The Origin of the Time Scale: A Crucial Issue for Predictive Microbiology

Alberto Schiraldi^1,

¹Formerly at the Department Food Environmental and Nutritional Sciences (DeFENS), University of Milan, Italy

Cite this paper:
Alberto Schiraldi. The Origin of the Time Scale: A Crucial Issue for Predictive Microbiology. Journal of Applied & Environmental Microbiology. 2022; 10(1):35-42. doi: 10.12691/jaem-10-1-4

Abstract

The collective behavior of microbial cells in a batch culture is the result of interactions among individuals and effects of the surrounding medium, which changes during the growth progress. A semi empirical model skips biological and physiological peculiarities of the microorganisms and focuses on the observed sigmoid shape of the growth curve that is a common feature of batch cultures of pro- and eukaryotic microorganisms. The model replaces the observed growth trend with the behavior of an ideal batch culture that undergoes an unperturbed duplication process. It leads one to recognize that: • the origin of the time scale for the microbes, θ, differs from that of the observer, t; • the absolute reference state for any batch culture is log (N) = 0 (no matter the log base) for θ = 0; • the cell duplication occurs after an active latency gap, θ₀, that decreases with increasing inoculum population, log₂(N₀) and increasing temperature; • θ₀ substantially differs from the lag phase, λ, considered by most authors; • the use of reduced variables allows gathering different growth curves in a single master plot; • the model applies to batch cultures which undergo change of the environmental conditions and predicts the width of the intermediate latency gap just after the change; • the expression for the decay trend of the microbial population allows definition of a parameter suitable to rank the effects of bactericidal drugs. The model justifies the demand of more restricted safety limits of microbial loads.

Keywords:
predictive model batch cultures latency gap time scale

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Zwietering, M. H., Jongenburger I., Rombouts F. M., van't Riet, K. 1990. Modeling of the bacterial growth curve. Appl. Environ. Microbiol., 56, 1875-1881.
[2]	Baranyi, J., Roberts, T. A. 1994. A dynamic approach to predicting bacterial growth in food. Int. J. Food Microbiol. 23, 277-294.
[3]	Baranyi, J., Roberts, T. A. 1995. Mathematics of predictive food microbiology. Int. J. Food Microbiol. 26, 199-218.
[4]	Baranyi, J. 1998. Comparison of stochastic and deterministic concepts of bacterial lag. J. Theor. Biol., 192, 403-408.
[5]	Baranyi, J., Pin, C. 2001. A parallel study on bacterial growth and inactivation. J. Theor. Biol., 210, 327-336.
[6]	Whiting, R.C., Bagi, L.K. 2002. Modeling the lag phase of Listeria monocytogenes. Int. J. Food Microbiol., 73, 291-295.
[7]	Swinnen, I.A.M., Bernaerts, K., Dens, E.J.J., Geeraerd, A.H., Van Impe, J.F. 2004. Predictive modelling of the microbial lag phase: a review. Int. J. Food Microbiol., 94, 137-159.
[8]	Kutalik, Z., Razaz, M., Baranyi, J. 2005. Connection between stochastic and deterministic modelling of microbial growth. J. Theor. Biol., 232, 285-299.
[9]	Neidhardt F. C. 1999. “Bacterial growth: constant obsession with dN/dt,” Journal of Bacteriology, vol. 181, no. 24, pp. 7405-7408.
[10]	Yates, G. T. and Smotzer, T. 2007. On the lag phase and initial decline of microbial growth curves. J. Theor. Biol., 244, 511-517.
[11]	Baranyi, J., George, S.M., Kutalik, Z. 2009. Parameter estimation for the distribution of single cell lag times. J. Theor. Biol., 259, 24-30.
[12]	Bertrand, R. L. 2019. Lag phase is a dynamic, organized, adaptive, and evolvable period that prepares bacteria for cell division. J. Bacteriol., 201 (7) 1-21.
[13]	Ziv, N., Brandt, N.J., Gresham, D. The Use of Chemostats in Microbial Systems Biology. J. Vis. Exp., 80 (2013) e50168.
[14]	A. Cavagna, A. Cimarelli, I. Giardina, G. Parisi, R. Santagati, F. Stefanini and M. Viale, Scale-free correlations in starling flocks, PNAS, 107, 26 (2010) 11865-11870. Supporting Information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1005766107/-/DCSupplemental.
[15]	M. Ballerini, N. Cabibbo, R. Candelier, A. Cavagna, E. Cisbani, I. Giardina, V. Lecomte, A. Orlandi, G. Parisi, A. Procaccini, M. Viale and V. Zdravkovic, Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study, PNAS , 105, 29 (2008) 1232-1237.
[16]	D. Gonze, K. Z Coyte, L. Lahti and K. Faust, Microbial communities as dynamical systems, Curr. Opinion Microbiol., 44 (2018) 41-49.
[17]	S.López, M. Prieto, J. Dijkstra, M.S.Dhanoa and J. France Statistical evaluation of mathematical models for microbial growth, Int. J. Food Microbiol., 96 (2004) 289-300.
[18]	A. Schiraldi, Microbial growth in planktonic conditions, Cell Develop. Biol., 6 (2) (2017) 185.
[19]	Schiraldi A.2017. “A self-consistent approach to the lag phase of planktonic microbial cultures,” Single Cell Biology, vol. 6, no. 3, p. 3.
[20]	Schiraldi A. 2020. Growth and decay of a planktonic microbial culture. Int. J. Microbiology, Article ID 4186468.
[21]	Schiraldi A., Foschino R. 2021. An alternative model to infer the growth of psychrotrophic pathogenic bacteria. J. Appl. Microbiol., and related “Supporting Information”.
[22]	Schiraldi A. Foschino R. 2021. Time scale of the growth progress in bacterial cultures: a self-consistent choice. RAS Microbiology and Infectious Diseases, 1(3) 1-8.
[23]	A. Schiraldi, Batch Microbial Cultures: A Model that can account for Environment Changes, Adv. Microbiol., 11 (2021) 630-645.
[24]	M. Deforet, D. van Ditmarsch, and J. B. Xavier, Cell-Size Homeostasis and the Incremental Rule in a Bacterial Pathogen, Biophys. Journal, 109 (2015) 521-528.
[25]	M. Schaechter, From growth physiology to system biology, Int. Microbiol., 9 (2006) 157-161.
[26]	Tyrer H, Ainsworth P, Ibanŏglu S, Bozkurt H (2004) Modelling the growth of Pseudomonas fluorescens and Candida sake in ready-to-eat meals. J Food Eng 65: 137-143.
[27]	E.J. Dens, K. Bernaerts, A.R. Standaert, J.F. Van Impe. Cell division theory and individual-based modeling of microbial lag Part I. The theory of cell division. Int. J. Food Microbiol., 101 (2005) 303-318.
[28]	E.J. Densa, K. Bernaertsa, A.R. Standaerta, J.-U. Kreftb, c,1, J.F. Van Impe. Cell division theory and individual-based modeling of microbial lag Part II. Modeling lag phenomena induced by temperature shifts. J. Food Microbiol., 101 (2005) 319-332.
[29]	I.A.M. Swinnen, K. Bernaerts, K. Gysemans, J.F. Van Impe. Quantifying microbial lag phenomena due to a sudden rise in temperature: a systematic macroscopic study. Int. J. Food Microbiol., 100 (2005) 85-96.
[30]	Egli T., Microbial growth and physiology: a call for better craftsmanship, Frontiers in Microbiology, 6, 287 (2015) 1-12.
[31]	K. Koutsoumanis, Predictive Modeling of the Shelf Life of Fish under Non isothermal Conditions, Appl. Environ.l Microbiol., 67 (2001) 1821-29. 2001.
[32]	R.J. Leiphart, D. Chen, A.P. Peredo, A. E. Loneker, P.A. Janmey, Mechanosensing at Cellular Interfaces, Langmuir, 35 (2019) 7509-7519.
[33]	V. Antolinos, M. Muñoz-Cuevas, M. Ros-Chumillas, P.M. Periago, P.S. Fernández, Y. Le Marc. Modelling the effects of temperature and osmotic shifts on the growth kinetics of Bacillus weihenstephanensis in broth and food products. Int. J. Food Microbiol., 158 (2012) 36-41.
[34]	I.A. Taub, F.E. Feeherry, E.W. Ross, K. Kustin, and C.J. Doona. A Quasi-Chemical Kinetics Model for the Growth and Death of Staphylococcus aureus in Intermediate Moisture Bread. J Food Sci., 68(8) (2003) 2530-37.
[35]	C.J. Doona, F.E. Feeherry, E.W. Ross. A quasi-chemical model for the growth and death of microorganisms in foods by non-thermal and high-pressure processing. Int. J. Food Microbiol., 100 (2005) 21-32.