Abstract
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.
Highlights
A biofilm is an aggregation of microorganisms that form on both natural and abiotic surfaces, and are irreversibly attached to a substrate or each other and embedded in a matrix of extracellular polymeric substances that they produce [31, 54]
The focus of this paper is to gain some fundamental understanding of the mechanisms of biofilm initiation. Modeling this particular stage leads to a better understanding of the whole process, which, leads to the ability of either inhibiting a detrimental biofilms or accelerating the formation of a beneficial biofilm. This stage is governed by bacterial chemotaxis towards the sensing molecules that leads to finding the surface and the attachment
Two positive facts making bacteria choose to live within a biofilm instead of the planktonic state, are: (1) the ability to differentiate into types that differ in their nutrient requirements, which means there are fewer competitors for a particular nutrient; (2) when conditions deteriorate in a biofilm, some bacteria sacrifice themselves for the other bacteria to have a better life
Summary
A biofilm is an aggregation of microorganisms that form on both natural and abiotic surfaces, and are irreversibly attached to a substrate or each other and embedded in a matrix of extracellular polymeric substances that they produce [31, 54]. Each particular type of biofilm models has its own assumptions and its own computational and mathematical tools These models usually consider that biofilm’s structure is determined by the substrate concentration and bacterial movement and they generally deal with final stages of biofilm formation [42, 51, 48]. Modeling this particular stage leads to a better understanding of the whole process, which, leads to the ability of either inhibiting a detrimental biofilms or accelerating the formation of a beneficial biofilm This stage is governed by bacterial chemotaxis towards the sensing molecules that leads to finding the surface and the attachment.
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