**1. Introduction**

Rhodopsins are photosensitive membrane proteins that have been discovered in many species across all three life domains. The natural diversity of the rhodopsins' first absorption band maxima (*λmax*) is achieved via the variation of the proteins' amino acid compositions during evolutionary processes [1,2]. The same strategy is used in modern technologies to obtain rhodopsin variants with an optimal *λmax* [3–6]. In this context, it is desirable to develop methodologies for prediction of the *λmax* change caused by the modifications of the primary protein structure, e.g., single or multiple amino acid substitutions (Δ*λmax*).

Site-directed mutagenesis is a common experimental technique that allows for Δ*λmax* evaluation. In many studies, amino acid substitutions are introduced into rhodopsins to measure Δ*λmax* and, consequently, to estimate the substituted residue contribution to the absorption maximum [7–9]. The objectives of these studies are to evaluate the correlations

**Citation:** Shtyrov, A.A.; Nikolaev, D.M.; Mironov, V.N.; Vasin, A.V.; Panov, M.S.; Tveryanovich, Y.S.; Ryazantsev, M.N. Simple Models to Study Spectral Properties of Microbial and Animal Rhodopsins: Evaluation of the Electrostatic Effect of Charged and Polar Residues on the First Absorption Band Maxima. *Int. J. Mol. Sci.* **2021**, *22*, 3029. https://doi.org/ 10.3390/ijms22063029

Academic Editor: Małgorzata Borówko

Received: 24 February 2021 Accepted: 5 March 2021 Published: 16 March 2021

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**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

between the type/position of a rhodopsin residue and the contribution of this residue to *λmax* and, ultimately, to establish general rules that allow for controlling *λmax*. However, the interpretation of the measured Δ*λmax* is not straightforward. Generally, a substitution of a single residue can lead to reorganization of the protein internal H-bond network changing positions of other residues and, therefore, their impact on the spectral properties. For such substitutions, a measured Δ*λmax* cannot be attributed exclusively to the mutated residue, and the aforementioned effects must be taken into account. Apparently, this indirect spectral tuning due to reorganization of the internal H-bond network is common for rhodopsins. For example, such H-bond network reorganization is responsible for the origin of the spectral shift between anion-free and chloride-ion-bound forms of halorhodopsin from *Natronomonas pharaonis* [10], evolutionary switch between ultraviolet and violet vision in vertebrates [11], and between visual rhodopsins from *Alloteuthis subulata* and *Loligo forbesii* squids [12].

In addition to experimental studies, computational modeling can be involved. In general, computational models enable not only the calculation of Δ*λmax* but also the evaluation of its direct and indirect parts. Currently, hybrid quantum mechanics/molecular mechanics (QM/MM) models are able to reproduce experimental *λmax* and Δ*λmax* values with good accuracy (within 20–30 nm and just a few nm from experiment, respectively), assuming that a high-quality three-dimensional protein structure is provided [11,13–18]. However, evaluation of QM/MM Δ*λmax* values is computationally expensive and not always easy. Thus, alternative less-demanding models are desirable for the interpretation of experimental data and initial rational design. These models can be less general and rigorous than QM/MM models, but they should allow for fast and simple Δ*λmax* prediction.

Here, for visual and microbial rhodopsins, we proposed such simple models that allow us to estimate the direct electrostatic part of Δ*λmax* for charged/polar amino acid substitution. The models are based on the precalculated high-level ab initio data. Application of these models requires only three-dimensional structures of rhodopsins, i.e., either X-ray structures or structures generated by comparative modeling. As a test, these models were applied to estimate the direct part of Δ*λmax* for charged and polar residue substitutions in bovine rhodopsin and sodium pumping rhodopsin KR2. The obtained data were validated both against more sophisticated ab initio QM/MM calculations and against experiment.
