MATHEMATICAL CORRELATION OF IC50 AND MIC OF HYDROPHOBIC ANTIBIOTICS FOLLOWING COMPETITIVE INHIBITION IN THE DISK DIFFUSION METHOD
DOI:
https://doi.org/10.63456/aamc-2-2-114Keywords:
MIC, , Zone of Inhibition,, Binding affinity, antibiotic resistance, IC50, Competative Inhibition, Disk diffusion.Abstract
Objective: This study explores the mathematical link between binding affinity, drug resistance, IC50, MIC, and Zone of Inhibition (ZOI) in the disc diffusion method for antimicrobial susceptibility testing. We consider ZOI (x) as a response to antibiotic concentration, showing that x is proportional to –log (MIC) and correlated with the binding free energy (exp ΔG). Our findings establish a clear relationship between binding affinity, MIC, ZOI, and antibiotic concentration (c) for hydrophobic antibiotics under competitive inhibition in the disk diffusion method, the value of half Maximal inhibitory concentration IC50 is equal to the twice of minimum inhibitory concentration to the multiple of exponent of fraction of Zone of Inhibition ‘x’ and dissipative term “V” by twice the diffusion term. It will Contributing to a better understanding of resistance mechanisms.
Methods: The mathematical derivations are been validated by the published data available from the journal such as MIC, diffusion constant (D), ZOI (x) and IC50 values and Dissipative Value (V) has been calculated and calculated, IC50 values are compared with reported values.
Result: The data had been validated for ∆G, Dissipative Value (V), IC50 values from predictive to reported it had been observed that while calculating IC50 values of resistance and non-resistance susceptibility, the MIC value for resistance group is more hence the value of IC50 will depreciates and depend more on values of ZOI (x) and V the dissipative term Table 1 revels while analysing the ratio between resistance and non-resistance MIC and IC50 shows direct relationship it can be cross verified by reported and calculated values, Levofloxacin IC50 values ranges from 9.81- 3.2 µg/ml while calculated value is 10-1.6 µg/ml, binding energy ∆G reported is -6.57 and calculated is -7.72 to 7.82 K Cal/mol (Table 1) similarly with ciprofloxacin the value of IC50 for non-resistant to resistant is 3.5- 10 µg/ml where Mic is 0.001-0.5 µg/ml, binding energy reported -7.13 and calculated was 8.37 Kcal/mol. In the case of Tetracycline, the value of reported IC50 was 35- 47 µg/ml and calculated is 54-60 µg/ml and value of reported and calculated ∆G is -12.48 and -7.62 to 7.07K Cal/mol respectively. The reason behind difference of ∆G is, large value of V 4.16 and 2.23 for tetracycline.
Significance: The equations and derivation give better understanding between ZOI (x) and Dissipative Value (V) we can predict the resistance and factors effecting resistance which give low value of ZOI (x) against same concentration of antibiotics against non-resistance bacteria
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