Kinetic study of the thermal inactivation of Lactobacillus plantarum during bread baking

Figures & data

Table 1. List of some studies on kinetic modeling of the inactivation of micro-organisms during dynamic drying processes.

Micro-organism strain	Medium	Drying condition	Kinetic model^a	Variables	Reference
Lactococcus lactis ssp. cremoris	reconstituted skim milk (10 wt%, 20 wt% solids content)	convective air drying (70, 90, 110 °C)	$k_d=k_0\text{exp}(-\frac{E_d}{RT})$	T	[16]
Lactobacillus plantarum	starch	fluidized-bed drying (Tinlet 30, 50, 60 °C)	$\ln \left(k_d\right)=\left[\left(a_1-\frac{a_2}{RT}\right)X+\left(b_1-\frac{b_2}{RT}\right)\right]+\left[1-\text{exp}(p{X}^q)\right]\left[\left(a_1^{\mathrm{\prime }}-\frac{a_2^{\mathrm{\prime }}}{RT}\right)X+\left(b_1^{\mathrm{\prime }}-\frac{b_2^{\mathrm{\prime }}}{RT}\right)\right]$	T, X	[17]
Listeria monocytogenes Scott A	macerated potato	surface dry heating (90, 100 °C)	sigmoidal-like primary inactivation model Bigelow type secondary inactivation model	T, aw	[18]
Lactococcus lactis ssp. cremoris ASCC930119	water droplet	convective air drying (45 ∼ 95 °C)	$k_d=k_{d,ref}\left[1-\frac{E_a}{R}(\frac{1}{T}-\frac{1}{T_{ref}})\right]$	T	[19]
Salmonella enterica serovar Enteritidis	potato omelet	microwave (300, 450, 600, and 800 W)	Weibull model $\text{log}\left(\frac{N(t)}{N_0}\right)=-b·t^n,\mathrm{ }b=b\left(T\right),\mathrm{ }n=n(T)\mathrm{ }$	T	[20]
Lactobacillus plantarum WCFS1	20 % w/w maltodextrin DE 6	flat-flow air drying (50, 60, 70 °C)	A modified Weibull model $\mathrm{l}\mathrm{n}\left(\frac{N(t)}{N_0}\right)=-{\left(\frac{t}{\alpha }\right)}^{\beta },\mathrm{ }\alpha =f\left(T,X\right),\mathrm{ }\beta =1$	T, X	[21]
Lactobacillus paracasei ssp. paracasei F19	water	vacuum drying	$k_d(a_w,T)=k_1\text{exp}(m·T)+k_2·\text{exp}(\frac{E_a}{RT}-0.5{\left(\frac{a_w-a_{w0}}{b}\right)}^2)$	T, aw	[22]
Saccharomyces cerevisiae ATCC 2601	0.39 wt% yeast/water suspension	infrared drying (60, 70, 90 °C)	rate-dependent secondary model $k_d=k_o(1+a\left|\frac{dX}{dt}\right|)(1+b\left|\frac{dT}{dt}\right|)\text{exp}(-\frac{E_d}{RT})$	T, dT/dt, dX/dt	[23]
Bifidobacterium infantis Bb1, Streptococcus thermophilus St10	milk droplet (10 wt% solids content)	flat-flow air drying (70, 90, 110 °C)	rate-dependent secondary model $k_d=k_o(1+a\left|\frac{dX}{dt}\right|+b{\left|\frac{dX}{dt}\right|}^2)\text{exp}(-\frac{E_d}{RT})$	T, dX/dt	[24]
Escherichia coli B200	n.a.	non-isothermic conditions (T 52.05 ∼ 63.10 °C, pH 3 ∼ 9, aw 0.928 ∼ 0.995)	$\ln \left(k\right)=C_0+C_1/T+C_{2}pH+C_3{pH}^2+C_4{a}_w^2$	T, pH, aw	[25]

^a Primary level model was first-order reaction model except mentioned, and the meaning of each parameter is referred to the original publications.

Table 2. Rate-dependent models tested in this study to describe the inactivation rate constant k_d of Lactobacillus plantarum P8 inactivation during bread baking.

Model No.	Expression	Variables
1	$k_d=k_o\text{exp}(-\frac{E_d}{RT})$	T
2	$k_d=k_o\text{exp}(aX-\frac{E_d+bX}{RT})$	T, X
3	$k_d=k_o(1+a\left|\frac{dX}{dt}\right|+b{\left|\frac{dX}{dt}\right|}^2)\text{exp}(-\frac{E_d}{RT})$	T, dX/dt
4	$k_d=k_o(1+a\left|\frac{dX}{dt}\right|)(1+b\left|\frac{dT}{dt}\right|)\text{exp}(-\frac{E_d}{RT})$	T, dT/dt, dX/dt
5	$k_d=k_o(1+a\left|\frac{dT}{dt}\right|)\text{exp}(-\frac{E_d}{RT})$	T, dT/dt
6	$k_d=k_o(1+a\left|\frac{dT}{dt}\right|)\text{exp}(bX-\frac{E_d}{RT})$	T, X, dT/dt

Figure 1. Experimental and simulated inactivation data of L. plantarum in the crust of 30 g bread during baking at different temperatures (experimental data: ×, 175 °C; *, 205 °C, ○, 235 °C; simulated data: _{······,} 175 °C; - - -, 205 °C; – _·· –, 235 °C), Simulated survival curves fitted with different rate-dependent models: (a) ∼ (f) for model No. 1 ∼ 6 in Table 2 (R², square of correlation coefficient). Error bars indicate the standard deviation of the experimental data.

Table 3. Optimal parameters of the rate-dependent models based on the inactivation data of Lactobacillus plantarum P8 in the crust of 30 g bread.

Model No.	k0 (s^−1)	Ed (J·mol^−1)	a	b	MSE	AICc
1	0.186	6.085 × 10^3	–	–	0.262	−188
2	27.731	5.271 × 10^4	31.550	9.979	0.303	−165
3	0.345	8.048 × 10^3	0	99.400	0.287	−171
4	0.175	1.087 × 10^4	0.863	16.873	0.131	−286
5	0.469	1.087 × 10^4	4.365	–	0.084	−351
6	0.110	1.392 × 10^4	12.788	5.309	0.029	−504

Figure 2. Validation of the rate-dependent model No. 4 in Table 2 using different inactivation datasets (a: 0.1 g; b: 5 g; c: 60 g) and a parity plot of the experimental and the simulated values of the residual viability of L. plantarum in the crust during baking (d: ▲30 g, Δ 0.1 g, □ 5 g, ◊ 60 g). Lines represent predicted survival curves calculated using parameters derived from 30 g dataset; Error bars indicate the standard deviation of the experimental data, R² the square of correlation coefficient.

Figure 3. Validation of the rate-dependent model No. 6 in Table 2 using different inactivation datasets (a: 0.1 g; b: 5 g; c: 60 g) and a parity plot of the experimental and the simulated values of the residual viability of L. plantarum in the crust during baking (d: ▲30 g, Δ 0.1 g, □ 5 g, ◊ 60 g). Lines represent predicted survival curves calculated using parameters derived from 30 g dataset; Error bars indicate the standard deviation of the experimental data, R² the square of correlation coefficient.

Figure 4. Experimental and simulated inactivation data of L. plantarum in the crumb of bread during baking at different temperatures (experimental data: □, 175 °C; ◊, 205 °C, Δ, 235 °C; simulated data: _{······,} 175 °C; - - -, 205 °C; – _·· –, 235 °C), Simulated survival curves fitted with different rate-dependent models: (a) ∼ (c) for model No. 4 and (d) ∼ (f) for model No. 6 in Table 2 (R², square of correlation coefficient). Error bars indicate the standard deviation of the experimental data.

Fu, N.; Woo, M. W.; Selomulya, C.; Chen, X. D. Inactivation of Lactococcus Lactis Ssp. Cremoris Cells in a Droplet During Convective Drying. Biochem. Eng. J. 2013, 79, 46–56. DOI:10.1016/j.bej.2013.06.015.

 Web of Science ®Google Scholar

Lievense, L. C.; Verbeek, M. A. M.; Taekema, T.; Meerdink, G.; Riet, K. V. Modelling the Inactivation of Lactobacillus Plantarum During a Drying Process. Chemical Engineering Science 1992, 47, 87–97. DOI:10.1016/0009-2509(92)80203-O.

 Web of Science ®Google Scholar

Valdramidis, V. P.; Geeraerd, A. H.; Gaze, J. E.; Kondjoyan, A.; Boyd, A. R.; Shaw, H. L.; Impe, J. F. V. Quantitative Description of Listeria Monocytogenes Inactivation Kinetics with Temperature and Water Activity as the Influencing Factors; Model Prediction and Methodological Validation on Dynamic Data. J. Food Eng. 2006, 76, 79–88. DOI:10.1016/j.jfoodeng.2005.05.025.

 Web of Science ®Google Scholar

Ghandi, A.; Powell, I.; Chen, X. D.; Adhikari, B. Drying Kinetics and Survival Studies of Dairy Fermentation Bacteria in Convective Air Drying Environment using Single Droplet Drying. J. Food Eng. 2012, 110, 405–417. DOI:10.1016/j.jfoodeng.2011.12.031.

 Web of Science ®Google Scholar

Valero, A.; Cejudo, M.; García-Gimeno, R. M. Inactivation Kinetics for Salmonella Enteritidis in Potato Omelet using Microwave Heating Treatments. Food Control 2014, 43, 175–182. DOI:10.1016/j.foodcont.2014.03.009.

 Web of Science ®Google Scholar

Tan, D. T.; Poh, P. E.; Chin, S. K. Microorganism Preservation by Convective Air-Drying — A review. Drying Technol. 2018, 36(7), 764–779.

 Web of Science ®Google Scholar

Bayrock, D.; Ingledew, W. M. Fluidized Bed Drying of Baker’s Yeast: Moisture Levels, Drying Rates, and Viability Changes During Drying. Food Res. Int. 1997, 30, 407–415. DOI:10.1016/S0963-9969(98)00003-9.

 Web of Science ®Google Scholar

Perdana, J.; Bereschenko, L.; Fox, M. B.; Kuperus, J. H.; Kleerebezem, M.; Boom, R. M.; Schutyser, M. A. I. Dehydration and Thermal Inactivation of Lactobacillus Plantarum WCFS1: Comparing Single Droplet Drying to Spray and Freeze Drying. Food Res. Int. 2013, 54, 1351–1359. DOI:10.1016/j.foodres.2013.09.043.

 Web of Science ®Google Scholar

Foerst, P.; Kulozik, U. Modelling the Dynamic Inactivation of the Probiotic Bacterium L. Paracasei Ssp. Paracasei During a low-temperature Drying Process based on Stationary Data in Concentrated Systems. Food Bioprocess Technol. 2012, 5, 2419–2427. DOI:10.1007/s11947-011-0560-4.

 Web of Science ®Google Scholar

Huang, H.; Brooks, M. S.-L.; Huang, H.-J.; Chen, X. D. Inactivation Kinetics of Yeast Cells During Infrared Drying. Drying Technol. 2009, 27, 1060–1068. DOI:10.1080/07373930903218453.

 Web of Science ®Google Scholar