Trends in mathematical modeling of host-pathogen interactions

Optimal control of ribosome population for gene expression under periodic nutrient intake

Translation of proteins is a fundamental part of gene expression that is mediated by ribosomes. As ribosomes significantly contribute to both cellular mass and energy consumption, achieving efficient management of the ribosome population is also crucial to metabolism and growth. Inspired by biological evidence for nutrient-dependent mechanisms that control both ribosome-active degradation and genesis, we introduce a dynamical model of protein production, that includes the dynamics of resources and control over the ribosome population. Under the hypothesis that active degradation and biogenesis are optimal for maximizing and maintaining protein production, we aim to qualitatively reproduce empirical observations of the ribosome population dynamics. Upon formulating the associated optimization problem, we first analytically study the stability and global behaviour of solutions under constant resource input, and characterize the extent of oscillations and convergence rate to a global equilibrium. We further use these results to simplify and solve the problem under a quasi-static approximation. Using biophysical parameter values, we find that optimal control solutions lead to both control mechanisms and the ribosome population switching between periods of feeding and fasting, suggesting that the intense regulation of ribosome population observed in experiments allows to maximize and maintain protein production. Finally, we find some range for the control values over which such a regime can be observed, depending on the intensity of fasting.

Surrogate infection model predicts optimal alveolar macrophage number for clearance of Aspergillus fumigatus infections

The immune system has to fight off hundreds of microbial invaders every day, such as the human-pathogenic fungus Aspergillus fumigatus. The fungal conidia can reach the lower respiratory tract, swell and form hyphae within six hours causing life-threatening invasive aspergillosis. Invading pathogens are continuously recognized and eliminated by alveolar macrophages (AM). Their number plays an essential role, but remains controversial with measurements varying by a factor greater than ten for the human lung. We here investigate the impact of the AM number on the clearance of A. fumigatus conidia in humans and mice using analytical and numerical modeling approaches. A three-dimensional to-scale hybrid agent-based model (hABM) of the human and murine alveolus allowed us to simulate millions of virtual infection scenarios, and to gain quantitative insights into the infection dynamics for varying AM numbers and infection doses. Since hABM simulations are computationally expensive, we derived and trained an analytical surrogate infection model on the large dataset of numerical simulations. This enables reducing the number of hABM simulations while still providing (i) accurate and immediate predictions on infection progression, (ii) quantitative hypotheses on the infection dynamics under healthy and immunocompromised conditions, and (iii) optimal AM numbers for combating A. fumigatus infections in humans and mice.

Analytical and Numerical Boundedness of a Model with Memory Effects for the Spreading of Infectious Diseases

In this study, an integer-order rabies model is converted into the fractional-order epidemic model. To this end, the Caputo fractional-order derivatives are plugged in place of the classical derivatives. The positivity and boundedness of the fractional-order mathematical model is investigated by applying Laplace transformation and its inversion. To study the qualitative behavior of the non-integer rabies model, two steady states and the basic reproductive number of the underlying model are worked out. The local and global stability is investigated at both the steady states of the fractional-order epidemic model. After analytic treatment, a structure-preserving numerical template is constructed to numerically solve the fractional-order epidemic model. Moreover, the positivity, boundedness and symmetry of the numerical scheme are examined. Lastly, numerical experiment and simulations are accomplished to substantiate the significant traits of the projected numerical design. Consequences of the study are highlighted in the closing section.

Uncertainty Modeling of a Modified SEIR Epidemic Model for COVID-19

Based on SEIR (susceptible-exposed-infectious-removed) epidemic model, we propose a modified epidemic mathematical model to describe the spread of the coronavirus disease 2019 (COVID-19) epidemic in Wuhan, China. Using public data, the uncertainty parameters of the proposed model for COVID-19 in Wuhan were calibrated. The uncertainty of the control basic reproduction number was studied with the posterior probability density function of the uncertainty model parameters. The mathematical model was used to inverse deduce the earliest start date of COVID-19 infection in Wuhan with consideration of the lack of information for the initial conditions of the model. The result of the uncertainty analysis of the model is in line with the observed data for COVID-19 in Wuhan, China. The numerical results show that the modified mathematical model could model the spread of COVID-19 epidemics.

Pathogen within-host dynamics and disease outcome: what can we learn from insect studies?

Parasite proliferations within/on the host form the basis of the outcome of all infectious diseases. However, within-host dynamics are difficult to study in vertebrates, as it requires regularly following pathogen proliferation from the start of the infection and at the organismal level. Invertebrate models allow for this monitoring under controlled conditions using population approaches. These approaches offer the possibility to describe many parameters of the within-host dynamics, such as rate of proliferation, probability to control the infection, and average time at which the pathogen is controlled. New parameters such as the Pathogen Load Upon Death and the Set-Point Pathogen Load have emerged to characterize within-host dynamics and better understand disease outcome. While contextualizing the potential of studying within-host dynamics in insects to build fundamental knowledge, we review what we know about within-host dynamics using insect models, and what it can offer to our knowledge of infectious diseases.

Agent-based modelling of iron cycling bacteria provides a framework for testing alternative environmental conditions and modes of action

Iron-reducing and iron-oxidizing bacteria are of interest in a variety of environmental and industrial applications. Such bacteria often co-occur at oxic-anoxic gradients in aquatic and terrestrial habitats. In this paper, we present the first computational agent-based model of microbial iron cycling, between the anaerobic ferric iron (Fe³⁺)-reducing bacteria Shewanella spp. and the microaerophilic ferrous iron (Fe²⁺)-oxidizing bacteria Sideroxydans spp. By including the key processes of reduction/oxidation, movement, adhesion, Fe²⁺-equilibration and nanoparticle formation, we derive a core model which enables hypothesis testing and prediction for different environmental conditions including temporal cycles of oxic and anoxic conditions. We compared (i) combinations of different Fe³⁺-reducing/Fe²⁺-oxidizing modes of action of the bacteria and (ii) system behaviour for different pH values. We predicted that the beneficial effect of a high number of iron-nanoparticles on the total Fe³⁺ reduction rate of the system is not only due to the faster reduction of these iron-nanoparticles, but also to the nanoparticles' additional capacity to bind Fe²⁺ on their surfaces. Efficient iron-nanoparticle reduction is confined to pH around 6, being twice as high than at pH 7, whereas at pH 5 negligible reduction takes place. Furthermore, in accordance with experimental evidence our model showed that shorter oxic/anoxic periods exhibit a faster increase of total Fe³⁺ reduction rate than longer periods.

BioSANS: A software package for symbolic and numeric biological simulation

Modeling biochemical systems can provide insights into behaviors that are difficult to observe or understand. It requires software, programming, and understanding of the system to build a model and study it. Softwares exist for systems biology modeling, but most support only certain types of modeling tasks. Desirable features including ease in preparing input, symbolic or analytical computation, parameter estimation, graphical user interface, and systems biology markup language (SBML) support are not seen concurrently in one software package. In this study, we developed a python-based software that supports these features, with both deterministic and stochastic propagations. The software can be used by graphical user interface, command line, or as a python import. We also developed a semi-programmable and intuitively easy topology input method for the biochemical reactions. We tested the software with semantic and stochastic SBML test cases. Tests on symbolic solution and parameter estimation were also included. The software we developed is reliable, well performing, convenient to use, and compliant with most of the SBML tests. So far it is the only systems biology software that supports symbolic, deterministic, and stochastic modeling in one package that also features parameter estimation and SBML support. This work offers a comprehensive set of tools and allows for better availability and accessibility for studying kinetics and dynamics in biochemical systems.

Antimicrobial Stewardship Programs: A Review of Strategies to Avoid Polymyxins and Carbapenems Misuse in Low Middle-Income Countries

Antibiotics misuse and overuse are concerning issues worldwide, especially in low middle-income countries. These practices contribute to the increasing rates of antimicrobial resistance. One efficient strategy to avoid them is antimicrobial stewardship programs. In this review, we focus on the possible approaches to spare the prescription of polymyxins and carbapenems for the treatment of Acinetobacter baumannii, carbapenem-resistant Enterobacterales, and Pseudomonas aeruginosas infections. Additionally, we highlight how to implement cumulative antibiograms and biomarkers to a sooner de-escalation of antibiotics.

Dynamic optimization reveals alveolar epithelial cells as key mediators of host defense in invasive aspergillosis

Aspergillus fumigatus is an important human fungal pathogen and its conidia are constantly inhaled by humans. In immunocompromised individuals, conidia can grow out as hyphae that damage lung epithelium. The resulting invasive aspergillosis is associated with devastating mortality rates. Since infection is a race between the innate immune system and the outgrowth of A. fumigatus conidia, we use dynamic optimization to obtain insight into the recruitment and depletion of alveolar macrophages and neutrophils. Using this model, we obtain key insights into major determinants of infection outcome on host and pathogen side. On the pathogen side, we predict in silico and confirm in vitro that germination speed is an important virulence trait of fungal pathogens due to the vulnerability of conidia against host defense. On the host side, we found that epithelial cells, which have been underappreciated, play a role in fungal clearance and are potent mediators of cytokine release. Both predictions were confirmed by in vitro experiments on established cell lines as well as primary lung cells. Further, our model affirms the importance of neutrophils in invasive aspergillosis and underlines that the role of macrophages remains elusive. We expect that our model will contribute to improvement of treatment protocols by focusing on the critical components of immune response to fungi but also fungal virulence traits.

A Review of Using Mathematical Modeling to Improve Our Understanding of Bacteriophage, Bacteria, and Eukaryotic Interactions

Phage therapy, the therapeutic usage of viruses to treat bacterial infections, has many theoretical benefits in the ‘post antibiotic era.’ Nevertheless, there are currently no approved mainstream phage therapies. One reason for this is a lack of understanding of the complex interactions between bacteriophage, bacteria and eukaryotic hosts. These three-component interactions are complex, with non-linear or synergistic relationships, anatomical barriers and genetic or phenotypic heterogeneity all leading to disparity between performance and efficacy in in vivo versus in vitro environments. Realistic computer or mathematical models of these complex environments are a potential route to improve the predictive power of in vitro studies for the in vivo environment, and to streamline lab work. Here, we introduce and review the current status of mathematical modeling and highlight that data on genetic heterogeneity and mutational stochasticity, time delays and population densities could be critical in the development of realistic phage therapy models in the future. With this in mind, we aim to inform and encourage the collaboration and sharing of knowledge and expertise between microbiologists and theoretical modelers, synergising skills and smoothing the road to regulatory approval and widespread use of phage therapy.

Results of the Seventh Scientific Workshop of ECCO: Precision Medicine in IBD-What, Why, and How

Many diseases that affect modern humans fall in the category of complex diseases, thus called because they result from a combination of multiple aetiological and pathogenic factors. Regardless of the organ or system affected, complex diseases present major challenges in diagnosis, classification, and management. Current forms of therapy are usually applied in an indiscriminate fashion based on clinical information, but even the most advanced drugs only benefit a limited number of patients and to a variable and unpredictable degree. This 'one measure does not fit all' situation has spurred the notion that therapy for complex disease should be tailored to individual patients or groups of patients, giving rise to the notion of 'precision medicine' [PM]. Inflammatory bowel disease [IBD] is a prototypical complex disease where the need for PM has become increasingly clear. This prompted the European Crohn's and Colitis Organisation to focus the Seventh Scientific Workshop on this emerging theme. The articles in this special issue of the Journal address the various complementary aspects of PM in IBD, including what PM is; why it is needed and how it can be used; how PM can contribute to prediction and prevention of IBD; how IBD PM can aid in prognosis and improve response to therapy; and the challenges and future directions of PM in IBD. This first article of this series is structured on three simple concepts [what, why, and how] and addresses the definition of PM, discusses the rationale for the need of PM in IBD, and outlines the methodology required to implement PM in IBD in a correct and clinically meaningful way.

Models of Plant Resistance Deployment

Owing to their evolutionary potential, plant pathogens are able to rapidly adapt to genetically controlled plant resistance, often resulting in resistance breakdown and major epidemics in agricultural crops. Various deployment strategies have been proposed to improve resistance management. Globally, these rely on careful selection of resistance sources and their combination at various spatiotemporal scales (e.g., via gene pyramiding, crop rotations and mixtures, landscape mosaics). However, testing and optimizing these strategies using controlled experiments at large spatiotemporal scales are logistically challenging. Mathematical models provide an alternative investigative tool, and many have been developed to explore resistance deployment strategies under various contexts. This review analyzes 69 modeling studies in light of specific model structures (e.g., demographic or demogenetic, spatial or not), underlying assumptions (e.g., whether preadapted pathogens are present before resistance deployment), and evaluation criteria (e.g., resistance durability, disease control, cost-effectiveness). It highlights major research findings and discusses challenges for future modeling efforts.

Computational Discovery of SARS-CoV-2 NSP 16 Drug Candidates Based on Pharmacophore Modeling and Molecular Dynamics Simulation

Non-Structural Protein 16 (NSP-16) is one of the most suitable targets for discovery of drugs for corona viruses including SARS-CoV-2. In this study, drug discovery of SARS-CoV-2 nsp-16 has been accomplished by pharmacophore-based virtual screening among some analogs (FDA approved drugs) and marine natural plants (MNP). The comparison of the binding energies and the inhibition constants was determined using molecular docking method. Three compounds including two FDA approved (Ibrutinib, Idelalisib) and one MNP (Kumusine) were selected for further investigation using the molecular dynamics simulations. The results indicated that Ibrutinib and Idelalisib are oral medications while Kumusine, with proper hydrophilic and solubility properties, is an appropriate candidate for nsp-16 inhibitor and can be effective to control COVID-19 disease.

Will SARS-CoV-2 Become Just Another Seasonal Coronavirus?

The future prevalence and virulence of SARS-CoV-2 is uncertain. Some emerging pathogens become avirulent as populations approach herd immunity. Although not all viruses follow this path, the fact that the seasonal coronaviruses are benign gives some hope. We develop a general mathematical model to predict when the interplay among three factors, correlation of severity in consecutive infections, population heterogeneity in susceptibility due to age, and reduced severity due to partial immunity, will promote avirulence as SARS-CoV-2 becomes endemic. Each of these components has the potential to limit severe, high-shedding cases over time under the right circumstances, but in combination they can rapidly reduce the frequency of more severe and infectious manifestation of disease over a wide range of conditions. As more reinfections are captured in data over the next several years, these models will help to test if COVID-19 severity is beginning to attenuate in the ways our model predicts, and to predict the disease.

Modeling the energy metabolism in immune cells

In this review, we summarize and briefly discuss various approaches to modeling the metabolism in human immune cells, with a focus on energy metabolism. These approaches include metabolic reconstruction, elementary modes, and flux balance analysis, which are often subsumed under constraint-based modeling. Further approaches are evolutionary game theory and kinetic modeling. Many immune cells such as macrophages show the Warburg effect, meaning that glycolysis is upregulated upon activation. We outline a minimal model for explaining that effect using optimization. The effect of a confrontation with pathogen cells on immunometabolism is highlighted. Models describing the differences between M1 and M2 macrophages, ROS production in neutrophils, and tryptophan metabolism are discussed. Obstacles and future prospects are outlined.

Competitive exclusion during co-infection as a strategy to prevent the spread of a virus: A computational perspective

Inspired by the competition exclusion principle, this work aims at providing a computational framework to explore the theoretical feasibility of viral co-infection as a possible strategy to reduce the spread of a fatal strain in a population. We propose a stochastic-based model—called Co-Wish—to understand how competition between two viruses over a shared niche can affect the spread of each virus in infected tissue. To demonstrate the co-infection of two viruses, we first simulate the characteristics of two virus growth processes separately. Then, we examine their interactions until one can dominate the other. We use Co-Wish to explore how the model varies as the parameters of each virus growth process change when two viruses infect the host simultaneously. We will also investigate the effect of the delayed initiation of each infection. Moreover, Co-Wish not only examines the co-infection at the cell level but also includes the innate immune response during viral infection. The results highlight that the waiting times in the five stages of the viral infection of a cell in the model—namely attachment, penetration, eclipse, replication, and release—play an essential role in the competition between the two viruses. While it could prove challenging to fully understand the therapeutic potentials of viral co-infection, we discuss that our theoretical framework hints at an intriguing research direction in applying co-infection dynamics in controlling any viral outbreak’s speed.

Population Genomics of Plant Viruses: The Ecology and Evolution of Virus Emergence

The genomics era has revolutionized studies of adaptive evolution by monitoring large numbers of loci throughout the genomes of many individuals. Ideally, the investigation of emergence in plant viruses requires examining the population dynamics of both virus and host, their interactions with each other, with other organisms and the abiotic environment. Genetic mechanisms that affect demographic processes are now being studied with high-throughput technologies, traditional genetics methods, and new computational tools for big-data. In this review, we discuss the utility of these approaches to monitor and detect changes in virus populations within cells and individuals, and over wider areas across species and communities of ecosystems. The advent of genomics in virology has fostered a multidisciplinary approach to tackling disease risk. The ability to make sense of the information now generated in this integrated setting is by far the most substantial obstacle to the ultimate goal of plant virology to minimize the threats to food security posed by disease. To achieve this goal, it is imperative to understand and forecast how populations respond to future changes in complex natural systems.

Interdisciplinary Approaches to COVID-19

The coronavirus disease 2019 (COVID-19) pandemic has been a significant concern worldwide. The pandemic has demonstrated that public health issues are not merely a health concern but also affect society as a whole. In this chapter, we address the importance of bringing together the world's scientists to find appropriate solutions for controlling and managing the COVID-19 pandemic. Interdisciplinary cooperation, through modern scientific methods, could help to handle the consequences of the pandemic and to avoid the recurrence of future pandemics.

Structure and Hierarchy of SARS-CoV-2 Infection Dynamics Models Revealed by Reaction Network Analysis

This work provides a mathematical technique for analyzing and comparing infection dynamics models with respect to their potential long-term behavior, resulting in a hierarchy integrating all models. We apply our technique to coupled ordinary and partial differential equation models of SARS-CoV-2 infection dynamics operating on different scales, that is, within a single organism and between several hosts. The structure of a model is assessed by the theory of chemical organizations, not requiring quantitative kinetic information. We present the Hasse diagrams of organizations for the twelve virus models analyzed within this study. For comparing models, each organization is characterized by the types of species it contains. For this, each species is mapped to one out of four types, representing uninfected, infected, immune system, and bacterial species, respectively. Subsequently, we can integrate these results with those of our former work on Influenza-A virus resulting in a single joint hierarchy of 24 models. It appears that the SARS-CoV-2 models are simpler with respect to their long term behavior and thus display a simpler hierarchy with little dependencies compared to the Influenza-A models. Our results can support further development towards more complex SARS-CoV-2 models targeting the higher levels of the hierarchy.

Using optimal control to understand complex metabolic pathways

BACKGROUND

Optimality principles have been used to explain the structure and behavior of living matter at different levels of organization, from basic phenomena at the molecular level, up to complex dynamics in whole populations. Most of these studies have assumed a single-criteria approach. Such optimality principles have been justified from an evolutionary perspective. In the context of the cell, previous studies have shown how dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point, and a single objective for the optimality criteria.

RESULTS

Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework which has been designed with scalability and efficiency in mind, including mechanisms to avoid the most common pitfalls. Third, we illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments.

CONCLUSIONS

We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we also show how to consider general cost/benefit trade-offs. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction or gene regulatory networks.

The urgent need for integrated science to fight COVID-19 pandemic and beyond

The COVID-19 pandemic has become the leading societal concern. The pandemic has shown that the public health concern is not only a medical problem, but also affects society as a whole; so, it has also become the leading scientific concern. We discuss in this treatise the importance of bringing the world's scientists together to find effective solutions for controlling the pandemic. By applying novel research frameworks, interdisciplinary collaboration promises to manage the pandemic's consequences and prevent recurrences of similar pandemics.

Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

Biofilms are composed of microorganisms attached to a solid surface or floating on top of a liquid surface. They pose challenges in the field of medicine but can also have useful applications in industry. Regulation of biofilm growth is complex and still largely elusive. Oscillations are thought to be advantageous for biofilms to cope with nutrient starvation and chemical attacks. Recently, a minimal mathematical model has been employed to describe the oscillations in Bacillus subtilis biofilms. In this paper, we investigate four different modifications to that minimal model in order to better understand the oscillations in biofilms. Our first modification is towards making a gradient of metabolites from the center of the biofilm to the periphery. We find that it does not improve the model and is therefore, unnecessary. We then use realistic Michaelis-Menten kinetics to replace the highly simple mass-action kinetics for one of the reactions. Further, we use reversible reactions to mimic the diffusion in biofilms. As the final modification, we check the combined effect of using Michaelis-Menten kinetics and reversible reactions on the model behavior. We find that these two modifications alone or in combination improve the description of the biological scenario.

Differential equation-based minimal model describing metabolic oscillations in Bacillus subtilis biofilms

Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.

Systems biology: current status and challenges

We put together a special issue on current approaches in systems biology with a focus on mathematical modeling of metabolic networks. Mathematical models have increasingly been used to unravel molecular mechanisms of complex dynamic biological processes. We here provide a short introduction into the topics covered in this special issue, highlighting current developments and challenges.