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.

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.

Most unicellular organisms live in communities and express different phenotypes. Many efforts have been made to study the population dynamics of such complex communities of cells, coexisting as well-coordinated units. Minimal models based on ordinary differential equations are powerful tools that can help us understand complex phenomena. They represent an appropriate compromise between complexity and tractability; they allow a profound and comprehensive analysis, which is still easy to understand. Evolutionary game theory is another powerful tool that can help us understand the costs and benefits of the decision a particular cell of a unicellular social organism takes when faced with the challenges of the biotic and abiotic environment. This work is a binocular view at the population dynamics of such a community through the objectives of minimal modelling and evolutionary game theory. We test the behaviour of the community of a unicellular social organism at three levels of antibiotic stress. Even in the absence of the antibiotic, spikes in the fraction of resistant cells can be observed indicating the importance of bet hedging. At moderate level of antibiotic stress, we witness cyclic dynamics reminiscent of the renowned rock–paper–scissors game. At a very high level, the resistant type of strategy is the most favourable.

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 massaction 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. Biofilms, a complex aggregation of cells embedded in a polysaccharide matrix, have been of interest for a long time in history-right when Antoine van Leuwenhoek examined a scraping of his tooth plaqueunder a microscope that he had built 1. Since then, our understanding of biofilms has greatly broadened. We now know that living as a close aggregation provides several advantages to bacteria, such as the efficient distribution of macronutrients, removal of waste products, defense from chemical stress, and better gaseous exchange in the case of pellicle biofilms on the surface of liquids 2,3. Biofilms are an elaborate system of coexisting individual cells that exhibit several social dynamics, including the division of labour 4-7. In experiments using a microfluidics chamber, oscillations were observed in the growth of Bacillus subtilis 4 which was supplied with glutamate on one end of the chamber while the waste products of the biofilm were washed off at the other end at a constant rate. The peripheral cells of the biofilm have the advantage of direct access to glutamate. On the downside, they lose small molecules like ammonia which is an important source of nitrogen 8. Cells in the interior, on the other hand, depend on the leftover glutamate that diffuses inwards in the biofilm, but do not lose gaseous molecules as rapidly as the peripheral cells. Thus cells in different regions of the biofilm will likely exhibit differences in their metabolic behavior 7. The interior cells produce ammonia, which is required to produce glutamine. Glutamine is a proxy for the protein content and thus for the growth of the biofilm 9. The peripheral cells depend on the ammonia diffusing from the interior for their growth. Thus, interior cells control the growth of the peripheral ...

The biotrophic fungus Sporisorium reilianum exists in two host-adapted formae speciales that cause head smut in maize (S. reilianum f. sp. zeae; SRZ) and sorghum (S. reilianum f. sp. reilianum; SRS). In sorghum, the spread of SRZ is limited to the leaves. To understand the plant responses to each forma specialis, we determined the transcriptome of sorghum leaves inoculated either with SRS or SRZ. Fungal inoculation led to gene expression rather than suppression in sorghum. SRZ induced a much greater number of genes than SRS. Each forma specialis induced a distinct set of plant genes. The SRZ-induced genes were involved in plant defense mainly at the plasma membrane and were associated with the Molecular Function Gene Ontology terms chitin binding, abscisic acid binding, protein phosphatase inhibitor activity, terpene synthase activity, chitinase activity, transmembrane transporter activity and signaling receptor activity. Specifically, we found an upregulation of the genes involved in phospholipid degradation and sphingolipid biosynthesis, suggesting that the lipid content of the plant plasma membrane may contribute to preventing the systemic spread of SRZ. In contrast, the colonization of sorghum with SRS increased the expression of the genes involved in the detoxification of cellular oxidants and in the unfolded protein response at the endoplasmic reticulum, as well as of the genes modifying the cuticle wax and lipid composition through the generation of alkanes and phytosterols. These results identified plant compartments that may have a function in resistance against SRZ (plasma membrane) and susceptibility towards SRS (endoplasmic reticulum) that need more attention in the future.

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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 perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasisteady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. We also specifically select parameters that are more suitable for the biological scenario of biofilm oscillations. 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.