Equation: Determine kcat

Introduction

The Vmax of an enzyme is the maximum enzyme velocity extrapolated to maximum substrate concentrations. The Vmax is determined by how many enzyme sites are present and the rate at which the enzyme can convert substrate to product. If you know the concentration of enzyme sites, you can fit kcat, the rate at each enzyme site can convert substrate to product.

Entering data

Create an XY data table. Enter substrate concentration into X, and enzyme velocity into Y. If you have several experimental conditions, place the first into column A, the second into column B, etc.

You can also choose Prism's sample data: Enzyme kinetics -- Michaelis-Menten.

After entering data, click Analyze, choose nonlinear regression, choose the panel of enzyme kinetics equations, and choose Kcat.

Constrain Et to a constant value

You must constrain Et to a constant value, based on other experiments. Et is the concentration of enzyme catalytic sites. If the enzyme has multiple subunits, note that Et is the concentration of catalytic sites, which can be larger than the concentration of enzyme molecules. The Y values are entered in units of concentration per time, and Et must be entered in those same concentration units.

To constrain the value of Et, go to the Constrain tab of the nonlinear regression dialog, make sure that the drop down next to Et is set to "Constant equal to" and enter the value. For the sample data, enter 100 as the value of Et.

If you don't know the value of Et, you cannot fit the kcat, but instead should fit the Vmax. It is not possible for Prism to fit both the kcat and Et, as the two parameters are intertwined, and a substrate-velocity curve gives no information about their individual values.

The model

Y = Et*kcat*X/(Km + X)

Interpret the parameters

kcat is the turnover number, the number of times each enzyme site converts substrate to product per unit time. This is expressed in the inverse of the time units of the Y axis. For example, if Y is in micromoles of substrate per minute, then Et is the number of molecules of substrate produced per catalytic site per minute.

Km is the Michaelis-Menten constant, in the same units as X. It is the substrate concentration needed to achieve a half-maximum enzyme velocity.

Vmax is the maximum enzyme velocity in the same units as Y. It is the velocity of the enzyme extrapolated to very high concentrations of substrate, so is almost always higher than any velocity measured in your experiment. It is computed by multiplying Et times kcat.

Notes