Delayed differential equations as a $\textit{Salmonella}$ biofilm model

Year 2025, Volume: 74 Issue: 2, 318 - 332, 19.06.2025

Hale Elçin Latifi , İrem Özgökkurt Işıkdoğan , Kağan Özdemir , Nefise Akçelik , Nuri Ozalp , Mustafa Akçelik

https://doi.org/10.31801/cfsuasmas.1532891

Abstract

$\textit{Salmonella}$ is a widespread bacterial pathogen that is the primary cause of many foodborne illnesses worldwide. It gains significant strength against antibacterial treatments when it forms the biofilm structure, which can be considered a multicellular-like form where the pathogen is compartmentalized based on function in which each part communicates, further adding to the capabilities of resistance. To overcome this problem, it is important for practitioners to know how $\textit{Salmonella}$ biofilms will evolve through time under the presence of various carbon resources which are mostly present in food products. In this work, a mathematical model of $\textit{Salmonella}$ biofilm trajectories was made using Delayed Logistic Differential Equations after an experimental procedure which comprised treatments with seven carbon sources of six different concentrations. This model proved to be efficient for modeling $\textit{Salmonella}$ biofilm formation even without significant amount of data.

Keywords

$\textit{Salmonella}$ , biofilm , mathematical modeling , carbon source

Supporting Institution

Ankara Üniversitesi Bilimsel Araştırma Projeleri (BAP)

Project Number

FYL-2023-2891

References

• Allen, L. J. S., An Introduction to Mathematical Biology, Prentice Hall, 2007.
• Bowden, S. D., Rowley, G., Hinton, J. C., Thompson, A., Glucose and glycolysis are required for the successful infection of macrophages and mice by Salmonella enterica serovar typhimurium, Infection and Immunity, 77(7) (2009), 3117-3126. https://doi.org/10.1128/iai.00093-09.
• Brown, C., Differential Equations: A Modeling Approach, Vol. 150., Sage, 2007.
• Cadena, M., Kelman, T., Marco, M. L., Pitesky, M., Understanding antimicrobial resistance (AMR) profiles of Salmonella biofilm and planktonic bacteria challenged with disinfectants commonly used during poultry processing, Foods, 8(7) (2019), 275. https://doi.org/10.3390/foods8070275.
• De la Fuente-Núñez, C., Reffuveille, F., Fernández, L., Hancock, R. E., Bacterial biofilm development as a multicellular adaptation: antibiotic resistance and new therapeutic strategies, Current Opinion in Microbiology, 16(5) (2013), 580-589. https://doi.org/10.1016/j.mib.2013.06.013.
• Flemming, HC., Wingender, J., Szewzyk, U. Steinberg, P., Rice, S.A., Kjelleberg, S., Biofilms: an emergent form of bacterial life, Nat Rev Microbiol, 14 (2016), 563– 575. https://doi.org/10.1038/nrmicro.2016.94.
• Hutchinson, G. E., Circular causal systems in ecology, Ann. NY Acad. Sci, 50(4) (1948), 221-246.
• Kalai Chelvam, K., Yap, K. P., Chai, L. C., Thong, K. L., Variable responses to carbon utilization between planktonic and biofilm cells of a human carrier strain of Salmonella enterica serovar typhi, PLoS One, 10(5) (2015), e0126207. https://doi.org/10.1371/journal.pone.0126207.
• Kenyon, W. J., Thomas, S. M., Johnson, E., Pallen, M. J., Spector, M. P., Shifts from glucose to certain secondary carbon-sources result in activation of the extracytoplasmic function sigma factor σE in Salmonella enterica serovar Typhimurium, Microbiology, 151(7) (2005), 2373-2383. https://doi.org/10.1099/mic.0.27649-0.
• Pal, M. K., Lavanya, M., Microbial influenced corrosion: understanding bioadhesion and biofilm formation, Journal of Bio-and Tribo-Corrosion, 8(3) (2022), 76. https://doi.org/10.1007/s40735-022-00677-x.
• Paytubi, S., Cansado, C., Madrid, C., Balsalobre, C., Nutrient composition promotes switching between pellicle and bottom biofilm in Salmonella, Frontiers in Microbiology, 8 (2017), 2160. https://doi.org/10.3389/fmicb.2017.02160.
• Roy, P. K., Ha, A. J. W., Mizan, M. F. R., Hossain, M. I., Ashrafudoulla, M., Toushik, S. H., Ha, S. D., Effects of en- vironmental conditions (temperature, pH, and glucose) on biofilm formation of Salmonella enterica serotype Kentucky and virulence gene expression, Poultry Science, , 100(7) (2021), 101209. https://doi.org/10.1016/j.psj.2021.101209.
• Speranza, B., Corbo, M. R., Sinigaglia, M., Effects of nutritional and environmental conditions on Salmonella sp.biofilm formation, Journal of Food Science, 76(1) (2011), M12-M16. https://doi.org/10.1111/j.1750-3841.2010.01936.x.
• Steenackers, H., Hermans, K., Vanderleyden, J., De Keersmaecker, S. C., Salmonella biofilms: an overview on occur-rence, structure, regulation and eradication, Food Research International, 45(2) (2012), 502-531. https://doi.org/10.1016/j.foodres.2011.01.038.
• Stepanovic, S., Vukovic, D., Dakic, I., A modified microtiter-plate test for quantification of staphylococcal biofilm formation, Journal of Microbiological Methods, 40(2) (2000), 175–179. https://doi.org/10.1016/S0167-7012(00)00122-6.
• Toyofuku, M., Inaba, T., Kiyokawa, T., Obana, N., Yawata, Y., Nomura, N., Environmental factors that shape biofilm formation, Bioscience, Biotechnology, and Biochemistry, 80(1) (2016), 7-12. https://doi.org/10.1080/09168451. 2015.1058701.
• Verotta, D., Haagensen, J., Spormann, A. M., Yang, K., Mathematical modeling of biofilm structures using COMSTAT data, Computational and Mathematical Methods in Medicine, 2017(1) (2017), 7246286. https://doi.org/10.1155/2017/7246286.
• Wright, E. M., The non-linear difference-differential equation, The Quarterly Journal of Mathematics, (1) (1946), 245-252. https://doi.org/10.1093/qmath/os-17.1.245.
• Yin, B., Zhu, L., Zhang, Y., Dong, P., Mao, Y., Liang, R., Niu L., Luo, X., The characterization of biofilm formation and detection of biofilm-related genes in Salmonella isolated from beef processing plants, Foodborne pathogens and disease, 15(10) (2018), 660-667. https://doi.org/10.1089/fpd.2018.2466.
• Zheng, L., Shi, C., Ma, W., Lu, Z., Zhou, L., Zhang, P., Bie, X., Mechanism of biofilm formation by Salmonella typhimurium ST19 in a high-glucose environment revealed by transcriptomics, Food Bioscience, 50 (2022), 102074. https://doi.org/10.1016/j.fbio.2022.102074.