Trends in mathematical modeling of host–pathogen interactions

Ewald, Jan; Sieber, Patricia; Garde, Ravindra; Lang, Stefan N.; Schuster, Stefan; Ibrahim, Bashar

doi:10.1007/s00018-019-03382-0

Cited by 38 publications

(29 citation statements)

References 136 publications

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“…Our results above show that ODEs yield satisfactory results as well. ODE systems must involve at least two variables to describe limit-cycle oscillations 15,16,24 . When only linear and bilinear kinetics is www.nature.com/scientificreports www.nature.com/scientificreports/ used, at least three variables are needed 17,18 .…”

Section: Resultsmentioning

confidence: 99%

Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

Garde

Ibrahim

Schuster

2020

Sci Rep

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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 ...

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Section: Resultsmentioning

confidence: 99%

Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

Garde

Ibrahim

Schuster

2020

Sci Rep

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“…However, these oscillations only occur under very special or even artificial conditions. In living cells, metabolic oscillations are rare, while being quite frequent in signalling systems [13,14,49,50]. The lights of a car are a helpful analogy: the headlights illuminate the street in a permanent way; there is no point in oscillations.…”

Section: Discussionmentioning

confidence: 99%

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

et al. 2020

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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 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.

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“…Dynamic simulation, game theory, and spatial modeling play an increasing role in understanding the biology of complex systems. These methods can also illustrate the dynamics of the relationship between pathogens and their host [27].…”

Section: Mathematics and Computer Sciencementioning

confidence: 99%

“…Worldwide, public health agencies use these frameworks coupled with information technologies such as bioinformatics, big data analytics, machine learning, artificial learning, sensors, and image recognition to assess and establish strategies for ever-emerging infectious diseases and to respond to outbreaks [27,[32][33][34].…”

Section: Mathematics and Computer Sciencementioning

confidence: 99%

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

et al. 2020

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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.

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Trends in mathematical modeling of host–pathogen interactions

Cited by 38 publications

References 136 publications

Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

Extending the minimal model of metabolic oscillations in Bacillus subtilis biofilms

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

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

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