Inhibition of Enzyme Reactions in Continuous Stirred-Tank Reactor and Batch Reactors

Inhibitors decrease the rates that enzymes bind to substrates and convert them to products. Three types of inhibition (competitive, uncompetitive, noncompetitive/mixed) and reaction with no inhibitor are compared for an enzyme reaction that obeys Michaelis-Menten kinetics. Substrate concentration is plotted versus time for a continuous stirred-tank reactor (CSTR) and for a batch reactor. Change the "inhibitor concentration", which remains constant during reaction, with a slider. Change the "initial substrate concentration" for the batch reactor or the "feed substrate concentration" for the CSTR with a slider. Select "reaction pathway" to see the reaction steps, pathways, and a brief description of the type of inhibition. In competitive inhibition, the inhibitor attacks the enzyme to form an enzyme-inhibitor complex (E-I); adding more substrate minimizes the inhibitor effect. In uncompetitive inhibition, the inhibitor attacks the enzyme-substrate complex (E-S); adding more substrate does not overcome this type of inhibition since the inhibitor does not compete with the substrate for the enzyme sites. In noncompetitive inhibition, the inhibitor attacks the enzyme to form an enzyme-inhibitor complex (E-I) or it attacks the enzyme-substrate complex (E-S) to form an enzyme-substrate-inhibitor complex (E-S-I).

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Details
For a CSTR the material balance is written in the form of a differential equation:

for a batch reactor the material balance is:
where CS is the substrate concentration (kmol/m3), CS,i is the feed substrate concentration (kmol/m3), rs is the rate of substrate consumption for various types of inhibition (kmol/[m3 min], τ is residence time (min), and t is time (min).

Rate laws are different for each type of inhibition:
where CI is the inhibitor concentration (kmol/m3), KI and KM are inhibitor and Michaelis constants (kmol/m3), and Vmax is the rate of reaction (kmol/[m3 min]).