Tutorial: analyze Km data of CODHs

This is the first post of a series in which we will provide the readers with simple tutorial approaches to reproduce the data analysis of some of our published papers. All our data analysis is performed using QSoas. Today, we will show you how to analyze the $K_m$ experiments we used to characterize the behaviour of an enzyme, the Nickel-Iron CO dehydrogenase IV from Carboxytothermus hydrogenoformans. The experiments we analyze here are described in much more details in the original publication, Domnik et al, Angewandte Chemie, 2017. The only things you need to know for now are the following:

• the data is the evolution of the current over time given by the absorbed enzyme;
• at a given point, a certain amount of CO (50 µM) is injected, and its concentration decreases exponentially over time;
• the enzyme has a Michaelis-Menten behaviour with respect to CO.

This means that we expect a response of the type: $$i(t) = \frac{i_m}{1 + \frac{K_m}{[\mathrm{CO}](t)}}$$ in which $$[\mathrm{CO}](t) = \begin{cases} 0, & \text{for } t < t_0 \\ C_0 \exp \frac{t_0 - t}{\tau}, & \text{for }t\geq t_0 %> \end{cases}$$

To begin this tutorial, first download the files from the github repository (direct links: data, parameter file and ruby script). Start QSoas, go to the directory where you saved the files, load the data file, and remove spikes in the data using the following commands:

QSoas> cd
QSoas> l Km-CODH-IV.dat
QSoas> R

First fit

Then, to fit the above equation to the data, the simplest is to take advantage of the time-dependent parameters features of QSoas. Run simply:

QSoas> fit-arb im/(1+km/s) /with=s:1,exp

This simply launches the fit interface to fit the exact equations above. The im/(1+km/s) is simply the translation of the Michaelis-Menten equation above, and the /with=s:1,exp specifies that s is the result of the sum of 1 exponential like for the definition of $[\mathrm{CO}](t)$ above. Then, load the Km-CODH-IV.params parameter files (using the "Parameters.../Load from file" action at the bottom, or the Ctrl+L keyboard shortcut). Your window should now look like this:

To fit the data, just hit the "Fit" button ! (or Ctrl+F).

Including an offset

The fit is not bad, but not perfect. In particular, it is easy to see why: the current predicted by the fit goes to 0 at large times, but the actual current is below 0. We need therefore to include an offset to take this into consideration. Close the fit window, and re-run a fit, but now with this command:

QSoas> fit-arb im/(1+km/s)+io /with=s:1,exp

Notice the +io bit that corresponds to the addition of an offset current. Load again the base parameters, run the fit again... Your fit window show now look like:

See how the offset current is now much better taken into account. Let's talk a bit more about the parameters:

• im is \(i_m\), the maximal current, around 120 nA (which matches the magnitude of the original current).
• io is the offset current, around -3nA.
• km is the \(K_m\), expressed in the same units as s_1, the first "injected" value of s (we used 50 because the injection is 50 µM CO). That means the value of \(K_m\) determined by this fit is around 9 nM ! (but see below).
• s_t_1 is the time of the injection of CO (it was in the parameter files you loaded).
• Finally, s_tau_1 is the time constant of departure of CO, noted \(\tau\) in the equations above.

Taking into account mass-transport limitations

However, the fit is still unsatisfactory: the predicted curve fails to reproduce the curvature at the beginning and at the end of the decrease. This is due to issues linked to mass-transport limitations, which are discussed in details in Merrouch et al, Electrochimica Acta, 2017. In short, what you need to do is to close the fit window again, load the transport.rb Ruby file that contains the definition of the itrpt function, and re-launch the fit window using:

QSoas> ruby-run transport.rb
QSoas> fit-arb itrprt(s,km,nFAm,nFAmu)+io /with=s:1,exp

Load again the parameter file... but this time you'll have to play a bit more with the starting parameters for QSoas to find the right values when you fit. Here are some tips:

• the curve predicted with the current parameters (use "Update" to update the display) should "look like" the data;
• apart from io, no parameter should be negative;
• there may be hints about the correct values in the papers...

A successful fit should look like this:

Here you are ! I hope you enjoyed analyzing our data, and that it will help you analyze yours ! Feel free to comment and ask for clarifications.

About QSoas

QSoas is a powerful open source data analysis program that focuses on flexibility and powerful fitting capacities. It is released under the GNU General Public License. It is described in Fourmond, Anal. Chem., 2016, 88 (10), pp 5050–5052. Current version is 2.2. You can download its source code or buy precompiled versions for MacOS and Windows there.