Bulletin of Mathematical Biology

, Volume 80, Issue 7, pp 1736–1775

# Simulation-Based Exploration of Quorum Sensing Triggered Resistance of Biofilms to Antibiotics

• Maryam Ghasemi
• Burkhard A. Hense
• Hermann J. Eberl
• Christina Kuttler
Original Article

## Abstract

We present a mathematical model of biofilm response to antibiotics, controlled by a quorum sensing system that confers increased resistance. The model is a highly nonlinear system of partial differential equations that we investigate in computer simulations. Our results suggest that an adaptive, quorum sensing-controlled, mechanism to switch between modes of fast growth with little protection and protective modes of slow growth may confer benefits to biofilm populations. It enhances the formation of micro-niches in the inner regions of the biofilm in which bacteria are not easily reached by antibiotics. Whereas quorum sensing inhibitors can delay the onset of increased resistance, their advantage is lost after up-regulation. This emphasizes the importance of timing for treatment of biofilms with antibiotics.

## Keywords

Antibiotics Biofilm Mathematical model Nonlinear diffusion Quorum sensing Simulation

## Mathematics Subject Classification

92D25 35K65 65N08 34C60

## Notes

### Acknowledgements

This study was supported in parts by the Natural Science and Engineering Research Council of Canada (NSERC) with a Discovery Grant and a Research Tools and Infrastructure Grant awarded to HJE, and a postgraduate scholarship awarded to MG. A visit of MG to the TU Munich for collaborative work was supported in parts by the Technical University of Munich with an Entrepreneurial Award for Global Challenges in The Mathematical Sciences, awarded to CK.

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© Society for Mathematical Biology 2018

## Authors and Affiliations

• Maryam Ghasemi
• 1
• Burkhard A. Hense
• 2
• Hermann J. Eberl
• 1
• Christina Kuttler
• 3
1. 1.Department of Mathematics and StatisticsUniversity of GuelphGuelphCanada
2. 2.Institute for Computational BiologyHelmholtz Zentrum MünchenOberschleissheimGermany
3. 3.Zentrum MathematikTU MünchenGarchingGermany