A New Mathematical Modeling Approach to Inferring the Distribution of Microbial Resistance From Time-Kill Experiments

Tuesday, November 9, 2010: 4:55 PM
250 C Room (Salt Palace Convention Center)
Pratik Bhagunde, Chemical and Biomolecular Engineering Department, University of Houston, Houston, TX, Vincent H. Tam, College of Pharmacy, University of Houston, Houston, TX and Michael Nikolaou, Chemical and Biomolecular Engineering, University of Houston, Hoston, TX

Time-kill experiments are in vitro experiments where the response of a bacterial population to an antibiotic at a number of fixed concentrations is measured. The main purpose for such experiments is the quick (24-hour) assessment of whether a bacterial population can be completely eradicated by an antibiotic or whether it may eventually regrow due to the presence of resistant subpopulations. Such assessment is important either in developing new antibiotics (a lengthy and laborious process) or for rapid selection of an appropriate antibiotic in a clinical setting.

Because bacterial populations are heterogeneous (namely consist of subpopulations of varying degrees of resistance) yet only the entire bacterial population size is measured over time in time-kill experiments, it is difficult to develop a dynamic model that fits time-kill data and can make longer-term predictions from short-term data.

In prior work, we developed and experimentally verified a general model structure that can describe, with some heuristic approximations, the dynamics of heterogeneous bacterial populations under linear dynamics, as is the case with bacterial populations declining under antibiotic treatment. In this work, we extend this model structure in two important ways: First, the general case of either total population decline or logistic growth is handled. Second, and more important, the distribution of resistance (expressed in terms of the bacterial kill rate distribution) can be inferred from short-term measurements of the entire population. Such inference is importance for both antibiotic development and therapeutic use.

The proposed approach is tested experimentally on in vitro measurements of both an entire bacterial population over time and a resistant subpopulation (with three times the minimum inhibitory concentration (MIC) of the average). The results indicate that the accuracy of the inferred resistance distribution over the population is acceptable and useful conclusions can be drawn for the efficacy of an antibiotic on a heterogeneous bacterial population.

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