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Modeling of the Bacillus subtilis Bacterial Biofilm Growing on an Agar Substrate.

Wang X, Wang G, Hao M - Comput Math Methods Med (2015)

Bottom Line: Bacterial biofilms are organized communities composed of millions of microorganisms that accumulate on almost any kinds of surfaces.Our results show biofilm growth evolution characteristics such as biofilm thickness, active biomass, and nutrient concentration in the agar substrate.We provide an alternative mathematical method to describe other kinds of biofilm growth such as multiple bacterial species biofilm and also biofilm growth on various complex substrates.

View Article: PubMed Central - PubMed

Affiliation: School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China ; School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.

ABSTRACT
Bacterial biofilms are organized communities composed of millions of microorganisms that accumulate on almost any kinds of surfaces. In this paper, a biofilm growth model on an agar substrate is developed based on mass conservation principles, Fick's first law, and Monod's kinetic reaction, by considering nutrient diffusion between biofilm and agar substrate. Our results show biofilm growth evolution characteristics such as biofilm thickness, active biomass, and nutrient concentration in the agar substrate. We quantitatively obtain biofilm growth dependence on different parameters. We provide an alternative mathematical method to describe other kinds of biofilm growth such as multiple bacterial species biofilm and also biofilm growth on various complex substrates.

No MeSH data available.


Related in: MedlinePlus

The parameter effect on the biofilm thickness. (a) The yield coefficient Y  (MMn−1) describes the ratio of the amount of biomass produced to the amount of substrate consumed [25]. (b) The maximum specific growth rate VT  (MnM−1T−1) describes the maximum proliferation ability of microorganisms. (c) The diffusion coefficient D  (L2T−1) reflects the nutrient diffusion ability into biofilm and (d) the biofilm biomass density ρ  (ML−3) indicates the biomass in unit volume. Moreover, the biofilm thickness as a function of time for different (b) VT (MnM−1T−1) and (c) ρ (ML−3) at a steady state (inset) is shown.
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fig6: The parameter effect on the biofilm thickness. (a) The yield coefficient Y  (MMn−1) describes the ratio of the amount of biomass produced to the amount of substrate consumed [25]. (b) The maximum specific growth rate VT  (MnM−1T−1) describes the maximum proliferation ability of microorganisms. (c) The diffusion coefficient D  (L2T−1) reflects the nutrient diffusion ability into biofilm and (d) the biofilm biomass density ρ  (ML−3) indicates the biomass in unit volume. Moreover, the biofilm thickness as a function of time for different (b) VT (MnM−1T−1) and (c) ρ (ML−3) at a steady state (inset) is shown.

Mentions: We find that when yield coefficient Y and the maximum specific growth rate VT increase, the biofilm thickness increases accordingly, as shown in Figures 6(a) and 6(b), while yield coefficient Y has significant effect on biofilm final thickness, as shown in Figure 6(a). It was approved that a larger yield coefficient Y would enlarge cell growth rate, and increase of the maximum specific growth rate VT would increase time-rate-of-change of biomass [33]. The maximum specific growth rate VT can have positive effect on the maximum value of active biomass volume fraction f(t) during the first day; at the same time, active biofilm volume fraction f(t) decreases more rapidly with higher value of VT after the first day, as shown in inset of Figure 7(a). The reason is that the higher the VT is, the more the bacteria multiply, which causes more nutrient consumption and competition between bacteria cells. Active biomass volume fraction f(t) also decreases with increase of rate of active biomass inactivation b, as shown in Figure 7(b). Similarly, Kluge et al. found that the inactivation rate of active biomass b can cause a negative growth rate of active biomass [34].


Modeling of the Bacillus subtilis Bacterial Biofilm Growing on an Agar Substrate.

Wang X, Wang G, Hao M - Comput Math Methods Med (2015)

The parameter effect on the biofilm thickness. (a) The yield coefficient Y  (MMn−1) describes the ratio of the amount of biomass produced to the amount of substrate consumed [25]. (b) The maximum specific growth rate VT  (MnM−1T−1) describes the maximum proliferation ability of microorganisms. (c) The diffusion coefficient D  (L2T−1) reflects the nutrient diffusion ability into biofilm and (d) the biofilm biomass density ρ  (ML−3) indicates the biomass in unit volume. Moreover, the biofilm thickness as a function of time for different (b) VT (MnM−1T−1) and (c) ρ (ML−3) at a steady state (inset) is shown.
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fig6: The parameter effect on the biofilm thickness. (a) The yield coefficient Y  (MMn−1) describes the ratio of the amount of biomass produced to the amount of substrate consumed [25]. (b) The maximum specific growth rate VT  (MnM−1T−1) describes the maximum proliferation ability of microorganisms. (c) The diffusion coefficient D  (L2T−1) reflects the nutrient diffusion ability into biofilm and (d) the biofilm biomass density ρ  (ML−3) indicates the biomass in unit volume. Moreover, the biofilm thickness as a function of time for different (b) VT (MnM−1T−1) and (c) ρ (ML−3) at a steady state (inset) is shown.
Mentions: We find that when yield coefficient Y and the maximum specific growth rate VT increase, the biofilm thickness increases accordingly, as shown in Figures 6(a) and 6(b), while yield coefficient Y has significant effect on biofilm final thickness, as shown in Figure 6(a). It was approved that a larger yield coefficient Y would enlarge cell growth rate, and increase of the maximum specific growth rate VT would increase time-rate-of-change of biomass [33]. The maximum specific growth rate VT can have positive effect on the maximum value of active biomass volume fraction f(t) during the first day; at the same time, active biofilm volume fraction f(t) decreases more rapidly with higher value of VT after the first day, as shown in inset of Figure 7(a). The reason is that the higher the VT is, the more the bacteria multiply, which causes more nutrient consumption and competition between bacteria cells. Active biomass volume fraction f(t) also decreases with increase of rate of active biomass inactivation b, as shown in Figure 7(b). Similarly, Kluge et al. found that the inactivation rate of active biomass b can cause a negative growth rate of active biomass [34].

Bottom Line: Bacterial biofilms are organized communities composed of millions of microorganisms that accumulate on almost any kinds of surfaces.Our results show biofilm growth evolution characteristics such as biofilm thickness, active biomass, and nutrient concentration in the agar substrate.We provide an alternative mathematical method to describe other kinds of biofilm growth such as multiple bacterial species biofilm and also biofilm growth on various complex substrates.

View Article: PubMed Central - PubMed

Affiliation: School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China ; School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.

ABSTRACT
Bacterial biofilms are organized communities composed of millions of microorganisms that accumulate on almost any kinds of surfaces. In this paper, a biofilm growth model on an agar substrate is developed based on mass conservation principles, Fick's first law, and Monod's kinetic reaction, by considering nutrient diffusion between biofilm and agar substrate. Our results show biofilm growth evolution characteristics such as biofilm thickness, active biomass, and nutrient concentration in the agar substrate. We quantitatively obtain biofilm growth dependence on different parameters. We provide an alternative mathematical method to describe other kinds of biofilm growth such as multiple bacterial species biofilm and also biofilm growth on various complex substrates.

No MeSH data available.


Related in: MedlinePlus