# How to Plot a Michaelis-Menten Curve

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Many biochemical reactions are naturally slow unless catalyzed by enzymes that increase their reaction rate. Enzyme kinetics measures the single substrate enzymatic reaction rate using the Michaelis-Menten equation, v= [S] Vmax/ [S] Km. The Michaelis-Menten equation, named after biochemist Leonor Michaelis and physician Maud Menten, "describes the relationship between the rate of substrate conversion by an enzyme (V) and the concentration of the substrate ([S])," according to the Davidson College Chemistry website. Based on this equation, the Michaelis-Menten curve can be plotted with the x-axis representing [S] in millimoles and the y-axis representing V in seconds/micromole.

## Understanding the Michaelis-Menten Equation

Understand the purpose of each value in the equation and what it represents. V is the rate of conversion or the reaction rate, [S] is the substrate concentration, Vmax is the maximum rate of conversion, and Km (the Michaelis constant) is the substrate concentration at which the rate of conversion is half of Vmax.

Find the values for each variable in the equation. [S] is the known concentration for the substrate being analyzed, and changing this value will affect the rate of the enzyme-catalyzed reaction. Km and Vmax values are usually listed with the substrate as well in terms of millimoles and sec-1 when given in a problem.

Solve the appropriate equation for each value if the values are not given. According to the Mills College Biochemistry website, begin with the steady state equation k1[Efree][S] = (k-1 + k2)[ES]. Define Km using the equation Km-1 = k1/ (k-1 + k2). Solve for [ES] using the equation [ES] = [S][Et]/(Km + [S]) to get [Ef] and [S]. Use [Ef] to define Vmax using the equation vmax = kcat [Et]. Consult a college level biochemistry guide or textbook for detailed instructions on how to solve each of these equations and for specific definitions of each variable.

Insert Km, [S] and Vmax into the Michaelis-Menten equation and solve for V, the velocity or rate of reaction.

## Plotting the Michaelis-Menten Curve

Using graph paper, draw an x- and y-axis. Label the x-axis mM of [S] or concentration of substrate. Label the y ax- sec/micro-mole of V or velocity of reaction.

Insert different values of [S] into the Michaelis-Menten equation, along with the values found for Km and Vmax, to solve for V.

Plot the values for [S] on the x-axis and the corresponding solved values for V on the y-axis. The graph should look like a rectangular hyperbola where higher concentrations of substrate equate to faster enzymatic reactions.

#### Things You'll Need

• Michaelis-Menten equation
• Calculator
• Graph paper
• Pencil
• College biochemistry guide or textbook