## 2 Materials and Methods
In brief, the single protein is represented by a set of nodes, one for each considered amino acid, identified by its C\({}_{\alpha}\) atom, and a set of links, each connecting a couple of nodes when their distance, \(l_{j,k}\), is below an appropriate cut-off value, D [9; 14; 24; 25]. In this way, the complete graph representing the single protein is described by a Boolean  
\begin{table} \begin{tabular}{c c c c c} \hline \hline
**PDB Code** & **Illumination** & **pH** & **\(\Phi\) (meV)** & **\(\rho\) (\(\Omega\)Å)** \\ \hline
2 uww & no & 6.5 & 0.219 & \(2.7\times 10^{12}\)–\(5.4\times 10^{10}\) \\
2 uws & yes & 6.5 & 0.206–0.219 & \(2.7\times 10^{12}\) \\
2j8c & no & 8.0 & 0.219 & \(2.7\times 10^{12}\) \\
2 ux3 & no & 9.0 & 0.219 & \(2.7\times 10^{12}\) \\
2 uxj & no & 10 & 0.219 & \(2.7\times 10^{12}\) \\ \hline \hline \end{tabular}  b\(RC\), a 307-amino acid protein, is part of the photosynthetic unit, a set of pigments, proteins, and inorganic molecules which harvest and transform energy from light. Specifically, b\(RC\) mediates a charge separation and transfer inside the cell, involving a couple of quinones (primary and secondary) to which electrons are transferred. Finally, protons are pumped outside the cell membrane. In performing this activity, the protein adapts its structure to the new function, this reshaping being called conformational change. In performing experiments with proteins that have a well-defined structure, the outcome depends on the orientation they take on the layer on which they were deposited [7; 12]. As a matter of fact, the orientation of b\(RC\) in the host cell maximizes its performance by arranging its three chains, say H, L, M, in a cylindrical symmetry, elongating from the Periplasm to the Cytoplasm [11; 12]. Chains L and M extend across the cell membrane while chain H mainly faces the cytoplasmic side and only one helix parallels the other two chains. When this symmetry is accounted for in experiments that try to reproduce the natural functioning of this protein, the results are amplified [7]. Indeed, the protein arrangement fulfills a transmembrane electron transfer which goes with a proton pumping and proceeds along the protein axes. In Reference [11] the role of pH on the structure conformation has been analyzed, mainly with respect to the relative orientation of the secondary quinone, and a large set of structures were deposited in the Protein Data Bank (PDB) [10]; some of them are accounted for in the present study. ### Theory  
The electrical properties of the bRC are investigated making use of the 3D structures listed in Table 1, describing the single protein crystallized in different values of pH, both in dark and in light. To this purpose, firstly we analyze the linear impedance response as a function of the frequency under a small, applied voltage, typically of a few mV, and represented by Nyquist and Bode plots that can be measured through a standard EIS technique. Secondly, we analyze the steady-state current-voltage (I-V) characteristics of a typical nanostructure at increasing values of applied voltages, up to 1 Volt, where deviations from-linear regimes can be achieved by means of a standard CAFM technique. In brief, the single protein is represented by a set of nodes, one for each considered amino acid, identified by its C\({}_{\alpha}\) atom, and a set of links, each connecting a couple of nodes when their distance, \(l_{j,k}\), is below an appropriate cut-off value, D [9; 14; 24; 25]. In this way, the complete graph representing the single protein is described by a Boolean \begin{table} \end{table} 
Table 1: List of the analyzed b\(RC\) structures. Each structure is identified by a code in the Protein Data Bank [10; 11]; illumination conditions and the pH value of the solution in which they were crystallized are reported. The values of the barrier height, \(\Phi\), used for the \(I\)-\(V\) calculations, as well as of the link resistivity, \(\rho\), used in the impedance calculations are reported.