Mathematical Modelling of Hydrophilic Antibiotic Concentration, Binding Dynamics, and Drug Resistance under Competitive Inhibition in Disc Diffusion Assays

Abstract

Understanding the intricate relationship between minimum inhibitory concentration binding Affinity and drug resistance is paramount for developing effective antimicrobial strategies, in this paper, we explore a mathematical relationship between these factors, under the condition of the disc diffusion method of antimicrobial susceptibility testing of antibiotics.
In our study we considered the response as (ZOI) Zone of Inhibition denoted by "X" in mm, the response X is directly proportional to the concentration of antibiotics, Zone of Inhibition X is directly proportional to binding affinity and ΔG binding free energy of receptor. X is directly proportional to the -log of minimum inhibitory concentration (MIC), which contributes to resistance upon certain values by our mathematical derivation, we tried to give the direct relationship among binding affinity, minimum inhibitory concentration (MIC), zone of inhibition (ZOI) i.e. X and antibiotic concentration 'c' on the hypothesis of enzymatic kinetics the dimensions of Cheng–Prusoff, binding affinity, IC50, were calculated. For hydrophilic antibiotics following competitive inhibition kinetics.