A mathematical model for determining minimal inhibitory concentrations (MICs) via diffusion assays

Area of Science:

• Mathematical modeling
• Biotechnology
• Toxicology

Background:

• Diffusion bioassays are crucial for determining microbial sensitivity to toxic substances.
• Quantifying the toxic response in these assays is essential for evaluating chemical safety.
• Existing methods may lack efficiency or require extensive parameter data.

Purpose of the Study:

• To develop a mathematical model for accurately describing inhibition zones in diffusion bioassays.
• To enable precise calculation of the inhibitory concentration (ctox) from observed toxic zone radii (rtox).
• To create a computational tool for routine, quantitative toxicity screening of chemicals.

Main Methods:

• A two-dimensional diffusion equation was formulated to model drug concentration changes.
• The non-linear diffusion equation was solved numerically using a computer-based solver.
• A "best-fit" simulation program was developed to determine unknown experimental parameters.

Main Results:

• The mathematical model accurately describes the formation of inhibition zones in diffusion bioassays.
• The method allows for the straightforward calculation of the inhibitory concentration (ctox).
• The developed computational tools were tested and found to be fast, efficient, and inexpensive.

Conclusions:

• The presented mathematical model and computational tools offer a robust approach for toxicity assessment.
• This method can be utilized for routine quantitative screening of chemical toxicity.
• The approach enhances the evaluation of microorganism sensitivity to toxic substances.