A study of the kinetics of the enzyme inhibitor Draculin

Documenting calculations: A study of the kinetics of the enzyme inhibitor Draculin

In this activity we can examine the use of both Vernier's Graphical Analysis, and TI's Derive

Context: Here's a real life real problem taken from the introductory module of the Open University course Molecules in Medicine S807 - an excellent course dealing with the nature of medicine at a molecular level, and an perfect resource if you're using a Salter's approach to student learning in Chemistry.

Activity

This is the actual introduction of a scientific paper published in Biochimica et Biophysica Acta in 1999. At the very end of the paragraph below, there are a couple of phrases for you to complete, which indicate the way the drug behaves.

Activation of Factor X is a common point between the intrinsic and extrinsic pathway of blood coagulation. Activated factor X (FXa) is the sole enzyme that catalyses the conversion of prothrombin into thrombin, the key enzyme in the coagulation cascade; therefore inhibitors of this step are of considerable mechanistic and pharmacological interest. In addition to the two known physiological inhibitors of this serine protease, antirhrombin III (AT-III) and the tissue factor phatway inhibitor (TFPI), several low molecular mass natural occurring polypeptides inhibitors have been described, such as Antistasin, a 119-residue protein isolated from the Mexican leech Haementeria officinalis; the tick anticoagulant peptide (TAP), a 60-amino acid protein derived from the tick Ornithodoros moubata; Ecotin, a periplasmic protein found in Escherichia coli; and the Ancylostoma caninum anticoagulant peptide (AcAP). These peptides behave as reversible, slow tight-binding inhibitors of FXa, where Antistasin and Ecotin are slowly cleaved by FXa, while TAP is not affected by the protease. Recently, we described a new natural FXa inhibitor, isolated from the saliva of the vampire bat Desmodus rotundus, which was named Draculin. Draculin is an 88.5 kDa glycoprotein, which selectively inhibits both FXa and activated factor IX (FIXa). Furthermore, the anticoagulant activity of Draculin is highly dependent on the proper glycosylation of the polypeptide backbone. The results described in this paper indicate that, ___________________, Draculin behaves as __________________ inhibitor of FXa.

Preincubation of FXa with Draculin inhibits the catalytic activity of the enzyme. From the progress plots, inhibited (Vi) and uninhibited (Vo) initial rates were calculated.

Using the rate of inhibition (V) values and the concentration of substrate (S), Lineweaver-Burk plots were plotted to establish the mode of inhibition of FXa by Draculin (competitive, non-competitive) and whether it is concentration dependent inhibition.

(a) In the table above are given the values for rate of inhibition (V) and substrate (S), concentration for constant concentration of FXa (4nM) and Draculin concentrations of 21.36, 32.18, and 41.20 nM. Using these values, construct the Lineweaver-Burk plots for each set of data in a single graph, decide whether the data indicate competitive or non-competitive inhibition, and calculate Km for each of the plots.

What are your conclusions so far?

source:  Open University, S807, Molecules in Medicine, 2003 (part question). The full paper detailing Draculin and containing the kinetic data can be found in this paper: Fenandez (2003)

 

For bright students, particularly those who are seriously looking at either biochemistry or medicine as a career, this question has great potential for studying the Biochemistry option as well as the Medicines and Drugs option in tandem. It also offers great potential for using software solutions in the service of clarity and presentation.

Taking the data given:

Substrate concentration [S]/µM	Initial rate v / (arbitrary units)
	Control (no Draculin)	[Draculin] = 21.36 nM	[Draculin] = 32.18 nM	[Draculin] = 41.20 nM
80	505	246	169	100
120	600	324	228	126
160	686	355	246	150
240	813	400	255	157

we will plotting these out using Vernier's Graphical Analysis software available from www.vernier.com
Purchasing one copy buys also a license for the school and it's students for home use.

 

First enter the data into a Graphical Analysis data window (similar to a spreadsheet). The columns to the right hand side are calculated columns of 1/rate corresponding to the different concentrations of the inhibitor Draculin as given.

In the background the data has been plotted on the graph but we need lines of best fit.

To complete this we use Graphical Analysis' own internal line fitting:

Note the linear regression data that appears in the data boxes on the graph. We need to change the scaling of the graph to identify the region of convergence. Clicking on the graph itself opens up the property boxy with two tabs. In the Graph Options tab we'll estabish a title for the graph,

and in the Axes Options tab, we'll play with the scale until we're happy with the layout.

finishing with the plot below which clearly indicates that Draculin is a non-competitive inhibitor.

and the Derive document within the Derive interface:

the 1/v value where the uninhibited (control) data line intercepts the y axis is 0.003401 with units of 1/rate (arbitrary units)

From a Lineweaver-Burk plot this intercept corresponds in value to 1/Vmax

Using our computer running Derive as a calculator recording all steps in our calculation, we have

For users of TI-83's and other TI calculators, there is little to learn. The embellishments include the annotations and comments between lines of calculations, simply inserted to make the document readable.

There are a full set of graphical and statistical functions, and these would have particular potential for the Biology students.

Resources:

Derive 5 or Derive 6 software
http://education.ti.com/us/product/software/derive/down/download.html

Introduction to Derive
http://education.ti.com/downloads/guidebooks/eng/product/derive5bk.pdf

Derive Tutorials
http://education.ti.com/us/training/online/freederivetutorials.html