### Abstract

It is widely accepted that β-lactam antimicrobials cause cell death through a mechanism that interferes with cell wall synthesis. Later studies have also revealed that β-lactams modify the autolysis function (the natural process of self-exfoliation of the cell wall) of cells. The dynamic equilibrium between growth and autolysis is perturbed by the presence of the antimicrobial. Studies with Staphylococcus aureus to determine the minimum inhibitory concentration (MIC) have revealed complex responses to methicillin exposure. The organism exhibits four qualitatively different responses: homogeneous sensitivity, homogeneous resistance, heterogeneous resistance and the so-called 'Eagle-effect'. A mathematical model is presented that links antimicrobial action on the molecular level with the overall response of the cell population to antimicrobial exposure. The cell population is modeled as a probability density function F(x,t) that depends on cell wall thickness x and time t. The function F(x,t) is the solution to a Fokker-Planck equation. The fixed point solutions are perturbed by the antimicrobial load and the advection of F(x,t) depends on the rates of cell wall synthesis, autolysis and the antimicrobial concentration. Solutions of the Fokker-Planck model are presented for all four qualitative responses of S. aureus to methicillin exposure.

Original language | English (US) |
---|---|

Pages (from-to) | 438-445 |

Number of pages | 8 |

Journal | Journal of Theoretical Biology |

Volume | 257 |

Issue number | 3 |

DOIs | |

State | Published - Apr 7 2009 |

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### Keywords

- Cell wall
- Eagle-effect
- Fokker-Planck equation
- Heterogeneous resistance
- Mathematical model
- Methicillin
- Staphylococcus aureus

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Journal of Theoretical Biology*,

*257*(3), 438-445. https://doi.org/10.1016/j.jtbi.2008.12.003

**A model of the complex response of Staphylococcus aureus to methicillin.** / Pienaar, Elsje; Whitney, Scott E.; Viljoen, Hendrik J; van Rensburg, Nicolaas F J.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 257, no. 3, pp. 438-445. https://doi.org/10.1016/j.jtbi.2008.12.003

}

TY - JOUR

T1 - A model of the complex response of Staphylococcus aureus to methicillin

AU - Pienaar, Elsje

AU - Whitney, Scott E.

AU - Viljoen, Hendrik J

AU - van Rensburg, Nicolaas F J

PY - 2009/4/7

Y1 - 2009/4/7

N2 - It is widely accepted that β-lactam antimicrobials cause cell death through a mechanism that interferes with cell wall synthesis. Later studies have also revealed that β-lactams modify the autolysis function (the natural process of self-exfoliation of the cell wall) of cells. The dynamic equilibrium between growth and autolysis is perturbed by the presence of the antimicrobial. Studies with Staphylococcus aureus to determine the minimum inhibitory concentration (MIC) have revealed complex responses to methicillin exposure. The organism exhibits four qualitatively different responses: homogeneous sensitivity, homogeneous resistance, heterogeneous resistance and the so-called 'Eagle-effect'. A mathematical model is presented that links antimicrobial action on the molecular level with the overall response of the cell population to antimicrobial exposure. The cell population is modeled as a probability density function F(x,t) that depends on cell wall thickness x and time t. The function F(x,t) is the solution to a Fokker-Planck equation. The fixed point solutions are perturbed by the antimicrobial load and the advection of F(x,t) depends on the rates of cell wall synthesis, autolysis and the antimicrobial concentration. Solutions of the Fokker-Planck model are presented for all four qualitative responses of S. aureus to methicillin exposure.

AB - It is widely accepted that β-lactam antimicrobials cause cell death through a mechanism that interferes with cell wall synthesis. Later studies have also revealed that β-lactams modify the autolysis function (the natural process of self-exfoliation of the cell wall) of cells. The dynamic equilibrium between growth and autolysis is perturbed by the presence of the antimicrobial. Studies with Staphylococcus aureus to determine the minimum inhibitory concentration (MIC) have revealed complex responses to methicillin exposure. The organism exhibits four qualitatively different responses: homogeneous sensitivity, homogeneous resistance, heterogeneous resistance and the so-called 'Eagle-effect'. A mathematical model is presented that links antimicrobial action on the molecular level with the overall response of the cell population to antimicrobial exposure. The cell population is modeled as a probability density function F(x,t) that depends on cell wall thickness x and time t. The function F(x,t) is the solution to a Fokker-Planck equation. The fixed point solutions are perturbed by the antimicrobial load and the advection of F(x,t) depends on the rates of cell wall synthesis, autolysis and the antimicrobial concentration. Solutions of the Fokker-Planck model are presented for all four qualitative responses of S. aureus to methicillin exposure.

KW - Cell wall

KW - Eagle-effect

KW - Fokker-Planck equation

KW - Heterogeneous resistance

KW - Mathematical model

KW - Methicillin

KW - Staphylococcus aureus

UR - http://www.scopus.com/inward/record.url?scp=61449252834&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61449252834&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2008.12.003

DO - 10.1016/j.jtbi.2008.12.003

M3 - Article

C2 - 19135063

AN - SCOPUS:61449252834

VL - 257

SP - 438

EP - 445

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 3

ER -