ABM simulation. The scheme was implemented using a client-server protocol allowing the results of each iteration to be analyzed and visualized on the server (i.e., in-situ) while the simulation is running on the same server. The resulting simulation and visualization software enables users to interact with and steer the course of the simulation in real-time as needed. This high-resolution 3D ABM framework was used for a case study of surgical vocal fold injury and repair. The new framework is capable of completing the simulation, visualization and remote result delivery in under 7 s per iteration, where each iteration of the simulation represents 30 min in the real world. The case study model was simulated at the physiological scale of a human vocal fold. This simulation tracks 17 million biological cells as well as a total of 1.7 billion signaling chemical and structural protein data points. The visualization component processes and renders all simulated biological cells and 154 million signaling chemical data points. The proposed high-performance 3D ABM was verified through comparisons with empirical vocal fold data. Representative trends of biomarker predictions in surgically injured vocal folds were observed.

Data-based Reconstruction of Gene Regulatory Networks of Fungal Pathogens

In the emerging field of systems biology of fungal infection, one of the central roles belongs to the modeling of gene regulatory networks (GRNs). Utilizing omics-data, GRNs can be predicted by mathematical modeling. Here, we review current advances of data-based reconstruction of both small-scale and large-scale GRNs for human pathogenic fungi. The advantage of large-scale genome-wide modeling is the possibility to predict central (hub) genes and thereby indicate potential biomarkers and drug targets. In contrast, small-scale GRN models provide hypotheses on the mode of gene regulatory interactions, which have to be validated experimentally. Due to the lack of sufficient quantity and quality of both experimental data and prior knowledge about regulator–target gene relations, the genome-wide modeling still remains problematic for fungal pathogens. While a first genome-wide GRN model has already been published for Candida albicans, the feasibility of such modeling for Aspergillus fumigatus is evaluated in the present article. Based on this evaluation, opinions are drawn on future directions of GRN modeling of fungal pathogens. The crucial point of genome-wide GRN modeling is the experimental evidence, both used for inferring the networks (omics ‘first-hand’ data as well as literature data used as prior knowledge) and for validation and evaluation of the inferred network models.

How to Predict Molecular Interactions between Species?

Organisms constantly interact with other species through physical contact which leads to changes on the molecular level, for example the transcriptome. These changes can be monitored for all genes, with the help of high-throughput experiments such as RNA-seq or microarrays. The adaptation of the gene expression to environmental changes within cells is mediated through complex gene regulatory networks. Often, our knowledge of these networks is incomplete. Network inference predicts gene regulatory interactions based on transcriptome data. An emerging application of high-throughput transcriptome studies are dual transcriptomics experiments. Here, the transcriptome of two or more interacting species is measured simultaneously. Based on a dual RNA-seq data set of murine dendritic cells infected with the fungal pathogen Candida albicans, the software tool NetGenerator was applied to predict an inter-species gene regulatory network. To promote further investigations of molecular inter-species interactions, we recently discussed dual RNA-seq experiments for host-pathogen interactions and extended the applied tool NetGenerator (Schulze et al., 2015). The updated version of NetGenerator makes use of measurement variances in the algorithmic procedure and accepts gene expression time series data with missing values. Additionally, we tested multiple modeling scenarios regarding the stimuli functions of the gene regulatory network. Here, we summarize the work by Schulze et al. (2015) and put it into a broader context. We review various studies making use of the dual transcriptomics approach to investigate the molecular basis of interacting species. Besides the application to host-pathogen interactions, dual transcriptomics data are also utilized to study mutualistic and commensalistic interactions. Furthermore, we give a short introduction into additional approaches for the prediction of gene regulatory networks and discuss their application to dual transcriptomics data. We conclude that the application of network inference on dual-transcriptomics data is a promising approach to predict molecular inter-species interactions.