2.1 Generation of sequence logos and subfamily logos

The LaTeX package TeXshade (version 1.26) was used to calculate and display protein sequence logos and subfamily logos.¹⁰ For the aquaporin logos, 147 sequences were analyzed of which 34 represented the GlpF subfamily. Escherichia coli GlpF served as the reference sequence¹¹ for which a high-resolution crystal structure is available¹² (PDB# 1FX8). For formate-nitrite transporter (FNT) logos, a total of 71 sequences were used, 41 of which were from eukaryotic microbial species. Here, the FNT from Plasmodium falciparum was the reference for sequence¹³ and structure¹⁴ (PDB# 6VQQ). The sequence logos and subfamily logos were calculated without frequency correction. Both sets of sequences were used before for the experimental evaluation of structure-function relationships of the aquaporin and FNT protein families. The sequence and subfamily logos of this paper are supplied as Data S1 (S1, S2, S6, S8).

2.2 Implementation of structure memes in TeXshade

A new LaTeX command \structurememe[⟨filename⟩]{⟨seqref⟩} was defined to generate a Chimera-compatible output file (suffixes .cmd or .com) from a calculated logo with ⟨seqref⟩ stating the reference sequence. For the amino acid color grouping \memeRed{⟨residues⟩}, and accordingly \memeYellow, \memeBlue, \memeWhite, and \memeBlack were introduced; \memeStandardcolors sets the definitions described in this paper: D, E (Red), C, G, N, Q, S, T, Y (Yellow), H, K, R (Blue), A, P, V (White), F, I, L, M, W (Black). For the radius of the α-carbon spheres the logo information bit-value was used, which remained scalable by using \chimeraballScale{⟨factor⟩} from 0 to 1. The residue composition at a sequence position was stored in a name label of the respective α-carbon. To eliminate irrelevant residues from the name label a bit-value was set by implementation of \memelabelcutoff{⟨bit-value⟩}. The symbols “>”, “:”, and “.” indicate the 3, 2, and 1 bit levels in the name label. Structure meme files from subfamily logos contain instructions for the Chimera software¹⁵ to duplicate the protein structure model. To set the translational direction for a side-by-side presentation of the models \chimeraxisdistance{⟨x-dist⟩}{⟨y-dist⟩}{⟨z-dist⟩} in Angstrom was defined. Conversion of the red-yellow-blue (RYB) color scheme into RBG space with 16 bit per channel (FFFF_hex) was also implemented in TeXshade¹⁰ by using the algorithm¹⁶ by Sugita and Takahashi. The generated Chimera command files are in commented ASCII and human-readable, see Data S1 (S3–S5, S7, S9).

2.3 Display of structure memes using Chimera

The TeXshade-generated structure meme command files can be opened directly in the molecular structure visualization program Chimera¹⁵; ChimeraX uses different commands and is not compatible. After loading the file, a file selector window will appear where a suitable protein structure file is chosen. For the aquaporin structure memes use PDB# 1FX8,¹² and for the FNT PDB# 6VQQ.¹⁴ A structure file can be stated in the command file by employing the new TeXshade command \echostructurefile{⟨strucref⟩}. If a 3D structure file contains more than one protein chain, the structure meme can be shown on one selected chain using \chimerachain{⟨chainlabel⟩}. The Chimera command file will change the color, sphere radius, and name label of the α-carbon atoms of the loaded protein structure. All other structure data will remain unchanged and usable, for example, for displaying selected sidechains.

3.1 Using the red-yellow-blue color scheme for integrative visualization of up to five distinct amino acid properties

A strength of sequence logos is the explicit display of readable residue symbols indicating the amino acid composition and relevance at a specific sequence position. Such a degree of detail, however, would be overwhelming when projected onto protein structure data. Therefore, the information was converted into a color code. In the subtractive RYB color space (based on light absorption), up to five contributions can be visually recognized and relative proportions estimated¹⁶ (Figure 2). Therefore, groups of amino acids with similar properties were attributed to one of the three primary colors red, yellow, and blue, plus black and white (Figure 2). This way, positively charged, polar uncharged, negatively charged, as well as large and small nonpolar amino acid residues, respectively, can be differentiated. Other amino acid groupings are certainly valid and depend on the question of investigation.

The RYB color scheme has a century-long tradition in the visual arts and is intuitive with respect to predicting mix colors or, inversely, extracting primary color information and the brightness level from a color mix.¹⁷ Figure 3 displays the logos of Figure 1 recolored according to the defined RYB amino acid groups. If one group predominates, a rather pure primary color, or either black or white will be visible (see eg, red sphere in Figure 3A, position 152, or white sphere in Figure 3C, position 211). Relevant contributions of two amino acid groups will result in a predictable mix color, that is, green from blue and yellow, orange from yellow and red, or purple from red and blue (Figure 2), yet the relative intensity proportions will remain discernable (see yellowish green sphere in Figure 3C, position 215). A third property will become visible, for example, as light orange or dark green (see Figure 3B, position 214). Contributions of more than three groups will result in a gray tone corresponding to the low information content at such a position in a protein alignment (see sphere in Figure 3A, position 151; note that blue is absent giving the sphere a warm tint).

Technically, the R, Y, and B intensities at sequence position i are calculated from:

(1)

(2)

(3)

with I_max being the maximal intensity per channel (eg, eight bit, ie, 255_dec or FF_hex), and p(∑a_R,i), p(∑a_Y,i), p(∑a_B,i), p(∑a_Blk,i), p(∑a_Wht,i) being the proportion of the sum of amino acids with red, yellow, blue, black, and white shading at this site.

Computer monitors use the additive RGB color scheme (based on emission) with red, green, and blue as primary colors matching the stimulating wavelengths of the human retinal photoreceptors.¹⁸ Other than the RYB color scheme, mix colors in the RGB space are not intuitive and are interpretable only after training. Conversion of RYB colors into an RGB output is achieved by generating RGB “green” from extracting equal proportions from the RYB “yellow” and “blue” channels; the color impression “yellow” requires equal distribution into the RGB “red” and “green” channels. An algorithm rearranging the RYB color proportions into the RGB channels is published,¹⁶ and was employed here.

3.2 The information content is displayed as sphere radius at the α-carbon site

The coloring representing amino acid composition and relative frequency was then projected onto spheres at the α-carbon position of each available residue position in the protein structure. Sites that are present in certain sequences of the logo display yet are absent in the structure data of the reference sequence will be omitted. The sphere radius was adjusted to the information content, that is, the height of the stacks in a logo (Figure 3). The maximal information content of a protein sequence logo is log₂20 = 4.32 bit¹ (the bit value can be somewhat higher when the amino acid frequencies are corrected for the real distribution in a set of proteins). The 0 to 4 number range was found to be quite suitable for direct use as the Angstrom radius of the spheres (Figure 4) but remains scalable by the displaying software in case too large diameters obscure the view. Alternatively, a scaling factor for the sphere radius can be set already in the software that generates the Chimera command file (here implemented as \chimeraballScale{⟨factor⟩} for the TeXshade alignment and logo package¹⁰). To generate a structure meme, the output was restricted to the shaded α-carbon spheres connected by sticks. However, the complete structure data were retained in the files for display as needed.

3.3 Example depicting sequence logo information on an aquaporin protein structure

Shown is a structure meme in rotated side views of a protomer (PDB# 1FX8) of the homotetrameric aquaporin proteins (Figure 4, S3). The logo information readily indicates general features of the aquaporin protein family¹⁹ in a structural context. The transmembrane region is mainly composed of nonpolar (black, white) and some uncharged polar residues (yellow). Several positively charged residues (blue, and as mix color green) at the cytoplasmic protein side illustrate the “positive-inside rule” for membrane proteins.²⁰ The highest degree of conservation (larger spheres) is found in the central plane of the transmembrane domain where the water/solute pore is located. The view at 0° rotation shows four prominent white spheres representing Pro and Ala of two NPA aquaporin signature motifs.⁶ Aquaporins further feature several conserved interacting pairs of Gly residues at helix crossings in the center of the membrane.⁸ These appear as pairs of large yellow spheres (Figure 4, 90°/180°/270° views). To emphasize the Pro and Gly residues, the amino acids were grouped differently and the structure model was recolored (Figure 4B, S4). Sulfur-containing residues were additionally shaded in yellow. Weak yellow intensity levels indicate that Cys and Met have no general role in the aquaporins, even though certain aquaporins are inhibitable by covalent Cys-modifiers such as organomercurials.²¹

3.4 Visualization of aquaporin subfamily-specific structure features

Next, a subfamily logo for the GlpF subfamily of aquaporins vs the water-selective aquaporins (AQP) was projected as a structure meme (Figure 5, S5, PDB# 1FX8). Contrary to sequence logo information, here, differences between the subfamilies appear as prominent spheres in the structure memes. A side-by-side placement of the GlpF and AQP subfamily structure memes (top down view) allows for rapid visual site comparisons (Figure 5A,B). For instance, the previously mentioned GlpF-specific charged residues D207 and R/K211 (see Figure 3B) are now found in close spatial proximity indicating salt-bridge formation.⁹

The example further illustrates that the residue composition at a site is stored in the file and is accessible via name labels when pointing to a sphere of interest. The displayed list of residues is ranked from left to right according to the logo information. The level of information is given by the separating symbols “>” (3 bit), “:” (2 bit), and “.” (1 bit). For clarity, an additional, adjustable cut-off threshold of 0.1 bit was set for residues to appear in the label.

3.5 Structure memes of complex proteins maintain clarity

To increase complexity, structure memes were calculated for homopentameric FNT^{13, 14} (Figure 6, S6–S9, PDB# 6VQQ). Despite the large number of more than 1500 residues the display remains clear. Generally, as for other protein structure information, the three-dimensionality of the display is best viewed when rotating the molecule on a computer screen. Similar to the aquaporins, the residues that form the channel-like transport paths through each protomer are most conserved (Figure 6A). There are slight functional differences in terms of substrate selection between prokaryotic and eukaryotic FNTs. Prokaryotic FNTs mainly select for the small substrates formate and nitrite, whereas eukaryotic FNTs, for example, from the malaria parasite P falciparum additionally transport somewhat larger lactate molecules.^{22, 23} Substrate size selection appears to occur mainly via two positions (I and III) of a filter site within each protomer²² (Figure 6B, left inset). The structure memes picked up and highlighted the underlying differences in the sidechain sizes of the involved residues (Figure 6B, right inset) demonstrating the validity of the method.