## 4 Discussion and Conclusions  
By using the tertiary structure of the b\(RC\) protein, its electrical characteristics are investigated under dark and light conditions and at different values of the pH of the crystallized solution, ranging from weak acid up to strong alkaline values. Theoretical calculations are carried out in the framework of the proteotronics, a structure-minded approach to the recent field of protein-based electronics. Analysis explores the macromolecule electrical response in both linear and non-linear regime.  
The procedure starts by mapping the macromolecule onto a graph which accounts for the protein structure. The graph is used to describe the electrical response of the protein in the philosophy of the lumped-element model, thus becoming an electrical network. A percolative-like process allows the analysis of the structure by using an ideal flow of charge that goes through the protein. The resistance that the network opposes to the charge flow measures its degree of connectivity and is a powerful tool to discriminate among different (although, sometimes, very similar) structures. In the present case, different pH values or different illumination conditions produce different networks, thus different electrical responses.  
Specifically, in the linear regime, i.e., at sufficiently low values of an applied bias, calculations of the electro-chemical impedance spectroscopy suggest that b\(RC\) is significantly sensitive to the pH value of the solution in which it is crystallized. The protein undergoes a resistance reduction when the pH changes from weak acid (pH = 6.5) to alkaline conditions with pH values up to 10, where this change appears even more evident. In the non-linear regime, i.e., at applied voltage values up to few Volts, theory makes use of a stochastic Monte Carlo approach to mimic a charge transport based on a sequential-tunneling mechanism including direct and injected tunneling regimes. Current voltage characteristics evidence a super-linear behavior with an increase of the current above the Ohmic value up to about a factor of two, and to keep the sensitivity to the value of the pH and the presence of the light. The current-voltage characteristics compare qualitatively well with available experiments performed in quasi-neutral conditions and in dark.  
These kinds of analysis should be of relevance for both basic and applied research. In the former case, the microscopic characterizations of proteins are still in their infancy when compared with simple inorganic materials, thus justifying the phenomenological approach used for the theoretical model. In the latter case, future application of these proteins in several branches of technology, medicine, solar energy harvesters, etc. are found to be very promising. From one side, they highlight the primary role of environment (here limited to the amount of cations on solution) in the physical-chemical (here electrical) response of biomaterial and how its effects are recognizable in the structure. Similar investigations concerning, for example, the role of temperature on structure and function of b\(RC\), which should complement present data are at present not available, although desirable. From another side, they can be used, for example, to regulate resistance in such devices. Finally, the present investigation can be thought to provide a valuable hint for designing pH-sensors.  
Conceptualization, methodology, validation, writing and editing E.A. and L.R.; software, E.A. All authors have read and agreed to the published version of the manuscript.  
This research was funded by EEC, grant number 228685-2.  
The data that support the findings of this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.