Analyzing a steady-state phenomenon using an ensemble of sequential transient events: A proof of concept on photocurrent of bacteriorhodopsin upon continuous photoexcitation

The proton pump activity of bacteriorhodopsin in aqueous solution upon excitation with modulated continuous light was monitored electrochemically and analyzed by superimposing a series of transient proton translocation events Hi+(t). An evolution function f(t)=he−lt+kh+k, including a decay and a stationary offset, was introduced to weight the contribution of the individual transient events evolving with time in the envelope of the steady-state event. The evolution of the total proton concentration can be treated as an ensemble of weighted sequential transient events, Htotal+(t)=∑i=0nHi+(t)⋅f(t), and the temporal profile of the photocurrent is derived by differentiating the proton concentration with respect to time, I(t)∝dHtotal+(t)dt. The temporal profiles of the bacteriorhodopsin photocurrent in pH range of 6.3–8.1 were analyzed using a well-defined kinetics model and restricted mathematical formulization, and fitted temporal behaviors agreed with the observations. This successful proof-of-concept study on analyzing a steady-state phenomenon using an ensemble of sequential transient events can be generalized to quantify other phenomena upon continuous stimulation, such as estimation of the light-driven ion pump activities of the photosynthetic proteins upon illumination.