Consider Example 16.1, where we demonstrated that two...

Consider Example 16.1, where we demonstrated that two bacteria competing for a single nutrient in a chemostat (well-mixed) could not coexist. Consider the situation where $B$ can adhere to a surface but $A$ cannot. Redo the balance equations, where $a$ is the surface area available per unit reactor volume and the rate of attachment is first order in $X_{B}$ with a rate constant $k_{a B}$. The sites available for attachment will be $\left(X_{B M}^{A t}-X_{B}^{A t}\right) a V$. The attached cells can detach with a first-order dependence on the attached cell concentration $\left(X_{B}^{A t}\right)$ with a rate constant of $k_{d B}$. Attached cells grow with the same kinetics as suspended cells. a. Without mathematical proofs, do you think coexistence may be possible? Why or why not? b. Consider the specific case below and solve the appropriate balance equations for $D=0.4 \mathrm{~h}^{-1}$ : $$ \begin{aligned} \mu_{m A} &=1.0 \mathrm{~h}^{-1} ; \quad \mu_{m B}=0.5 \mathrm{~h}^{-1} \\ K_{S A} &=K_{S B}=0.01 \mathrm{~g} / \mathrm{l} \\ Y_{A / S} &=Y_{B / S}=0.5 \mathrm{~g} / \mathrm{g} \\ S_{0} &=5 \mathrm{~g} / 1, \quad a=10 \mathrm{~cm}^{2} / \mathrm{cm}^{3} \\ X_{B M}^{A t} &=1 \times 10^{-4} \mathrm{~g} / \mathrm{cm}^{2} \\ k_{d B} &=0.5 \mathrm{~h}^{-1}, \quad k_{a B}=1000 \mathrm{~cm}^{3} / \mathrm{g}-\mathrm{h} \end{aligned} $$

Consider Example 16.1, where we demonstrated that two bacteria competing for a single nutrient in a chemostat (well-mixed) could not coexist. Consider the situation where $B$ can adhere to a surface but $A$ cannot. Redo the balance equations, where $a$ is the surface area available per unit reactor volume and the rate of attachment is first order in $X_{B}$ with a rate constant $k_{a B}$. The sites available for attachment will be $\left(X_{B M}^{A t}-X_{B}^{A t}\right) a V$. The attached cells can detach with a first-order dependence on the attached cell concentration $\left(X_{B}^{A t}\right)$ with a rate constant of $k_{d B}$. Attached cells grow with the same kinetics as suspended cells.
a. Without mathematical proofs, do you think coexistence may be possible? Why or why not?
b. Consider the specific case below and solve the appropriate balance equations for $D=0.4 \mathrm{~h}^{-1}$ :
$$
\begin{aligned}
\mu_{m A} &=1.0 \mathrm{~h}^{-1} ; \quad \mu_{m B}=0.5 \mathrm{~h}^{-1} \\
K_{S A} &=K_{S B}=0.01 \mathrm{~g} / \mathrm{l} \\
Y_{A / S} &=Y_{B / S}=0.5 \mathrm{~g} / \mathrm{g} \\
S_{0} &=5 \mathrm{~g} / 1, \quad a=10 \mathrm{~cm}^{2} / \mathrm{cm}^{3} \\
X_{B M}^{A t} &=1 \times 10^{-4} \mathrm{~g} / \mathrm{cm}^{2} \\
k_{d B} &=0.5 \mathrm{~h}^{-1}, \quad k_{a B}=1000 \mathrm{~cm}^{3} / \mathrm{g}-\mathrm{h}
\end{aligned}
$$

Key Concepts

Surface Attachment and Detachment Kinetics

This concept introduces the additional dynamics of microbial attachment to and detachment from surfaces within a bioreactor. The attachment of cells adds a spatial component where microbes can adhere to surfaces, altering their effective concentration in the suspended phase, while detachment returns them to the bulk. These processes are typically modeled as first-order kinetics with specific constants, and they can significantly influence overall microbial behavior and potential coexistence.

Mass Balance Equations in Biological Systems

Mass balance equations are used to model the rates of change of concentrations of substrates and cells within a system. In microbial ecology and bioprocess engineering, these differential equations capture the essential dynamics of growth, substrate consumption, and cell removal (or retention in the case of attached cells). They are crucial for predicting system behavior under various operating conditions and modifications such as adhesion.

Chemostat Dynamics

This concept involves the study and control of microbial growth in a continuously operated bioreactor where fresh nutrient medium is continuously added and culture liquid containing microorganisms is continuously removed at the same rate. It is central to understanding how steady-state conditions are maintained, how dilution rate influences growth, and how nutrient supply affects microbial kinetics in well-mixed systems.

Microbial Competition

Microbial competition examines how different microbial species or strains interact and compete for limited resources within an environment. In the context of continuous cultures like chemostats, understanding competitive dynamics is important due to the competitive exclusion principle, which in many cases predicts that one species will outcompete another for a single limiting nutrient, thereby preventing coexistence under simple conditions.

Competitive Exclusion and Coexistence Mechanisms

While classic chemostat models often predict competitive exclusion when two species compete for a single nutrient, additional mechanisms such as spatial segregation (e.g., one species adhering to surfaces) can provide niches that allow for coexistence. This concept explores how modifications, like differential attachment/detachment abilities, can alleviate direct competition and enable multiple species to persist in the same environment.

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