Microbial growth and isothermal microcalorimetry: Growth models and their application to microcalorimetric data

Thermochimica Acta 555 (2013) 64–71

Contents lists available at SciVerse ScienceDirect

Thermochimica Acta journal homepage: www.elsevier.com/locate/tca

Review

Microbial growth and isothermal microcalorimetry: Growth models and their application to microcalorimetric data O. Braissant a,b,∗ , G. Bonkat a,b , D. Wirz b , A. Bachmann a,b a b

Department of Urology, University Hospital Basel, Spitalstrasse 21, CH-4031 Basel, Switzerland Laboratory for Biomechanics and Biocalorimetry, University of Basel, c/o Biozentrum – Pharmazentrum, Klingelbergstrasse 50-70, CH-4056 Basel, Switzerland

a r t i c l e

i n f o

Article history: Received 29 August 2012 Received in revised form 12 November 2012 Accepted 12 December 2012 Available online 14 January 2013 Keywords: Isothermal microcalorimetry Growth rate Growth models Microbiology

a b s t r a c t Over the last 10 years use of isothermal microcalorimetry in the biological and biomedical field has been a increasing. Several biomedical applications such as detection and characterization of pathogens, drug testing, parasitology, and tissue engineering have been investigated. Similarly in environmental science isothermal microcalorimetry has been shown to provide insight in soil science or in geomicrobiology. Often it is useful to convert the isothermal microcalorimetry data into biologically meaningful data such as growth rate, lag phase, or maximum growth. In this study we review not only the various approaches used for such conversion but we also carefully look at the advantages, the drawbacks and underlying assumption of each approach. Understanding of these assumptions is a critical point into applying the right model to the right portion of the microcalorimetric data. © 2012 Elsevier B.V. All rights reserved.

Contents 1. 2. 3. 4.

5. 6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Typical measurements and typical misconceptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimating growth parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Simple exponential models using different approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1. Heat flow data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2. Heat data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. More complex models using heat data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Special cases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. Introduction Isothermal microcalorimetry is often used to monitor bacterial activity and bacterial growth in various types of samples ranging from soil to liquid cultures. Furthermore, in biotechnology, calorimetry as a quantitative analytical technique can provide useful real time informations about the yield, the growth rate or

∗ Corresponding author at: Laboratory for Biomechanics and Biocalorimetry, University of Basel, c/o Biozentrum – Pharmazentrum, Klingelbergstrasse 50-70, CH-4056 Basel, Switzerland. Tel.: +41 61 265 64 64. E-mail address: [email protected] (O. Braissant). 0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tca.2012.12.005

64 65 65 67 67 67 67 68 69 69 69 69

the stoichiometry of a specific biological process (see [1–3] for a review). Using isothermal microcalorimetry, liquid cultures are often preferred for rapid detection of bacterial growth, for example in clinical settings [4–7], or to test antimicrobial compounds [8–10]. However, since microcalorimetry passively measures heat, cultures on solid or viscous medium as well as in opaque matrix are used in the area of food microbiology for example [11,12] or to grow microorganisms that prefer solid medium such as mycobacteria and fungi [13–15]. Translating microcalorimetry data into useful microbiological data can be challenging and often paper present isothermal microcalorimetry data which are not supported or validated by any microbiological measurements such as optical density, cell counts, or metabolic assays (Alamar blue or tetrazolium salt reduction assays). Although some microcalorimeters

O. Braissant et al. / Thermochimica Acta 555 (2013) 64–71

65

Fig. 1. Simplified sketch showing a typical microbial growth curve (A) and a typical microcalorimetric measurement of a Enterococcus faecalis 3 ml culture (B) (author’s unpublished data).

were designed to be able to monitor several additional parameter [16] they never became commercially available. On the other hand some reaction calorimeters allow to have such monitoring but at the cost of higher sample volume and very low throughput (usually reaction calorimeters can only perform one measurement at a time). In addition to technical errors often encountered in microcalorimetry [17], this can result in misinterpretation of the data with respect to their microbiological significance and strongly weakens any further conclusion. Among microbiological parameters, the growth rate () and the generation time (g) are often used to indicate how fast a culture actually grows. A change in these 2 parameters can indicate a positive or negative effect of a particular treatment on cultures. These parameters can be useful when investigating new antimicrobial compounds for example. Similarly, in the context of biotechnology, the production of several compounds is optimal when the growth rate is maintained at a certain level [18,19]. The models involving determination of the growth rate from the calorimetric data are usually quite well described in these studies using reaction calorimeter and large scale calorimeters. In addition, these studies also validate the use of a model using a parallel set of data and investigate the range of applicability of such considered [20,21]. This is often possible because these calorimeters allow measurement of numerous parameters such as substrate consumption, oxygen consumption, carbon dioxide production, biomass production and pH for example. In isothermal microcalorimeters using smaller static ampoules (usually 4 or 20 ml), many studies determine the growth rate using common microbial growth model without discussing the underlying assumptions. Similarly the limitation in the range of applications of these models is often not discussed in the studies involving static ampoules. Finally, the same approach is used in many publications using different organisms, but once again no attempt is made to investigate the growth model that fits data the best and is the most meaningful in terms of microbiology. Therefore, the aim of the present study is to review several approach to monitor bacterial growth in static ampoules (the most commonly used). For this purpose, author’s data or previously published and datasets where small volume closed ampoules isothermal microcalorimetry data can be correlated with microbiological data were used.

2. Data collection Data from peer-reviewed published paper and used here to illustrate the various example where collected using datathief III (version 1.5, Bas Tummers, www.datathief.org). Briefly, pdf versions of the different studies were obtained and high-resolution screenshots of ss containing interesting dataset of data were made.

Images were cleaned using Gimp (version 2.4.5, www.gimp.org) and exported as png files. The resulting png files where then imported in datathief III and data were extracted and saved as text files. Further calculations presented in this paper have been performed using Qtiplot or R (version 2.11.1, [22]) and the grofit package [23]. In addition unpublished data of the authors have also been used as example.

3. Typical measurements and typical misconceptions As microbial growth occur in a batch culture it goes through 4 main phases: the lag phase, the exponential growth phase, the stationary phase and the death phase (or decline phase) ([24], Fig. 1A). Similarly, a typical heat flow curve during a microbial growth experiment also follows a rise and decline (Fig. 1B). However, the similarity between curve shapes does not imply that similar processes are involved. For example a decline in the heat flow does not always mean a decrease of the cell number. When microbes are confronted to different carbon sources, they might consume these substrates sequentially resulting in diauxic growth [25]. The transition from one substrate to another often requires the synthesis of new enzymes (that can be subjected to catabolite repression such as ␤-galactosidase). During this time, heat flow of the culture tends to decrease [26,27] (Fig. 2A). Such change in the stoichiometry energy sources resulting in double maxima in the heat flow curve are not only observed in liquid culture but also in milk fermentation or solid state fermentation as in rye sourdough for example [12,28]. In addition, metabolic transition in electron acceptor for example switching from aerobic respiration to fermentation will result in the same momentary decrease [16,29] (Fig. 2B). Similarly, the return of the heat flow to its baseline at the end of the experiment does not imply that all cell are dead or suddenly disappeared from the growth medium. In most cases, the return to the baseline indicates that the heat producing reaction (i.e., the microbial metabolism) has ceased, however the number of cells in the medium remains rather constant (Fig. 2C, after Ref. [30]). For example as growth related heat production last for ca 10 h [30], survival of Escherichia coli after growth can last up to several days without a significant decrease in the cell number [31,32]. This phenomenon might be even more pronounced for microorganisms able to enter dormancy or to form spores or endospores. On the other hand of the spectrum, cell number can rapidly decrease when a bacteriophage kills the bacteria for example [33] (Fig. 2D) or if specific antimicrobial or disinfectants are introduced in the culture. Similarly in slow growing, more fragile microorganisms lysis can be observed at the end of the culture. Although in this case the heat flow decreases faster than the cell number [34–36] they do show a similar pattern. As a consequence one realizes that heat

O. Braissant et al. / Thermochimica Acta 555 (2013) 64–71

A

800 Heatflow in µW

Heatflow in µW•ml-1

150

100

50

B

0.3

600

0.2

400

0.1

Oxygen in mM

66

200 0

0 2

4

6

8

10

12

14

1

2

Time in hours

4

5

6

Time in hours

C

D

0.4

0.06

30 0.2 20

0.05 10 0.04 5

0.1

10

OD 600nm

0.3

40

Heatflow in µW

15 OD 600nm

Heatflow in µW

50

3

0.03 0

0 0

2

4

6

8

0

2

Time in hours

4

6

8

10

12

14

Time in hours

Fig. 2. Different heatflow pattern and their interpretation. (A) Diauxic event described by Schaarschmidt and Lamprecht [27] with S. cerevisiae using fructose and maltose. (B) Heatflow pattern recorded by Johansson and Wadsö [16] showing the growth of E. coli with the decrease of oxygen in red. The increase in the cell number measured by the optical density is indicated in green for comparison. Note the steep decrease in the heatflow pattern when E. coli is forced to switch from respiration (i.e., oxygen is present) to fermentation (i.e., oxygen is depleted). (C) Heatflow pattern from E. coli in culture and cell number measured by the optical density (in red). Note that heatflow returned to a zero baseline as still high optical density is measured. Redrawn after Fan et al. [30]. (D) Heatflow pattern of an E. coli culture infected with T4 bacteriophages. Note that metabolic heat production decreases as cell are lyzed by the bacteriophage (data from Guosheng et al. [33]). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

flow data alone does not allow deciphering about the viability of cells. Similarly one also realizes that using heat flow as a proxy for the cell number can be true only as long as there is a correlation between heat flow and cell count or optical density. Such correlation only exists during early growth. This lack of correlation between the heat flow and the CFU counts is clearly described in reference [37]. Although in this study a mixed population was used, the observation can be made using other datasets from pure culture. For example in Fig. 2C, the cell number measured using optical density (which is the most commonly used proxy for cell density) is still increasing as the heatflow decreases, thus clearly showing that correlation between heatflow and cell count measured by this

60

5

A

raw data fitted model µ = 0.0357

50

B

raw data fitted model µ = 0.0357

4 3

40

ln(heatflow)

Heatflow in µW

mean has to be considered with care. However, although the relation between the optical density and the viable counts is generally good, the relation between these 2 variables can be affected by several parameters such as temperature, pH and water activity [38], therefore drawing conclusion out of optical density should also be made with care and under the assumption that optical density is a good proxy for viable cell number in the specific conditions of the study performed. As the example provided in Fig. 2C is rely on optical density data the reader can also find similar example using the cell number determined by outplating in Fig. 5 (see Section 4.2), in the graphical abstract of this paper, or in the literature using microscopy to perform a direct cell count [8]. Overall this shows

30 20

2 1

10

0

0

-1 -2

-10 0

100

200

300

Time in minutes

400

500

0

100

200

300

400

500

Time in minutes

Fig. 3. Example of growth rate calculation using simple exponential model (A) and linear model with natural logarithm of the data (B). Note that in both case the calculated growth rate is equal, however the exponential part of the curve might be easier to find on the raw data. Data processed with a simple spreadsheet software QtiPlot. Original data from Fan et al. [30].

O. Braissant et al. / Thermochimica Acta 555 (2013) 64–71

67

Fig. 4. Example of growth rate calculation using simple exponential model applied on the heat over time data. (A) Raw data from Chen et al. [48] showing the heatflow pattern of P. putida as well as the heat and the optical density at 600 nm of the culture. (B) Heat data fitted with a exponential growth models from Eq. (4) in red and Eq. (5) in green. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

that it is necessary to correlate the data observation with microbiological measurements, or alternatively based on its reasoning previously published data.

the growth rate (Fig. 3B). Example of use of this approach can be seen in Refs. [41–43].

4. Estimating growth parameters

In addition it is also relatively easy to include terms in the equation taking care of the microcalorimeter baseline drift and baseline shift as shown below.

As mentioned above there is a strong need to translate the microcalorimetric data into usable microbiological data. In this section the commonly used models to obtain growth rate and/or lag phase duration and maximum growth will be described and their use will be discussed. 4.1. Simple exponential models using different approaches 4.1.1. Heat flow data A commonly encountered approach to estimate bacterial growth is to directly use heat flow data to estimate the growth rate with a simple exponential model (see example in Refs. [8,9,39,40]). As explained above this can be done only during early exponential growth and under the assumption that the heat production rate per cell (or CFU) remains constant and that all cells are metabolically active (i.e., producing heat). The latter assumptions can be considered as true over a sufficiently short period of time. Appling this model outside of these boundaries will results in irrelevant estimation of growth such as null or negative growth rate for example. In the case of diauxic growth (or other metabolic shifts) for example, this approach can be used 2 or more times on the appropriate portions of the heat flow curve (i.e., rising portions). Therefore one has to choose carefully the portion of curve to be fitted and to keep in mind that depending on the curve portion chosen, there can be variations in the calculated growth rate. In Xie et al. [40], the equation used to fit the data is described as follows. nt · w = n0 · w · e(t) → ˚t = ˚0 · e(t)

(1)

where nt is the number of cells at time t, n0 is the initial number of cells, w is the specific heat production rate per cell (or the “power output of each bacterium” as defined in [40]), and  is the specific growth rate. Assuming that w is constant one can use ˚ (the heat flow) directly to calculate the growth rate (˚0 being the initial heatflow and ˚t being the heatflow at time t). Although this model is limited by the assumptions and limitation stated above, it is widely used because of its simplicity and applicability. Preparing, plotting, and performing the appropriate curve fitting allows obtaining the growth rate easily. This can be done using a simple spreadsheet software (Fig. 3A). Similarly, taking advantage of the fact that natural logarithm is the inverse of the exponential function (i.e., ln ex = x) and using a logarithmic notation (see Eq. (2)) makes these operations even easier since only a linear regression is needed to extract

ln(˚t ) = ln(˚0 ) +  · t

˚t = ˚0 · e(t) + ˚0 · A · t + C

(2)

(3)

where A is a constant and ˚·A·t represents the baseline drift over time and C is a constant representing the baseline shift [44]. However due to the properties of logarithm, it becomes quite difficult to find a simple logarithmic notation for such equation. Also it has to be noted that many calorimeters nowadays have very small baseline drift or shift. Similarly the manufacturer software often corrects the baseline drift and shift prior to extraction of the data to spreadsheet software. 4.1.2. Heat data Heat is the integral of the heat flow over time. The heat over time curve has been recognized as a proxy for the growth for 3 decades [45–47]. However, in many cases the heat curves are simply not considered. As the heat production rate per cell can vary quite a lot depending on the metabolism and the growth phase, the energetic cost of a cell should remain quite constant under certain conditions. Therefore the amount of heat generated to produce a cell should also be quite constant. However one has to keep in mind that the biomass related enthalpy of reaction can be dependent on the pathway [2]. When looking at data from [48] (Fig. 4A and B) one might see that there is quite a good relationship between heat and the biomass determined using optical density. Similarly, this can be seen by the heat content of the biomass per unit of carbon formula (UCF). Such values have been measured for E. coli and Saccharomyces cerevisiae and are 5.003 kJ mol−1 (UCF) and 5.266 kJ mol−1 (UCF) respectively (see [49] for a review). Then to estimate the growth rate data one would use the same exponential model as in equation 1 however with heat instead of heat flow data. Qt = Q0 · e(t)

(4)

where Q is the heat, and  the specific growth rate. Example of use of such approach can be seen in Fig. 4B. As before (see Eq. (2)), the logarithmic notation can be used for this simple equation. Similarly, to estimate growth rate from the heat data, Takahashi and colleagues used the following equation [45–47]. Qt = AN0 · e(t) + BN0 ≈ Qt = aQ0 · e(t) + bQ0

(5)

where Q is the heat, N0 is the inoculum size (in any units, cell number or dry weight for example),  is the specific growth rate and A,

1.5 0.5

OD600

2.5

CFU·108

0 1 2 3 4 5

200 0 6 4

original equations of these models have been modified so the growth parameters appear clearly. Early already the Gompertz curve (Eq. (6), according to [53]) was recognized a valuable proxy for the growth curve [54,55]. However many other models exist and were reviewed by Zwietering et al. [53] (see Eqs. (7) and (8) for example). The application of these models to microcalorimetric data is more restricted. For example, when two or more peaks are observed in the heat flow curve, this results in a heat over time curve exhibiting a “staircase pattern”. Of course, such pattern cannot be fitted using such models. This can happen when mixed populations are growing or when diauxic growth occurs. The most commonly used equation for such growth model are listed below (Eqs. (6)–(8), see [53] for details). y = A · e−e[(m ·e/A)·(−1)+1]

OD600

2.5 1.5 0.5

C

4

6

0

2

B

2

heat in joules

A

(modified Gompertz equation)

y = A · {1 +  · e(1+) · e[(m /A)·(1+)(1+(1/))·(−t)] }

(6)

(−1/)

(modified Richards equation)

(7)

0

heat in joules

500

O. Braissant et al. / Thermochimica Acta 555 (2013) 64–71

heatflow in µW

68

0

2

4 6 Time in hours

8

Fig. 5. Example of growth rate calculation using the Richards and the Gompertz growth model applied on the heat over time curve of a Staphylococcus aureus culture (authors unpublished data). (A) Raw data with heatflow (dashed line), CFU counts (circles). Heat (plain black line) is indicated for comparison only (see scale in B and C). (B) Heat data (black line) fitted with the Gompertz model (red line) in parallel with the optical density data (circles). Calculated growth rate was 1.96 h−1 using the Gompertz model. (C) Heat data (black line) fitted with the Richards model (red line) in parallel with the optical density data (circles). The calculated growth rate was 1.90 h−1 using the Richards model. Note that the growth rate calculated using the OD and CFU data were 1.59 h−1 and 0.93 h−1 , respectively. Both growth rates were calculated using R (version 2.11.1, [22]) and the grofit package [23]. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

B, a and b are constants. These constant come from the integration process where the authors also took into account the lag phase (see details in [45]). Again, also this was not the original intent from the authors, since heat is directly proportional to the number of cells produced in many cases, one might replace N0 by Q0 resulting in the right part of Eq. (2) (see example of use in Fig. 4B). The major assumption of this approach is that all cell produced remain in the medium and can be counted using different means, even if they are not active (i.e., not producing heat anymore), using dry weight for example which shows a good agreement with the heat data [50]. If cell lysis occurs, discrepancies will rapidly appear between the heat evolution and the cell count. However one can still correlate the heat evolution with metabolic products that will remain in the medium such as proteins, reducing sugars, nitrite for nitrate reducing bacteria and sulfide for sulfate reducing bacteria respectively [51,52]. As for the previous model the calculations are quite easy and can be performed in simple spreadsheet software. However one as to remain careful in the choice of the curve portion to be fitted. Finally it has to be noted that this model is appropriate for “bumpy” or “noisy” heat flow curve as the integral will be rather smooth compared to the original data (see example in Fig. 4). 4.2. More complex models using heat data When a full growth related heat flow pattern is collected so that heat flow is allowed to rise and return to levels close to baseline (Fig. 5), the heat over time curve usually looks like a sigmoid curve. As simple exponential models only focus on the early part of the curve, obtaining a complete growth curve allows using more complex growth model having a sigmoid shape. Often the

y=

A {1 + e[(4m /A)(−t)+2] }

(modified logistic equation)

(8)

In these equations y can represent the cell number, but also the optical density or other parameters. As for simple exponential models y can be replaced by the heat Q keeping in mind the assumption that the energy to produce a new cells remains fairly constant (see above). Note that the growth rate is not considered anymore and is replaced by the maximum growth rate denoted m . This is because  is time dependent and can be calculated on any interval of the curve, there is only one possible value for m due to the mathematical nature of the sigmoid curves which have only one inflection point where the slope is maximum and to which logistic, Gompertz and Richards equation belong.  represents the duration of the lag phase and A the maximum growth (i.e., the maximum cell number or heat produced). Assuming that these equations are applicable, their use provides more informations on the curve. The additional informations gained might be useful in deciphering between the bactericidal or bacteriostatic effect of a substance that is when mostly  or m are affected. In this context, a bacteriostatic agent will mostly affect m as a bactericidal agent will mostly affect  [56]. Such information is not directly available using the simple exponential models and must be estimated by the experimenter. Similarly, estimation an inoculum size for example after use of disinfectant based on  is also possible assuming that a standard curve has been previously build [57]. In this context it seems that can be a valuable indicator for the efficiency of disinfectants and bacteriostatic agents. Another advantage of these models is that they consider the whole curve. There is no need for the experimenter to arbitrarily choose a portion of the curve to be fitted, therefore different experimenter analyzing the same set of data using the same model will get the same results. Therefore one might expect to get a higher reproducibility using these models. Despite the advantages noted here, these models are less commonly used in microcalorimetry. One reason hindering the use of such models is that much more data processing is involved to extract the data of interest (m , , A). In some cases better fits might be obtained using equation with an additional parameters such as  which is a curve shape factor (see Richards equation (Eq. (7))). However the biological interpretation of such parameter is difficult [53]. Nevertheless these models seems to be particularly appropriated for growth on solid medium [58] (authors personal observations). Using non calorimetric data with fixed  values Dalgaard et al. [59] found that m was determined more accurately using Richards model compared to Gompertz and logistic models.

O. Braissant et al. / Thermochimica Acta 555 (2013) 64–71

69

Table 1 Summary of the different approaches to estimate the growth rate and other parameters based on the microcalorimetric data. Model

Data

Data range

Assumptions

Ease of use

Exponential model

Heatflow

Local

Easy

Linear model

Ln (heatflow)

Local

Exponential model

Heat

Local

Gompertz

Heat

Global

Richards

Heat

Global

Logistic

Heat

Global

Constant w Active cells Constant w Active cells Cell remain Constant cell cost 1 main peaka Cell remain Constant cell cost 1 main peaka Cell remain Constant cell cost 1 main peaka Cell remain Constant cell cost 1 main peaka

Remarks

Easy Easy

1

Moderate

1,2

Moderate to difficult

1,2,3

Easy to moderate

1,2

a Indicate that the heatflow data should present one main peak or a closely similar shape (i.e., peak with a shoulder, or two or very close peaks without big decrease in the heatflow in between). (1) Indicate the possibility to analyze substrate consumption when using a defined medium or metabolic byproducts when they can be determined easily. This assumes that H values are known. (2) Additional parameter such as lag phase duration can be obtained using this model. (3) Indicate that a curve shape parameter is used in the model. This curve shape parameter is difficult to relate to a biological parameter, making interpretation more difficult.

Finally it must be noted that accuracy and use of different models is still subject to a lot of investigation [60,61]. 5. Special cases Fitting growth models to isothermal microcalorimetry data is appealing because it allows reducing the power-time curve to only a few parameters which are easier to handle for further statistical analysis. However one must recognize that in some cases it is rather difficult not to say impossible to use this approach. For example metabolic oscillation during growth described for yeast [62] or parasites [35] are rather difficult to handle with simple models. In other case net growth might cease (i.e., the cell number might remain more or less constant) but the metabolic activity might remain high. This is commonly observed in biofilm, in which cell number increases during the initial establishment of the biofilm and then remain fairly constant when a mature biofilm is formed [63–65]. Also the heterogeneity of biofilms even when produced under the same conditions results in strong variation in the powertime curves [66]. Similarly, in many adherent animal cell line culture, cells growth until they reach confluence, then metabolic activity remain quite high but without cell density increase [67]. Finally, we tend to admit that cells (mostly microorganisms) use energy in an efficient manner, however this is not always true and there is many cases were microorganisms engage in futile cycle [68], therefore spilling energy without any metabolic gain. In the case of intense competition between organisms futile cycle might be a way to prevent potential competitors to access resources. In human energy spilling may be related to cancer, aging, ischemia and cardiac failure (see [69] for a review). Therefore the use of calorimetry associated with such models in these so-called “complicated cases” would be rather useful in the future. 6. Concluding remarks Isothermal microcalorimetry can generate large amount of data and quite large dataset. Comparison of individual power-time curve can be performed visually as some differences are sometime obvious or using specific mathematical analysis such as crosscorrelation analysis [70], discriminant analysis [71] or support vector machines [72]. However, isothermal microcalorimetry data are usually not used alone. For example combining isothermal microcalorimetry data with HPLC, physico–chemical data (such as pH or water activity) or microscopy could valuable in studying microorganisms relevant for the food industry [11,12,36]. Therefore, in order to include microcalorimetric data in wider datasets

allowing further statistical analysis for example, it is often required to reduce them to simple parameter such as growth rate, lag phase duration or maximum growth. To achieve such reduction to simple parameters the use of growth models is required. From the data presented above it is clear that every model has its advantages, drawbacks and assumptions. In addition, there are still some discrepancies between the growth rate calculated using the heatflow data and the growth rate measured by conventional methods (plate counts or OD measurements). One also has to remember that systematic differences exist between the measurement of optical density and the viable counts [59]. However in most of the studies the discrepancies between values obtained using optical density, viable counts and isothermal microcalorimetry are perfectly acceptable. A summary of the various features of each model is presented in Table 1. Also it is quite clear that the choice of a specific model should be motivated by previously gathered data, parallel set of data, or previous publications. In addition to the models presented here several other models exist and although they were not described here it might be helpful to consider them to interpret microcalorimetry data [73]. Finally, it must be noted that there is still a lot of scenarios (biofilm, adherent animal cell lines, metabolic oscillations,. . .) where accurate models are not available. To promote further use of microcalorimetry in microbiology and cell biology it would be helpful that such model appear and become available to the isothermal microcalorimeter end user. This is even truer considering the emergence of new microcalorimeter design with higher throughput such as well plate microcalorimeter (www.symcel.se) and flow through chip calorimeter [74–76] which could be used in many biomedical and biotechnological area where microbiology play an important role. Acknowledgements The authors wish to thanks the two anonymous reviewers who critically read this paper and greatly contributed to improve the original manuscript. References [1] T. Maskow, R. Kemp, F. Buchholz, T. Schubert, B. Kiesel, H. Harms, What heat is telling us about microbial conversions in nature and technology: from chip- to megacalorimetry, Microb. Biotechnol. 3 (2010) 269–284. [2] T. Maskow, H. Harms, Real time insights into bioprocesses using calorimetry: state of the art and potential, Eng. Life Sci. 6 (2006) 266–277. [3] U. Von Stockar, The use of calorimetry in biotechnology, Adv. Biochem. Eng. Biotechnol. 40 (1989) 94–136.

70

O. Braissant et al. / Thermochimica Acta 555 (2013) 64–71

[4] D. Baldoni, H. Hermann, R. Frei, A. Trampuz, A. Steinhuber, Performance of microcalorimetry for early detection of methicillin resistance in clinical isolates of Staphylococcus aureus, J. Clin. Microbiol. 47 (2009) 774–776. [5] A.E. Beezer, B.Z. Chowdhry, Microcalorimetric investigations of drugs, Biol. Microcalorim. (1980) 195–246. [6] O. Braissant, D. Wirz, B. Goepfert, A.U. Daniels, Biomedical use of isothermal microcalorimeters, Sensors 10 (2010) 9369–9383. [7] A. Trampuz, A. Steinhuber, M. Wittwer, S.L. Leib, Rapid diagnosis of experimental meningitis by bacterial heat production in cerebrospinal fluid, BMC Infect. Dis. 7 (2007) 116. [8] W.-J. Kong, Y.-L. Zhao, X.-H. Xiao, Z.-L. Li, Y.-S. Ren, Action of palmatine on Tetrahymena thermophila BF5 growth investigated by microcalorimetry, J. Hazard. Mater. 168 (2009) 609–613. [9] W.-J. Kong, J.B. Wang, C. Jin, Y.L. Zhao, C.M. Dai, X.H. Xiao, Z.L. Li, Effect of emodin on Candida albicans growth investigated by microcalorimetry combined with chemometric analysis, Appl. Microbiol. Biotechnol. 83 (2009) 1183–1190. [10] U. von Ah, D. Wirz, A.U. Daniels, Isothermal micro calorimetry – a new method for MIC determinations: results for 12 antibiotics and reference strains of E. coli and S. aureus, BMC Microbiol. 9 (2009) 106. [11] N. Kabanova, I. Stulova, R. Vilu, Microcalorimetric study of the growth of bacterial colonies of Lactococcus lactis IL1403 in agar gels, Food Microbiol. 29 (2012) 67–79. [12] A. Mihhalevski, I. Sarand, E. Viiard, A. Salumets, T. Paalme, Growth characterization of individual rye sourdough bacteria by isothermal microcalorimetry, J. Appl. Microbiol. 110 (2011) 529–540. [13] O. Braissant, D. Wirz, B. Goepfert, A.U. Daniels, “The heat is on”: rapid microcalorimetric detection of mycobacteria in culture, Tuberculosis 90 (2010) 57–59. [14] E. Oriol, R. Conteras, M. Raimbault, Use of microcalorimetry for monitoring the solid state culture of Aspergillus niger, Biotechnol. Tech. 1 (1987) 79–84. [15] L. Wadso, Y. Li, J. Bjurman, Measurements on two mould fungi with a calorespirometric method, Thermochim. Acta 422 (2004) 63–68. [16] P. Johansson, I. Wadsö, An isothermal microcalorimetric titration/perfusion vessel equipped with electrodes and spectrophotometer, Thermochim. Acta 342 (1999) 19–29. [17] I. Wadsö, L. Wadsö, Systematic errors in isothermal micro- and nanocalorimetry, J. Therm. Anal. Calorim. 82 (2005) 553–558. [18] I. Marison, J.-S. Liu, S. Ampuero, U. Von Stockar, B. Schenker, Biological reaction calorimetry: development of high sensitivity bio-calorimeters, Thermochim. Acta 309 (1998) 157–173. [19] M.M. Schuler, I.W. Marison, Real-time monitoring and control of microbial bioprocesses with focus on the specific growth rate: current state and perspectives, Appl. Microbiol. Biotechnol. 94 (2012) 1469–1482. [20] M.M. Schuler, S. Sivaprakasam, B. Freeland, A. Hama, K.-M. Hughes, I.W. Marison, Investigation of the potential of biocalorimetry as a process analytical technology (PAT) tool for monitoring and control of Crabtree-negative yeast cultures, Appl. Microbiol. Biotechnol. 93 (2011) 575–584. [21] S. Sivaprakasam, M.M. Schuler, A. Hama, K.-M. Hughes, I.W. Marison, Biocalorimetry as a process analytical technology process analyser; robust inline monitoring and control of aerobic fed-batch cultures of Crabtree-negative yeast cells, J. Therm. Anal. Calorim. 104 (2011) 75–85. [22] R. Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, 2008. [23] M. Kahm, G. Hasenbrink, H. Lichtenberg-Fraté, J. Ludwig, M. Kschischo, Grofit: fitting biological growth curves with R, J. Stat. Softw. 33 (2001) 1–8. [24] M.T. Madigan, J.M. Martinko, J. Parker, Brock: Biology of Microorganisms, Prentice-Hall, London, 2000. [25] J. Monod, The growth of bacterial culture, Annu. Rev. Microbiol. 3 (1949) 371–394. [26] O. Braissant, D. Wirz, B. Goepfert, A.U. Daniels, Use of isothermal microcalorimetry to monitor microbial activities, FEMS Microbiol. Lett. 303 (2010) 1–8. [27] B. Schaarschmidt, I. Lamprecht, Microcalorimetric study of yeast growth, utilization of different carbohydrates, Thermochim. Acta 22 (1978) 333–338. [28] I. Stulova, A. Kabanova, T. Kriˇscˇ iunaite, T.-M. Laht, R. Vilu, The effect of milk heat treatment on the growth characteristics of lactic acid bacteria, Agron. Res. 9 (2009) 473–478. [29] U. von Stockar, B. Birou, The heat generated by yeast cultures with a mixed metabolism in the transition between respiration and fermentation, Biotechnol. Bioeng. 34 (1989) 86–101. [30] D.D. Fan, L.-H. Wang, L.-A. Shang, H.-J. Shi, X.-X. Ma, Y. Mi, K.-Z. Xua, A microcalorimetric method for studying the biological effects of Mg2+ ion on recombinant Escherichia coli, Chem. Biochem. Eng. 22 (2008) 363–368. [31] J. Hrenovic, T. Ivankovic, Survival of Escherichia coli and Acinetobacter junii at various concentrations of sodium chloride, EurAsian J. Biosci. (2009) 144–151. [32] R.D. Reinders, S. Biesterveld, P.G.H. Bijker, Survival of Escherichia coli O157:H7 ATCC 43895 in a model apple juice medium with different concentrations of proline and caffeic acid, Appl. Environ. Microbiol. 67 (2001) 2863–2866. [33] L. Guosheng, Study on interaction between T4 phage and Escherichia coli B by microcalorimetric method, J. Virol. Methods 112 (2003) 137–143. [34] K. Ljungholm, I. Wadsö, P.-A. Mardh, Microcalorimetric detection of growth of mycoplasmatales, J. Gen. Microbiol. 96 (1976) 283–288. [35] T. Wenzler, T. Steinhuber, S. Wittlin, C. Scheurer, R. Brun, A. Trampuz, Isothermal microcalorimetry, a new tool to monitor drug action against Trypanosoma brucei and Plasmodium falciparum, PLoS Negl. Trop. Dis. 6 (2012) e1668.

[36] N. Kabanova, A. Kazarjan, I. Stulova, R. Vilu, Microcalorimetric study of growth of Lactococcus lactis IL1403 at different glucose concentrations in broth, Thermochim. Acta 496 (2009) 87–92. [37] C. Alklint, L. Wadsö, I. Sjöholm, Accelerated storage and isothermal microcalorimetry as methods of predicting carrot juice shelf-life, J. Sci. Food Agric. 85 (2005) 281–285. [38] K. Francois, F. Devlieghere, A.R. Standaert, A.H. Geeraerd, I. Cools, J.F. Van Impe, J. Debevere, Environmental factors influencing the relationship between optical density and cell count for Listeria monocytogenes, J. Appl. Microbiol. 99 (2005) 1503–1515. [39] L. Xiaoyan, L. Yi, L. Peng, Z. Juncheng, l. Lin, Q. Songsheng, Y. Ziniu, Microcalorimetric study of Bacillus thuringiensis growth with differenet plasmid number and various promoters, J. Therm. Anal. Calorim. 79 (2005) 649–652. [40] C.-L. Xie, T. Hou-Kuan, S. Zhau-Hua, Q. Song-Sheng, Microcalorimetric study of bacterial growth, Thermochim. Acta 123 (1988) 33–41. [41] L.N. Yang, F. Xu, X.N. Sun, Z.B. Zhao, G.C. Song, Microcalorimetric studies on the action of different cephalosporins, J. Therm. Anal. Calorim. 93 (2008) 417–421. [42] J. Yao, L. Tian, F. Wang, H.L. Chen, C.Q. Xu, C.-L. Su, M.-F. Cai, T. Maskow, G. Zaray, Y.-X. Wang, Microcalorimetric study on effect of chromium(III) and chromium(VI) species on the growth of Escherichia coli, Chin. J. Chem. 26 (2008) 101–106. [43] Y.-L. Zhao, J.-B. Wang, P. Zhang, L.-M. Shan, R.-S. Li, X.-H. Xiao, Microcalorimetric study of the opposing effects of ginsenosides Rg1 and Rb1 on the growth of mice splenic lymphocytes, J. Therm. Anal. Calorim. 104 (2010) 357–363. [44] D. Przybylski, Simple ampoule calorimetric measurements of anaerobic bacterial growth: overcoming weaknesses and biases, in: International Society for Biological Calorimetry Meeting, Leipzig, 2012. [45] M. Hashimoto, K. Takahaschi, Calorimetric studies of microbial growth: quantitative relation between growth thermograms and inoculum size agric, Biol. Chem. 46 (1982) 1559–1564. [46] T. Kimura, K. Takahashi, Calorimetric studies of soil microbes: quantitative relation between heat evolution during microbial degradation of glucose and changes in microbial activity in soil, J. Gen. Microbiol. 131 (1985) 3083–3089. [47] S. Wirkner, K. Takahashi, M. Furuta, B. Hayashi, Calorimetric study on the effect of 60 Co g-rays on the growth of microorganisms, Radiat. Phys. Chem. 63 (2002) 327–330. [48] H.-L. Chen, J. Yao, F. Wang, E. Bramanti, T. Maskow, G. Zaray, Acute toxic effects of three pesticides on Pseudomonas putida monitored by microcalorimeter, J. Environ. Sci. Health B 44 (2009) 157–163. [49] E.H. Battley, Absorbed heat and heat of formation of dried bacterial biomass: studies on the thermodynamics of microbial growth, J. Therm. Anal. Calorim. 74 (2003) 709–721. [50] I.W. Marison, U. Vonstockar, The application of a novel heat-flux calorimeter for studying growth of Escherichia coli W in aerobic batch culture, Biotechnol. Bioeng. 28 (1986) 1780–1793. [51] P. Monk, Aerobic growth thermograms of Streptococcus lactis obtained with a complex medium containing glucose, J. Bacteriol 135 (1978) 373–378. [52] A.S. Traoré, C.E. Hatchikian, J. Le Gall, J.-P. Belaich, Microcalorimetric studies of the growth of sulfate-reducing bacteria: comparison of the growth parameters of some Desulfovibrio species, J. Bacteriol 149 (1982) 606–611. [53] M. Zwietering, I. Jongenburger, F. Rombout, K. van’t Riet, Modeling of the bacterial growth curve, Appl. Environ. Microbiol. 56 (1990) 1875–1881. [54] C. Winsor, The Gompertz curve as a growth curve, Proc. Natl. Acad. Sci. U.S.A. 18 (1932) 1–8. [55] A. Schiraldi, Microbial growth and metabolism: modelling and calorimetric characterization, Pure Appl. Chem. 67 (1995) 1873–1878. [56] M. Howell, D. Wirz, A.U. Daniels, O. Braissant, Application of a microcalorimetric method for determining drug susceptibility in Mycobacterium species, J. Clin. Microbiol. 50 (2011) 16–20. [57] M. Astasov-Frauenhoffer, O. Braissant, I. Hauser-Gerspach, A.U. Daniels, D. Wirz, R. Weiger, T. Waltimo, Quantification of vital adherent Streptococcus sanguinis cells on protein-coated titanium after disinfectant treatment, J. Mater. Sci.: Mater. Med. 22 (9) (2011) 2045–2051. [58] D. Rodríguez, A.U. Daniels, J.L. Urrusti, D. Wirz, O. Braissant, Evaluation of a low-cost calorimetric approach for rapid detection of tuberculosis and other mycobacteria in culture, J. Appl. Microbiol. 111 (2011) 1016–1024. [59] P. Dalgaard, T. Ross, L. Kamperman, K. Neumeyer, T. McMeekin, Estimation of bacterial growth rates from turbidimetric and viable count data, Int. J. Food Microbiol. 23 (1994) 391–404. [60] F. Baty, J.P. Flandrois, M.L. Delignette-Muller, Modeling the lag time of Listeria monocytogenes from viable count enumeration and optical density data, Appl. Environ. Microbiol. 68 (2002) 5816–5825. [61] S. Perni, P.W. Andrew, G. Shama, Estimating the maximum growth rate from microbial growth curves: definition is everything, Food Microbiol. 22 (2005) 491–495. [62] I. Lamprecht, Calorimetry and thermodynamics of living systems, Thermochim. Acta 405 (2003) 1–13. [63] J.W. Costerton, K.J. Cheng, G.G. Geesey, T.I. Ladd, J.C. Nickel, M. Dasgupta, T.J. Marrie, Bacterial biofilms in nature and disease, Annu. Rev. Microbiol. 41 (1987) 435–464. [64] J.W. Costerton, Z. Lewandowski, D.E. Caldwell, D.R. Korber, H.M. Lappin-Scott, Microbial biofilms, Annu. Rev. Microbiol. 49 (1995) 711–745. [65] L. Hall-Stoodley, J.W. Costerton, P. Stoodley, Bacterial biofilms: from the natural environment to infectious diseases, Nat. Rev. Microbiol. 2 (2004) 95–108.

O. Braissant et al. / Thermochimica Acta 555 (2013) 64–71 [66] M. Astasov-Frauenhoffer, O. Braissant, I. Hauser-Gerspach, A.U. Daniels, R. Weiger, T. Waltimo, Isothermal microcalorimetry provides new insights into biofilm variability and dynamics, FEMS Microbiol. Lett. 337 (1) (2012) 31–37. [67] R. Santoro, O. Braissant, B. Müller, D. Wirz, A.U. Daniels, I. Martin, D. Wendt, Real-time measurements of human chondrocyte heat production during in vitro proliferation, Biotechnol. Bioeng. 108 (2011) 3019–3024. [68] J.B. Russel, G.M. Cook, Energetics of bacterial growth: balance of anabolic and catabolic reactions, Microbiol. Rev. 59 (1995) 48–62. [69] J.B. Russell, The energy spilling reactions of bacteria and other organisms, J. Mol. Microbiol. Biotechnol. 13 (2007) 1–11. ˜ J.G. Lorén, J. Bermúdez, Analysis of microcalorimetric curves [70] D. López, M. Vinas, for bacterial identification, Can. J. Microbiol. 33 (1987) 6–11. ˜ [71] J. Bermúdez, D. López, A. Sanahuja, M. Vinas, J. Lorén, Discriminant analysis of microcalorimetric data of bacterial growth, Can. J. Microbiol. 34 (1988) 1058–1062.

71

[72] N. Cristianini, J. Shawe-Taylor, An Introduction to Support Vector Machines, Cambridge University Press, Cambridge, 2006. [73] J. Baranyi, T.A. Roberts, A dynamic approach to predicting bacterial growth in food, Int. J. Food Microbiol. 23 (1994) 277–294. [74] J. Lerchner, A. Wolf, G. Wolf, V. Baier, E. Kessler, M. Nietzsch, M. Krugel, A new micro-fluid chip calorimeter for biochemical applications, Thermochim. Acta 445 (2006) 144–150. [75] S.-I. Yoon, M.-H. Lim, S.-C. P., J.-S. Shin, Y.-J. Kim, BCG detection based on a splitflow microcalorimetric biosensor for the diagnosis of tuberculosis, Biochip J. 2 (2008) 52–59. [76] S. Yoon, M.-H. Lim, S.C. Park, J.-S. Shin, Y.-J. Kim, Neisseria meningitidis detection based on a microcalorimetric biosensor with a split-flow microchannel, J. Microelectromech. Syst. 17 (2008) 590–598.