Modeling bacterial attachment to surfaces as an early stage of biofilm development
Biofilms are present in all natural, medical and industrial surroundings where bacteria live. Biofilm formation is a key factor in the growth and transport of both beneficial and harmful bacteria. While much is known about the later stages of biofilm formation, less is known about its initiation wh...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.821 |
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| author | Fadoua El Moustaid Amina Eladdadi Lafras Uys |
| author_facet | Fadoua El Moustaid Amina Eladdadi Lafras Uys |
| author_sort | Fadoua El Moustaid |
| collection | DOAJ |
| description | Biofilms are present in all natural, medical and industrial surroundings where bacteria live. Biofilm formation is a key factor in the growth and transport of both beneficial and harmful bacteria. While much is known about the later stages of biofilm formation, less is known about its initiation which is an important first step in the biofilm formation.In this paper, we develop a non-linear system of partial differential equations of Keller-Segel type model in one-dimensional space, which couples the dynamics of bacterial movement to that of the sensing molecules. In this case, bacteria perform a biased random walk towards the sensing molecules. We derive the boundary conditions of the adhesion of bacteria to a surface using zero-Dirichlet boundary conditions, while the equation describing sensing molecules at the interface needed particular conditions to be set.The numerical results show the profile of bacteria within the space and the time evolution of the density within the free-space and on the surface. Testing different parameter values indicate that significant amount of sensing molecules present on the surface leads to a faster bacterial movement toward the surface which is the first step of biofilm initiation.Our work gives rise to results that agree with the biological description of the early stages of biofilm formation. |
| format | Article |
| id | doaj-art-10f447c5e82c4893b90b545487da05b1 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-10f447c5e82c4893b90b545487da05b12025-01-24T02:26:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-03-0110382184210.3934/mbe.2013.10.821Modeling bacterial attachment to surfaces as an early stage of biofilm developmentFadoua El Moustaid0Amina Eladdadi1Lafras Uys2African Institute for Mathematical Sciences, 6 Melrose road, Muizenberg, 7945African Institute for Mathematical Sciences, 6 Melrose road, Muizenberg, 7945African Institute for Mathematical Sciences, 6 Melrose road, Muizenberg, 7945Biofilms are present in all natural, medical and industrial surroundings where bacteria live. Biofilm formation is a key factor in the growth and transport of both beneficial and harmful bacteria. While much is known about the later stages of biofilm formation, less is known about its initiation which is an important first step in the biofilm formation.In this paper, we develop a non-linear system of partial differential equations of Keller-Segel type model in one-dimensional space, which couples the dynamics of bacterial movement to that of the sensing molecules. In this case, bacteria perform a biased random walk towards the sensing molecules. We derive the boundary conditions of the adhesion of bacteria to a surface using zero-Dirichlet boundary conditions, while the equation describing sensing molecules at the interface needed particular conditions to be set.The numerical results show the profile of bacteria within the space and the time evolution of the density within the free-space and on the surface. Testing different parameter values indicate that significant amount of sensing molecules present on the surface leads to a faster bacterial movement toward the surface which is the first step of biofilm initiation.Our work gives rise to results that agree with the biological description of the early stages of biofilm formation.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.821bacterial biofilmkeller-segel modelchemotaxissensing molecules. |
| spellingShingle | Fadoua El Moustaid Amina Eladdadi Lafras Uys Modeling bacterial attachment to surfaces as an early stage of biofilm development Mathematical Biosciences and Engineering bacterial biofilm keller-segel model chemotaxis sensing molecules. |
| title | Modeling bacterial attachment to surfaces as an early stage of biofilm development |
| title_full | Modeling bacterial attachment to surfaces as an early stage of biofilm development |
| title_fullStr | Modeling bacterial attachment to surfaces as an early stage of biofilm development |
| title_full_unstemmed | Modeling bacterial attachment to surfaces as an early stage of biofilm development |
| title_short | Modeling bacterial attachment to surfaces as an early stage of biofilm development |
| title_sort | modeling bacterial attachment to surfaces as an early stage of biofilm development |
| topic | bacterial biofilm keller-segel model chemotaxis sensing molecules. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.821 |
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