## 2 Materials and Methods  
### Synthesis  
In this work, we used laminar nanoclays from different sources and size particles: MMT with trade name Gel white(r), and Laponite(r) (LAP) with trade name XLG. The chemical composition of MMT is 80% SiO\({}_{2}\), 13% Al\({}_{2}\)O\({}_{3}\) and 3% Fe\({}_{2}\)O\({}_{3}\) (molecular formula: Al\({}_{2}\)H\({}_{2}\)O\({}_{12}\)Si\({}_{4}\)) [39]. The cation exchange capacity (CEC) of M is approximately 90-145 cmol\(\cdot\)kg\({}^{-1}\). Synthetic L (Si\({}_{8}\)[Mg\({}_{5}\).5 Li\({}_{0.4}\)H\({}_{4.0}\)O\({}_{24}\)]\({}_{0.7}-\)Na\({}_{0.7}\)\({}^{+}\)) is a 2D clay disc-shaped silicate that is approximately 1 nm thick. Its diameter is 25 nm. The adsorption capacity of L-based hydrogels and their CEC is 74 cmol\(\cdot\)kg\({}^{-1}\)[40]. They were supplied by from BYK Additives Ltd. (Wesel, Germany), and Rockwood, (Widness, UK), respectively. First we attempted to also use hydrotalcite nanoclay as we did before with other natural dyes [41]. However, this was not possible due to the nanoclay pH in dispersion, not even with the calinated one. pH remained above 4 and it could not be lowered with HCl\({}^{-}\) as we did with M or L. Both PC and PE lost their color under these pH conditions and only hydrotalcite optical properties remained. This was why we finally selected the M and L clays. As nanoclay organic modifiers, we employed surfactant cetylpyridinium bromide (SURF) C\({}_{21}\)H\({}_{38}\)BrN\(\cdot\)6H\({}_{2}\)O, 384.44 g/mol, purity 98%, and silane compound (SIL) 3-aminopropyltriethoxysilane, H\({}_{2}\)N(CH\({}_{2}\))\({}_{3}\)Si(OCH\({}_{3}\))\({}_{3}\), 179.29 g/mol, purity 99%. The pH variation during the synthesis process was controlled by chloridic acid HCl\({}^{-}\) (37%). All these products were supplied by Sigma-Aldrich (Madrid, Spain). Both PC and PE were extracted and purified as in our previous works using buffer phosphate solutions [42; 43]. The structure of biliproteins depends on the environment in which they are found (physical state, pH, ionic strength, etc. ), and can be a complex mixture of trimers, hexamers or monomers. Figure 1 depicts as an example of the 3D structure and its dimensions for PC and PE in the hexameric state. The hybrid synthesis process via water adsorption under stirring conditions has also been followed after taking into the account the incorporation time of additives according to our former works [38]. In this study, both nanoclays were dispersed at 1800 rpm for 20 h. The L dispersions were prepared at 18 g\(\cdot\)L\({}^{-1}\) to avoid gel formation in distilled water, while the M dispersions were prepared at 33 g\(\cdot\)L\({}^{-1}\). In both nanoclay dispersions, pH was adjusted to 4 using 37% HCl\({}^{-}\)[44,45]. Dye solutions (PC and PE) were prepared in buffer phosphate at [250 mM] and were added to the nanoclay dispersions at three concentrations over clay mass: 0.5%, 1% and 3%. The surface modifiers concentration fell within a 0-1% range over nanoclay mass. The solvent separation and drying process by lyophilization were carried out as in our previous works [46]. The experimental conditions were defined using a multilevel factorial DOE by selecting only 16 from the multifactorial 3\({}^{1}\cdot\)2\({}^{1}\) experiment conditions according to the D-Optimization criteria (Table 1). We included the dye concentration at three levels, namely the nanoclay origin, and the silane or surfactant concentration, as synthesis factors to control synthesis performance and hybrid pigment properties. Figure 1 shows the images from the different synthesis steps with both the PC and PE dyes and fine powders obtained under distinct synthesis conditions.