Analysis of the lag phase to exponential growth transition by incorporating inoculum characteristics A.J. Verhulst, A.M. Cappuyns, E. Van Derlinden, K. Bernaerts, J.F. Van Impe * CPMF2 1 e Flemish Cluster Predictive Microbiology in Foods, Chemical and Biochemical Process Technology and Control (BioTeC), Department of Chemical Engineering, Katholieke Universiteit Leuven, W. de Croylaan 46, B-3001 Leuven, Belgium article info Article history: Received 10 March 2010 Received in revised form 2 July 2010 Accepted 11 July 2010 Available online 16 July 2010 Keywords: Predictive food microbiology Individual-based modelling Biomass distributions Single-cell abstract During the last decade, individual-based modelling (IbM) has proven to be a valuable tool for modelling and studying microbial dynamics. As each individual is considered as an independent entity with its own characteristics, IbM enables the study of microbial dynamics and the inherent variability and heteroge- neity. IbM simulations and (single-cell) experimental research form the basis to unravel individual cell characteristics underlying population dynamics. In this study, the IbM framework MICRODIMS, i.e., MICRObial Dynamics Individual-based Model/Simulator, is used to investigate the system dynamics (with respect to the model and the system modelled). First, the impact of the time resolution on the simulation accuracy is discussed. Second, the effect of the inoculum state and size on emerging individual dynamics, such as individual mass, individual age and individual generation time distribution dynamics, is studied. The distributions of individual characteristics are more informative during the lag phase and the transition to the exponential growth phase than during the exponential phase. The first generation time distributions are strongly influenced by the inoculum state. All inocula with a pronounced heterogeneity, except the inocula starting from a uniform distribution, exhibit commonly observed microbial behaviour, like a more spread first generation time distribution compared to following generations and a fast stabilisation of biomass and age distributions. Ó 2010 Elsevier Ltd. All rights reserved. 1. Introduction By combining microbiological knowledge, experimental data and mathematical techniques, predictive (food) microbiology designs models in order to describe, understand and predict microbial dynamics in food products. Traditionally, microbial growth is modelled from a macroscopic viewpoint by describing the dynamics of a population parameter (e.g., total cell number) as a function of time (e.g., model of Baranyi and Roberts, 1994). These models are able to predict microbial dynamics under uncomplicated environ- mental conditions, but fail to provide accurate predictions when more complex situations occur, such as, adaptation phenomena (e.g., lag phase) and microbial dynamics in structured food products (Brocklehurst, 2004). Individual-based Modelling (IbM) provides a framework to model complex microbial dynamics. By considering the individual cell as the basic modelling unit, it is more natural to include (i) mechanistic knowledge on the behaviour and interactions of the microbial cell, (ii) individual biological variability, and (iii) interactions between the cells and their environment. During the last decade, IbM has proven to be an important tool for modelling microbial dynamics (e.g., Kreft et al., 1998; Dens et al., 2005; Prats et al., 2006; Ferrer et al., 2008; Hellweger and Bucci, 2009). Emergence of population dynamics is investigated via the fundamental unit of bacterial life, i.e., an individual cell. Each indi- vidual is considered as an independent entity with its own state (e.g., mass, age,.) and behaviour. Nevertheless, all individuals are of the same type (i.e., bacterium or yeast) and have the same potential regarding state and behaviour. As individual microbial behaviour is translated into rules and/or equations, IbM provides a suitable framework to study microbial behaviour at both the individual and the population level. IbM is a leverage to gain more information, e.g., concerning the distributions of individual characteristics, and is always complementary to experimental research. Individual and emerging population dynamics should be validated against experi- mental data and prior knowledge (e.g., Dens et al., 2005). Advances in single-cell research result in an increasing amount of biological knowledge (e.g., Elfwing et al., 2004; Wakamoto et al., 2005; * Corresponding author. Tel.: þ32 16 32 14 66; fax: þ32 16 32 29 91. E-mail addresses: anke.verhulst@cit.kuleuven.be (A.J. Verhulst), astrid.cappuyns@ cit.kuleuven.be (A.M. Cappuyns), eva.vanderlinden@cit.kuleuven.be (E. Van Derlinden), kristel.bernaerts@cit.kuleuven.be (K. Bernaerts), jan.vanimpe@cit.kuleuven.be (J.F. Van Impe). 1 www.cpmf2.be. Contents lists available at ScienceDirect Food Microbiology journal homepage: www.elsevier.com/locate/fm 0740-0020/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.fm.2010.07.014 Food Microbiology 28 (2011) 656e666