Substrate inhibition in bioreactors occurs when the concentration of substrate (such as glucose, salts, or phenols) exceeds the optimal parameters and reduces the growth rate of the cells within the bioreactor. This is often confused with substrate limitation, which describes environments in which cell growth is limited due to of low substrate. Limited conditions can be modeled with the Monod equation; however, the Monod equation is no longer suitable in substrate inhibiting conditions. A Monod deviation, such as the Haldane (Andrew) equation, is more suitable for substrate inhibiting conditions. These cell growth models are analogous to equations that describe enzyme kinetics, although, unlike enzyme kinetics parameters, cell growth parameters are generally empirically estimated.
General Principles Cell growth in bioreactors depends on a wide range of environmental and physiological conditions such as substrate concentration. With regards to bioreactor cell growth, substrate refers to the nutrients that the cells consume and is contained within the bioreactor medium. Cell growth can either be substrate limited or inhibited depending on whether the substrate concentration is too low or too high, respectively. The Monod equation accurately describes limiting conditions, but substrate inhibition models are more complex. Substrate inhibition occurs when the rate of microbial growth lessens due to a high concentration of substrate. Higher substrate concentrations are usually caused by osmotic issues, viscosity, or inefficient oxygen transport. By slowly adding substrate into the medium, fed-batch bioreactor systems can help alleviate substrate inhibition. Substrate inhibition is also closely related to enzyme kinetics which is commonly modeled by the Michaelis–Menten equation. If an enzyme that is part of a rate-limiting step of microbial growth is substrate inhibited, then the cell growth will be inhibited in the same manner. However, the mechanisms are often more complex, and parameters for a model equation need to be estimated from experimental data. Additionally, information on inhibitory effects caused by mixtures of compounds is limited because most studies have been performed with single-substrate systems.
Types of Inhibition
Enzyme Kinetics Overview One of the most well known equations to describe single-substrate enzyme kinetics is the Michaelis-Menten equation. This equation relates the initial rate of reaction to the concentration of substrate present, and deviations of model can be used to predict competitive inhibition and non-competitive inhibition. The model takes the form of the following equation:
ν = V m [ S ] K M + [ S ] {\displaystyle \nu ={\frac {V_{m}[S]}{K_{M}+[S]}}} (Michaelis-Menten equation) Where
K M {\displaystyle K_{M}} is the Michaelis constant
ν {\displaystyle \nu } is the initial reaction rate
V m {\displaystyle V_{m}} is the maximum reaction rate If the inhibitor is different from the substrate, then competitive inhibition will increase Km while Vmax remains the same, and non-competitive will decrease Vmax while Km remains the same. However, under substrate inhibiting effects where two of the same substrate molecules bind to the active sites and inhibitory sites, the reaction rate will reach a peak value before decreasing. The reaction rate will either decrease to zero under complete inhibition, or it will decrease to a non-zero asymptote during partial inhibition. This can be described by the Haldane (or Andrew) equation, which is a common deviation of the Michaelis-Menten equation, and takes the following form:
ν = V m [ S ] K M + [ S ] + [ S ] 2 K I {\displaystyle \nu ={\frac {V_{m}[S]}{K_{M}+[S]+{\frac {[S]^{2}}{K_{I}}}}}} (Haldane equation for single-substrate inhibition of enzymatic reaction rate) Where
K I {\displaystyle K_{I}} is the inhibition constant
Cell Growth in Bioreactors Bioreactor cell growth kinetics is analogous to the equations presented in enzyme kinetics. Under non-inhibiting single-substrate conditions, the specific growth rate of biomass can be modeled by the well-known Monod equation. The Monod equation models the growth of organisms during substrate limiting conditions, and its parameters are determined through experimental observation. The Monod equation is based on a single substrate-consuming enzyme system that follows the Michaelis-Menten equation. The Monod takes the following familiar form:
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