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\begin{document}

\title{TD-DFT Modeling of Electronic Spectra of Biliverdins in Different
Environments}



\author[1]{Gonzalo Diaz Mirón}%
\author[2]{Dar"o A. Estrin}%
\author[3]{Sara Bari}%
\author[2]{Mariano González Lebrero}%
\affil[1]{Consejo Nacional de Investigaciones Científicas y Técnicas}%
\affil[2]{Universidad de Buenos Aires Facultad de Ciencias Exactas y Naturales}%
\affil[3]{Consejo Nacional de Investigaciones Cientificas y Tecnicas}%


\vspace{-1em}



  
  \date{May 21, 2024}


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\selectlanguage{english}
\begin{abstract}
Non covalent biliproteins are found in a growing number of living
organisms and even in viruses, such as SARS-CoV-2. Unlike the well
described covalent biliproteins, such as the phytochromes, they present
a vast structural and functional diversity, and often with limited
experimental information. A very important tool (and sometimes the only
one available) to study these systems is the UV-Vis spectrum, which is
modulated both by conformational changes of the biliverdin chromophore
and specific interactions with the apoprotein. In this work we present a
theoretical study of the microscopic determinants of the UV-Vis spectrum
of these compounds through the use of hybrid QM(TD-DFT)/MM techniques
and molecular dynamics simulations. Comparing our results with existing
experimental data, we prove that it is possible to predict spectroscopic
properties, such as relative position and intensity ratio of main bands,
with affordable methods, and to provide a microscopic explanation of
them. This systematic information can be very useful for the study of
described biliproteins or for those yet unknown.%
\end{abstract}%



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\section*{\sffamily \Large SI.1. Validation of PBE0/6-31G}
Figure \ref{fig:func} shows the calculated absorption spectra using different combinations of functionals and basis set functions for biliverdins in ZZZsss and ZZZssa conformations.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/functionals/functionals}
\caption{{\label{fig:func} Absorption spectra of biliverdins using different functionals and basis set functions for ZZZsss (left panel) and ZZZssa (right panel) conformations.%
}}
\end{center}
\end{figure}

Table \ref{tb:BVD_func} shows the intensity ratio and wavelength difference of Q and S bands for different combinations of functionals and basis set functions, and its comparison with the experimental results.\selectlanguage{english}
\begin{table}[H]
\begin{center}
\begin{tabular}{l l l l}
\hline
 & & \multicolumn{2}{c}{calculated} \\
\hline
BVD & functional/basis & $\Delta(\lambda_{maxQ}-\lambda_{maxS}) [nm]$ & $A_Q/A_S$ \\
conformation & & &   \\
\hline
 \multirow{5}{*}{ZZZsss} & PBE0/6-31G & 276 & 0.20 \\
 & CAM-B3LYP/6-31G & 260 & 0.31 \\
 & LC-BLYP/6-31G & 212 & 0.32 \\
 & CAM-B3LYP/DZVP & 267 & 0.31 \\
 & LC-BLYP/DZVP & 210 & 0.36 \\
 Experimental\hyperref[csl:1]{(Iturraspe et al., 1989)} & - & 278 & 0.27 \\
\hline
 \multirow{5}{*}{ZZZssa} & PBE0/6-31G & 218 & 0.89 \\
 & CAM-B3LYP/6-31G & 216 & 0.86 \\
 & LC-BLYP/6-31G & 194 & 0.89 \\
 & CAM-B3LYP/DZVP & 232 & 0.88 \\
 & LC-BLYP/DZVP & 201 & 0.86 \\
 Experimental\hyperref[csl:1]{(Iturraspe et al., 1989)} & - & 285 & 0.90 \\
\hline
\end{tabular}
\caption{{Comparison of calculated ratio and difference of Q and S bands using different combinations of functional and basis set functions.}}
\label{tb:BVD_func}
\end{center}

\end{table}

\section*{\sffamily \Large SI.2. Full Optimizations vs Intermediate Optimizations.}
The correct prediction of absorption spectra of systems in complex environments requires a large number of configurations, both of the environment, such as solvents molecules, and for the chromophore. The methodology used in this work resorts to the use of MM simulations to obtain solvent configurations and then perform a QM/MM optimization, where the solvent molecules remain "frozen". However, this strategy is still computationally expensive in the case of biliverdins in solution. Figure \ref{fig:bvd_opt} we show in the upper panels the absorption spectra, wavelengths and intensities for different configurations of biliverdins in the protonated ZZZssa conformations, in methanol during an optimization (upper panels), and the same variables for different configurations of the same system but performing a full optimization (lower panels).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/bvd-opt/bvd-opt}
\caption{{\label{fig:bvd_opt} Absorption spectrum, wavelengths and intensities of the Q and S band for protonated ZZZssa BV$\alpha$ in methanol. The upper panels correspond to different configurations obtained during an optimization. The lower panels correspond to different configurations, each of them obtained from a full optimization%
}}
\end{center}
\end{figure}

As we can see in the Figure \ref{fig:bvd_opt}, the wavelengths of the Q and S band converge in step 20 of the optimization (upper middle panel), but the intensities (especially of the S band) present some variability (upper right panel). When we observe the intensities of the bands for the different configurations resulting from a full optimization, the variability is even greater (lower right panel). Therefore, the conclusion is that performing an incomplete optimization with many configurations is better than few configurations with a more rigorous optimization.

\section*{\sffamily \Large SI.3: Validation of the performance of the TDDFT}
Figure \ref{fig:bvd_propionat} shows the absorption spectra of biliverdin IX$\alpha$ in the ZZZsss conformation with and without propionates side chains.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/bvd-propionates/bvd-propionates}
\caption{{\label{fig:bvd_propionat} Calculated absorption spectra of biliverdin IX$\alpha$ including (blue) and excluding (orange) the propionate side chains.%
}}
\end{center}
\end{figure}

Figure \ref{fig:bvd_mos} depicts the frontier molecular orbitals involved in the Q and S band in the absorption spectra of biliverdin IX$\alpha$ in the ZZZsss conformation.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/all-MO/all-MO}
\caption{{\label{fig:bvd_mos} Frontier molecular Oobitals involved in the Q and S band in the UV-Vis absorption spectra of biliverdin IX$\alpha$ in ZZZsss conformation.%
}}
\end{center}
\end{figure}

\section*{\sffamily \Large SI.4: Prediction of the absorbance spectra of biliverdins of different conformations in vacuo. Impact of the --CH2CH2- intramolecular linkages in the absorption spectra of biliverdins in extended conformations in vacuo}
In order to evaluate the impact of the intramolecular restrictions in the results, and to reproduce more closely the bilin structures present in biliproteins, we deleted the -$CH_2CH_2$- linkages that covalently assure the anti conformations, for the extended biliverdins 2, 3, and 4 in Figure 2 (main text). The alkyl substituent were replaced by H atoms. The results are presented in Figure \ref{fig:bvd_links} and Table \ref{tb:BVD_link}, and show that the -$CH_2CH_2$- linkages do not impact in the absorption spectra of the extended biliverdins, and that the agreement with the experimental data is maintained for the difference in the positions of both maxima and for the ratio $A_Q/A_S$.\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/bvd-links/bvd-links}
\caption{{\label{fig:bvd_links} Comparison of UV-Vis absorption spectra for a selected BVDs conformers with (blue) and without (orange) the -$CH_2CH_2$- linkages.%
}}
\end{center}
\end{figure}\selectlanguage{english}
\begin{table}[H]
\begin{center}
\begin{tabular}{l l l l}
\hline
 & \multicolumn{3}{c}{$A_Q/A_S$} \\
\hline
Biliverdin & calculated & experimental & Ref.$^{[a]}$\\
conformation & & &  \\
\hline
ZZZass & 0.93 & 0.90 & \hyperref[csl:1]{(Iturraspe et al., 1989)} \\
\hline
ZZZasa & 4.20 & 4.50 & \hyperref[csl:1]{(Iturraspe et al., 1989)} \\
\hline
ZEZsas & 8.23 & 8.00 & \hyperref[csl:1]{(Iturraspe et al., 1989)} \\
\hline
\end{tabular}
\caption{{Comparison of calculated ratios $A_Q/A_S$ for modeled non-helical biliverdins with experimental data of synthetic biliverdins in the same conformations. [a] Reference for experimental data.}}
\label{tb:BVD_link}
\end{center}
Reference for experimental data.

\end{table}

\section*{\sffamily \Large SI.5. Hypothetical conformers of biliverdin IX$\alpha$.}
In this section we show the predicted UV-Vis absorption spectra for some proposed conformers of BV$\alpha$ for which there is no experimental information available (Figure \ref{fig:bvd_no_exp}).\selectlanguage{english}
\begin{figure}[H]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/bvd-no-exp/bvd-no-exp}
\caption{{\label{fig:bvd_no_exp} Calculated UV-Vis absorption spectra of hypothetical BV$\alpha$ conformations. The absorption lines were convoluted with a FWHM of 5 nm%
}}
\end{center}
\end{figure}

\selectlanguage{english}
\FloatBarrier
\section*{References}\sloppy
\phantomsection
\label{csl:1}{Total synthesis of extended biliverdins. The relation between their conformation and their spectroscopic properties}. (1989). \textit{Journal of the American Chemical Society}, \textit{111}(4), 1525–1527.

\end{document}

