A wealth of information on the reactions of redox-active sites in proteins can be obtained by voltammetric studies in which the protein sample is arranged as a layer on an electrode surface. For instance, by carrying out cyclic voltammetry over a wide range of scan rates and exploiting the ability to poise or pulse the electrode potential between cycles, data are obtained that are conveniently (albeit simplistically) analysed in terms of plots of peak potentials against scan rate. A simple reversible electron-transfer process gives rise to a trumpet-shaped plot because the oxidation and reduction peaks separate increasingly at high scan rate; the electrochemical kinetics are then determined by fitting to Butler-Volmer or Marcus models. Much more interesting though are the ways in which this trumpet plot is altered, often dramatically, when electron transfer is coupled to biologically important processes such as proton transfer, ligand exchange, or a change in conformation. It is then possible to derive particularly detailed information on the kinetics, energetics and mechanism of reactions that may not be revealed clearly or even at all by other methods [1, 2]. Thus, from the electrode current response of such voltammetric experiments, information about the underlying/coupled/parallel mechanisms of electron transfer can be drawn.

Hitherto, the voltammetric investigations of immobilised proteins has been conducted almost exclusively using cyclic voltammetry [1-3]. This is due to the fact that the ‘simple' input utilised by cyclic voltammetry, a voltage ramp, simplified the following fitting process using standard electrochemical dynamics models. Lately, more complicated voltage excitations have been investigated to interrogate such systems. Among them, ac voltammetry, which uses a superposition of a ‘slower' dc ramp with a high-amplitude/high-frequency harmonic as excitation, has emerged as a very prominent candidate [4]. The major advantage of such novel excitation waveforms is the fact that they offer a number of input degrees of freedom which the experimentalist can utilise to address/target different protein function-related mechanisms. In order to interpret though the voltammetry of coupled systems using such ‘complicated' voltage excitations, it is important to be able to define the ideal behaviour for systems that are expected to show simple and uncoupled electron transfer.

The major difficulty of voltammetric methods lies in their interpretation. Electrochemical signals are intrinsically nonlinear and nonstationary. Additionally, double layer capacitance effects due to the re-organisation of ions at the electrode surface often distort the current response severely. Hitherto there have been few alternatives to the fast Fourier transform technique for frequency analysis although fundamental assumptions of the theory, namely periodicity, continuity and linearity, are not satisfied. The Hilbert transform (HT) offers an alternative tool of data analysis that can overcome these difficulties. It results in instantaneous frequency and amplitude as a function of time providing a viable method for nonstationary, nonlinear signal processing [5]. Recently, the HT was used to study the voltammetric time series of a population of electrochemical oscillators [6] as well as for purely electroanalytical purposes [7].

In this contribution we show how kinetic and thermodynamic properties of surface bound molecules can be estimated accurately using ac voltammetry as excitation perturbation and the time domain patterns resulting from the HT analysis. We will illustrate theoretically how the macroscopic parameters that characterise electron transfer, i.e. k₀, α, E₀ from the Butler-Volmer methodology can be estimated with high accuracy from our pattern formation analysis. This method proves extremely robust even in the presence of large capacitive currents, which normally preclude quantitative analysis with conventional tools. From the HT analysis of simulated ac voltammograms we introduce parameters (γ, Δτ) which allow the determination of these physical properties directly from the time domain [8, 9]. Furthermore, we will attempt to show how microscopic electron-transfer parameters such as recombination energy &lamda or gating effects which are of significance in numerous biological/environmental processes influence our time domain-analysis. Additionally, we shall derive from our analysis the optimal voltage excitation parameters for the investigation of the analyte/protein of interest. Experimental data with azurin, a blue copper protein, will support our theoretical evidence.

References

[1] Armstrong FA, Heering HA, Hirst J. Reactions of complex metalloproteins studied by protein-film voltammetry. Chem. Soc. Rev., 1997; 26: 169.

[2] Chen K, Hirst J, Camba R, Bonagura CA, Stout CD, Burgess BK, Armstrong FA. Atomically defined mechanism for proton transfer to a buried redox centre in a protein. Nature, 2000; 405: 814.

[3] Chi QJ, Farver O, Ulstrup J. Long-range protein electron transfer observed at the single-molecule level: In situ mapping of redox-gated tunneling resonance. Proc. Natl. Acad. Sci. USA 2005; 102: 16203.

[4] Fleming BD, Barlow NL, Zhang J, Bond AM, Armstrong FA. Application of power spectra patterns in Fourier transform square wave voltammetry to evaluate electrode kinetics of surface-confined proteins. Anal. Chem. 2006; 78: 2948.

[5] Gabor D, Proc. IEE 1946; 93: 429.

[6] Kiss IZ, Zhai YM, Hudson JL. Emerging coherence in a population of chemical oscillators. Science 2002; 296: 1676.

[7] Anastassiou CA, Ducros N, Parker KH, O'Hare D. Characterisation of AC voltammetric Reaction-Diffusion Dynamics: From Patterns to Physical Parameters. Anal. Chem. (in press) DOI: 10.1021/ac060122v.

[8] Anastassiou CA, Parker KH, O'Hare D. Determination of kinetic and thermodynamic parameters of surface confined species through ac voltammetry and a nonstationary signal processing technique: the Hilbert transform. Anal. Chem. 2005; 77: 3357.

[9] Anastassiou CA, Parker KH, O'Hare D. AC voltammetry exploration of microscopic electron-transfer effects using Marcus DOS theory (submitted)