# Exploring Bacterial Colonies in Solid Foods or Model Foods Using Non-Destructive Techniques

Anne Thierry, Sophie Jeanson, Sylvie Lortal

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Anne Thierry, Sophie Jeanson, Sylvie Lortal (Dir.). Exploring Bacterial Colonies in Solid Foods or Model Foods Using Non-Destructive Techniques. Frontiers in Microbiology, Février 2016, 103 p., 2016, Frontiers in Microbiology, 978-2-88919-743-9. 10.3389/978-2-88919-743-9 . hal-01276165

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Distributed under a Creative Commons Attribution 4.0 International License
EXPLORING BACTERIAL
COLONIES IN SOLID
FOODS OR MODEL FOODS
USING NON-DESTRUCTIVE
TECHNIQUES

EDITED BY: Sophie Jeanson, Sylvie Lortal and Anne Thierry

PUBLISHED IN: Frontiers in Microbiology

<figure><img src="image_2.png" /></figure>

frontiers Research Topics
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ISSN 1664-8714
ISBN 978-2-88919-743-9
DOI 10.3389/978-2-88919-743-9

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EXPLORING BACTERIAL COLONIES IN
SOLID FOODS OR MODEL FOODS USING
NON-DESTRUCTIVE TECHNIQUES

Topic Editors:

**Sophie Jeanson**, French National Institute for Agricultural Research (INRA), UMR1253,
France

**Sylvie Lortal**, French National Institute for Agricultural Research (INRA), UMR1253, France

**Anne Thierry**, French National Institute for Agricultural Research (INRA), UMR1253, France

<figure><img src="image_4.png" /></figure>

Colony of lactic acid bacteria (Lactococcus lactis) in cheese, surrounded by fat-protein network, observed
by confocal laser-scanning microscopy. Bacteria are shown in green, protein matrix in black, lipids in red.

Image by Marie-Noëlle Madec, INRA, STLO, France

Bacteria are always present in foods, either as initial contamination or as technological agents. In solid foods, they are immobilized and develop as colonies. So far, there is a lack of knowledge about the bacteria in colonies, growth and physiology. Non-destructive and resolute techniques, such as fluorescent microscopy, now allow investigating the world of bacteria in colonies and their surroundings in food, at the microscopic scale.

**Citation:** Jeanson, S., Lortal, S., Thierry, A., eds. (2016). Exploring Bacterial Colonies in Solid Foods or Model Foods Using Non-Destructive Techniques. Lausanne: Frontiers Media. doi: 10.3389/978-2-88919-743-9
Table of Contents

**04 Editorial: Exploring Bacterial Colonies in Solid Foods or Model Foods Using Non-Destructive Techniques**

Sophie Jeanson and Anne Thierry

**06 Bacterial Colonies in Solid Media and Foods: A Review on Their Growth and Interactions with the Micro-Environment**

Sophie Jeanson, Juliane Floury, Valérie Gagnaire, Sylvie Lortal and Anne Thierry

**26 Colonial vs. planktonic type of growth: mathematical modeling of microbial dynamics on surfaces and in liquid, semi-liquid and solid foods**

Panagiotis N. Skandamis and Sophie Jeanson

**35 Recent trends in non-invasive in situ techniques to monitor bacterial colonies in solid (model) food**

María M. Lobete, Estefania Noriega Fernandez and Jan F. M. Van Impe

**44 Growth and location of bacterial colonies within dairy foods using microscopy techniques: a review**

Cian D. Hickey, Jeremiah J. Sheehan, Martin G. Wilkinson and Mark A. E. Auty

**52 In situ examination of Lactobacillus brevis after exposure to an oxidizing disinfectant**

Yu Zhao, Susanne Knöchel and Henrik Siegumfeldt

**60 Laser-induced speckle scatter patterns in Bacillus colonies**

Huisung Kim, Atul K. Singh, Arun K. Bhunia and Euiwon Bae

**69 Microcalorimetric study of the growth of Streptococcus thermophilus in renneted milk**

Irina Stulova, Natalja Kabanova, Tiina Kriščiunaite, Kaarel Adamberg, Tiiu-Maie Laht and Raivo Vilu

**82 Measurement of pH micro-heterogeneity in natural cheese matrices by fluorescence lifetime imaging**

Zuzana Burdikova, Zdenek Svindrych, Jan Pala, Cian D. Hickey, Martin G. Wilkinson, Jiri Panek, Mark A. E. Auty, Ammasi Periasamy and Jeremiah J. Sheehan

**92 Diffusion of solutes inside bacterial colonies immobilized in model cheese depends on their physicochemical properties: a time-lapse microscopy study**

Juliane Floury, Ilham El Mourdi, Juliana V. C. Silva, Sylvie Lortal, Anne Thierry and Sophie Jeanson
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CrossMark

# Editorial: Exploring Bacterial Colonies in Solid Foods or Model Foods Using Non-Destructive Techniques

Sophie Jeanson<fnref n="1" />,<fnref n="2" />* and Anne Thierry<fnref n="1" />,<fnref n="2" />

**Keywords:** bacterial colonies, growth, physiology, solid foods, modeling, non-destructive techniques

## The Editorial on the Research Topic

### Exploring Bacterial Colonies in Solid Foods or Model Foods Using Non-Destructive Techniques

Bacteria are present in all foods, whether they are indigenous or inoculated. They can be beneficial to the quality of foods, responsible for food spoilage, or even pathogens. In solid food products, bacteria are immobilized. They thus grow as colonies entrapped within the food products or on the food surfaces. In both cases, bacteria interact with the solid matrix, sometimes facing difficulties to access the nutrients as nutrients have to diffuse from the matrix to the bacterial colonies. Bacterial development can thus be impaired in solid matrices in comparison to planktonic growth. To control the growth of bacteria in solid foods is then of major importance. In the case of pathogens, it is crucial for safety issues to predict how the bacteria present as initial contaminants will develop. In the case of inoculated bacteria, such as lactic acid bacteria, it is also crucial to control their development because they are responsible for the final quality of the food products. However, studies on the growth of bacteria have been essentially focused on growth in liquid media. Resolute techniques, which include both microcopy approaches and quantitative techniques, have now been developed to observe colonies at the microscopic scale. They allow studying the variation of growth in different contexts either in model growth culture media or in model foods.

This Research Topic starts with four review papers. A first comprehensive review about bacterial colonies redraws the history of the studies on colonies, synthetizes the conditions of growth in which growth in colonies differs from planktonic growth, and finally presents concepts of the interaction of bacterial colonies with the food matrix in which they grow, with cheese as an example (Jeanson et al.). The second review demonstrates the importance of modeling the growth of bacterial colonies in solid foods despite a lack of knowledge. The different types of models and their potential consequences on decisions are presented and discussed (Skandamis and Jeanson). The third review shows how non-invasive techniques can be used to observe bacterial growth and also quantify the bacterial metabolism in colonies at the microscopic scale (Lobete et al.). The last review paper shows how microscopy techniques are particularly valuable to increase knowledge about bacterial colonies in model foods and foods. Fluorescent microscopy allows targeting metabolites and understand the physiology of bacteria within colonies (Hickey et al.).

The five following papers present original results in the field. Using an automated microscope coupled with fluorescence dyes, it was possible to demonstrate that the exposure to an oxidizing disinfectant led to different morphologies of cells depending on the strains and that dead cells were randomly distributed within the micro-colonies (Zhao et al.). The following study demonstrates the

**OPEN ACCESS**

Edited and reviewed by:

Giovanna Suzzi,
Università degli Studi di Teramo, Italy

*Correspondence:

Sophie Jeanson
sophie.jeanson@rennes.inra.fr

**Specialty section:**

This article was submitted to
*Food Microbiology,*
a section of the journal
*Frontiers in Microbiology*

Received: 12 November 2015

Accepted: 03 December 2015

Published: 22 December 2015

**Citation:**

Jeanson S and Thierry A (2015)
*Editorial: Exploring Bacterial Colonies in Solid Foods or Model Foods Using Non-Destructive Techniques.*
*Front. Microbiol.* 6:1440.
doi: 10.3389/fmicb.2015.01440

<footnote n="1">¹ Institut National de la Recherche Agronomique, UMR1253, Science and Technology of Milk and Eggs, Rennes, France,</footnote>

<footnote n="2">² AGROCAMPUS OUEST, UMR1253, Science and Technology of Milk and Eggs, Rennes, France</footnote>
accuracy of a phenotyping technology based on laser-induced speckle scatter patterns in *Bacillus* colonies. The authors showed that the distribution of speckle size is modified during the growth of colonies (Kim *et al.*).

The three following studies investigate bacterial colonies of lactic acid bacteria in their food environment in model cheeses or investigate the pH in their surrounding micro-environment in Cheddar cheeses. Physiology and growth of *Streptococcus thermophilus* colonies was compared in liquid milk and renneted milk using microcalorimetry. The results showed that above a threshold size of colonies (low inoculation levels), growth rates and metabolism in renneted milk differed from the one observed in liquid milk (Stulova *et al.*). The use of fluorescence lifetime imaging was shown to be relevant to investigate the pH micro-heterogeneity in Cheddar cheeses (Burdikova *et al.*). These results suggest that the surroundings of bacterial colonies within cheeses could differ from homogeneous growth conditions in liquid medium. The last study questioned the access of bacteria in colonies to their nutrients, through the assessment of diffusion of solutes inside colonies. The diffusion of high molecular weight molecules was assessed inside *Lactococcus lactis* colonies grown in a model cheese. The results led to the conclusion that diffusion of molecules inside bacterial colonies depends on the physicochemical properties of the molecules (Floury *et al.*).

In conclusion, since bacteria mainly grow in colonies in foods, increase knowledge on growth and physiology of bacteria growing as colonies is now a crucial issue. This is achieved by the recent development of non-invasive techniques that allows investigating at the microscopic scale with time lapse and quantitative analyses. Knowledge about the growth and the adaptive response of bacteria to the food environment will continue to grow by addressing the remaining questions about interactions between bacterial colonies and their food environment.

## AUTHOR CONTRIBUTIONS

SJ: wrote the editorial. AT: revised and improved the editorial.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2015 Jeanson and Thierry. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
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# Bacterial Colonies in Solid Media and Foods: A Review on Their Growth and Interactions with the Micro-Environment

Sophie Jeanson¹,²*, Juliane Floury¹,², Valérie Gagnaire¹,², Sylvie Lortal¹,² and Anne Thierry¹,²

¹INRA, UMR1253, Science and Technology of Milk and Eggs, Rennes, France, ²AGROCAMPUS OUEST, UMR1253, Science and Technology of Milk and Eggs, Rennes, France

**OPEN ACCESS**

**Edited by:**

Jean-Christophe Augustin,
Ecole Nationale Vétérinaire d'Alfort,
France

**Reviewed by:**

Ilkin Yucel Sengun,
Ege University, Turkey
Kostas Koutsoumanis,
Aristotle University of Thessaloniki,
Greece

*Correspondence:

Sophie Jeanson
sophie.jeanson@rennes.inra.fr

**Specialty section:**

This article was submitted to
*Food Microbiology,*
a section of the journal
*Frontiers in Microbiology*

**Received:** 03 September 2015

**Accepted:** 31 October 2015

**Published:** 01 December 2015

**Citation:**

Jeanson S, Floury J, Gagnaire V, Lortal S and Thierry A (2015) Bacterial Colonies in Solid Media and Foods: A Review on Their Growth and Interactions with the Micro-Environment. *Front. Microbiol.* 6:1284.
doi: 10.3389/fmicb.2015.01284

Bacteria, either indigenous or added, are immobilized in solid foods where they grow as colonies. Since the 80's, relatively few research groups have explored the implications of bacteria growing as colonies and mostly focused on pathogens in large colonies on agar/gelatine media. It is only recently that high resolution imaging techniques and biophysical characterization techniques increased the understanding of the growth of bacterial colonies, for different sizes of colonies, at the microscopic level and even down to the molecular level. This review covers the studies on bacterial colony growth in agar or gelatine media mimicking the food environment and in model cheese. The following conclusions have been brought to light. Firstly, under unfavorable conditions, mimicking food conditions, the immobilization of bacteria always constrains their growth in comparison with planktonic growth and increases the sensibility of bacteria to environmental stresses. Secondly, the spatial distribution describes both the distance between colonies and the size of the colonies as a function of the initial level of population. By studying the literature, we concluded that there systematically exists a threshold that distinguishes micro-colonies (radius <100–200 µm) from macro-colonies (radius >200 µm). Micro-colonies growth resembles planktonic growth and no pH microgradients could be observed. Macro-colonies growth is slower than planktonic growth and pH microgradients could be observed in and around them due to diffusion limitations which occur around, but also inside the macro-colonies. Diffusion limitations of milk proteins have been demonstrated in a model cheese around and in the bacterial colonies. In conclusion, the impact of immobilization is predominant for macro-colonies in comparison with micro-colonies. However, the interaction between the colonies and the food matrix itself remains to be further investigated at the microscopic scale.

**Keywords:** bacterial colony, spatial distribution, diffusion limitation, porosity, cheese, Growth
# INTRODUCTION

Bacteria in food products, whether those added as inocula or those naturally present, are always immobilized. They develop as colonies, either on the surface of or embedded within the food matrices and interact with their micro-environment (Hickey et al., 2015). As previously stated (Hills, 2001), the bacterial cells of the colony "consume the nutrients from the surrounding (food) matrix and in return, liberates end-products into the surrounding matrix modifying its micro-environment."

Bacterial colonies and biofilms are both formed by clusters of bacteria. Whilst published research focusing on biofilms is abundant (Flemming and Wingender, 2010), that based on the bacterial colony is relatively scarce, especially with respect to food. The question remains unanswered whether there are different phenotypes of bacteria making up biofilms and colonies (and especially surface colonies). A biofilm is well-defined as: "a microbiologically derived sessile community characterized by cells that are irreversibly attached to a substratum or interface or to each other, are embedded in a matrix of extracellular polymeric substances that they have produced, and exhibit an altered phenotype with respect to growth rate and gene expression" (Donlan and Costerton, 2002). On the other hand, bacterial colonies are not so well-defined. In this review, a bacterial colony is taken as a clonal group of cells developed either on the surface of or embedded within a gel-type solid (culture medium or food) from which it takes its growth substrates. Unlike biofilms, a colony is limited by size displaying a definite maximum radius ranging between a few µm to a few mm. As the production of extracellular polymeric substances has never been investigated in colonies, we considered not to be a mandatory property. This review will focus only on bacterial colonies and exclude biofilms.

The literature on growth and metabolism of bacteria growing in colonies is scarce. Usually, growth and metabolism of food bacteria (whether desirable or undesirable) are studied in broth media, i.e., in planktonic cultures. However, in order to predict the growth of bacteria in food, it is preferable to perform the study in conditions that closely reflect the natural condition, i.e., in solid model foods. Furthermore, it has been shown that the predictive models of growth built from data taken from liquid cultures are not accurate in describing immobilized growth, especially under stressful conditions that exist in a food medium (Pipe and Grimson, 2008; Skandamis and Jeanson, 2015). Although, the context of most studies cited in this review relates to food, all of them were performed using laboratory media, such as agar or gelatine media, mimicking the growth parameters of food (*a*<sub>w</sub>, pH, NaCl concentration, etc.). It is only very recently that model foods, such as a model cheese, have been used to study the growth of bacterial colonies *in situ*. Both agar/gelatine and foods are matrices in which bacterial colonies can be embedded (submerged colonies), or on which bacterial colonies can attach (surface colonies). However, there is a major difference between agar/gelatine based media and food matrices. Agar/gelatine media are "neutral" matrices because agar and gelatine are not themselves modified by bacteria, whilst food matrices constitute both a structure and a bound substrate for the bacteria. For example, caseins in cheese are a gel-type structure

and also provide nitrogen sources to bacteria. This means that food matrices may change by the bacterial activity.

The aim of this review is to describe the growth of colonies by pointing out when and how it differs from the planktonic growth. We particularly discuss the occurrence of variability at the microscopic scale of the physiological states inside the colony, of pH inside and around colonies and of oxygen around the colonies. The diffusion of substrates within the matrix and the access of bacteria to the substrates is also a major concern for the bacterial activity. The second objective is to build concepts on the different situations when growth of bacteria is impacted by the growth in colonies or not, depending on the initial level of population and two other concepts on the different ways of interacting with a food matrix, i.e., "bubble" or "sponge" concepts. Finally, experimental exploration of these two concepts will be examined in model cheese. Furthermore, a large table assembles the main parameters of growth and size of colonies for different experimental culture conditions studied with several bacterial species (Table 1).

# HISTORICAL PERSPECTIVE OF THE SCIENTIFIC COMMUNITY WORKING ON BACTERIAL COLONIES

As early as the 60's, Pirt, of the University of London, had started to take into account the immobilization of bacteria in the predictive growth models (Pirt, 1967). More recently the 90's, Wimpenny, from the University of Wales, started to study the consequences for bacteria by growing as colonies. Wimpenny et al. (1995), Thomas and Wimpenny (1996b), and McKay et al. (1997) performed studies on pathogenic bacteria, mostly as large colonies (>500 µm), either surface or submerged, on an agar medium. They determined several characteristics of the behavior in colonies comparing with planktonic growth, such as growth rates under different conditions, and pH gradients within and around colonies of different sizes. Before the research on this topic stopped at the University of Wales, Wimpenny collaborated with Brocklehurst (Walker et al., 1997; Wilson et al., 2002) of the Institute of Food Research (Norwich, UK) who was also working on the immobilized growth of pathogenic bacteria. Brocklehurst and his group (Parker et al., 1998; Wright et al., 2000; Meldrum et al., 2003) developed and patented the Gel Cassette System (Brocklehurst et al., 1995). This system has become the ideal tool to study submerged colonies in gelatine and agar media, which was associated with a non-destructive and *in situ* microscopic examination. It comprises a 2 mm thick frame in a PVC sleeve shown to be permeable to gas. The inoculated medium solidifies inside the frame and the immobilized cells develop as colonies within the formed solid gel. Subsequently, Brocklehurst collaborated with Malakar (Wageningen University, Netherlands) who worked on pH microgradients, introducing imaging techniques (Malakar et al., 2000), and on interactions between colonies of lactic acid bacteria (Malakar et al., 2003) and at a later date with Van Impe (Leuven University, Belgium) whose group still works at improving predictive growth models for immobilized pathogenic
<table><caption>TABLE 1 | Summary of the main studies about growth kinetics and distribution (size and neighboring distances) of bacterial colonies, with details of experimental conditions, and main conclusions.</caption><thead><tr><th>Influent parameters</th><th>Inoculation level or number of cells per colony</th><th>Experimental/Growth conditions</th><th>R<sub>col</sub> = colony radius R<sub>bnd</sub> = boundary radius (μm) d<sub>2D</sub> and d<sub>3D</sub> = distance 2D or 3D (μm)</th><th>Maximal growth rate (μ<sub>max</sub> in h<sup>-1</sup>) Generation time (T<sub>g</sub> in h)</th><th>Conclusions or comments</th><th>References</th></tr></thead><tbody><tr><td colspan="7"><strong>BACILLUS CEREUS</strong></td></tr><tr><td>[agar]</td><td>10 cfu/ml</td><td>B-H<br>30°C<br>pH 7.2<br>+ D<sub>1</sub>[6,3H] glucose<br>+ 125I-rhIGF-I (human<br>insulin-like growth factor)</td><td>[agar] = 1% &harr; R<sub>col</sub> = <strong>162</strong><br>[agar] = 5-7% &harr; R<sub>col</sub> = <strong>32</strong></td><td></td><td></td><td>Stacchini et al., 1998</td></tr><tr><td colspan="7"><strong>ESCHERICHIA COLI</strong></td></tr><tr><td>pH</td><td>10<sup>-3</sup>-10<sup>4</sup> cfu/ml</td><td>B-H agar</td><td></td><td>Temp. 10°C:</td><td>Only the effect of temperature was significant. Adequate correlation between area and viable counts.</td><td>Skandamis et al., 2007</td></tr><tr><td>Temperature</td><td></td><td>Submerged colonies (Gel cassette®)</td><td></td><td>Temp. 20°C:</td><td>Majority of cases (60%) where the model disagree with literature data on foods, the predictions were “fail-safe,” i.e., overestimated.</td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>Temp. 30°C:</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 5 &harr; μ<sub>max</sub> = <strong>0.405</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 6 &harr; μ<sub>max</sub> = <strong>0.561</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 7 &harr; μ<sub>max</sub> = <strong>0.653</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>Temp. 40°C:</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 5 &harr; μ<sub>max</sub> = <strong>1.365</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 6 &harr; μ<sub>max</sub> = <strong>1.451</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 7 &harr; μ<sub>max</sub> = <strong>1.622</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>Temp. 30°C:</td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 5 &harr; μ<sub>max</sub> = <strong>1.688</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 6 &harr; μ<sub>max</sub> = <strong>1.719</strong></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>pH 7 &harr; μ<sub>max</sub> = <strong>1.925</strong></td><td></td><td></td></tr><tr><td>Size of colonies</td><td>1 cfu/ml</td><td>Log(surface) = fn(viable cells)<br>100 pixels = 0.32 mm<sup>2</sup><br>= 10<sup>6</sup> cells/col</td><td>R<sub>col</sub> = <strong>160-224</strong> at 11 h<br>R<sub>col</sub> = <strong>746</strong> at 23 h</td><td></td><td></td><td>Mertens et al., 2012</td></tr><tr><td colspan="7"><strong>LACTOBACILLUS CURVATUS</strong></td></tr><tr><td>Inoculation level</td><td>5 cfu/ml<br>10<sup>2</sup> cfu/ml<br>10<sup>3</sup> cfu/ml</td><td>MRS + gelatine<br>20°C</td><td>R<sub>col</sub> = <strong>75</strong> at 150 h<br>R<sub>col</sub> = <strong>190</strong> at 380 h<br>R<sub>col</sub> = <strong>215</strong> at 239 h</td><td></td><td>Micro-gradients of pH observed for 5 and 100 cfu/ml (intra-colony interactions), but not for 1000 cfu/ml (inter-colony interactions)</td><td>Malakar et al., 2000</td></tr><tr><td>pH</td><td>Cells/colony when inter-colony interactions started:<br>6.10<sup>5</sup> cells/colony<br>&harr; 10<sup>2</sup> cfu/ml<br>10<sup>6</sup> cells/colony &harr;<br>1 cfu/ml</td><td>MRS + agar<br>30°C</td><td>R<sub>col</sub> when inter-colony interactions started:<br>pH 6 &harr; R<sub>col</sub> = <strong>113</strong><br>pH 7 &harr; R<sub>col</sub> = <strong>134</strong></td><td></td><td>For pH 7 and pH 6, if R<sub>col</sub> &lt;200 μm, the equations for growth are relevant; diffusion limitations start when the number of cells in a colony&gt; 10<sup>5</sup></td><td>Malakar et al., 2002a</td></tr></tbody></table>

(Continued)
<table><caption>TABLE 1 | Continued</caption><thead><tr><th>Influent parameters</th><th>Inoculation level or number of cells per colony</th><th>Experimental/Growth conditions</th><th>R<sub>col</sub> = colony radius R<sub>bnd</sub> = boundary radius (µm) d<sub>2D</sub> and d<sub>3D</sub> = distance 2D or 3D (µm)</th><th>Maximal growth rate (µ<sub>max</sub> in h<sup>-1</sup>) Generation time (T<sub>g</sub> in h)</th><th>Conclusions or comments</th><th>References</th></tr></thead><tbody><tr><td colspan="7"><strong>LACTOCOCCUS LACTIS</strong></td></tr><tr><td>[gelatine]</td><td>10<sup>3</sup> cfu/ml</td><td>BHIY + glucose 1% ± gelatine 12°C</td><td></td><td>Broth ⇌ µ<sub>max</sub> = 0.200 Gelatine: [gelatine] = 5% ⇌ µ<sub>max</sub> = 0.145 [gelatine] = 30% ⇌ µ<sub>max</sub> = 0.097</td><td>The increase of [gelatine] decreases the µ<sub>max</sub> of L. lactis, more sensitive than L. innocua</td><td>Antwi et al., 2007 Theys et al., 2009a</td></tr><tr><td>Inoculation level</td><td>Inoculation levels (cfu/ml): a- 2.0x10<sup>5</sup> b- 1.6x10<sup>6</sup> c- 9.6x10<sup>6</sup></td><td>Model cheese 19°C</td><td>a- R<sub>col</sub> = 10.4 (±2.6) b- R<sub>col</sub> = 5.2 (±1.6) c- R<sub>col</sub> = 4.0 (±0.5) a- d<sub>2D</sub> = 123 b- d<sub>2D</sub> = 50 c- d<sub>3D</sub> = 34 Cf. Table 2</td><td>Surface between colonies and cheese matrix increased when R<sub>col</sub> decreased: a- S = 1.32 cm<sup>2</sup>/cm<sup>3</sup> b- S = 5.19 cm<sup>2</sup>/cm<sup>3</sup> c- S = 9.49 cm<sup>2</sup>/cm<sup>3</sup></td><td>Jeanson et al., 2011</td><td></td></tr><tr><td>[glucose]</td><td>From 10<sup>6</sup> to 10<sup>6</sup> cfu/ml</td><td>CMR agar 1% 35°C</td><td></td><td>Colonies up to 10<sup>5</sup> cells/colony grow with similar growth rate than planktonic cultures, bigger colonies have lower growth rate</td><td></td><td>Kabanova et al., 2012</td></tr><tr><td>[glucose]</td><td>10<sup>2</sup> cfu/ml</td><td>M17 L agar 1% 35°C</td><td>[glucose] = 2 g/l ⇌ R<sub>col</sub> = 105 [glucose] = 6 g/l ⇌ R<sub>col</sub> = 120 [glucose] = 10 g/l ⇌ R<sub>col</sub> = 105</td><td>µ<sub>broth</sub> ≈ µ<sub>agar</sub> ⇌ no diffusion limitations for glucose – much less lactic acid produced for the same [glucose] consumed, final pH higher</td><td></td><td>Kabanova et al., 2013</td></tr><tr><td>Planktonic vs. immobilized</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Strain (n=6)</td><td>A few colonies</td><td>Synthetic amino acid medium + glucose 0.5% 30°C</td><td>Surface after 134 h of growth: From 20 to 165 pixels</td><td>Generation time (min): From 63 (strain IL1403) to 123 Rmq: strain IL1403 had the fastest growth Rmq: wide variability of colony size for a same strain</td><td>The proportion of dead cells was related to the surface from 18 to 50%, randomly distributed within the colony</td><td>Ryssel et al., 2013</td></tr><tr><td colspan="7"><strong>NISIN-PRODUCING LACTOCOCCUS LACTIS AND LISTERIA MONOCYTOGENES</strong></td></tr><tr><td>±CaCO<sub>3</sub></td><td>a- 7.8,10<sup>5</sup> cfu/ml b- 1.7,10<sup>5</sup> cfu/ml c- 7.8,10<sup>2</sup> cfu/ml d- 7.8,10<sup>1</sup> cfu/ml</td><td>BHIY + glucose + agar 30°C</td><td>a- d<sub>2D</sub> = 100 b- d<sub>2D</sub> = 200 c- d<sub>2D</sub> = 1100 d- d<sub>2D</sub> = 5000</td><td></td><td>Critical distance (&lt;5000 µm) exists for the inhibition L. monocytogenes by the nisin produced by L. lactis only if the medium is not buffered</td><td>Thomas et al., 1997</td></tr><tr><td colspan="7"><strong>LISTERIA INNOCUA</strong></td></tr><tr><td>[gelatine]</td><td>10<sup>3</sup> cfu/ml</td><td>BHIY + glucose 1% ± gelatine 12°C</td><td></td><td>Broth ⇌ µ<sub>max</sub> = 0.120 [gelatine] = 5% ⇌ µ<sub>max</sub> = 0.097 [gelatine] = 30% ⇌ µ<sub>max</sub> = 0.076</td><td>The increase in [gelatine] decreases the µ<sub>max</sub> of Listeria innocua</td><td>Antwi et al., 2007 Theys et al., 2009a</td></tr></tbody></table>

(Continued)
<table><caption>TABLE 1 | Continued</caption><thead><tr><th>Influent parameters</th><th>Inoculation level or number of cells per colony</th><th>Experimental/Growth conditions</th><th>R<sub>col</sub> = colony radius R<sub>bnd</sub> = boundary radius (μm) d<sub>2D</sub> and d<sub>3D</sub> = distance 2D or 3D (μm)</th><th>Maximal growth rate (μ<sub>max</sub> in h<sup>-1</sup>) Generation time (T<sub>g</sub> in h)</th><th>Conclusions or comments</th><th>References</th></tr></thead><tbody><tr><td>[gelatine]</td><td rowspan="4">10<sup>3</sup> cfu/ml</td><td rowspan="4">TSBY + glucose 1% ± gelatine Gelatine 10% for submerged colonies Gelatine 10% or 20% for surface colonies 20°C pH = 7</td><td rowspan="4">Broth: [sucrose] = 0% &harr; μ<sub>max</sub> = <b>0.90</b> [sucrose] = 20% &harr; μ<sub>max</sub> = <b>0.55</b> [sucrose] = 30% &harr; μ<sub>max</sub> = <b>0.32</b> Submerged: [sucrose] = 0% &harr; μ<sub>max</sub> = <b>0.80</b> [sucrose] = 20% &harr; μ<sub>max</sub> = <b>0.48</b> [sucrose] = 30% &harr; μ<sub>max</sub> = <b>0.30</b> Surface: [sucrose] = 0% &harr; μ<sub>max</sub> = <b>0.68</b> [sucrose] = 20% &harr; μ<sub>max</sub> = <b>0.30</b> [sucrose] = 30% &harr; μ<sub>max</sub> = <b>0.0</b></td><td rowspan="4">Whatever the [sucrose], μ<sub>broth</sub> &harr; μ<sub>submerged</sub> &harr; μ<sub>surface</sub> Surface colonies have greater vulnerability to inhibition than submerged colonies, but no effect of [gelatine] up to 20%</td><td rowspan="4">Brocklehurst et al., 1997</td></tr><tr><td>[sucrose]</td><td>Centre of colony &harr; μ<sub>max</sub> = <b>0.37</b> &gt;200 μm from the center &harr; μ<sub>max</sub> = <b>0.69</b></td><td>Regional variations of μ within the colony, μ<sub>max</sub> outside the colony while μ &lt; μ<sub>max</sub> in the center of the colony</td></tr><tr><td>1 colony/plate</td><td>BHI agar 1% pH 7 30°C</td><td>R<sub>col</sub> &gt; 200</td><td>McKay et al., 1997</td></tr><tr><td>Inoculation level</td><td>TSB + gelatine 10% (gel cassettes®) 20°C</td><td>Inoculation 10<sup>3</sup> cfu/ml: pH 5 &harr; R<sub>col</sub> = <b>300</b> pH 7 &harr; R<sub>col</sub> = <b>450</b> Inoculation 1 cfu/ml: pH 5, [glc] = 0 or 0.1% &harr; R<sub>col</sub> = <b>400</b> pH 5, [glc] = 1% &harr; R<sub>col</sub> = <b>800</b> pH 7, [glc] = 0 or 1% &harr; R<sub>col</sub> = <b>1300</b> pH 5, [glc] = 0.1% &harr; R<sub>col</sub> = <b>1600</b></td><td>Acidification is more dependent on the [glucose] than on the inoculation level. Rings of pH (microgradients) were still observed after 5 d when [glucose] was 1% while pH microgradients disappeared when the colony aged 5–6 d when [glucose] = 0.1%</td></tr><tr><td>Initial pH</td><td>10<sup>3</sup> cfu/ml</td><td></td><td></td><td></td><td></td></tr><tr><td>[glucose]</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Planktonic vs. immobilized</td><td>10<sup>4</sup> cfu/ml</td><td>TSB + glucose 1% + gelatine 10% pH 7 20°C Final population (cfu/ml): 2.84, 1.0<sup>3</sup> &harr; 10<sup>5</sup> cells/colony</td><td>d<sub>2D</sub> = <b>464</b></td><td>μ<sub>max</sub> = <b>0.550</b></td><td>Slower growth in gelatine than in broth—physiological heterogeneity within a colony of bacteria growing in a gel matrix</td><td>Walker et al., 1998</td></tr><tr><td>Planktonic vs. immobilized</td><td>10<sup>3</sup> cfu/ml</td><td>TBS ± gelatine 20% 20°C</td><td>Broth: pH 7 &harr; R<sub>col</sub> = <b>8.8</b> ±0.1 pH 5 &harr; R<sub>col</sub> = <b>8.6</b> ±0.2</td><td></td><td></td><td></td></tr><tr><td>pH</td><td></td><td>Final population (cfu/ml): Broth, pH 7 &harr; 6.3.10<sup>8</sup> pH 5 &harr; 4.10<sup>8</sup> Gelatine, pH 7 &harr; 4.10<sup>8</sup> pH 5 &harr; 6.3.10<sup>8</sup></td><td>Gelatine: pH 7 &harr; R<sub>col</sub> = <b>8.6</b> ±0.3 pH 5 &harr; R<sub>col</sub> = <b>8.8</b> ±0.2</td><td></td><td>Growth rates are significantly higher in broth but the final counts were similar. Faster consumption of glucose occurred in broth compared in gelatine because of aerobic metabolism</td><td>Skandamis et al., 2000</td></tr></tbody></table>

(Continued)
<table><caption>TABLE 1 | Continued</caption><thead><tr><th>Influent parameters</th><th>Inoculation level or number of cells per colony</th><th>Experimental/Growth conditions</th><th>R<sub>col</sub> = colony radius R<sub>bnd</sub> = boundary radius (µm) d<sub>2D</sub> and d<sub>3D</sub> = distance 2D or 3D (µm)</th><th>Maximal growth rate (µ<sub>max</sub> in h<sup>-1</sup>) Generation time (T<sub>g</sub> in h)</th><th>Conclusions or comments</th><th>References</th></tr></thead><tbody><tr><td></td><td>10<sup>3</sup> cfu/ml</td><td>20°C, 10% gelatine, 0.5% NaCl, pH 7<br>Final population = 10<sup>9</sup> cfu/ml</td><td>R<sub>col</sub> = 90</td><td>µ<sub>max</sub> = 1.1</td><td>Linear correlation between Log/volume of the colony) and normalized doubling time. The volume continue to increase while Log(cfu/ml) is stable</td><td>Wright et al., 2000</td></tr><tr><td>Planktonic vs. immobilized</td><td>10<sup>3</sup> cfu/ml</td><td>TSB without glucose<br>20°C<br>Petri dish for gelatine 1%<br>Gel cassettes® for gelatine 5%</td><td></td><td></td><td>Broth:<br>pH 4.5, a<sub>w</sub> = 0.970 ⇏ µ<sub>max</sub> = <b>0.10</b><br>a<sub>w</sub> = 0.990 ⇏ µ<sub>max</sub> = <b>0.45</b><br>pH 5.5, a<sub>w</sub> = 0.970 ⇏ µ<sub>max</sub> = <b>0.45</b><br>a<sub>w</sub> = 0.990 ⇏ µ<sub>max</sub> = <b>0.70</b><br>[gelatine] = 1%:<br>pH 4.5, a<sub>w</sub> = 0.970 ⇏ µ<sub>max</sub> = <b>0.08</b><br>a<sub>w</sub> = 0.990 ⇏ µ<sub>max</sub> = <b>0.35</b><br>pH 5.5, a<sub>w</sub> = 0.970 ⇏ µ<sub>max</sub> = <b>0.30</b><br>a<sub>w</sub> = 0.990 ⇏ µ<sub>max</sub> = <b>0.45</b><br>[gelatine] = 1%:<br>pH 4.5, a<sub>w</sub> = 0.970 ⇏ µ<sub>max</sub> = <b>0.1</b><br>a<sub>w</sub> = 0.990 ⇏ µ<sub>max</sub> = <b>0.35</b><br>pH 5.5, a<sub>w</sub> = 0.970 ⇏ µ<sub>max</sub> = <b>0.30</b><br>a<sub>w</sub> = 0.990 ⇏ µ<sub>max</sub> = <b>0.45</b></td><td></td><td>a<sub>w</sub> seems to have a higher influence on growth than pH. Planktonic vs. gelatine 1% has an effect on growth but not the increase of [gelatine] from 1 to 5%</td><td>Theys et al., 2008</td></tr><tr><td>pH</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>a<sub>w</sub></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>10<sup>3</sup> cfu/ml</td><td>TSB + gelatine 5%<br>Final population = 5.10<sup>8</sup> cfu/ml</td><td>pH = 5.25, a<sub>w</sub> = 0.980<br>⇨ R<sub>max</sub> = <b>68</b><br>pH = 4.50, a<sub>w</sub> = 0.975<br>⇨ R<sub>30h</sub> = <b>54</b></td><td>pH 5.5, a<sub>w</sub> = 0.990<br>⇨ µ<sub>max</sub> = <b>0.45</b><br>pH 5.25, a<sub>w</sub> = 0.980<br>⇨ µ<sub>max</sub> = <b>0.36</b><br>pH 4.50, a<sub>w</sub> = 0.975<br>⇨ µ<sub>max</sub> = <b>0.15–0.19</b></td><td>Exponential growth until appearance of a dead fraction: 34% at pH 5.25<br>72% at pH 4.50</td><td>Theys et al., 2009b</td></tr><tr><td>[gelatine]</td><td>10<sup>3</sup> cfu/ml</td><td>a<sub>w</sub> = 0.099 or [NaCl] = 1.5%<br>pH = 5.5<br>20°C</td><td></td><td>[gelatine] from 0 to 5%, a<sub>w</sub> = 0.99<br>⇨ µ<sub>max</sub> = <b>0.54</b><br>[gelatine] = 1%, [NaCl] = 1.5%<br>⇨ µ<sub>max</sub> = <b>0.53</b><br>[gelatine] = 5%, [NaCl] = 1.5%<br>⇨ µ<sub>max</sub> = <b>0.47</b><br>[gelatine] = 0%, ∀ a<sub>w</sub> and [NaCl]<br>⇨ µ<sub>max</sub> = <b>0.85</b></td><td></td><td></td><td></td></tr><tr><td>Planktonic vs. immobilized</td><td>10<sup>3</sup> cfu/ml</td><td>25°C<br>LB ± pluronic acid<br>Final population = 10<sup>9</sup> cfu/ml</td><td>In mid-exponential phase<br>⇨ R<sub>col</sub> = <b>100</b><br>In late stationary phase<br>⇨ R<sub>col</sub> = <b>190</b></td><td>Broth:<br>⇨ µ<sub>max</sub> = <b>0.87</b> ±0.04<br>Colonies:<br>⇨ µ<sub>max</sub> = <b>0.82</b> ±0.09</td><td>+3h of lag phase but less virulence in immobilized growth compared to planktonic growth</td><td>Knudsen et al., 2012</td></tr></tbody></table>

Bold values are the measured values in the studies, normal values are the experimental conditions.
bacteria in gelatine media (Antwi et al., 2007; Mertens et al., 2012; Boons et al., 2013). Van Impe studied mostly large pathogen bacterial colonies grown in agar or gelatine media and used micro-electrodes to measure pH. More recently, high resolution imaging techniques have allowed the (i) exploration of small colonies (<100 µm), (ii) measurement of pH down to a resolution of a few µm, and (iii) increasing numbers of monitored parameters like variability of shape, of growth in which single-cell variability, and of metabolism (Bae et al., 2011a; Gonzalez et al., 2012; Knudsen et al., 2012; Koutsoumanis and Lianou, 2013; Ryssel et al., 2013; Vilain et al., 2014). Other research groups have recently compared planktonic and immobilized bacterial growth using molecular techniques to study the difference of gene expression (Knudsen et al., 2012) and protein expression (Knudsen et al., 2012; Vilain et al., 2014). Microcalorimetry has been recently used to study the carbon metabolism at different inoculation levels (Kabanova et al., 2012). The techniques used to study the immobilized bacterial colonies are described in a recent review (Lobete et al., 2015). Imaging fluorescent techniques have allowed the observation of colonies within an opaque matrix such as model cheese. Our group, at the French National Institute for Agricultural Research (INRA, Rennes, France), explores small colonies of lactic acid bacteria (LAB) and their dynamic micro-environment in a model cheese (pH, diffusion of substrates in and around colonies, etc.) in order to better understand the role of LAB during cheesemaking and ripening at the microscopic scale (Jeanson et al., 2011, 2013; Floury et al., 2013, 2015). We also investigated the role of the size of colonies during ripening by combining omics techniques (Le Boucher et al., 2013, 2015a).

## WHAT DOES IMMOBILIZATION IMPLY FOR THE GROWTH OF BACTERIA?

The growth of colonies has been studied using a qualitative approach and several publications have described how a bacterial colony grew on and within a solid matrix, how they were distributed depending on the inoculation level, and how neighboring colonies interacted with each other either from the same or different species.

### Growth of Immobilized Colonies

Since the first studies, it has been demonstrated that the growth of bacterial colonies on the surface is a concentric pattern (Wimpenny, 1992). Cell division starts from the initial immobilized cell, with the colony expanding progressively at the periphery thus following a concentric pattern (Wimpenny, 1992; Pipe and Grimson, 2008). In the exponential growth phase, the number of cultivable cells is linearly correlated to the Log(colony volume) (Wright et al., 2000; Theys et al., 2009b) for submerged colonies or to the Log(colony area) (Guillier et al., 2006; Skandamis et al., 2007; Mertens et al., 2012) for surface colonies. Image analysis techniques have thus been proposed to replace the time-consuming plating techniques. The height of a bacterial colony growing on a surface of a medium was modeled as a function of the glucose concentration of the medium. Indeed, the glucose concentration is low on the top of the colony. It has

been suggested that the growth of bacteria and the development of pH profiles in and around the colony were determined by the local presence, and diffusion of glucose, in the medium beneath the colony (Wimpenny, 1992). This was the main reason offered to explain why the growth of immobilized cells may be different from that of planktonic cells. It has been demonstrated that most of the mathematical models based on a laboratory broth overestimate the bacterial growth in milk, and even more so its growth in cheese-like media (Theys et al., 2009a).

In conclusion, all the studies on bacterial colony growth have suggested that the growth of colonies (growth rate, final size, and shape) was determined by local concentration of substrates and thus by possible limitations of the diffusion of substrates or end-products in solids (McKay et al., 1997; Walker et al., 1997; Malakar et al., 2002b; Pipe and Grimson, 2008).

### Distribution of Colonies: Size of Colonies and Distances between Colonies

When considering the dimensions of a colony, there are two radii of particular importance: the colony radius from the center of the colony to its periphery ($R_{col}$), and the boundary radius from the center of the colony to the limit of its influence on the medium ($R_{bnd}$) (Malakar et al., 2002a). **Figure 1** illustrates these two radii: the colony itself is defined by the radius ($R_{col}$) and its “living space” is defined as the region around the colony ($R_{bnd}$) within which the activity of the bacterial cells is measurable (dashed line), for example by the consumption of substrates and/or production of end-products. The larger the colony (large $R_{col}$), the higher the activity of the colony, the greater the “living spaces” (large $R_{bnd}$). Furthermore, the larger the radius $R_{bnd}$, the greater the distance for the substrate to diffuse to reach the colony. The value of $R_{bnd}$ at the moment of an inoculation of 1 cfu/ml was estimated to be five times longer than for an inoculation of 100 cfu/ml (Malakar et al., 2002a).

The spatial distribution of bacterial colonies is defined by the size of colony and the distances between neighboring colonies. It was measured for the first time in a model cheese, varying with the inoculation levels of a *prt*⁻ strain of *Lactococcus lactis* ranging from $10^5$ to $10^7$ cfu/ml, i.e., within the range used in cheese manufacture (Jeanson et al., 2011). The theoretical distances

<figure><img src="image_7.png" /><figcaption>**FIGURE 1** | Representation of the colony and its surrounding “living space” (the area within which the colony is active) with the two respective radii $R_{col}$ and $R_{bnd}$; *d* is the distance between two neighboring colonies. Adapted from Malakar et al. (2002a) and Wimpenny (1992).</figcaption></figure>
between colonies were first estimated assuming that (i) all the cells in the inoculum gave rise to a colony and (ii) that they were randomly distributed (Poisson $l a_w$). These two assumptions were confirmed from experimental data obtained by confocal image analysis. It was also demonstrated that the final population was always the same regardless of the inoculation level (Jeanson et al., 2011). As a consequence, the size of colonies was negatively correlated to the level of inoculation, that is, the lower was the inoculation level, the larger the colonies. The distances between neighboring colonies were 123 and 34 µm for inoculation levels of $2 \times 10^5$ and $9.6 \times 10^6$ cfu/ml, respectively (Table 1). A separate study (Kabanova et al., 2012), carried out using agar, gave the spatial distribution parameters from experimental data of a larger scale of inoculation levels of a strain of *L. lactis* (from $10^0$ to $10^6$ cfu/ml). The values of distances and radii measured were slightly smaller than those reported by Jeanson et al. (2011) (Table 2). However, the latter used isothermal microcalorimetry which is based on dynamic measurements of heat flow rate. Measurements and calculations of colony radii are mostly in agreement for the strains of the two species (*Lactococcus lactis* and *Streptococcus thermophilus*) reaching final populations over $10^9$ cfu/ml whether they were grown in agar medium or in milk gel/model cheese (Table 2). In the agar medium, the shape of colonies was lenticular; this may explain the difference between the measured and the calculated values. Moreover, the *L. lactis* strain ($lac^-/prt^-$) producing Green Fluorescent Protein (GFP) used by Jeanson et al. (2011) produced smaller colonies in the model cheese because it reached a lower final population ($5 \times 10^8$ cfu/ml).

For a given inoculation level, the variation of the radii of bacterial colonies followed a Normal distribution centered on the mean radius. Indeed, considering that a colony arises from

a single cell, the asynchrony of division of any bacterial culture (Kreft et al., 1998) may explain the variability of the colony radii. Some immobilized cells start their division later than others but all cells stopped to grow at the same time. As a result, different numbers of divisions may occur in neighboring colonies (Koutsoumanis and Lianou, 2013).

## Distances between Colonies and Interactions between Different Bacterial Species

If the distance between two neighboring colonies (denoted as *d*) is greater than $R_{bnd}$, one can consider that there is no interaction between the colonies, but if it is closer one can consider that some level of interaction exists (Figure 2 and Table 1). This applies whether the neighboring colonies comprise the same strain or are formed from different strains or species. Interactions between different species may be in the form of competition for the same substrate (Thomas and Wimpenny, 1996b) or of inhibition because of production of metabolites such as a bacteriocin like nisin (Thomas and Wimpenny, 1996a) or lactic acid (Antwi et al., 2007). This review focuses on the few studies on colonies taking into account the distances between the inhibiting and the affected colonies. Wimpenny et al. (1995) introduced the concept of “propinquity” defined as the maximum distance between neighboring colonies at which there is still interaction.

A strain of *Salmonella enterica* subsp. *enterica* serotype Enteritidis (named S. Enteritidis thereafter) inhibited a strain of *Pseudomonas fluorescens*, while a strain *L. lactis* subsp. *lactis* inhibited a strain of *Listeria monocytogenes* on agar media (Wimpenny et al., 1995). The results showed that the inhibition only occurred if the inoculation level of the inhibiting strain was

<table><caption>TABLE 2 | Size of colonies (calculated by microcalorimetric method or measured from micrographs) as a function of different inoculation levels of two different species of lactic acid bacteria grown in agar, milk gels, or in model cheese.</caption><thead><tr><th rowspan="2">Inoculation levels (cfu/ml)</th><th colspan="3">Agar<sup>a</sup></th><th colspan="2">Model cheese</th><th colspan="2">Milk gel<sup>d</sup></th></tr><tr><th>R<sub>col</sub> (µm) measured</th><th>R<sub>col</sub> (µm) calculated</th><th>Total number of cells/colony (calculated)</th><th>R<sub>col</sub> (µm) measured<sup>b</sup></th><th>R<sub>col</sub> (µm) measured<sup>c</sup></th><th>R<sub>col</sub> (µm) calculated</th><th>Total number of cells/colony (calculated)</th></tr></thead><tbody><tr><td>10<sup>0</sup></td><td>546</td><td></td><td>1.4 × 10<sup>8</sup></td><td></td><td></td><td></td><td></td></tr><tr><td>10<sup>1</sup></td><td>523 ± 98</td><td>150</td><td>1.2 × 10<sup>7</sup></td><td></td><td></td><td>331 ± 1</td><td>1.4 × 10<sup>8</sup></td></tr><tr><td>10<sup>2</sup></td><td>192 ± 16</td><td>66</td><td>2.2 × 10<sup>6</sup></td><td></td><td></td><td>160 ± 4</td><td>1.6 × 10<sup>7</sup></td></tr><tr><td>10<sup>3</sup></td><td>92 ± 18</td><td>32</td><td>2.5 × 10<sup>5</sup></td><td>55 ± 1</td><td></td><td>74 ± 0.2</td><td>1.6 × 10<sup>6</sup></td></tr><tr><td>10<sup>4</sup></td><td>52 ± 13</td><td>14</td><td>2.3 × 10<sup>4</sup></td><td>32 ± 4</td><td></td><td>34 ± 0.5</td><td>1.6 × 10<sup>5</sup></td></tr><tr><td>10<sup>5</sup></td><td>25 ± 3</td><td>6</td><td>1.8 × 10<sup>3</sup></td><td>5 ± 1</td><td>16–23</td><td>16 ± 0.3</td><td>1.6 × 10<sup>4</sup></td></tr><tr><td>10<sup>6</sup></td><td>10 ± 1</td><td>3</td><td>1.8 × 10<sup>2</sup></td><td>3 ± 1</td><td></td><td>7 ± 0.01</td><td>1.6 × 10<sup>3</sup></td></tr><tr><td>10<sup>7</sup></td><td></td><td></td><td></td><td>2 ± 0.2</td><td>4 ± 0.4</td><td></td><td></td></tr></tbody></table>

<footnote><sup>a</sup> Kabanova et al. (2012): *Lactococcus lactis* subsp. *lactis* strain, in CRM agar 35°C, $R_{col}$ and total numbers of cells/colony calculated from the microcalorimetric study for a final population between $10^9$ and $10^{10}$ cfu/ml, $R_{col}$ measured from micrographs.</footnote>

<footnote><sup>b</sup> Jeanson et al. (2011): *Lactococcus lactis* subsp. *cremoris* strain producing GFP, in a model cheese, final population measured at $5 \times 10^8$ cfu/ml ($lac^-/prt^-$ strain), from confocal microscopy images.</footnote>

<footnote><sup>c</sup> Jeanson et al. (2011), Floury et al. (2015) and Le Boucher et al. (2015b): *Lactococcus lactis* subsp. *idem lactis* strain, in a model cheese, final population measured at $5 \times 10^9$ cfu/ml ($lac^+/prt^+$ strain), from confocal microscopy images.</footnote>

<footnote><sup>d</sup> Stulova et al. (2015): *Streptococcus thermophilus* strain, in renneted milk gel, calculated final population of between 1.4 and $1.6 \times 10^9$ cfu/ml from a microcalorimetric study. The corresponding total number of cells per colony is also given when calculated in the study.</footnote>
above 30–100 cfu/ml which corresponded to an average distance between the colonies of 1.4–2.2 mm. These results were then confirmed in another study (Thomas et al., 1997) with strains of *L. monocytogenes* and *L. lactis*. The *Listeria* strain was inhibited either by nisin from a nisin-producer *Lactococcus* strain or, to a lesser extent, by lactic acid production from a non nisin-producer strain. In both cases, the inhibition increased when the distance between colonies of the two species fell from 11 mm to 100 µm. A maximum inhibition distance of 5000 µm was determined, for the inoculation levels of 12 and 4 cells/ml for *L. lactis* and *L. monocytogenes*, respectively, beyond which there was no further inhibition (Thomas et al., 1997).

In conclusion, as low inoculation levels correspond to the formation of colonies far apart ($d > 1.5–5$ mm), it has been suggested that for inoculation levels of 100 cfu/ml and below, no interactions between colonies will occur (Malakar et al., 2000). On the other hand, for an inoculation level greater than 100 cfu/ml, interactions between colonies can be expected **(Figure 2)**.

## GROWTH IN COLONIES: WHEN AND HOW IT DIFFERS FROM PLANKTONIC GROWTH

The growth of bacteria as colonies is subjected to several constraints that are absent in planktonic cultures, such as a necessary diffusion of substrates through the solid matrix, with potentially limited access to the substrates. Predictive growth models for bacteria have mainly been based around parameters taken from planktonic cultures and led to the observation that they were not applicable for modeling immobilized growth (Pipe and Grimson, 2008; Skandamis and Jeanson, 2015). Attention was thus given to understand when and how immobilized growth differed from planktonic growth, especially under the stressful conditions of the food environment. In this section, two aspects of the consequences of immobilization of bacteria are presented: (i) their responses to conditions of stress and (ii) on the micro-heterogeneity of the micro-environment inside and around the colonies.

### **Narrower Boundaries of Growth/No Growth Regions under Stressful Conditions**

The environment existing in food products rarely provides optimal conditions for the growth of microorganisms. The main factors affecting the bacterial growth in food are temperature, pH, NaCl concentration, water activity ($a_w$) and substrate concentration. Increasing the NaCl or sucrose concentrations also decreases the $a_w$ and increases the osmotic pressure, with combined negative effects. Several studies have modified these parameters to determine the conditions leading to growth and no growth conditions comparing planktonic and immobilized bacterial growth. Most of these studies have focused on pathogenic species, aiming at predicting or preventing their growth in food. The experimental details and results from the most cited studies in the literature are listed in **Table 1**.

The growth of a strain of *Salmonella enterica* subsp. *enterica* serotype Typhimurium (named S. Typhimurium thereafter) in gelatine medium was compared to its growth in broth, at different

conditions of pH and NaCl (Brocklehurst et al., 1995). The results show that S. Typhimurium behaves the same when growing in colonies and in a planktonic culture when under optimal conditions ($pH = 7$ and NaCl concentration of 0.5%). However, the generation time $t$ ($t = \log2/\mu$ where $\mu$ is the growth rate) was increased by a factor between 1.3 and 2 in the more stressful conditions ($pH = 5$ and NaCl concentration of 3.5%). The growth rates of this bacterial strain were thus ordered as follow: $\mu_{\text{planktonic}} > \mu_{\text{submerged}} > \mu_{\text{surface}}$ regardless of the $a_w$ when the NaCl concentration was 0.5%, and regardless of the NaCl concentration for maximum $a_w$ (Brocklehurst et al., 1997). The maximum viable cell counts were less affected by a low value of $a_w$ reduced by high sucrose and NaCl concentrations if the colony was submerged rather than on the surface. An explanation could be that the substrates are only accessible through the small area of the underside of surface colonies, whilst it is accessible all around the colony on a bigger area when submerged. By comparing a strain of S. Typhimurium growing as submerged colonies or in planktonic culture, it was shown that the $a_w$ was the most influential parameter on the growth rates (Theys et al., 2008). However, decreasing $a_w$ by increasing NaCl concentration was relatively more harmful to the growth of colonies, because of the combined effect on osmotic pressure, than by increasing gelatine concentrations of the media (Theys et al., 2010). In agreement with the latter, a lower growth rate of growth was observed in planktonic cultures than in submerged colonies of a strain of S. Typhimurium and the growth in colonies increased its sensitivity to the inhibition exerted by oregano oil (Skandamis et al., 2000). Surprisingly, the growth rate of submerged colonies of S. Typhimurium was found lower in broth than in agar medium, but lower in gelatine medium than in broth (Walker et al., 1998). Furthermore, when the growth rate was not affected by the immobilization of bacteria, the lag phase was increased in comparison to planktonic growth (Knudsen et al., 2012; Nielsen

<figure><img src="image_8.png" /><figcaption>**FIGURE 2** | Representation of two situations of neighboring colonies. (A) When the production of lactic acid of one colony does not impact on its neighbors and (B) when the production of lactic acid of one colony does impact on its neighbors. Adapted from Malakar et al. (2002a) and Wimpenny (1992).</figcaption></figure>
et al., 2013). **Figure 3** is an example of the detrimental effect of immobilization of bacteria on their growth when under severe conditions such as low pH and high concentration of NaCl.

Similarly, a strain of *L. monocytogenes* always displayed a lower growth rate when in submerged colonies than in the planktonic form regardless of the sucrose concentration (ranging from 0 to 60%) and the initial pH of the medium. Furthermore, the minimal pH for enabling growth was higher (pH = 5) in colonies than in a planktonic culture (Meldrum et al., 2003). *L. monocytogenes* growth was also shown to be affected by immobilization at low pH and low *a*<sub>w</sub> (Koutsoumanis et al., 2004) as shown on **Figure 4**. However, in this study, *a*<sub>w</sub> had been decreased by increasing the NaCl concentration, the harmful effects of both the NaCl and a low *a*<sub>w</sub> were thus combined.

The growth of a strain of *Listeria innocua* inoculated at 10³ cfu/ml in milk and in gelatinized milk was compared. The growth rates substantially decreased when the concentration of gelatine in the medium was raised from 0 to 50% (Theys et al., 2009a). Under the same conditions, a strain of *L. lactis* was even more detrimentally affected by the increase in gelatine in pasteurized

milk (Antwi et al., 2007). The same conclusions were drawn for two LAB strains: the growth rate as colonies was lower than in a broth but only when the inoculation level was lower than 10³ cfu/ml for *L. lactis* (Kabanova et al., 2012) or lower than 100 cfu/ml for *Lactobacillus curvatus* (Malakar et al., 2002a). Two studies, using the same *Lactococcus* strain grown in M17 media, showed that, for inoculation levels above 10² or 10⁴ cfu/ml (Kabanova et al., 2012, 2013): (i) there was no glucose diffusion limitation in agar at 1%, (ii) the value of µ<sub>max</sub> in agar was similar to that in broth during the exponential growth phase, (iii) the LAB strain switched to a heterofermentative metabolism in agar, thus producing less lactic acid with the same amount of glucose, and stopping growth at a higher pH in agar (Kabanova et al., 2013).

The conclusion from all these results is that the growth of bacteria in colonies differs from the planktonic growth, (i) below a specific inoculation level (depending on the species or the strain of bacteria) and (ii) especially in stressful conditions because of narrower boundaries of conditions conducive to growth.

## Heterogeneity in and Around Colonies (Growth, pH, Oxygen)

The heterogeneity in and around the colonies results from different aspects of the bacterial activity: growth rates (or lysis), substrate consumption and metabolic activity. The potential existence of microgradients within and around the colony would suggest that the environmental conditions (pH, oxygen, redox potential, etc.) experienced by the cells of the colony are not those of the mean values for the medium (Hills, 2001). The metabolic action, either with respect to the consumption of substrates or the production of end-products, is likely to create microgradients of concentration that cause the heterogeneity of bacterial activity inside the colony. Firstly, the studies about the heterogeneity of growth and metabolic activity inside colonies are discussed. Then, with the technical evolution from micro-electrodes to the recent imaging techniques, the possible existence of microgradients in the environmental parameters inside and around the colony is discussed. These parameters include the pH, resulting from production of lactic acid, and oxygen concentration, resulting from its consumption by bacteria. In order to measure the different types of spatial heterogeneity, all studies were performed on large colonies, mostly on the surface of agar/gelatine media (see **Table 1** for details).

## Heterogeneity of Growth Rate and Metabolic Activity between Cells of the Colony

Two types of heterogeneity within the colony have been shown: (i) a gradient of growth rates or metabolite production from the center to the periphery of the colony arising because of the concentrical growth pattern (Wimpenny, 1992), and (ii) a random heterogeneity due to random differences of division or gene expression between cells (Mikkelsen et al., 2007) which has been observed even in small colonies. Different aspects of the heterogeneity can be observed: morphology, growth rates, or metabolic activity (metabolite pattern).

<figure><img src="image_9.png" /></figure>

<figure><img src="image_10.png" /></figure>
For large colonies, rings exhibiting different morphologies were described (R<sub>col</sub> = 750 µm) for *Escherichia coli* with cells modifying their morphology when aging (Shapiro, 1987), as well as rings with different cell densities for colonies (R<sub>col</sub> = 250–450 µm) of different species of *Bacillus* (Kim et al., 2014). The spatial heterogeneity of colony growth, between active growth for the periphery cells and maintenance activity for the central cells where glucose was scarce, was modeled for *Bacillus* (Kreft et al., 1998). Growth rates were measured in the center and at the periphery of a large (R<sub>col</sub> > 200 µm) colony of S. Typhimurium (McKay et al., 1997). Soon after the formation of the colony (13 h), the growth rate at its periphery was twice that of the center, demonstrating that the periphery of a large colony was the region of maximum metabolic activity (Figure 5 and Table 1). The growth slowed down in the center of the colony due to the accumulation of lactic acid possibly combined with the depletion of glucose or carbon sources.

Metabolic heterogeneity has been described by the
observation of gradients in lysis activity, as well as gradients of
metabolite production or enzyme activity within the colony. An
intense lysis of cells was observed in the center of colonies of
*Vibrio cholerae* by using a vital stain of the cells (Wimpenny,
1992). Large surface colonies (R<sub>col</sub> ≈ 350 µm) of *Enterobacter
cloacae* were sliced (10 µm) from top to bottom, to measure the
NADH oxidase activity (Wimpenny, 1992). As oxygen is more
available at the surface of the colony, higher activities were found
in the upper 100 µm layer. The same conclusion was drawn from
using Fourier transform infrared (FT-IR) microspectroscopic
mapping of large colonies of *Bacillus megaterium* (obligate
aerobes) and *Legionella bozemanii* (microaerophiles). The cells
at the top and in the center bottom layers (the “oldest” cells)
got the maximum concentrations of capsule components for
*B. megaterium* and of poly-β-hydroxybutyric acid, a storage
material present in intracellular granules, for *L. bozemanii* (Ngo
Thi and Naumann, 2007). In *E. coli* colonies (R<sub>col</sub> = 1 mm),
vibrational spectroscopy spectra also showed that for the oldest
cells in the surface layers, the RNA level was lower than that in
younger cells in the deeper layers (Choo-Smith et al., 2001).

For smaller colonies, results are less clear. For example, the
adenylate pool which includes ATP has been shown to be affected
by the growth in submerged colonies of S. Typhimurium (Walker

et al., 1998). The authors suggested that the variation of adenylate
production through incubation time, in comparison with broth
culture, could be due to an heterogeneity within colonies but this
heterogeneity has never been proved. In small colonies (R<sub>col</sub> =
40–60 µm) of *E. coli*, three distinct zones could be observed
(center, intermediate and edge) using FT-IR spectra (Ngo-Thi
et al., 2003). On the other hand, elastic-scattering patterns of
small colonies (R<sub>col</sub> = 50–100 µm) of *L. monocytogenes*, *E.
coli*, and *Salmonella* Montevideo, showed no microgradients of
metabolite concentration (Ngo-Thi et al., 2003; Bae et al., 2011a),
indicating that their mean profile was representative of the whole
colony. Small colonies (R<sub>col</sub> = 25 µm) of *E. coli* have also been
shown to be quite homogeneous using vibrational spectroscopy
and it was even suggested that 6 h colonies were the most suitable
for building an identification data base (Choo-Smith et al.,
2001). Identification at early stage of growth of bacterial colonies
was possible using a new highly sensitive and non-destructive
technique, chromatic confocal microscopy (Drazek et al., 2015).

Finally, the variability of phenotype randomly occurs when
a sub-population develops under stressful conditions, either
in colonies or in planktonic cultures. This phenomenon was
observed under acid stress conditions for small colonies of *L.
plantarum* (Ingham et al., 2008) and for *B. cereus* under severe
salt stress (den Besten et al., 2007). Heterogeneity of division
and shape was observed in small colonies of *L. brevis* (from an
initial cluster of a few cells through to several generations) after
exposure to an oxidizing disinfectant (Zhao et al., 2014). In small
colonies of six different strains of *L. lactis*, the area of dead cells,
measured using propidium iodide in microscopy, correlated with
growth rates. The dead cells were randomly distributed until 38 h,
and were then concentrated in the center of the colony at 134 h
(Ryssel et al., 2013).

In conclusion, putting aside the natural random variability
of phenotype, these results show, by mapping the growth and
the metabolites of large colonies (R<sub>col</sub> > 250 µm), that cells
differentiate during the stage of growth within the colony. For
this reason, small colonies are homogeneous because all cells
exhibit the same growth state.

Gradients of pH in and Around Colonies

The production of lactic acid from bacteria has often been
suggested to be the reason why growth stops, due to the
accumulation of lactic acid in and around colonies. Using
micro-electrodes and then pH-sensitive fluorophores, pH
microgradients were recorded only in the case of large colonies,
in and around colonies grown on agar/gelatine. However, the
question remained if there were also pH microgradients around
small colonies or in food such as cheese.

Using micro-electrodes, the first pH profiles were performed
only on large colonies because of the poor resolution of the
technique. Microgradients of pH were observed in and around
large colonies (R<sub>col</sub> ≈ 10 mm) of *Bacillus cereus* (Wimpenny,
1992) and large surface colonies (R<sub>col</sub> = 800 µm) of S.
Typhimurium (Walker et al., 1997). Inoculated at 1 cfu/ml with
supplementation of glucose at 1%, a difference of 2 pH units
was generated between the center of the colony and the edge of
the gel (a distance of 1.2 mm); this difference was only 0.5 pH

<figure><img src="image_11.png" /><figcaption>**FIGURE 5** | Simplified model illustrating the spatial variations in the specific growth rate (µ) within a growing bacterial colony of a facultative anaerobe, such as *Salmonella Typhimurium*. Adapted from McKay et al. (1997).</figcaption></figure>
units in a medium supplemented with glucose at 0.1% (Figure 6 and Table 1). For submerged colonies ($R_{col} = 200~\mu m$) of S. Typhimurium in agar gels, Wimpenny et al. (1995) observed a span of pH of 0.8 pH units from the periphery of the colony to the surface of the agar gel (a distance of 3 mm). In contrast, colonies of S. Typhimurium inoculated at $10^3$ cfu/ml ($R_{col} = 200~\mu m$) did not generate measurable pH gradients but modified the pH in the whole bulk medium (Walker et al., 1997). Using ratio-imaging fluorescence, pH microgradients were observed in and around submerged colonies of *L. curvatus* when inoculated at between 5 and 100 cfu/ml (leading to colonies of $R_{col} = 215$ and 190 µm, respectively) but no pH variation was observed when inoculated at 1000 cfu/ml ($R_{col} = 75~\mu m$) (Malakar et al., 2000).

In order to confront the observations in agar and gelatine to a real food medium, pH was measured at the microscopic level in a model cheese and in real commercial cheeses. Using ratio-imaging fluorescence, local pH was measured during the acidification of colonies of *L. lactis* whose radii ranged from 17.5 to 55.5 µm, corresponding to the lowest inoculation levels possible in cheesemaking, ranging from 1.3 × $10^3$ to 1.6 × $10^5$ cfu/ml, respectively (Jeanson et al., 2013). Regardless of the observed colony size, no pH microgradients could be observed around colonies (Figure 7). Furthermore, in the same model cheese, the same strain of *L. lactis* displayed no evidence of acid stress at the gene expression level (Cretenet et al., 2011). These results are in agreement with those described above and observed in a gelatine medium for colonies of *L. curvatus* up to 150 µm (Malakar et al., 2000). These consistent results demonstrate that the diffusion of lactic acid was not the limiting factor for growth neither in gelatine nor in a model cheese containing colonies which radius was smaller than 150 µm. Furthermore, in ripened commercial Cheddar cheeses, pH microgradients have been observed at the microscopic scale of a few µm using the fluorescence life-time (FLIM), but not especially around colonies

(Burdikova et al., 2015). The accumulation of lactic acid around the colonies has been suggested as the main explanation for the lower growth rate in renneted milk gels when compared with that in liquid milk (Stulova et al., 2015). The simplified composition (no fat, no NaCl) and the homogeneous structure of the model cheese (Jeanson et al., 2013) may explain the non-accumulation of lactic acid around small colonies whilst in commercially available cheeses (Burdikova et al., 2015), lactic acid concentration may vary at the microscopic scale because of a more heterogeneous microstructure.

## Gradients of Oxygen Concentration around Colonies

Oxygen ($O_2$) is one of the most important parameters for determining the behavior of bacterial growth. Depending on the species, $O_2$ can be favorable to growth (aerobes) or inhibiting (anaerobes), or even “neutral” (microaerophilic). For example, for facultative anaerobes such as S. aureus or E. coli, the cell division has been shown to be more intense on the bottom layer of the colony where $O_2$ is scarce and substrates are abundant (Reyrolle and Letellier, 1979). On the other hand, for aerobes such as *Pseudomonas putida*, the top layer of the colony was the zone of the most intense cell division (Reyrolle and Letellier, 1979). Oxygen gradients were first measured inside a colony of *B. cereus* in 1983 using micro-electrodes (Pipe and Grimson, 2008). It has been measured mainly on large surface colonies because $O_2$ is present over the whole surface of the colony. The $O_2$ concentration decreases with depth moving within the colony and also in depth through the medium below and around the colony in all directions (Wimpenny, 1992). The aerobic zone is considered to exist through 30–40 µm depth in a gelatine medium (Walker et al., 1997). However, Tammam et al. (2001), questions the use of micro-electrodes because they can give non-reproducible results due to the poisoning of the platinum electrodes by other ions. Instead, these authors developed *in situ* mass spectroscopy measurements to investigate the concentrations of $O_2$ and $CO_2$ concentrations in MRS agar inoculated with a strain of *L. paracasei* (Tammam et al., 2001). Their results show that $O_2$

<figure><img src="image_12.png" /></figure>

<figure><img src="image_13.png" /></figure>
was rapidly consumed by LAB metabolism, while CO2 was produced as expected. They showed that in the aerobic zone, there was a gradient of O2 concentration through a 5 mm depth in agar after 24 h of inoculation whilst gradients of CO2 concentration occurred in the same zone but through a 20 mm depth (Figure 8).

For the first time in Cheddar cheeses, these authors also investigated the evolution of the concentrations of O₂ and CO₂ at depth just below the rind (Tammam et al., 2001). These innovative results concluded that the O₂ concentration ranged between 350 and 0 µM between the surface of the cheese and 16 mm depth, respectively, after 2 days of ripening. After 15 days, no O₂ could be measured at a depth of 4 mm (Figure 9). The small colonies of lactococci, observed within the curd by confocal microscopy, were suggested as responsible for the consumption of O₂ leading to the decrease of the redox potential known in Cheddar cheese manufacture, for example (Caldeo and McSweeney, 2012). The CO₂ concentration was also directly linked to the heterofermentation of lactococci colonies, which produced up to 16 mM of CO₂ after 200 days of ripening at a depth of 15 mm. A chemically reducing environment, (i.e., low redox potential), in cheese has been suggested to be essential in the development of flavor and stability (Kristoffersen, 1985). However, in contrast to pH, local variation of the redox potential around colonies has never been investigated at the microscopic scale.

In conclusion, it seems clear that heterogeneity can occur within and around the colonies of bacteria with respect to several parameters directly linked to the bacterial metabolic activity. However, the size of the colonies, and thus the inoculation level, is a major factor determining heterogeneity and the existence of such microgradients.

## DIFFUSION LIMITATIONS WITHIN THE SOLID MATRICES

To sustain the growth of bacteria in colonies, substrates have to diffuse from the solid (food) matrix to the colony. At the same time, end-products have to diffuse away from the colony to the matrix, especially if they inhibit bacterial growth such as lactic acid.

The existence of diffusion limitations is the first hypothesis put forth to explain slower growth of the cells in the center of the colony and the microgradients arising in and around the colony. This paradigm has been widely used by different groups to explain their results (Brocklehurst et al., 1997; McKay et al., 1997; Walker et al., 1997; Stecchini et al., 1998; Malakar et al., 2000; Pipe and Grimson, 2008; Kabanova et al., 2012). Even if microgradients of pH and O₂ have been measured, to our knowledge, microgradients of redox potential, inhibitors, or substrates have not, and their existence is still to be shown. Furthermore, some of these studies initially suggested diffusion limitations of the substrates, but then concluded, in the case of numerous and small colonies in favorable growth conditions, that there were no mass transfer limitations of substrates and lactic acid (Stecchini et al., 1998; Malakar et al., 2002b; Kabanova et al., 2012, 2013). For instance, Malakar et al. (2002b) concluded after they measured the effective diffusion coefficient of lactic acid in gelatine medium that the diffusion of lactic acid was not limiting for growth, and that the growth rate was determined only by the generation time of *L. curvatus*, a LAB strain. They obtained a mean diffusion coefficient of 2.81 × 10⁻¹⁰ m²/s in MRS with 10% gelatine at 20°C, which they compared with

<figure><img src="image_14.png" /><figcaption>**FIGURE 8** | CO₂ and O₂ concentration profiles with depth at 24 h (♦) and 48 h (■) after inoculation with *Lactobacillus paracasei* CI3 in MRS 0.1% agar. A MIMS (membrane inlet mass spectrometric) probe was inserted through column of growth. Adapted from Tammam et al. (2001).</figcaption></figure>

<figure><img src="image_15.png" /><figcaption>**FIGURE 9** | O₂ concentration profiles under the rind of Cheddar cheese at 2 days (♦), 9 days (■), and 15 days (▲) of maturation. Adapted from Tammam et al. (2001).</figcaption></figure>
a diffusion coefficient of $1.74 \times 10^{-10}$ m²/s in water at 25°C previously measured by Cussler (1997). Therefore, Malakar et al. (2002b) concluded that because both values were of the same order of magnitude in the gel and in the aqueous solution, lactic acid produced by bacteria can easily diffuse through gels. This conclusion is questionable though, because others studies such as those conducted by Ribeiro et al. (2005) and Øyaas et al. (1995) reported values of diffusion coefficient of lactic acid in water much higher than that of Cussler (1997) of between $7 \times 10^{-10}$ and $10 \times 10^{-10}$ m²/s at 25°C, meaning that diffusion of lactic acid in the gel media was around 4–6 times lower than in the aqueous solution. It may only be for large colonies (more than $10^5$ cells/colony or 100 cfu/ml), producing a large amount of lactic acid, that mass transfer limitations can be significant (Malakar et al., 2002a). Furthermore, the diffusion coefficient of glucose at 5°C in a 0.8% agar medium was $3.27 \times 10^{-10}$ m²/s and was found to decrease linearly with an increase of the agar concentration (Mignot and Junter, 1990). These results demonstrated that the diffusion coefficient of glucose was dependent on the gel microstructure because it decreased with the pore size of the gel network. On the other hand, the diffusion rate of glucose and a small protein (insulin-like growth factor) was shown to be independent of the pore size of the gel with an increased concentration of agar (Stechini et al., 1998). Finally, the little number of studies on diffusion in gels does not allow clear conclusions on the limiting effect of diffusion of substrates or inhibitors.

In cheese, diffusion of small molecules (water, NaCl, lactose) has been studied while knowledge on diffusion of macro-molecules lacks of data (Floury et al., 2010). Recently, Fluorescence Recovery After Photobleaching was adapted to a model cheese (Floury et al., 2012) in order to measure the diffusion coefficients of fluorescent dextrans of different molecular sizes as well as a range of milk proteins. The major conclusion was that the dextrans (which are flexible and charge-neutral molecules) as large as 2000 kDa were able to diffuse through the model cheese as well as the milk proteins (which are rigid and charged molecules). However, the milk proteins were more hindered in the cheese protein network than dextran molecules of similar hydrodynamic radii (Silva et al., 2013). From these studies, it remains very difficult to draw specific conclusions about the potential effects of diffusion limitations of substrates or end-products on bacterial growth and metabolic activity. Indeed, these diffusion rates have now to be compared to enzymatic reaction rates in immobilized conditions, which are, to our knowledge, still unknown and difficult to determine experimentally. We can only suggest that diffusion within the model cheese matrix is probably not the most limiting factor for the growth of cells at the periphery of colonies where the concentration of the substrates is very high. However, one can wonder what happens to the molecules, especially large molecules, upon reaching the center of the colony. In other words, is the colony porous enough to large molecules, either to penetrate the colony or to be expelled from the colony when released after bacterial lysis?

# INTEGRATED ANALYSIS AND NEW CONCEPTS OF THE BEHAVIOR OF BACTERIAL COLONIES

This section outlines the consequences of the immobilization of bacteria in colonies on their growth and metabolic activity in order to identify general principles and theoretical concepts of importance for fermented food products.

## How the Spatial Distribution of Colonies Has a Crucial Impact on Growth

When immobilized as colonies in a solid matrix, bacteria experience multiple constraints on their growth pattern: they develop as colonies and diffusion limitations may limit their access to the substrates. Micro-colonies have previously been defined as colonies displaying a radius $R_{col}$ as small as 1.5 µm up to 100 µm (Choo-Smith et al., 2001; Bae et al., 2011b; Zhao et al., 2014) and macro-colonies as those with a radius as large as 2.5 mm (Ngo Thi and Naumann, 2007). However, all these studies were either focused on micro- or on macro-colonies but never integrated data on both. The present overview of literature led to the conclusion that micro- and macro-colonies were two different conditions of growth depending on a threshold of size, determined by the initial level of population. Figure 10 illustrated the two conditions of colonies along with the planktonic form of culture for comparison, defined as follows:

* Large colonies or macro-colonies => colony radii that are generally above a threshold of 100–200 µm ($R_{col} > 100–200$ µm), or typically more than $10^5$ cells per colony, usually generated by inoculation levels or initial populations below $10^2–10^3$ cfu/ml;

* Small colonies or micro-colonies => colony radii that are generally below 100–200 µm ($R_{col} < 100–200$ µm), or typically less than $10^4$ cells per colony, usually generated by inoculation levels or initial populations above $10^3–10^4$ cfu/ml.

The threshold between micro-colonies and macro-colonies is determined by the inoculation level above which growth in optimal conditions resembles to planktonic growth. The precise threshold depends on the bacterial species, but implies an inoculation level of between $10^2$ and $10^4$ cfu/ml.

The hypothesis of diffusion limitations around colonies seems relevant for macro-colonies but not for micro-colonies as the growth rate of bacteria is then comparable to that in the exponential phase of planktonic growth (McKay and Peters, 1995; Malakar et al., 2002a; Kabanova et al., 2012, 2013). On the one hand, if micro-colonies on agar/gelatine media display the same growth rate as that for planktonic growth, the most likely hypothesis is that the substrates can penetrate inside micro-colonies so that all the cells have access to the substrates. On the other hand, if there is heterogeneity of growth rates inside the macro-colonies, the hypothesis is that some of the substrates, most likely the larger molecules, do not reach the center of the colony so that those cells cannot access such substrates. These
<figure><img src="image_16.png" /><figcaption>FIGURE 10 | Schematic diagram of the three culture conditions for bacterial cells and their main characteristics; planktonic culture conditions are the most studied.</figcaption></figure>

<figure><img src="image_17.png" /><figcaption>FIGURE 11 | Schematic representations of the two concepts of interactions between the colony and the matrix; arrows show the diffusing molecules.</figcaption></figure>

hypotheses lead to the question: are colonies porous to large molecules?

## Two Possible Concepts for the Interactions between a Colony and the Surrounding Matrix: “Bubble” or “Sponge”

We imagined two extreme concepts of the colony (Figure 11): (i) the colony acts as a “bubble” impermeable to molecules and only the periphery cells are in contact with all of the substrates available from the matrix, (ii) or the colony acts as a “sponge” permeable to all the molecules, representing both substrates and end-products which migrate freely through the colony.

If we consider first the “sponge” scenario, the colony is then a group of individual cells all in contact with its micro-environment. The exchange between the micro-environment and the colony is thus that of each of the cells and depends neither

on the size of the colony, nor on their number. This concept is close to the planktonic condition in term of interaction of bacteria with the medium. On the contrary, in the “bubble” scenario, the colony can be considered as a tight cluster of cells and only those at the periphery of the colony are in contact with the micro-environment. Thus, for a given number of bacteria, the total exchange area is then determined by the size and the number of colonies, and is of major importance in governing the activity of the colonies within the matrix. The exchange surface (overall exchange surface per unit of medium volume) increases with the number of colonies as their size decreases (Jeanson et al., 2011). The activity of the colonies within the matrix will thus be increased by an increasing exchange surface if the colonies behave as in the “bubble” scenario whereas there will be no effect if colonies behave as in the “sponge” one. As a consequence, in the “bubble” concept, two different inoculation levels will result in two different values for the exchange surface, and thus two different activities for colonies of different sizes containing the same total number of cells. In the case of two different spatial distributions, labeled 1 and 2, the terms S₁ and S₂ represent two different exchange surfaces resulting from the two different inoculation levels I₁ and I₂. We assume that (i) the packing density of cells and the volume of individual cells inside the colonies are equal for both spatial distributions; (ii) the inoculation level is equal to the number of colonies (one cell gives one colony). Theoretically, for the same final populations, the ratio S₁/S₂ follows the following equation:

$$S_1/S_2 = (I_1/I_2)^{1/3}$$

However, as seen on Figure 12, the experimental data tend to overestimate the ratio of exchange surfaces (S₁/S₂) for a given ratio of inoculation levels (I₁/I₂) when compared to the theoretical model. The low precision of the experimental measurements may explain this difference. These concepts are
<figure><img src="image_18.png" /><figcaption>FIGURE 12 | Theoretical relation (black line) for two different spatial distributions, 1 and 2, between the ratio of the exchange surfaces (S₁/S₂) and the ratio of inoculation levels (I₁/I₂); (Δ) experimental data either manually measured or obtained from image analysis of confocal microscopy images from Jeanson et al. (2011) and from Le Boucher et al. (2013).</figcaption></figure>

theoretical but may be of great value in food processing. It is thus very important to experimentally explore the question: is the colony functioning as a “bubble” or a “sponge”?

## Experimental Exploration of the Two Concepts “Bubble” and “Sponge”

### The Porosity of Colonies with Respect to Different Types of Molecules

As described above, milk proteins and dextrans molecules up to 2000 kDa can diffuse within in a model cheese, but are these large molecules able to also diffuse in to the colony?

A first study explored the resistance to diffusion exerted by cells of *E. coli* and *Rhodospirillum rubrum* homogeneously immobilized in agar through which solutions of glucose and L-malic acid could diffuse (Mignot and Junter, 1990). The results showed that the diffusion of glucose and L-malic acid was negatively and linearly correlated with the increase in cell density in the agar, with an increasing resistance to diffusion over the range from $10^4$ to $10^8$ cells/ml, probably due to the increased tortuosity imposed by the higher density of cells. Considering the packing density of cells in a colony of about $10^{11}$ cells/ml (Malakar et al., 2002a), the resistance to diffusion of molecules within the colony might be expected to be even higher than for a cell density of $10^8$ cells/ml. We thus investigated the porosity of a bacterial colony to molecules of different sizes (Floury et al., 2013). The results showed that dextran molecules from 4 to 155 kDa could penetrate through lactococcal colonies ($R_{col} = 15 - 55 \mu m$) immobilized in an agar gel and in a model

cheese. Indeed, dextran molecules as big as 155 kDa (larger than milk proteins) can diffuse through a bacterial colony but their diffusion coefficient could be limited by their size. On the other hand, milk proteins such as bovine serum albumin, lactoferrin and $\alpha_{s1}$-casein did not penetrate inside the lactococcal colonies in a model cheese (Floury et al., 2015). We observed the same results with strains of *Lactobacillus rhamnosus* and *L. plantarum* (Jeanson, personal communication).

In conclusion, it was clearly demonstrated that the diffusion behavior of macromolecules through bacterial colonies immobilized in a model cheese did not depend so much on the size of the diffusing solute molecules, but mainly on their physicochemical properties (Floury et al., 2015). The colony acts like a “sponge” for the neutral and flexible dextran molecules whilst the colony acts like a “bubble” for all the tested proteins.

## Consequences of the Porosity of Bacterial Colonies in Food Fermentation: Example of Cheese

In cheese, carbon sources such as lactose are soluble and can diffuse freely as in agar or gelatine medium. On the contrary, nitrogen-based substrates are mostly caseins which are bound up in the network and cannot diffuse, except for a minor proportion of free caseins. Assimilable nitrogen substrates are peptides produced from the activity of bacterial cell-wall proteases. In the case of colonies embedded within cheese, only the cells on the periphery can theoretically access the caseins in the network. Taking cheese as an example, this raises the questions: (i) how does the spatial distribution of colonies influence the bacterial metabolism and (ii) how do the cells at the center of the colony access the nitrogen substrates, i.e., the caseins and the casein-derived peptides. If caseins are bound up, one might expect the “bubble” scenario but could the colony act as a “sponge” with respect to the peptides? In order to explore this hypothesis, we measured the influence of two different spatial distributions of micro-colonies of *L. lactis* on the cheese metabolomes during ripening. The inoculations levels, respectively, $1.6 \times 10^5$ and $3.1 \times 10^7$ cfu/ml thus $I_1/I_2= 191$, generated two sets of model cheeses called *small colonies* cheeses with $R_{col} = 3.9 \pm 0.2 \mu m$ and *big colonies* cheeses with $R_{col} = 26.8 \pm 0.2 \mu m$ (Le Boucher et al., 2015a). For exactly the same lactococci viable population in the two sets of cheeses, the results showed that lactococci distributed as “small” colonies tended to accelerate proteolysis during ripening in comparison with “big” colonies. As a consequence, *small colonies* cheeses contained higher amounts of amino acids and some of the peptides than *big colonies* cheeses. Nevertheless, the increase in concentration of metabolites between *small* and *big colonies* cheeses ranged from 1.2 to 2.0 for a ratio of $S_1/S_2$ equal to 5 (Le Boucher et al., 2015b). Under the hypothesis of a “bubble” scenario, there should have been an increase in the metabolite concentration close to the ratio $S_1/S_2$, i.e., 5. Under the hypothesis of a “sponge” scenario, there should not have been observed any changes between the proteolysis of the two different spatial distributions. The results obtained with the *small* and *big colony* cheeses are in agreement with the observations on the porosity of colonies. They suggest that the colony acts either as a “sponge” or a “bubble” according to the diffusing molecules, and that some molecules such as peptides may diffuse inside the
colony reaching the cells located in the center of the colony. The relatively small proportion of cells in the periphery could produce enough peptides for the cells of the whole colony. It has been previously demonstrated for milk that 10% of a *prt*⁺ strain of *L. lactis* could sustain the growth of 90% of the isogenic *prt*⁻ strain (Juillard and Richard, 1994). Another study performed in a renneted milk gel showed that the overall concentration of total free amino acids was 1.15 times higher than in liquid milk, both being inoculated with a strain of *Streptococcus thermophilus* at 10⁵ cfu/ml (Stulova et al., 2015). Even if rennet increased the hydrolysis of caseins into peptides, this result supports the idea that peptides diffuse inside the colony where they are further degraded into amino acids by intracellular aminopeptidases. Furthermore, for inoculation levels from 10² to 10⁶ cfu/ml, the growth rates were similar in renneted milk gel and liquid milk during the first exponential phase when the bacteria use the non-protein nitrogen sources initially present in the milk. However, the growth rates were subsequently lower in the milk gels than in milk during the second exponential phase when the bacterial strain had to synthesize its own cell-wall protease to sustain growth (Stulova et al., 2015). The hypothesis given by the authors was that there was an accumulation of lactic acid around colonies. However, the fact that the total number of bacteria was 13% higher in the milk gels than in milk at the end of the exponential growth phase, demonstrates that the growth rate was slower but growth lasted longer (Stulova et al., 2015). This result also supports the argument of a limited access to caseins, (leading to the slower growth rate), but to a free access to the peptides.

In conclusion, the interaction of the colony with its surrounding matrix is extremely complex and there are no simple mechanisms that describe how and when the “sponge” and “bubble” conceptions apply. Most likely, the colony acts as a selective filter depending on the properties of the diffusing molecules with a greater preference for flexible and neutral molecules regardless of their size.

## CONCLUSIONS

The objective of this review was a comprehensive understanding based on published literature of the impact of bacterial growth

as colonies in a food context. Overall, the term “bacterial colonies” embrace different situations depending on the spatial distribution of colonies (size and number of colonies) in the matrix. Finally, the spatial distribution emerges as the most crucial parameter in determining whether the immobilization of bacteria has an impact or not. The conclusions differ widely: (i) if colonies are small and numerous (micro-colonies), the implications of growing in colonies rather than as free planktonic growth are minor; (ii) whereas if colonies are large and relatively few in number (macro-colonies), the implications of such immobilization become significant, mostly in terms of a relatively lower growth rates and their lower resistance when under conditions of stress. In the case of bacterial contamination or indigenous microflora, the initial population is low and colonies thus develop as macro-colonies. It is thus important to increase the understanding on the behavior of pathogenic bacteria in solid matrices in order to improve the predictive growth models in solid foods. In the case of LAB in fermented foods, the inoculation levels are high and one can wonder if the growth in micro-colonies really impacts on the growth and the metabolic activity of bacteria in foods by comparison with that as planktonic growth. However, in fermented foods, the interactions between bacterial colonies and the food matrix itself remain unexplained and inadequately studied using agar/gelatine media. Moreover, interactions and even communication between colonies, like quorum sensing, is still unexplored in solid food media (Skandamis and Nychas, 2012). The newly available imaging techniques may open a great field of research in this respect.

## AUTHOR CONTRIBUTIONS

SJ: design and wrote the review manuscript. JF: expert in the diffusion of molecules in cheese and porosity of colonies; improved the review manuscript. VG: expert in proteolysis by bacteria; improved the review manuscript. SL: initiated the topic in the lab; improved the review manuscript. AT: head of the research group; design and extensively improved the review manuscript.

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2015 Jeanson, Floury, Gagnaire, Lortal and Thierry. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
<figure><img src="image_19.png" /></figure>

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# Colonial vs. planktonic type of growth: mathematical modeling of microbial dynamics on surfaces and in liquid, semi-liquid and solid foods

Panagiotis N. Skandamis<fnref n="1" />* and Sophie Jeanson²,³

## OPEN ACCESS

**Edited by:**
Jean-christophe Augustin,
Ecole Nationale Vétérinaire d'Alfort,
France

**Reviewed by:**
Laurent Guillier,
Agence Nationale de Sécurité
Sanitaire de l'Alimentation, de l'
Environnement et du Travail, France
Juan Aguirre,
Universidad Complutense, Madrid,
Spain

*Correspondence:
Panagiotis N. Skandamis
pskan@aua.gr

**Specialty section:**
This article was submitted to
Food Microbiology,
a section of the journal
Frontiers in Microbiology

**Received:** 09 July 2015
**Accepted:** 12 October 2015
**Published:** 29 October 2015

**Citation:**
Skandamis PN and Jeanson S (2015)
Colonial vs. planktonic type of growth:
mathematical modeling of microbial
dynamics on surfaces and in liquid,
semi-liquid and solid foods.
Front. Microbiol. 6:1178.
doi: 10.3389/fmicb.2015.01178

Predictive models are mathematical expressions that describe the growth, survival, inactivation, or biochemical processes of foodborne bacteria. During processing of contaminated raw materials and food preparation, bacteria are entrapped into the food residues, potentially transferred to the equipment surfaces (abiotic or inert surfaces) or cross-contaminate other foods (biotic surfaces). Growth of bacterial cells can either occur planktonically in liquid or immobilized as colonies. Colonies are on the surface or confined in the interior (submerged colonies) of structured foods. For low initial levels of bacterial population leading to large colonies, the immobilized growth differs from planktonic growth due to physical constrains and to diffusion limitations within the structured foods. Indeed, cells in colonies experience substrate starvation and/or stresses from the accumulation of toxic metabolites such as lactic acid. Furthermore, the micro-architecture of foods also influences the rate and extent of growth. The micro-architecture is determined by (i) the non-aqueous phase with the distribution and size of oil particles and the pore size of the network when proteins or gelling agent are solidified, and by (ii) the available aqueous phase within which bacteria may swarm or swim. As a consequence, the micro-environment of bacterial cells when they grow in colonies might greatly differs from that when they grow planktonically. The broth-based data used for modeling (lag time and generation time, the growth rate, and population level) are poorly transferable to solid foods. It may lead to an over-estimation or under-estimation of the predicted population compared to the observed population in food. If the growth prediction concerns pathogen bacteria, it is a major importance for the safety of foods to improve the knowledge on immobilized growth. In this review, the different types of models are presented taking into account the stochastic behavior of single cells in the growth of a bacterial population. Finally, the recent advances in the rules controlling different modes of growth, as well as the methodological approaches for monitoring and modeling such growth are detailed.

**Keywords:** bacterial colony, stochastic, stress response, lag time, microstructure, micro-environment

<footnote n="1">¹ Laboratory of Food Quality Control and Hygiene, Department of Food Science and Human Nutrition, University of Athens, Athens, Greece, ² Institut National de la Recherche Agronomique, UMR1253 Science and Technology of Milk and Eggs, Rennes, France, ³ AGROCAMPUS OUEST, UMR1253 Science and Technology of Milk and Eggs, Rennes, France</footnote>
# INTRODUCTION TO PREDICTIVE MICROBIOLOGY

Predictive food microbiology is a sub-discipline of food microbiology that uses models (i.e., mathematical equations) to describe the growth, survival, or inactivation of microbes in food systems. Mathematical models refer to a set of basic hypotheses supporting the target (bio-) processes which are to be simulated and are possibly algebraic functions and/or differential equations (Baranyi and Roberts, 1995). Therefore, with predictive microbiology, all the knowledge of microbial responses in different environmental conditions is summarized as mathematical equations. McMeekin et al. (2008), stated that "the model is often a simplified description of relationships between observations of the system (responses) and the factors that are believed to cause the observed responses."

The long roadmap of predictive microbiology over the last four decades, along with the advances toward understanding and quantifying microbial responses down to single cell level, have led to the appointment of predictive modeling as one of the most promising decision-support methodologies for food safety assessment by the Food Industry and competent authorities. Predictive modeling has been greatly benefitted by the technological and scientific evolution in both collection and processing of data, through the introduction of—omics (Rantsiou et al., 2011; Brul et al., 2012), the deployment of advanced microscopy techniques (e.g., confocal laser microscopy and fluorophores fused in the genome; Locke and Elowitz, 2009; Cox et al., 2010; Bridier et al., 2015), the application of chemometrics, data mining and the emergence of advanced data modeling techniques (e.g., artificial neural networks; Argyri et al., 2010; Panagou et al., 2011). As a next step, the rising trend for application of predictive modeling in daily practice has intensified the need to systematically exploit the vast number of available predictive models so far. Meeting this demand is being markedly achieved through the development of collective predictive modeling repositories (e.g., ComBase, Pathogen Modeling Program, iRisk, Food Spoilage and Safety Predictor, Sym'Previus, etc.). They are equipped with search engines for guided-retrieval of the appropriate food-specific or generic models (i.e., not food-specific) associated with particular hazards and built-in fitting or simulation modules, in order to visualize and numerically express the model outputs in comprehensive and ready to use formats. Such a variety of predictive models and risk assessment/risk ranking software tools may indeed help the food producers, researchers and food safety inspectors to apply the concepts of predictive modeling in quality-by-design, identification of safe product formulations and evaluation of products compliance with safety standards and microbiological criteria. A comprehensive and quite extensive review of the available software tools can be found in the study by Tenenhaus-Aziza and Ellouze (2014).

Models alone should be applied in caution and with proper disclaimers in the context of decision-making during Hazard Analysis Critical Control Point (HACCP) plan development. Use of models requires experience and judgment, both in modeling and food microbiology. Therefore, it is of vital importance

to clearly perceive that the predictive models and associated software tools should not replace the expert opinion, but rather assist the experts (and sometimes even the non-experts) to elicit a food safety plan (Tenenhaus-Aziza and Ellouze, 2014). When models alone are used to make a decision, those models must be shown to be valid for the food in question and should take into consideration lot-to-lot variation. Validation may be based on published or unpublished data for very similar or identical foods. Nonetheless, even in cases when the available predictions are obtained from lab-media based models, which may potentially overlook some significant food-specific impacts on microbial behavior, such predictions are still very useful in guiding more focused and targeted challenge testing (Baranyi and Roberts, 1995; McDonald and Sun, 1999; McMeekin et al., 2008).

# MODEL TYPES AND CLASSIFICATION

Based on microbial responses, expressed as change in numbers and stress tolerance, the combinations of intrinsic and extrinsic environmental determinants to which microorganisms may be exposed, are divided into the following major domains: the growth era and the domain including the combinations that allow survival or cause death of microorganisms (Booth, 2002). The conditions that lie between these two domains refer to a zone where microbial responses are uncertain and characterized by the growth/no growth interface (Le Marc et al., 2005). This zone is strongly associated with the so-called cardinal values (T, pH, $a_w$, etc.) for growth and outlines the bio-kinetic range of microbial proliferation. Such values are species- or even strain-dependent and thus, introduce significant variability in the assessment of the impact of marginal growth conditions on microbial growth, an issue commonly encountered in quantitative microbial risk assessment. To remedy that, models have been proposed which embed the theoretical growth-limiting values for critical hurdles, such as temperature, $a_w$, pH, $CO_2$ and preservatives as biological meaningful parameters in the model structure. Notably, a theoretical interface also exists between survival and inactivation separating combinations that cause growth cessation but not cellular death from those that are lethal (McKellar et al., 2002).

Depending on the conceptual modeling approach applied to the target biochemical process and the final algebraic form, the models can be characterized as empirical or phenomenological, which mathematically describe specific behavior, and mechanistic or theoretical models with a biological basis, which search for the underlying mechanisms driving already observed phenomena. Polynomial equations are the most common empirical models. These models are easy to use, straightforward and no knowledge of a particular process is required. However, polynomial models have no theoretical foundation and have numerous parameters without biological meaning. Therefore, they do not offer any knowledge to mechanisms underlying a process. Polynomial models are commonly represented as quadratic response surfaces describing the environment dependence of a parameter of a bacterial population (Gibson et al., 1988).

Based on the type of dependent variable that is predicted, the models can be classified as kinetic or probabilistic. Kinetic
models predict the extent and rate of growth or inactivation of a microorganism. The growth rate of a microorganism can be modeled in order to be used for making predictions based on the exponential growth of the corresponding microbial population. Kinetic models can be used to predict changes in microbial numbers with time, even if a controlling variable, which can affect growth, is changing (McDonald and Sun, 1999). This type of models constitutes a fundamental model category in predictive microbiology, especially for ready-to-eat foods, since they may assess the exposure of consumers to the doses (levels) of pathogenic bacteria at the time of consumption. The purpose of kinetic models is to estimate the time required for a specified growth or inactivation response to occur under certain intrinsic or extrinsic conditions. Such conditions include temperature, pH, a<sub>w</sub>, packaging atmosphere (e.g., CO<sub>2</sub> levels), redox potential (Eh), the rheological properties of the food (structure-associated variables), relative humidity, nutrient content and the concentration of antimicrobial compounds (Theys et al., 2009b; Mejlholm et al., 2010; Møller et al., 2013). Thermal inactivation was the first microbial inactivation process modeled since 1920 by the canned food industry, in order to control the risk of *Clostridium botulinum* toxigenesis. First-order inactivation models were used to describe a log-linear trend of *C. botulinum* spores in low acid canned food. Through the slope of inactivation curves the thermal death time was estimated and particularly in low acid canned foods, a 12-decimal reduction (12D) of *C. botulinum* spores was shown to require exposure to 121°C/15 psi for 15 min. Over the last decades the microbial inactivation modeling was expanded to account for non-thermal inactivation (Buchanan et al., 1997). In addition to the classical linear inactivation curve, the concept of biphasic death, associated with the pre-existence or emergence of a resistant sub-populations throughout exposure to lethal conditions was modeled with non-linear models (Whiting, 1993; Geeraerd et al., 2005). Probabilistic models constitute the corner stone of predicting microbial dynamics, acting as the filter, i.e., likelihood-based decision of the primary microbial response (growth or inactivation) and guiding the selection of the subsequent kinetic modeling tool, i.e., growth or inactivation model, for predicting the change in microbial numbers in time. As such, the fate of microbial populations in foods is eventually dependent on the probability of growth or inactivation phenomena defined by the intrinsic and extrinsic factors of foods and processing environment. From a closer perspective, the behavior of an isogenic (homogeneous) population is the cumulative and stochastic outcome of its individual cells (microscopic level; Kutalik et al., 2005). Each cell within a microbial population is characterized by a variable probability for growth initiation (Koutsoumanis, 2008), followed by a stochastically defined lag time, i.e., sampled from a probability distribution (Francois et al., 2005, 2006a, 2007; Guillier et al., 2005, 2006), both resulting in a fractional growth of the total population with various sub-populations (mesoscopic level) initiating growth on different times (McKellar and Knight, 2000; McKellar, 2001). It has been suggested that under given conditions the geometric lag, i.e., the intersection of the slope at exponential phase with horizontal asymptote at the initial population level, is essentially dependent

on the cumulative behavior of the fraction(s) of the initial population, which either possesses the shortest lag time (i.e., the earliest growth starters), and/or the fastest generation time (McKellar and Knight, 2000; Koutsoumanis, 2008). As a mirror image, under lethal conditions, e.g., pH < 3.0, or T > 60°C, the inactivation curve of a microbial population, represented by a curve of survivors (%) vs. time, is the result of the cumulative distribution of the individual cell death time, i.e., the time required to kill every single cell (Aspridou and Koutsoumanis, 2014). In explicit terms, probability models can be used to predict the likelihood of the occurrence of a microbial response as a function of intrinsic and extrinsic factors of foods and processing environment (Ross and Dalgaard, 2004). Microbial responses which have been modeled with this approach include spore germination, toxin formation by *C. botulinum*, growth initiation and survival or death of bacteria as a result of lethal pH and organic acid combinations. In the context of industrial practice, such models together with cardinal growth models may be of great assistance to HACCP, by offering science-based numerical evidence for setting critical limits, establishing process or product criteria and assessing the compliance of a given process to these limits or the legislative microbiological criteria (e.g., EC Regulation 2073/2005).

All the above model types may be further divided into the following categories, based on the combination of dependent (predicted) and independent (explanatory) variable (Whiting and Buchanan, 1993; McDonald and Sun, 1999):

i. the primary models, which are used to describe the changes of the microbial population density as a function of time using a limited number of kinetic parameters (e.g., lag time, growth or inactivation rate and maximum population density);

ii. the secondary models expressing the effect of environmental variables (e.g., temperature, NaCl, pH, etc.) on the kinetic parameters estimated by the primary models;

iii. the tertiary models, which are computer tools that integrate the primary and secondary models into user-friendly units. The wider use of models in the food industry and research depends on the availability of user-friendly software (Psomas et al., 2011; http://www.aua.gr/psomas/gropin/), which encompass predictive models and allow different users to retrieve information from them in a rapid and convenient way (McMeekin et al., 2008, 2013).

The impact on microbial growth of the aforementioned intrinsic and extrinsic variables described by the models is strongly dependent on the structure of food or the model substrate. Based on that, in the following lines, a review is performed of existing modeling approaches accounting for different forms of microbial growth on surfaces, or in the interior of food matrices, either in suspension or immobilized in colonies.

## Growth Rate of Microorganisms in Different Forms of Growth

In foods, microbial growth occurs in the aqueous phase. The structural characteristics (e.g., viscosity, 3D structured grid, also called “micro-architecture”) of this phase, resulting from
hydrophilic structure-inducing agents, in combination with the total concentration and dispersion of water compared to fat phase determine the form and rate of growth, i.e., the spatio-temporal microbial dynamics. Food may be characterized as liquid (e.g., juices), gelled (e.g., jellies, cottage, marmelades), oil-in-water emulsions (e.g., mayonnaise, milk), or water-in-oil emulsions (e.g., butter and margarine) and the composite form of gelled emulsions (i.e., an immobilized oil-in-water emulsion). The type of emulsion determines the distribution of available water (Møller et al., 2013). The growth rate of microorganisms in response to food structure, for a given set of intrinsic and extrinsic parameters, is dependent on the motility of cells in the aqueous phase, the extent of resulting (micro-)colony immobilization and the diffusion kinetics of nutrient, oxygen, and metabolites. Three different status of growth may occur depending on the food structure:

(1) If bacteria are suspended in liquids, their growth is planktonic and the motility of microorganisms may enable taxis to certain nutrient-rich sites of the food (Wilson et al., 2002). Access of cells to nutrients and transfer of metabolites away from cells contribute to the formation of a temporarily uniform environment, until the resources are depleted, or the microbial metabolites are accumulated at self-toxic levels.

(2) If bacteria are growing in structured aqueous phase, e.g., due to addition of thickeners, or gelling (structure-inducing) agents, such as gelatin, pectins, starch, gums, etc., microbial cells are immobilized within the gelled regions and constrained to grow as submerged colonies in three dimensions. Their growth rates as colonies tend to be lower than that of planktonically growing cells (Wilson et al., 2002; Theys et al., 2008; Boons et al., 2013a,b, 2014; Aspridou et al., 2014). This can be further enhanced by increasing the fat concentration on the expense of water phase, thereby increasing the size of oil droplets with concomitant trend of reversal of oil-in-water emulsion. At low fat concentrations and in the absence of any dense (3D structured) network, e.g., such as that formed by proteins, the water phase may allow cell motility that resembles planktonic growth. As the fat concentration increases and compresses water, growth is constrained and becomes colonial. In a homogeneous protein network, cocci bacterial colonies are spherical while when if fat is added within a protein network, such as cheese, cocci bacterial colonies display an irregular shape. A similar effect can be obtained by adding a structure-inducing agent, such as gelatin, instead of proteins. The type and density of the gelling agent impact the growth rate of bacteria by influencing the diffusion of nutrients and metabolites to and from the colonies, respectively, as well as through the interaction of the gelling agent with inhibitory compounds, i.e., quenching or reducing diffusivity (due to entrapment) of antimicrobial agents, or due to bound of NaCl to the gelling agent (Boons et al., 2013b; Tack et al., 2015). The size and maximum achievable population of viable cells in colonies immobilized inside a structured matrix are affected by the proximity of colonies as well as the oxygen diffusion, with growth rate reduced in hypoxic

or anoxic microenvironments (Noriega et al., 2008). The spatial distribution of cells of a population determines a critical population density level *per* colony, that renders the limitations in nutrient diffusion and the inhibition by metabolites sensible to adjacent colonies, leading to growth cessation (Malakar et al., 2003). Conversely, at population densities lower than the growth-limiting level, colony-to-colony interactions are negligible and cells divide without constraints. The latter critical level highly varies with the strain and the structure-inducing agent which in turn determines the chemical diffusion properties of the growth matrix.

(3) If bacteria are growing on the surface of foods, such as meat and vegetables, growth is also colonial, initially in two dimensions (mono-layer), whereas the center of colony gradually develops in the third dimension most likely upward, depending on aeration and nutrient availability. Replenishment of nutrients takes place only from the bottom or the perimeter of the colony and soon cells in the center of colony experience starvation and self-toxication. This places growth constraints to the surface colony as a whole and causes suppression of the growth rate as compared to submerged growth within the food matrix or planktonic growth. Thus, the growth rate of the aforementioned different forms of growth is known to follow the order: planktonic ≥ submerged > surface (Wilson et al., 2002; Theys et al., 2008). It needs to be noted however, that the differences in growth rates between these three modes of growth likely range from significant (i.e., 0.5-or 1-fold difference) to non-significant and/or not consistent, depending on the microorganism and the structure-inducing agent (Smet et al., 2015). The same accounts for lag times. In contrast, unequivocal increase in growth rate is induced by aeration of the growth medium, e.g., in shaking culture.

These observations have also been explored in relation to the stochastic behavior of individual cells growing in liquid media or immobilized inside or on the surface of solid media (Guillier et al., 2005, 2006; Manios et al., 2012; Koutsoumanis and Lianou, 2013; Tack et al., 2015). Starting from single cell level and simulating the formation of colony or the proliferation to high numbers in planktonic state, may assist in drawing useful conclusions on the expected behavior of large populations. These aspects are further discussed in the following paragraphs.

## Individual-based Modeling of Planktonic or Immobilized Cells

The growth of a microbial population depends on the cumulative behavior of individual cells. As described above, a great variability is commonly evident in the growth responses, i.e., lag time, generation time and probability of growth, among individual cells of a homogeneous (or isogenic) population, due to the so-called "noise" (Locke and Elowitz, 2009). This biological variability (also termed "biovariability"; Billon et al., 1997) markedly impacts the dynamics, e.g., geometrical lag and germination time and time to reach detectable levels, of low
populations such as 1–50 cells and increases with the intensity of environmental stresses (Billon et al., 1997; Smelt et al., 2002, 2008; Francois et al., 2005, 2006a; Guillier et al., 2005; Guillier and Augustin, 2006; Dupont and Augustin, 2009). For instance, the distribution of germination times (lag) of individual *C. botulinum* spores became less peaky (i.e., with lower *kyrtosis* coefficient) and less positively skewed (i.e., *skeweness* factor close to 1) as the incubation temperature decreased from 37 to 20°C, suggesting that the variance of germination times increased with the intensity of temperature stress (Billon et al., 1997; Stringer et al., 2011; Smelt et al., 2013). Variability in single cells behavior might be the result of diverse physiology of individual cells due to diverse exposure to environmental conditions in time and space of each daughter cell after the division of the mother cell. To eliminate the latter spatio-temporal diversity of the micro-environment of individual cells, microfluidic Lab-On-A-Chip systems have been proposed, such as Envirostat 2.0 (Dusny et al., 2012), which standardizes the experimental substrate under which the behavior of single cells is investigated.

However, the variable behavior of single cells is masked by the massive behavior of large populations, e.g., >500 cells or it is almost eliminated at optimal conditions (Llaudes et al., 2001; Smelt et al., 2002; Métris et al., 2006). Most of the available predictive models quantify the response of high microbial populations at a given set of conditions, which may be constant or varying with time. In order to model the variability of single cells (or single spores), stochastic modeling, i.e., where the input values are provided in the form of probability distributions describing the variability and uncertainty of the independent variables, may be applied, which is also the common approach in Quantitative Microbial Risk Assessment (Pérez-Rodríguez et al., 2007). Therefore, deterministic models, models based on input of single values for the independent variables, apply to population level, whereas stochastic models may describe the population dynamics taking into account the variability in both the input variables (i.e., extrinsic and intrinsic food parameters) and the responses (e.g., lag time and generation time) of microbial populations, either in large scale or at individual cell level.

Although deterministic models average the behavior of individual cells, the characteristics of the latter cannot be deduced from population measurements (Kutalik et al., 2005). Indeed, the growth of a population may be simulated by superimposing the evolution of independent subpopulations derived from single cells, each receiving a lag time value also termed “physiological lag,” different from the geometrical population lag (Baranyi et al., 2009), from a specific probability distribution. The evolution of a microbial population can be modeled as a Poisson birth process with constant birth intensity parameter µ (Baranyi, 1998; Baranyi and Pin, 2001). A cell capable of dividing, will divide after an initial delay consisting of the physiological lag and the generation time of the cell. Then each cell produces a subpopulation which consists of cells growing independently in the same habitat with a constant growth rate (Baranyi, 1998; McKellar, 2001). However, deviations from this rule are likely as a result of some novel non-thermal microbial inactivation treatments, such as pulsed light and electron beam irradiation, which may diversify the

growth rate, due to injury, of cell clusters within a homogeneous population exposed to the treatment (Aguirre et al., 2013, 2015). For simplification purposes, to model the process of consecutive generations of cells, it is assumed that (Baranyi, 2002; Métris et al., 2003): (i) after the first division of each cell, the daughter cells enter directly in the exponential phase, suggesting that the daughter cells have no additional lag time; (ii) daughter cells do not interact by any means, e.g., competition or quorum sensing. Both assumptions were applicable when the experimental method used to describe the variability in lag times was the time to detect visible changes in the optical density of the liquid medium containing a single cell derived by a series of 2-or 10-fold dilutions of a standard concentrated microbial suspension, or even by sorting with flow cytometry (Smelt et al., 2002, 2008; Francois et al., 2003; Standaert et al., 2005; Baranyi et al., 2009). Indeed, when the population is extremely low (i.e., down to a few cells) and the volume of the liquid surrounding medium is large, it is reasonable to speculate that the interaction between floating cells is negligible or that the probability of each cell being affected by the presence and metabolic activity of adjacent cells is very low. Individual lag times commonly follow Weibull, Gamma, Exponential, or Normal distribution (Francois et al., 2005, 2006a, 2007; Kutalik et al., 2005; Métris et al., 2006; Standaert et al., 2007). The development of sophisticated image analysis systems for real-time monitoring of single cell division (or spore germination) under the microscope, during continuous exposure of attached cells to flowing liquid media, allowed further insight in the variability assessment of single cells (Billon et al., 1997; Elfwing et al., 2004). By targeting specific cells, it was observed that the generation time of daughter cells removed after division, are not the same for all cells but they follow a distribution, the variance of which, decreases with the number of consecutive divisions (Kutalik et al., 2005; Métris et al., 2005, 2006; Pin and Baranyi, 2006).

Exposure of bacterial populations to stresses (sublethal or lethal), such as chlorine, heat shock, pH, osmotic stresses, those related to minimal processing, such as irradiation and pulsed light, as well as sub-optimal conditions in a new environment shift the distribution of the time to first division to higher mean values (i.e., movement of mean to the right) and increase its variance (Francois et al., 2005, 2006a; Guillier et al., 2005; Guillier and Augustin, 2006; Dupont and Augustin, 2009; Aguirre et al., 2012, 2015). Furthermore, stress may decrease the probability of a single cell to initiate growth and increase the number of cells needed for growth initiation (Koutsoumanis, 2008; Dupont and Augustin, 2009). As a result, both extension of individual lag times and reduction of single cell growth probability may lead to false negative detection, due to insufficient growth above the threshold level of enrichment or no growth at all during enrichment (Dupont and Augustin, 2009). Given that stress increases the biological variability, interactions between cells within colonies (e.g., due to competition for nutrients, or the release of inhibitory metabolic products) may be an additional indigenous stress factor, which possibly increases cell lag variation, while retarding the growth of the total population (Guillier et al., 2006).
## Real Time Monitoring of Single Cells and Derived Micro-colonies

Even though the variability of growth responses (e.g., individual lag times and generation times) of planktonic cells has been extensively characterized with OD or microscopic measurements, the variability in relevant parameters of colonial growth (i.e., doubling of cells attached on biotic surfaces) associated with intra-colony cell-to-cell interactions are rarely quantified due to technical difficulties (Aguirre et al., 2012), nor even by direct imaging of cells when the daughter cell is removed after division. Thus, as an alternative, direct time-lapse imaging of microbial populations growing on agar surfaces of different intrinsic properties has enabled the characterization of population heterogeneity taking into account the interactions between adjacent cells (Koutsoumanis and Lianou, 2013) and colonies (Guillier et al., 2006). It may also depict the history of cells residing in different sites of a colony and their physiological adaptations, resulting from exposure to stresses, such as starvation or anoxia and affecting their subsequent resistance to inimical factors, e.g., sanitizers or lethal acid stress (Zhao et al., 2014; Tack et al., 2015). Experimental protocols for direct imaging of surface-growing cells include the gel-cassette system (Brocklehurst et al., 1997), the systems introduced by Billon et al. (1997), Niven et al. (2006), and later on adopted by Koutsoumanis and Lianou (2013), consisting of an agar layer on top of a microscope slide, covered by a cover slip, sealed with paraffin wax and placed under the microscope and the anopore strips (Ingham et al., 2005). Applications of these methods at single cell or colony level may be found for E. coli O157:H7, for which a comparison between growth rates estimated from viable count data and changes in colony area (in pixels) is made (Skandamis et al., 2007), *Bacillus cereus* in response to salinity (den Besten et al., 2007, 2010) and *Salmonella* showing the distribution of living and dead cells, during the evolution of colonies in time and space (Theys et al., 2009a). These techniques may also allow for identification of injured or even dead sub-populations within bacterial micro-colonies as a result of exposure to stresses or entrance into stationary phase of growth. This is achievable through the use of well-established fluorophores, such as SYTO 9, that stains living cells and propidium iodide that stains cells with impaired membranes (Bunthof et al., 2001). For instance, coupling direct cell imaging with viability staining, made possible to monitor the evolution of injury of various *Lactobacillus brevis* cells growing on the surface of de Man Rogosa Sharp agar, in parallel to colony growth kinetics, expressed through $\mu_{max}$, after short exposure to peroxy-acetic acid (PAA), i.e., an strong oxidizing agent (Zhao et al., 2014). The experimental approach applied was able to unravel some interesting physiological responses that are impossible to detect by classical plate counting. In particular, not all cells that were unable to divide after exposure to PAA were appeared red (i.e., injured), suggesting that growth inhibition was not associated with membrane damage (Zhao et al., 2014). In addition, elongation or clumps of cells experiencing starvation is a very common cellular response that denotes a highly stressful physiological state of cells that cannot be detected by

plate counting and probably characterize the emergence of a viable-but-not culturable sub-population (Koutsoumanis and Lianou, 2013; Zhao et al., 2014; Tack et al., 2015).

Advances in individual-based modeling (IbM) have suggested that apart from the population measurements, the complete characterization of lag time also requires the evolution of total biomass and thus, the geometrical definition of lag time is not quite reliable (Prats et al., 2008). Furthermore, since geometrical lag depends on the time required by total viable population to exceed the detection limit of the enumeration method, a part of geometrical lag does not have practically biological meaning and can also be termed “pseudo-lag” (Koutsoumanis, 2008), because growth initiation of a fast growing sub-population, which will eventually give the detection signal, might have started quite earlier.

## Individual-based Modeling in Foods

The well-established variability of single cells in laboratory media is expected even more pronounced in natural food ecosystems (Ferrier et al., 2013). This may be attributable to the combination of multiple stress factors in foods, such as limitations in nutrient diffusion, competition with natural flora, accumulation of inhibitory metabolic products, structural constraints, and spatio-structural variability of microenvironments where microorganisms are located (Noriega et al., 2010). Despite the low number of studies dealing with single cell variability in foods, a common conclusion is that the behavior of low inocula (e.g., <10 CFU/g) cannot be accurately approximated by models based on the responses of higher inocula on the same food nor by broth-based models (Schvartzman et al., 2010; Manios et al., 2012). For instance, the time that *L. monocytogenes* required for a 100-fold increase on vacuum packaged frankfurters stored at 4 and 8°C, starting from 0.007 to 0.1 CFU/g was markedly higher than that expected based on the responses of 10–20 CFU/g on the safe food (Pal et al., 2009). Likewise, the simulated variability in log-numbers of *L. monocytogenes* cells in liver pâté at 7°C or lettuce and cabbage fresh cut salads, based on broth data, differed from the observed number (Francois et al., 2006b; Manios et al., 2012). Notably, Monte Carlo simulation based on stochastic description of lag times of individual *L. monocytogenes* cells from broth data slightly over-predicted the growth of single cells of *L. monocytogenes* after 12 days on lettuce. For instance, the model predicted that there was 60% likelihood a single cell of the pathogen to reach 1.5 log CFU/g, while the observed growth under the same probability was 1 log CFU/g (Manios et al., 2012). In contrast, remarked under-estimation of the observed growth in cabbage was recorded, as the predictions showed that 60% of the individual cells could grow at 0.5 log CFU/g, whereas the observed growth was 2.6 log CFU/g (Manios et al., 2012). It is imperative that the evaluation of the response of single cells in foods should receive more focus in parallel to the optimization of laboratory media assays, which provide further theoretical aspects under controlled conditions. Furthermore, improving our ability to quantitatively characterize the micro-environment surrounding single cells, e.g., by measuring the micro-scale pH, water activity, nutrient, etc., might increase the robustness of
predictions for growth or inactivation of these cells and explain their variable behavior based on spatio-temporal distribution of each cell (or cluster of cells) in the food matrix (Ferrier et al., 2013).

## CONCLUSION—FUTURE ASPECTS

The deviation of broth-based predictions from the observed growth in foods is a well-known challenge of numerous predictive models, including some pioneer models of the last decades, addressing the issue of poor transferability of broth-based data to foods. Indeed, broth-based data are collected easily and under controlled conditions, thereby requiring low labor costs and assuring high reproducibility. However, such models do not adequately encompass the effect of critical factors explaining bacterial behavior in real foods, especially structured foods. Such critical factors may be associated with the constraints of colonial growth because of food micro-structure, cell-to-cell or colony-to-colony (inter-/intra-species) interactions (Habimana et al., 2011), along with the limitations due to availability of nutrients and oxygen and/or the removal of bacterial metabolites away from colonies. The impact of these factors is amplified at low microbial populations, manifested by the stochastic behavior of single cells. Thus, extrapolating broth-based predictions of microbial growth from single cells to foods may lead to significant over- or under-estimation of actual microbial behavior in foods, with important consequences on food safety and spoilage. In this context, one of the current trends in predictive microbiology is to define food micro-architecture in quantifiable (metric) variables, so that their impact on microbial

growth or inactivation is quantitatively described. Advances in relevant instrumentation, such as Nuclear Magnetic Resonance (Møller et al., 2013) for assessing the distribution of water and oil particles in emulsified foods, or the development of micro-electrodes technology (Ferrier et al., 2013) measuring ion fluxes, pH or $a_w$ in the food microenvironment (i.e., measurements in micro-scale; Lobete et al., 2015) have enabled the collection of useful data for the above purpose. In addition, bottom-up approaches are more and more adopted by food microbiologists in the context of predictive modeling, i.e., investigating the behavior of single cells forming adjacent micro-colonies, as a means to predict the behavior of larger microbial populations in 2 or 3 dimensions, including biofilm formation (Habimana et al., 2011). Deep insights in this area, such as stochastic description of individual lag times in the form of probability distributions, are feasible *via* the use of time-lapse microscopy (e.g., confocal laser scanning microscope), coupled with the use of viability- respiratory activity- or gene expression-associated fluorophores at single cell level (Habimana et al., 2011; Bridier et al., 2015; Lobete et al., 2015). The latter, apart from assisting in visualization of cellular division and monitoring changes in cell number in real time, they may reveal physiological trends (e.g., virulence, stress resistance, protein expression, etc.) of single cells resulting from their interaction with the liquid or solid substrate they habituate. Finally, the challenge of integrating—omics data into predictive modeling is still open and microbiologists thrive to exploit the vast amount of such type of data collected so far so as to unravel the most critical aspects of the interaction between microorganisms and foods or between cell-to-cell interactions.

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**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2015 Skandamis and Jeanson. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
<figure><img src="image_20.png" /></figure>

# Recent trends in non-invasive *in situ* techniques to monitor bacterial colonies in solid (model) food

María M. Lobete<fnref n="1" />,<fnref n="2" />, Estefania Noriega Fernandez<fnref n="1" />,<fnref n="2" /> and Jan F. M. Van Impe<fnref n="1" />,<fnref n="2" />*

**Edited by:**

Sophie Jeanson, Institut National de la Recherche Agronomique, France

**Reviewed by:**

Raivo Vilu, Tallinn University of Technology, Estonia
Jean-Christophe Augustin, Ecole Nationale Vétérinaire d'Alfort, France

**\*Correspondence:**

Jan F. M. Van Impe, Chemical and Biochemical Process Technology and Control, Department of Chemical Engineering, Katholieke Universiteit Leuven, Willem de Croylaan 46, B-3001 Leuven, Belgium

e-mail: jan.vanimpe@cit.kuleuven.be

Planktonic cells typically found in liquid systems, are routinely used for building predictive models or assessing the efficacy of food preserving technologies. However, freely suspended cells often show different susceptibility to environmental hurdles than colony cells in solid matrices. Limited oxygen, water and nutrient availability, metabolite accumulation and physical constraints due to cell immobilization in the matrix, are main factors affecting cell growth. Moreover, intra- and inter-colony interactions, as a consequence of the initial microbial load in solid systems, may affect microbial physiology. Predictive food microbiology approaches are moving toward a more realistic resemblance to food products, performing studies in structured solid systems instead of liquids. Since structured systems promote microbial cells to become immobilized and grow as colonies, it is essential to study the colony behavior, not only for food safety assurance systems, but also for understanding cell physiology and optimizing food production processes in solid matrices. Traditionally, microbial dynamics in solid systems have been assessed with a macroscopic approach by applying invasive analytical techniques; for instance, viable plate counting, which yield information about overall population. In the last years, this approach is being substituted by more mechanistically inspired ones at mesoscopic (colony) and microscopic (cell) levels. Therefore, non-invasive and *in situ* monitoring is mandatory for a deeper insight into bacterial colony dynamics. Several methodologies that enable high-throughput data collection have been developed, such as microscopy-based techniques coupled with image analysis and OD-based measurements in microplate readers. This research paper provides an overview of non-invasive *in situ* techniques to monitor bacterial colonies in solid (model) food and emphasizes their advantages and inconveniences in terms of accuracy, performance and output information.

**Keywords:** bacterial colonies, growth dynamics, solid food (model) system, image analysis, food structure, optical density, microcalorimetry

## EFFECT OF SOLID STRUCTURES ON THE GROWTH OF BACTERIAL POPULATIONS

Microbial behavior is determined by structure as much as by environmental conditions and the chemical composition of the media (Robins and Wilson, 1994; Wilson et al., 2002; Antwi et al., 2006, 2007; Theys et al., 2008). In solid structures, substrates diffuse into the colonies and metabolic products outside, triggering concentration gradients in and around the colony, that concern cells availability to oxygen and nutrients (Wimpenny and Coombs, 1983; Wimpenny et al., 1995; Walker et al., 1997; Malakar et al., 2000, 2003; Kabanova et al., 2013). The outwards diffusion of metabolic acids in bacterial colonies gives rise to pH gradients, causing a potential degree of biochemical heterogeneity within and around the colony cells (Walker et al., 1997; Malakar et al., 2000). Studies focused on oxygen penetration's depth and its diffusion through the matrix have revealed to play also a key role on bacterial colonies growth, regarding their surface or submerged character (Wimpenny and Coombs, 1983; Peters et al., 1987;

Robinson et al., 1991). Solid structures has also been reported to affect certain bacterial characteristics, e.g., cell development, morphology, membrane permeability, surface tension, osmotic pressure and metabolism, as well as cell viability and physiological state (Dervakos and Webb, 1991; Wilson et al., 2002; Meldrum et al., 2003). Some authors stated that cell immobilization in a solid environment can also generate changes in cell susceptibility to antimicrobial compounds (Walker et al., 1997; Malakar et al., 2000; Skandamis et al., 2000; Dens and Van Impe, 2001) as well as acid tolerance responses (Malakar et al., 2000; Antwi et al., 2007).

Therefore, it seems of utmost importance to study colony behavior in solid structures, since most of the studies in literature have focused on planktonic growth in liquid systems. In fact, trends in predictive microbiology are moving toward a more realistic approach of microbial behavior in structured food products, including the study of surface and submerged colonies. This work gives an overview of the different available

<footnote n="1">¹ Flemish Cluster Predictive Microbiology in Foods, Leuven, Belgium</footnote>

<footnote n="2">² Chemical and Biochemical Process Technology and Control, Department of Chemical Engineering, Katholieke Universiteit Leuven, Leuven, Belgium</footnote>
techniques to characterize colony growth in solid model food systems.

# STUDYING BACTERIAL COLONIES IN SOLID MODEL FOOD SYSTEMS

## INVASIVE TECHNIQUES

To date, several approaches have been developed for a better understanding of bacterial colony behavior in solid systems. Most traditional measuring techniques provide information of overall microbial populations through invasive procedures, like viable plate count and microelectrodes. Traditional techniques enable growth dynamics estimation, the measurement of environmental conditions, etc. Hereunder are compiled some representative achievements in this field.

To study colony behavior at laboratory scale, bacterial colonies are often obtained from the inoculation of different solid culture media prepared by adding different gelling agents. Agar and gelatine are widely used in food microbiology, although their relevance is restricted to products with gelled microstructure like frankfurters (Mertens et al., 2009). In order to cover a wider range of model food systems, some authors assayed with different hardening agents such as xanthan gum, Carbopol, κ-carrageenan (Mertens et al., 2009, 2011; Noriega et al., 2010; Boons et al., 2013a) and Maxiren 180 (DSM Food Specialities, France), a coagulant agent used by Jeanson et al. (2011) for a model cheese. Studies on real solid food have also been performed, e.g., Katsaras and Leistner (1988) described for the first time the growth of submerged bacteria in fermented sausages; Noriega et al. (2010) described the role of the food structure in bacterial colonization of poultry products. The study of bacterial colonies also requires an adequate experimental setup to hold the solid structure in which colonies will be cultured, e.g., plastic or glass petri dishes and conical tubes. Special attention draws the gel-cassette system designed by Brocklehurst et al. (1995) at the Institute of Food Research (IFR, Norwich, UK). This system consists of a frame sealed with gas-permeable plastic film that holds the inoculated gelled media between two PVC transparent windows. The gelled media needs a separate preparation in order to be inoculated and introduced in the system before solidifying. Once the cassette is filled, it is sealed with the plastic films, being then ready for incubation. Sampling for viable count experiments from the gel-cassette requires blending the media to take an aliquot; while for colony observation it can be directly couple to a microscopy device. The gel-cassette is widely used to develop either submerged or surface colonies and has helped assessing overall population dynamics of several pathogenic bacteria, e.g., *Salmonella typhimurium* (Brocklehurst et al., 1995), *Listeria monocytogenes* (Meldrum et al., 2003) and mixed bacterial co-cultures (Tsigarida et al., 2003).

Among the traditional techniques to determine bacterial growth in solid structures, viable plate count remains as the most commonly used procedure. This technique generally entails the sampling of an aliquot from the inoculated system under study, its homogenization and dilution. Finally, the sample is spread on the corresponding agar plates for the following viable counting. This technique has been used to determine the overall growth dynamics of bacterial populations and thus, to elucidate the potential effect of different environmental factors. Brocklehurst

et al. (1995) assessed the effect of transient temperatures on the growth dynamics of *S. Typhimurium*. Noriega et al. (2013) used global viable counts to determine the effect of medium structure on the sublethal injure of *S. Typhimurium*, *L. monocytogenes* and *Escherichia coli* colonies. In Skandamis et al. (2007) viable plate count was compared with a non-invasive technique to study the effect of temperature and pH on the growth of *E. coli* colonies cultured in the gel-cassette. Although this methodology is widely applied in the study of bacterial colonies, viable plate count gives information of overall population dynamics, but not from the individual colonies; moreover, it requires a tedious, time consuming and costly work (Guillier et al., 2006; Jeanson et al., 2011; Mertens et al., 2012; Koutsoumanis and Lianou, 2013). Additionally, the heterogeneous behavior among individual cells is driving researches to study cell colonies individually, instead of as a whole population.

As previously described, colony growth in solid systems is affected by several diffusion limitations responsible for gradients of pH, oxygen, metabolites, etc. For a deeper insight in these localized gradients, an invasive technique based on direct measurements with microelectrodes has been developed. Wimpenny and Coombs (1983) published the first work in which microelectrodes were applied to measure oxygen penetration. Colonies of *Bacillus cereus* were cultured on the surface of tryptone soya broth agar (TSBA) contained in petri dishes and oxygen measurements were performed with an oxygen-sensitive microelectrode mounted on a prior micromanipulator. On the other hand, it has been reported the potential inaccuracy in the use of microelectrodes, due to oxygen leakage around the electrode and poisoning tip (Tammam et al., 2001). Microelectrodes have also been applied for measuring pH gradients, e.g., Walker et al. (1997) described the pH gradients within and around surface colonies of *S. Typhimurium* grown in an adapted gelatin cassette system. This technique is usually combined with viable plate count, so that, information about colony growth assist in interpreting the obtained measurements. Nowadays, few tools are available to monitor and identify the metabolic release patterns of growing microbial colonies. Among them, matrix-assisted laser desorption/ionization-time of light (MALDI-TOF) imaging mass spectrometry (IMS) has recently been proposed as a valuable source to detect and to (2D) and (3D) visualize the distribution of metabolites produced by microbial colonies (Gonzalez et al., 2012; Fang and Dorrestein, 2014). Through IMS, the whole bacterial colony is examined including the surrounding agar medium, defining a raster composed of greater that 1000 laser points of data collection, increasing thus the likelihood of detecting unique, discrete ion distribution patterns and hidden molecular phenotypes (Gonzalez et al., 2012). In addition, its combination with MALDI-TOF imaging unravels to visualize the spatial distribution of the detected compounds.

The study of microbial colonies and their peculiarities has also been extended to microbial identification and characterization. It is worth to mention certain techniques that although invasive, approach microbial colonies from an individual point of view. For instance, Fourier transform infra-red (FT-IR) spectrometry provides fingerprint-like patterns of microorganisms that enable to identify different species and strains due to their specific