## 4 Discussion  
_MiLPMO9H_ was immobilised on an electrode surface, ensuring that direct electron transfer is indeed possible for this enzyme with the immobilisation method used with an indication that, for the conventional scan, rated when using cyclic voltammetry, the kinetics were quasi-reversible. The signal was governed by capacitance, a common feature for immobilised enzymes on electrode surfaces. Despite this, still, an initial estimation of the standard electron transfer rate constant was intented through the computational reproduction of cyclic voltammograms. From the peak separation, it was predicted that the \(k^{0}\) would be around 5 s\({}^{-1}\), assuming an \(a\) equal to 0.5. Then FTacV was performed for two different amplitudes as various frequencies in order to assure that both quasi-reversibility and reversibility are achieved in order to apply the methodology to extract the \(k^{0}\) of immobilised species using FTacV. The extracted value was at \(4.6\pm 2.6\) s\({}^{-1}\) being in good accordance with what was expected from cyclic voltammetry. In order to validate the \(k^{0}\) value obtained experimentally, FTacV experiments were simulated numerically and a rather good agreement was found for transfer coefficient \(a\) equal to 0.57. In order to approximate the peak heights of the voltammograms, different values of \(\Gamma^{0}S\) were used for the two different amplitudes. At this point, the validity of the \(\Gamma^{0}S\) used shall be ascertained. Since the enzyme concentration is 5.5 mg mL\({}^{-1}\) and 8 mL were utilised, and they were dilluted in 10 mL to a final concentration of 4.4 mg mL\({}^{-1}\). From this, 2 mL were used, and, taking into consideration that the molecular weight of the enzyme is 65 kDa [22], the maximum moles that can be 1.35 \(\times\) 10\({}^{-10}\). Considering that not all of the enzymes would be bound to the matrix and from what was bound, not all would be oriented in such a way so as to interact with the enzyme, the values used for  
Figure 7: Experimental (black) versus computational (red dashed line) of the 5 th harmonic of _MiLPMO9H_ immobilised on a Co-f-MWCNTs modified GC electrode at 25 \({}^{\circ}\)C. Experimental conditions: acetate buffer 500 mM, pH 6, \(f=1\) Hz and **(a)**\(A_{0}=0.2\) and (b) 0.25 V. Computational parameters: a=0.57, \(f=1\) Hz, (a) \(A_{0}=0.2\) V, \(\Gamma^{0}S=3\times 10^{-13}\) mol and **(b)**\(A_{0}=0.25\) V, \(\Gamma^{0}S=1.2\times 10^{-12}\) mol. the simulation seem to be valid. Nevertheless, it has to be pointed out that the proposed experimental methodology for obtaining kinetic parameters does not require knowledge of the surface concentration of the immobilised species or the the value of the surface area. In general, it is common practice to compare computational with experimental results in order to ascertain the validity of the parameters used for the computational ones. The computational fits tend to reproduce most of the features of the voltammogram, just as in this case, where the basic features of the harmonics presented are fitted rather well [25; 26]. Regarding the precision of the comparison of the computational harmonics with the experimental ones, it should also be taken into account that the above analysis is valid only if the assumptions of the model are closely met, where the immobilised species must behave as a Langmuir monolayer and a dispersion of the electrochemical transfer rates should be absent. Otherwise, where kinetic or thermodynamic dispersion is present, more elaborate models have to be considered [27; 28; 29]. The influence of kinetic and thermodynamic dispersion might affect the waveform of the voltammograms [30], and other theories such as that of Marcus-Hush can applied, instead of the Butler-Volmer law [31]. Yet, in this case, the Butler-Volmer law seems to be rather sufficient for this case.