By Andy Pasquesi
Updated Aug 30, 2022

Enzymes accelerate chemical reactions by lowering the activation energy required for substrate conversion. The turnover number, k_cat, quantifies the catalytic efficiency of an enzyme by measuring the number of substrate molecules converted to product per enzyme active site per second under saturating substrate conditions.

1. Determining Initial Reaction Velocities

Step 1

Plot the product concentration versus time for the first test tube of your enzymatic assay. Use time on the horizontal axis and product concentration on the vertical axis.

Step 2

Calculate the slope of the linear portion of the curve (initial velocity, V₀). In Excel or a graphing calculator, the linear regression line will give you the slope directly. If you prefer a manual estimate, divide the change in product concentration between two consecutive data points by the corresponding change in time.

Step 3

Record this slope as the initial reaction velocity, V₀, for that test tube. In the regression equation [Product] = m·time + b, the coefficient m is V₀.

Step 4

Repeat steps 1–3 for each test tube in the assay to obtain a series of V₀ values at different substrate concentrations.

2. Calculating V_max Using the Lineweaver–Burk Plot

Step 1

Create a Lineweaver–Burk (double‑reciprocal) plot: plot 1/[S] (inverse substrate concentration) on the horizontal axis and 1/V0 (inverse initial velocity) on the vertical axis. For example, if a test tube has an initial substrate concentration of 50 µM and a V₀ of 80 µM s^–1, the plotted point would be (1/50 µM, 1/80 µM s^–1).

Step 2

Perform a linear regression on these points. The resulting equation takes the form 1/V0 = m·(1/[S]) + b, where b is the y‑intercept.

Step 3

Calculate the inverse of V_max by taking the reciprocal of the y‑intercept: 1/Vmax = 1/b.

Step 4

Invert the value from step 3 to obtain V_max:

Vmax = 1/(1/Vmax) = b

Step 5

Identify the enzyme concentration used in the assay (this value is constant across all test tubes and should be reported in the raw data).

Step 6

Compute k_cat by dividing V_max by the enzyme concentration:

kcat = Vmax / [E]

This yields the number of substrate molecules converted per enzyme active site per second.

Key Takeaway

By following these systematic steps—measuring initial velocities, constructing a Lineweaver–Burk plot, extracting V_max, and normalizing to enzyme concentration—you can accurately determine an enzyme’s turnover number, k_cat, a cornerstone metric in enzymology and drug development.