The aim of the study was a profound insight into the antibiotic resistance development in uropathogenic Escherichia coli strains with the use of some mathematical and statistical methods. During the previous study some antibiotics (amoxicillin, ciprofloxacin, gentamycin, and tobramycin) were applied to induce the resistance of E. coli strains, which led to the generation of ∼120 derivative strains with changed antibiotic susceptibility profiles. In this work, quantitative analysis was performed based on the strains defined as values of vectors of susceptibility for all the antibiotics' use. The Pearson correlation coefficient was used to define the correlation dissimilarity (distance) of the strains, which was further applied to hierarchical clustering. Analogously, the antibiotics were presented as vectors of susceptibility values of all the investigated strains. Correlation and cluster analysis were performed for antibiotics. The hclust method from the R system with the Ward method was used as a class agglomeration method. Mathematical analysis revealed two types of statistically relevant interactions-between antibiotics and derivative strains, as well as between the effect of individual antibiotics on the bacterial strains. These observed correlations can play a potential role for modeling uropathogenic E. coli (UPEC) resistant changes, based on the particular antibiotic used to initiate resistance development, or a model helping to predict drug resistance interactions in various UPEC strains. The obtained results can lead to development of much more sophisticated mathematical models, which, in turn, can be a potentially useful tool as a drug resistance trend predictor, both for clinicians and epidemiologists.
Keywords: UPEC; induced antibiotic resistance; mathematical analysis.