New Insights into Modelling Bacterial Growth with Reference to the Fish Pathogen Flavobacterium psychrophilum

Abstract

Simple Summary

Flavobacterium psychrophilum is a cold-water bacterium responsible for cold water disease and rainbow trout fry syndrome which has significant impacts on fish health and, by extension, negative economic impacts on aquaculture operations. Models can be applied to bacterial growth curves yielding parameter estimates describing rates of bacterial growth and the time it takes for a bacterium to reach its exponential phase of growth (lag time). These parameter estimates can be used to establish the relationship between microbial growth and environmental variables such as pH, temperature and effect of anti-microbial treatments. Two novel models are derived and their potential to describe bacterial growth assessed through their ability to mimic the growth of Flavobacterium psychrophilum on liquid media. Due to their mechanistic derivation, the proposed models result in flexible and robust growth functions that can be expressed as equations with biologically meaningful parameters. Based upon statistical measures of goodness-of-fit and cross-validation, the purposed models were able to describe satisfactorily the growth of Flavobacterium psychrophilum on various media. Furthermore, the proposed models also provide insight into underlying mechanisms that are driving microbial growth and how the current environment affects bacterial rate of growth.

Abstract

Two new models, based upon the principles promulgated by Baranyi and co-workers are presented and resulting growth functions evaluated based upon their ability to mimic bacterial growth of the fish pathogen Flavobacterium psychrophilum. These growth functions make use of a dampening function to suppress potential growth, represented by a logistic, and are derived from rate:state differential equations. Dampening effects are represented by a rectangular hyperbola or a simple exponential, incorporated into a logistic differential equation and solved analytically resulting in two newly derived growth equations, viz. logistic × hyperbola (log × hyp) and logistic × exponential (log × exp). These characteristics result in flexible and robust growth functions that can be expressed as equations with biologically meaningful parameters. The newly derived functions (log × hyp and log × exp), along with the Baranyi (BAR), simple logistic (LOG) and its modified form (MLOG) were evaluated based upon examination of residuals and measures of goodness-of-fit and cross-validation. Using these criteria, log × hyp, log × exp and BAR performed better than, or at least equally well as, LOG and MLOG. In contrast with log × exp and BAR, log × hyp can be easily manipulated mathematically allowing for simple algebraic expressions for time and microbial biomass at inflexion point, in addition to maximum and scaled maximum growth rates.