Modeling the light-induced electric potential difference ΔΨ across the thylakoid membrane based on the transition state rate theory

In photosynthesis, electron transport-coupled proton movement initiates the formation of the light-induced electric potential difference, ΔΨ, across the thylakoid membrane (TM). Ions are transported across the TM to counterbalance the charge of protons accumulated in the lumen. The objective of this work is to construct range of mathematical models for simulation of ΔΨ, using the transition state rate theory (TSRT) for description of movement of ions through the channels. The TSRT considers either single-ion (TSRT-SI) or multi-ion occupancy (TSRT-MI) in the channels. Movement of ions through the channel pore is described by means of energy barriers and binding sites; ions move in and out of vacant sites with rate constants that depend on the barrier heights and well depths, as well as on the interionic repulsion in TSRT-MI model. Three energy motifs are used to describe the TSRT-SI model: two-barrier one-site (2B1S), three-barrier two-site (3B2S), and four-barrier three-site (4B3S). The 3B2S energy motif is used for the TSRT-MI model. The accumulation of cations due to the TM surface negative fixed charges is also taken into account. A model employing the electro-diffusion theory instead of the TSRT is constructed for comparison. The dual wavelength transmittance signal (ΔA515-560 nm) measuring the electrochromic shift (ECS) provides a proxy for experimental light-induced ΔΨ. The simulated ΔΨ traces qualitatively agree with the measured ECS traces. The models can simulate different channel conducting regimes and assess their impact on ΔΨ. The ionic flux coupling in the TSRT-MI model suggests that an increase in the internal or external K+ concentration may block the outward or the inward Mg2+ current, respectively.