Simulations of frequency-dependent photoacoustic magnitude signals and their implications for bacteriorhodopsin photocycle energetics

The modulation frequency dependence of photoacoustic signals obtained from photoactive samples can provide information on the time-dependent enthalpy changes occurring during the light-induced process. The experimental requirements for this type of calorimetry, and the interpretation ot the results, are critically examined with reference to the light-driven proton pump bacteriorhodopsin. For a three-step unbranched model of the bacteriorhodopsin photocycle we derive an expression for the photoacoustic magnitude signal as a function of frequency. Simulations are performed for various values of the rate constants and energetic changes. It is shown that the net heat uptake during a low, final step postulated by some workers should be reflected in the photoacoustic magnitude frequency spectrum, giving rise to a characteristic maximum. However, this effect, which has been observed experimentally, may also be produced by a fast, strongly endothermic step occurring earlier. The precise chronology of an endothermic transition cannot be resolved unambiguously by magnitude measurements alone, although they are free from assumptions regarding difficult-to-measure phase relationships. Hence, the published photoacoustic observations showing the effect are consistent with a cyclic sequence of events in which the bacteriorhodopsin system first undergoes an increase of entropy, followed by a decrease on returning to the initial state, as well as the reverse. It is argued that the molecular disorder-order sequence is more probable.