Rhodopsin charge diffusion computations disclose contrasting color-tuning mechanisms

Our understanding of the rules controlling the spectral tuning of light absorbing proteins is limited. When looking at rhodopsins as canonical examples, the fact that the cavity incorporates the chromophore counterion in different positions and polar residues with different orientations, leads to patterns of electrostatic potential whose effect is not obvious. In this work we use a model of the optogenetic reporter Arch-3 capable to describe the effect of the diffusion of its counterion charge on both excitation energies ( ${\lambda }_{\max }^a$ ) and chromophore geometry. By optimizing such charge for a set of increasing ${\lambda }_{\max }^a$ values, we show that progression towards redder values occurs along two distinct paths featuring a "compact" or an "extended" charge diffusion respectively. These results are validated by showing that both paths replicate the experimentally observed relationships between ${\lambda }_{\max }^a$ and chromophore isomerization in different sets of Arch-3 variants, NeoR variants and other microbial rhodopsins from 16 different organisms.