Bacterial Normalized Binary Fission Growth Model

Mathematical models have traditionally been used to facilitate the interpretation of bacterial growth curves in order to more accurately understand and identify variations in bacterial proliferation. Here, a binary fission growth model was developed to normalize starting bacterial levels, allowing for the identification of changes in bacterial growth and the separation of a bacterial population as it correlates to size. This normalized binary fission model (NBF) relies on a multi-bin growth mode, where each bin is associated with a size range during a growth cycle. The proposed NBF model allows for a determination of the percentage of treated bacteria eradicated compared to a control sample, either generally across all bacterial binary fission sizes or specific to a size range or bin. Comparisons between the NBF model and experimental observations demonstrates that bacterial growth curves, and the ratio of sample growth to a control, can be used to both determine and normalize initial variations in bacterial size, and quantity, among test samples, as well as identify final nutrient levels and the percentage of bacteria affected by treatment. Significance StatementIt is difficult to determine the effectiveness of selective bacterial eradication based upon a bacterias characteristics size, related to acoustic resonance. Here we develop a binary fission model to analyze effect on growth curves of size depend eradications. Understanding the effect on growth curves provides a method to extract the eradication percentage and initial bacterial level differences between treated sample and control sample, by using the ratio of treated growth curve to control growth curve.