Abstract
A two-parameter model describes the microbial growth trend of planktonic cultures. Based on the assumption that cell duplication underlies the growth, the model defines an average generation time that depends on time and complies with the phenomenological evidence that the growth rate is naught at the start and at the end of the process. This is tantamount as to replace the real growth process with a virtual one, where all the generation lines stemming from the inoculum are synchronous and imply a duplication tree with no truncated branches. A simple function that complies with these constraints is τ=(a/t+bt), where a and b are parameters defined through a best fit treatment of the experimental plate count data. Surprisingly simple relationships come out for specific items of the growth trend, like maximum specific growth rate, eventual cell number, Nmax, duration of lag phase, etc., as well as some intriguing correlations between them. Published plate count data allowed testing the reliability of the model. The agreement is satisfactory being in line with the accuracy of the data (R2 ≥ 0.98).
Highlights
The phenomenology of microbial effects in food and animal or vegetal tissues is mainly related to the number of cells per unit volume or unit mass of the system
Based on the assumption that cell duplication underlies the growth, the model defines an average generation time that depends on time and complies with the phenomenological evidence that the growth rate is naught at the start and at the end of the process
The present paper suggests a model that does not take into account any specific growth mechanism, aiming to predict just the resultant of the cell duplication applied to a vast microbial population
Summary
The phenomenology of microbial effects in food and animal or vegetal tissues is mainly related to the number of cells per unit volume or unit mass of the system. Plate count data (number of CFU per unit volume, or unit mass) reflect the empirical resultant of the actual behavior of many thousands of cells. The best treatments of such data are those that strictly reflect their empirical nature This attitude is at the fundament of models [1,2,3] that made use of damped exponential functions to describe the sigmoid increase (or decrease) of the population density. The relevant expressions for the maximum growth rate, the maximum CFU density, the lag-time and the effect of temperature changes contain a number of parameters, many of which become adjustable quantities in the fitting treatment. Data sets reported in the literature for several microbial species allow a reliability test of the model: the accuracy of the fits obtained is in line (R2 ≥ 0.98) with the best ones so far achieved. Since the two parameters of the model reflect the potential growth extent and the sharpness of the growth trend, the model can be of help for defining protocols to tune the microbial growth on changing the environmental conditions
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