The Michaelis-Menten model describes the kinetics of enzyme mediated reactions: where S = substrate concentration (moles/L), m

The Michaelis-Menten model describes the kinetics of enzyme mediated reactions:

where S = substrate concentration (moles/L), νm = maximum uptake rate (moles/L/d), and k_s = the half-saturation constant, which is the substrate level at which uptake is half of the maximum [moles/L]. If the initial substrate level at t = 0 is S₀, this differential equation can be solved for

S = S₀ − ν_mt + k_s ln(S₀/S)
Develop an M-file to generate a plot of S versus t for the case where S₀ = 8 moles/L, vm = 0.7 moles/L/d, and k_s = 2.5 moles/L.

Transcribed Image Text:

ds dt || -Um S ks + S