Tutorial: analyze redox inactivations/reactivations

Redox-dependent inactivations are actually rather common in the field of metalloenzymes, and electrochemistry can be an extremely powerful tool to study them, providing one can analyze the data quantitatively. The point of this point is to teach the reader how to do so using QSoas. For more general information about redox inactivations and how to study them using electrochemical techniques, the reader is invited to read the review del Barrio and Fourmond, ChemElectroChem 2019.

This post is a tutorial to learn the analysis of data coming from the study of the redox-dependent substrate inhibition of periplasmic nitrate reductase NapAB, which has the advantage of being relatively simple. The whole processed is discussed in Jacques et al, BBA, 2014. What you need to know in order to follow this tutorial is the following:

• the whole inactivation/reactivation process can be modelled by a simple reversible reaction: $$ \mathrm{A} \rightleftharpoons \mathrm{I} $$ A is the active form, I the inactive form;
• the forward rate constant is \(k_i(E)\) (dependent on potential) and the backward rate constant is \(k_a(E)\), also dependent on potential;
• the experiment is done in a series of 5 steps at 3 different potentials: \(E_0\) then \(E_1\) then \(E_2\) then \(E_1\) then, finally, \(E_0\);
• the enzyme is assumed to be fully active at the beginning of the first step;
• a single experiment is used to obtain the values of \(k_i\) and \(k_a\) for the three potentials (although not reliably for the value at \(E_0\)
• the current given by the active species depends on potential (and it is negative because the enzyme catalyzes a reduction), and the inactive species gives no current;
• in addition to the reversible reaction above, there is an irreversible, potential-dependent loss.

You can download the data files from the GitHub repository. Before fitting the data to determine the values of the rate constants at the potentials of the experiment, we will first subtract the background current, assuming that the respective contributions of faradaic and non-faradaic currents is additive. Start QSoas, go to the directory where you saved the files, and load both the data file and the blank file thus:

QSoas> cd
QSoas> load 27.oxw
QSoas> load 27-blanc.oxw
QSoas> S 1 0

(after the first command, you have to manually select the directory in which you downloaded the data files). The S 1 0 command just subtracts the dataset 1 (the first loaded) from the dataset 0 (the last loaded), see more there. blanc is the French for blank...

Then, we remove a bit of the beginning and the end of the data, corresponding to one half of the steps at \(E_0\), which we don't exploit much here (they are essentially only used to make sure that the irreversible loss is taken care of properly). This is done using strip-if:

QSoas> strip-if x<30||x>300

Then, we can fit ! The fit used is called fit-linear-kinetic-system, which is used to fit kinetic models with only linear reactions (like here) and steps which change the values of the rate constants but do not instantly change the concentrations. The specific command to fit the data is:

QSoas> fit-linear-kinetic-system /species=2 /steps=0,1,2,1,0

The /species=2 indicates that there are two species (A and I). The /steps=0,1,2,1,0 indicates that there are 5 steps, with three different conditions (0 to 2) in order 0,1,2,1,0. This fits needs a bit of setup before getting started. The species are numbered, 1 and 2, and the conditions (potentials) are indicated by #0, #1 and #2 suffixes.

• The I_1 and I_2 are the currents for the species 1 and 2, so something for 1 (active form) and 0 for 2 (inactive form). Moreover, the parameters I_2_#0 (and _#1, _#2) should be fixed and not free (since we don't need to adjust a current for the inactive form).
• The k_11 and k_22 correspond to species-specific irreversible loss. It is generally best to leave them fixed to 0.
• k_12 is the formation of 2 (I) from 1 (A), and k_21 is the formation of A from I. Their values will be determined for the three conditions. The default values should work here.
• The k_loss parameters are the rates of irreversible loss that apply indiscriminately on all species (unlike k_11 and k_22). They are adjusted and ther default values should work too.
• alpha_1_0 and alpha_2_0 are the initial concentrations of species 1 and 2, so they should be fixed to 1 and 0.
• Last, the xstart_a and (_b, _c, _d and _e) correspond to the starting times for the steps, here, 0, 60, 120, 210 and 270.

For the sake of simplicity, you can also simply load the starting-parameters.params parameters to have all setup the correct way. Then, just hit Fit, enjoy this moment when QSoas works and you don't have to... The screen should now look like this:

Now, it's done ! The fit is actually pretty good, and you can read the values of the inactivation and reactivation rate constants from the fit parameters.

You can train also on the 21.oxw and 21-blanc.oxw files. Usually, re-loading the best fit parameters from other potentials as starting parameters work really well. Gathering the results of several fits into a real curve of rate constants as a function of potentials is left as an exercise for the reader (or maybe a later post), although you may find these series of posts useful in this context !

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 3.0. You can download its source code there (or clone from the GitHub repository) and compile it yourself, or buy precompiled versions for MacOS and Windows there.