Computational models for monitoring the trans-membrane potential with fluorescent probes: the DiSC₃(5) case

Fluorescent permeant charged probes are commonly used for monitoring the trans-membrane potential in lipid vesicles and biological membranes, which has been earlier described by various mathematical models. In the present study, we developed a more complex model based on the computational step-by-step analysis of the influence of various factors, such as the membrane surface potential, ionic strength, and the aggregation properties of cationic cyanine probe DiSC₃(5) in the membrane and aqueous phases, in addition to the Nernstian distribution of the probe across the membrane and the hydrophobic interaction with the lipid bilayer. The final full model allows prediction of the optimal experimental conditions for monitoring the trans-membrane potential, such as the probe/lipid ratio and the concentration of liposomes, with a given percentage of negatively charged phospholipids in the membrane, the ionic strength of the aqueous media, the "membrane-water" partition coefficient and the aggregation properties of the probe, as well as the most adequate mode of fluorescence measurement. In agreement with many experimental studies, this model showed high voltage sensitivity of the quantity of the aqueous phase DiSC₃(5) monomers, showing its almost exponential decrease with an increase in the trans-membrane potential value. The model also demonstrated the highest voltage sensitivity of the ratio of the quantity of DiSC₃(5) monomers in the aqueous phases to that in the membrane phase. A new combined parameter, the logarithmic function of this ratio, demonstrated almost linear changes within a wide range of the trans-membrane potential changes.