# How To Plot A Michaelis-Menten Curve

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

### Step 1

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.

### Step 2

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.

### Step 3

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.

### Step 4

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

### Step 1

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.

### Step 2

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

### Step 3

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 Needed

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

### Cite This Article

#### MLA

Junious, Brandi. "How To Plot A Michaelis-Menten Curve" *sciencing.com*, https://www.sciencing.com/plot-michaelismenten-curve-10044510/. 24 April 2017.

#### APA

Junious, Brandi. (2017, April 24). How To Plot A Michaelis-Menten Curve. *sciencing.com*. Retrieved from https://www.sciencing.com/plot-michaelismenten-curve-10044510/

#### Chicago

Junious, Brandi. How To Plot A Michaelis-Menten Curve last modified August 30, 2022. https://www.sciencing.com/plot-michaelismenten-curve-10044510/