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18/10/2014 Equation: Determine kcat
http://www.graphpad.com/guides/prism/6/curve-fitting/reg_kcat.htm?toc=0&printWindow 1/2
GraphPad Curve Fitting Guide
Equation: Determine kcat
Introduction
Kcat is the turnover number -- the number of substrate molecule each enzyme site converts to
product per unit time. If you know the concentration of enzyme sites, you can fit Kcat instead of Vmax
when analyzing a substrate vs. velocity curve.
The model
Y = Et*kcat*X/(Km + X)
X is the substrate concentration

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18/10/2014Equation: Determine kcathttp://www.graphpad.com/guides/prism/6/curve-fitting/reg_kcat.htm?toc=0&printWindow1/2
GraphPad Curve Fitting Guide
Equation: Determine kcat
Introduction
Kcat is the turnover number -- the number of substrate molecule each enzyme site converts toproduct per unit time. If you know the concentration of enzyme sites, you can fit Kcat instead of Vmaxwhen analyzing a substrate vs. velocity curve.
The model
Y = Et*kcat*X/(Km + X)
X
is the substrate concentration.
Y
is enzyme velocity.
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 inmicromoles of substrate per minute, then kcat 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 neededto achieve a half-maximum enzyme velocity.
Et
is the concentration of enzyme catalytic sites. If the enzyme has multiple subunits, note that Et isthe 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 sameconcentration units.
Vmax
is the maximum enzyme velocity in the same units as Y. It is not directly shown in the modelabove. It is the velocity of the enzyme extrapolated to very high concentrations of substrate, so isalmost always higher than any velocity measured in your experiment. It is computed by multiplying Ettimes kcat.
Relationship to the Michaelis-Menten model
The curve shown above is identical to the curve defined by the Michaelis-Menten model. You'll getidentical curves when you fit either model to your data, and identical values for Km.The Michaelis-Menten model finds the Vmax, which is the maximum enzyme velocity extrapolated outto very high concentrations of substrate. It is expressed in the same units you used to enter your Yvalues (enzyme activity). Usually it is straightforward to express this (or convert to ) moles/minute/mgof protein. The Vmax is determined by how many enzyme sites are present (Et) and the rate at whichthe enzyme can convert substrate to product (kcat).If you know the concentration of enzyme sites you've added to the assay (Et) then you can fit thecatalytic constant Kcat using the model above.When calculating Kcat, the concentration units cancel out, so Kcat is expressed in units of inversetime. It is the turnover number -- the number of substrate molecule each enzyme site converts to
18/10/2014Equation: Determine kcathttp://www.graphpad.com/guides/prism/6/curve-fitting/reg_kcat.htm?toc=0&printWindow2/2
product per unit time.
Fitting the model with Prism
1.
Create an XY data table. Enter substrate concentration into X, and enzyme velocity into Y. If youhave 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.
2.
After entering data, click Analyze, choose nonlinear regression, choose the panel of enzymekinetics equations, and choose
Kcat
.
3.
You must constrain
Et
to a constant value, based on other experiments. To constrain the value of Et, go to the Constrain tab of the nonlinear regression dialog, make sure that the drop down next toEt 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 notpossible for Prism to fit both the kcat and Et, as the two parameters are intertwined, and asubstrate-velocity curve gives no information about their individual values.
4.
With the sample data, Prism reports that Km= 5.886 with a 95% confidence interval ranging from3.933 to 7.839. The best fit value of kcat is 13.53 with a 95% confidence interval ranging from11.97 to 15.09.
Notes
ã
See the list of assumptions of all analyses of enzyme kinetics.
ã
This equation fits exactly the same curve as the equation that fits Vmax, ratherthan the turnover number Kcat. The product of Kcat times Et (the concentration of enzyme sites) equals the Vmax.
ã
This equation is related to the equation for allosteric enzymes. That allostericmodel adds an additional parameter: the Hill slope h. When h equals 1.0, the twomodels are identical.
© 1995-2014 GraphPad Software, Inc. All rights reserved.

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