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...hing that commonly occurs with amino acid substitution matrices or profile PSSMs. In our view, vertical evolutionary conservation of amino acids has been thoroughly explored using tools such as BLAST =-=[4,5]-=- and FASTA [42], while horizontal conservation of other protein properties has not. Thus, non-local properties of proteins, depending on correlations across residue positions, such as thermodynamic st...

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...lize that a probability model is specific to the type of data aligned and must also be recalibrated for a specific combination of W, C, and GapMax. The probability model for Kyte-Doolittle hydropathy =-=[35]-=-, averaged over a 15-residue window, is listed in Tables 1 and 2 and was built for the following HePCaT parameters: W=5 residues, GapMax=4 residues, C=0.4 with the local scaling of Equation 3. (Other ...

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...he blue cylinders indicate PSIPRED confidently predicted helical secondary structure of TC0624, the red cylinders indicate the actual helical secondary structure of d1cola_ domain as assessed by DSSP =-=[69]-=-. Numbers indicate the functionally important helical elements, as annotated by Cramer, et al. [65] Reasonable correspondence between the type and locations of secondary structure elements is observed...

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...red or blue regions. Equation 1 demonstrates a key conceptual difference from structure comparison algorithms that are usually based on distance or contact matrices restricted to only positive values =-=[32,33]-=-. This difference reflects the nature of the information being compared. For structure comparison, the distance between two atoms is identical whether it is computed between the first and second atom ...

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...red or blue regions. Equation 1 demonstrates a key conceptual difference from structure comparison algorithms that are usually based on distance or contact matrices restricted to only positive values =-=[32,33]-=-. This difference reflects the nature of the information being compared. For structure comparison, the distance between two atoms is identical whether it is computed between the first and second atom ...

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... two-variable formulae, it was empirically determined that these score distributions were statistically best fit by Scaled Inverse Chi-Squared probability density functions (Figure 2, Tables 1 and 2) =-=[37]-=-, PDFInverseChiSquared x; v,s 2DL ~ s2n 2 sn 2 e {s 2n 2x C n 2 x 1zn 2 ð5Þ In Equation 5, L is optimal alignment length, and C(x) is the Gamma function. [38] Parameters n and s2 were estimat...

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...tions (Figure 2, Tables 1 and 2) [37], PDFInverseChiSquared x; v,s 2DL ~ s2n 2 sn 2 e {s 2n 2x C n 2 x 1zn 2 ð5Þ In Equation 5, L is optimal alignment length, and C(x) is the Gamma function. =-=[38]-=- Parameters n and s2 were estimated by minimum chi-squared fits to the binned score data at each observed alignment length (Figure 2A). Binning and parameter estimation were performed using custom Mat...

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... protein with the profile of each member of the nonredundant set of 214 membrane proteins of known structure described above Secondary structure prediction was performed using the PSIPRED server [48] =-=[49]-=- and Hidden Markov Model sequence profile comparison was performed using the HHpred server [50], both with default parameters. Modeling was performed with a local installation of I-TASSER software [45...

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...7, using coefficients of Table 2. Clustering of membrane protein structures based on hydropathy All 1604 amino acid sequences corresponding to every membrane protein structure in SCOP 1.73 (class f ) =-=[39]-=- were obtained from the ASTRAL domain database [40] and clustered at 70% sequence identity by the cd-hit server [41], resulting in 214 representative sequences. The Kyte-Doolittle hydropathy values [3...

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...nly on the basis of hydropathy similarity (labeled sub-branches in Figure 3A). Interestingly, proteins belonging to f.13, annotated as ‘‘single transmembrane helix’’ and thus ‘‘not a true SCOP fold’’ =-=[56]-=-, are spread among several dispersed sub-branches, consistent with this provisional expert curation. Figure 3. Clustering of known membrane protein structures by hydropathy similarity. Dendrogram leav...

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... FASTA-aligning [42] amino acid sequences of the proteome with amino acid sequences of known GPCRs obtained from the GPCRDB [44]. Modeling was performed with a local installation of I-TASSER software =-=[45]-=- using default parameters. Structural similarity between the first I-TASSER model and known proteins was assessed using the DALI server [46]. Discovery of similarity between ORFan protein TC0624 and c...

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...sequences corresponding to every membrane protein structure in SCOP 1.73 (class f ) [39] were obtained from the ASTRAL domain database [40] and clustered at 70% sequence identity by the cd-hit server =-=[41]-=-, resulting in 214 representative sequences. The Kyte-Doolittle hydropathy values [35] for each sequence were averaged over a window size of 15 residues, with the average being assigned to the middle ...

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...nge [23,24], is described by a onedimensional sequence of numerical values (i.e. amide protection factors). These values are well-known to be a combination of sequence, structure, and solvent effects =-=[25]-=-, but no substitution matrix or distance measure exists for the objective comparison of two sets of protection factors. As such, important relationships could be overlooked, or worse, erroneous knowle...

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...as performed with a local installation of I-TASSER software [45] using default parameters. Structural similarity between the first I-TASSER model and known proteins was assessed using the DALI server =-=[46]-=-. Discovery of similarity between ORFan protein TC0624 and colicin pore-forming domain A dataset of 8812 ORFan protein sequences was obtained from Yomtovian, et al. [47] As described above, HePCaT was...

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...atistical artifact: this metallothionein is naturally short and contains a high frequency of cysteine residues; such low-complexity sequences are normally filtered out of amino acid sequence searches =-=[62]-=-, which was not done in the present study. Some of the proteins in this group are medically important, such as the hematological and neurological expressed-1 like protein, ephrin A4 isoforms, and the ...

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...stance and Ward’s minimum variance criterion as implemented in the Hierarchical Clustering Package of Mathematica 8.0 (Wolfram Research) to create a dendrogram. A similar tree was computed from FASTA =-=[42]-=- E-values of all pairwise sequence comparisons. Significance of each grouping was estimated using the bootstrap ‘‘Gap Test’’ option of the software. Hydropathy database search of the human proteome us...

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... (approximately 30% identity over 40 residues on average). Clearly, patterns of hydropathy, reflecting the well-known idea that protein structure similarity is more conserved than sequence similarity =-=[57,58]-=-, can be objectively recovered using pairwise HePCaT alignments in conjunction with the appropriate probability model described above. Database search using human adenosine receptor A2a as query Given...

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...robability models have been constructed and tested by the authors, including models based on eScape predicted native state thermodynamic stability [19], and predicted translation efficiency index tAI =-=[20,21]-=-, and are available upon request.) Construction of probability model Significance of the Equation 4 score of optimal HePCaT alignments was estimated with respect to the scores of optimal alignments of...

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...ORFan protein with the profile of each member of the nonredundant set of 214 membrane proteins of known structure described above Secondary structure prediction was performed using the PSIPRED server =-=[48]-=- [49] and Hidden Markov Model sequence profile comparison was performed using the HHpred server [50], both with default parameters. Modeling was performed with a local installation of I-TASSER softwar...

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...otential biological insight into proteins, have not been as thoroughly explored. For example, the local thermodynamic stability of a protein, as experimentally measured by deuterium-hydrogen exchange =-=[23,24]-=-, is described by a onedimensional sequence of numerical values (i.e. amide protection factors). These values are well-known to be a combination of sequence, structure, and solvent effects [25], but n...

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...f the software. Hydropathy database search of the human proteome using adenosine receptor A2a as query The human proteome was obtained from translation of the DNA sequences contained in the NCBI CDDS =-=[43]-=- build 36.3 A Horizontal Tool for Numerical Trend Discovery PLOS Computational Biology | www.ploscompbiol.org 4 October 2013 | Volume 9 | Issue 10 | e1003247 (April 30, 2008). Each amino acid in every...

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...brane protein structures based on hydropathy All 1604 amino acid sequences corresponding to every membrane protein structure in SCOP 1.73 (class f ) [39] were obtained from the ASTRAL domain database =-=[40]-=- and clustered at 70% sequence identity by the cd-hit server [41], resulting in 214 representative sequences. The Kyte-Doolittle hydropathy values [35] for each sequence were averaged over a window si...

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...dently produced model of the taste receptor, constructed using no HePCaT information (Figure 5C). Additionally, the original HePCaT match was demonstrated to be a useful template for a homology model =-=[61]-=- based on the A2a structure (data not shown). The validity of the hydropathy similarity between A2a and the taste receptor was further demonstrated to be robust with respect to the particular hydropho...

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...coli colicin A (Figure 6A). This match spanned the entire chain length of the ORFan protein and the experimentally-determined minimal length region of functional importance of the pore-forming domain =-=[64]-=-. The validity of the hydropathy similarity between colicin and TC0624 was further demonstrated to be robust with respect to the particular hydrophobicity scale used (Text S1; Figures S1 and S2 in Tex...

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... significantly matched by HePCaT (p,0.01, data not shown). The most significant ten matches are displayed in Figure 4. These hits fell into two categories: those that matched the transmembrane region =-=[59]-=- of A2a (Figure 4, blue) and those that mostly matched the tail region (Figure 4, red). The longest match to the transmembrane region was the A2b isoform, which is also 59% sequence identical to A2a (...

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...information, where available about the matches, could not be confidently transferred to the putatively disordered tail region of A2a, which is thought to be involved in ligand specificity of the GPCR =-=[63]-=-. These tail matches may also result from the local scaling (Equation 3), which could potentially be disabled, illustrating the sensitivity vs. specificity tradeoffs inherent to relative shape matchin...

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...en achieved for other types of numerical data, an alternative estimate of statistical significance is available. Specifically, the non-parametric statistics of theMIC score reported by Reshef, et al. =-=[68]-=- could potentially be used to evaluate a match returned by HePCaT. In this way, the significances of arbitrary pattern associations reported by Reshef, et al. could be greatly leveraged by using HePCa...

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... at most 40% different was counted as a matching shape. If Equation 3 were disabled, C would have to be adjusted empirically based on the dynamic ranges of data compared. The algorithm starts at cell =-=(1,1)-=- of S (i.e. the lower left corner of the matrix in Figure 1, Step 3), corresponding to the average difference between the scaled intraprotein distances of residues 1– 5 in Protein 1 and residues 1–5 i...

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...robability models have been constructed and tested by the authors, including models based on eScape predicted native state thermodynamic stability [19], and predicted translation efficiency index tAI =-=[20,21]-=-, and are available upon request.) Construction of probability model Significance of the Equation 4 score of optimal HePCaT alignments was estimated with respect to the scores of optimal alignments of...

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...preserved in the absence of strict conservation of the side chain atoms. In other words, similar properties could exist horizontally in a sequence even when recognizable vertical conservation is lost =-=[7]-=-. Even if such similarities are due to analogy rather than homology [8], approaches are needed that can augment sequence based analysis by matching patterns that may be independent of amino acid conse...

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...proteins of random amino acid sequence. Two random proteins of equal lengths between 10 and 500 residues were generated according to background amino acid frequencies as given by Robinson & Robinson. =-=[36]-=- Sets of at least 20,000 such pairs for each length were optimally aligned using HePCaT, and the distributions of Equation 4 scores for a given optimal alignment length from the entire pool were tabul...

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...hing that commonly occurs with amino acid substitution matrices or profile PSSMs. In our view, vertical evolutionary conservation of amino acids has been thoroughly explored using tools such as BLAST =-=[4,5]-=- and FASTA [42], while horizontal conservation of other protein properties has not. Thus, non-local properties of proteins, depending on correlations across residue positions, such as thermodynamic st...

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...ion are available. Citation: Hadzipasic O, Wrabl JO, Hilser VJ (2013) A Horizontal Alignment Tool for Numerical Trend Discovery in Sequence Data: Application to ?Protein Hydropathy. PLoS Comput Biol 9=-=(10)-=-: e1003247. doi:10.1371/journal.pcbi.1003247 Editor: Jacquelyn S. Fetrow, Wake Forest University, United States of America Received April 19, 2013; Accepted July 10, 2013; Published October 10, 2013 C...

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...otential biological insight into proteins, have not been as thoroughly explored. For example, the local thermodynamic stability of a protein, as experimentally measured by deuterium-hydrogen exchange =-=[23,24]-=-, is described by a onedimensional sequence of numerical values (i.e. amide protection factors). These values are well-known to be a combination of sequence, structure, and solvent effects [25], but n...

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...cin’s lethal ability to travel from a hydrophilic extracellular environment, insert into the hydrophobic membrane interior, and form toxic pores in its host [65]. TC0624 has independently been placed =-=[66]-=- in a class unique to Chlamydiae that is observed by experiment to also similarly partition into the membrane interior of the chlamydial inclusion [67]. These so-called ‘‘Inc’’ proteins, difficult or ...

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.... In other words, similar properties could exist horizontally in a sequence even when recognizable vertical conservation is lost [7]. Even if such similarities are due to analogy rather than homology =-=[8]-=-, approaches are needed that can augment sequence based analysis by matching patterns that may be independent of amino acid conservation at each position. Comparison of three-dimensional atomic struct...

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...cability to data types other than transmembrane protein hydrophobicity. In addition, the scoring functions for hydrophobicity analysis are often based on templatebased matching or absolute similarity =-=[30]-=-, and while this is effective at finding matches that are similar in both shape and magnitude, two sets of data that describe the same shape, but are offset by a scalar value, would be missed. For exa...

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...s, such as identification and alignment of the membrane spanning regions of non-globular proteins [26–28]. Although useful, these tools have historically incorporated family-specific scoring matrices =-=[29]-=- and empirical PLOS Computational Biology | www.ploscompbiol.org 1 October 2013 | Volume 9 | Issue 10 | e1003247 gap penalties. Such heuristics hinder the algorithms’ transferability to different prot...

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...SD calculation is executed after translation of both sets to data to their respective centers-of-mass, thus effects of a global offset between each data set are again minimized. Following Jia, et al. =-=[34]-=-, we define an Optimal Path Score (OPS) for this optimal alignment according to the formula: OPS~ RMSD L 1z Gaps L ð4Þ In Equation 4, L is the alignment length and Gaps is the total number of cell...

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...roteins, most membrane protein structures can be classified, independent of evolutionary relationships, into two main groups, ‘‘all-alpha’’ and ‘‘all-beta’’, based on structural characteristics alone =-=[51,52]-=-. One dominant characteristic is the requirement for stability within the nonpolar interior of the membrane, and this is reflected in recurring patterns of defined length hydrophobic segments, imposed...

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...thought to be functionally crucial for colicin’s lethal ability to travel from a hydrophilic extracellular environment, insert into the hydrophobic membrane interior, and form toxic pores in its host =-=[65]-=-. TC0624 has independently been placed [66] in a class unique to Chlamydiae that is observed by experiment to also similarly partition into the membrane interior of the chlamydial inclusion [67]. Thes...

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...sfully performed by amino acid sequence comparison [1–5]. However, it is well known that structure can be preserved even when sequence has diverged past the point of amino acid similarity recognition =-=[6]-=-, suggesting that sequences can bestow local, subglobal, and global properties to a protein that can be preserved in the absence of strict conservation of the side chain atoms. In other words, similar...

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... by side chain identity or structural similarity [14–18]. It may be the case that proteins can also be meaningfully characterized by other attributes, such as the energetic contributions to stability =-=[19]-=- or the predicted codon translation efficiency along the mRNA [20– 22]. Yet, such attributes are not easily accommodated by simple adaptation of current algorithms, largely because the scoring systems...

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...red local thermodynamic stabilities of proteins, where the relative stabilities of the same structural region of two homologs are observed to be strikingly similar, yet offset by a constant DDG value =-=[31]-=-. Finally, some of these previous tools lack the capability for large database searches or do not include estimates of statistical significance, limiting their usefulness and effectiveness even for th...

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... GPCRs were checked and annotated in our local copy of the human proteome by FASTA-aligning [42] amino acid sequences of the proteome with amino acid sequences of known GPCRs obtained from the GPCRDB =-=[44]-=-. Modeling was performed with a local installation of I-TASSER software [45] using default parameters. Structural similarity between the first I-TASSER model and known proteins was assessed using the ...

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...assessed using the DALI server [46]. Discovery of similarity between ORFan protein TC0624 and colicin pore-forming domain A dataset of 8812 ORFan protein sequences was obtained from Yomtovian, et al. =-=[47]-=- As described above, HePCaT was used to optimally align the Kyte-Doolittle averaged hydropathy profiles of each ORFan protein with the profile of each member of the nonredundant set of 214 membrane pr...

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...own structure described above Secondary structure prediction was performed using the PSIPRED server [48] [49] and Hidden Markov Model sequence profile comparison was performed using the HHpred server =-=[50]-=-, both with default parameters. Modeling was performed with a local installation of I-TASSER software [45] using default parameters. Structural similarity between the first I-TASSER model and known pr...

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...roteins, most membrane protein structures can be classified, independent of evolutionary relationships, into two main groups, ‘‘all-alpha’’ and ‘‘all-beta’’, based on structural characteristics alone =-=[51,52]-=-. One dominant characteristic is the requirement for stability within the nonpolar interior of the membrane, and this is reflected in recurring patterns of defined length hydrophobic segments, imposed...

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... (approximately 30% identity over 40 residues on average). Clearly, patterns of hydropathy, reflecting the well-known idea that protein structure similarity is more conserved than sequence similarity =-=[57,58]-=-, can be objectively recovered using pairwise HePCaT alignments in conjunction with the appropriate probability model described above. Database search using human adenosine receptor A2a as query Given...

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...xhibited a significant match to this region (Figure 4). As this taste receptor has insignificant pairwise sequence identity to A2a (Figure 5B) and its structure has not been experimentally determined =-=[60]-=-, this observed similarity was consistent with an independently produced model of the taste receptor, constructed using no HePCaT information (Figure 5C). Additionally, the original HePCaT match was d...

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... host [65]. TC0624 has independently been placed [66] in a class unique to Chlamydiae that is observed by experiment to also similarly partition into the membrane interior of the chlamydial inclusion =-=[67]-=-. These so-called ‘‘Inc’’ proteins, difficult or impossible to predict using existing computational tools [66], are nonetheless important for chlamydial survival and maturation within its human or ani...