Michaelis-Menten enzyme kinetics

[aritraroy24]

Trials and solutions of the Michaelis-Menten enzyme kinetics

[aritraroy24]

Key Points:

• This is my own version of Michaelis-Menten enzyme kinetics with the following reaction-
  
• Reaction Rate Equation ODEs and Stochastic Chemical Kinetics Jump Processes plots were plotted

Code:

using Catalyst, DifferentialEquations, Plots
reaction = @reaction_network begin
    k₁, S + E --> ES
    k₋₁, ES --> E + S
    k₂, ES --> E + P
    k₋₂, E + P --> ES
end
reactions(reaction)
p = (:k₁ => 0.00166, :k₋₁ => 0.0001, :k₂ => 0.1, :k₋₂ => 0.0005)
tspan = (0.0, 100.0)
u0 = [:S => 301.0, :E => 100.0, :ES => 0.0, :P => 0.0]

# solve ODEs
oprob = ODEProblem(reaction, u0, tspan, p)
osol = solve(oprob, Tsit5())

# solve JumpProblem
u0 = [:S => 301, :E => 100, :ES => 0, :P => 0]
dprob = DiscreteProblem(reaction, u0, tspan, p)
jprob = JumpProblem(reaction, dprob, Direct())
jsol = solve(jprob, SSAStepper())

plot(plot(osol; title="Reaction Rate Equation ODEs"),
    plot(jsol; title="Stochastic Chemical Kinetics Jump Processes");
    layout=(2, 1))

Generated Plots: