Patterny: A Troupe of Decipherment Helpers for Intrinsic Disorder, Low Complexity and Compositional Bias in Proteins

1. Introduction

Intrinsically-disordered regions are protein parts that remain unfolded during at least a part of their functioning. They have long been associated with lower ‘sequence complexity’, i.e., the sequences are generally simpler, more repetitive and sample residue types un-evenly [1,2]. Originally, the term ‘low-complexity’ as applied to proteins had a strictly algorithmic meaning, referring to sequence tracts that had lower information entropy, as calculated by the algorithm SEG by Wootton & Federhen [3]. ‘Compositional bias’ is a more general term that covers a range from highly biased and repetitive sequences to those that have a milder compositional skew [3,4]. Arguably, sequence complexity per se is less likely to be under selection in protein sequences than say a specific compositional bias for amino acids that has a functional role, and it is also not clear where an imaginary boundary around the concept of ‘low-complexity’ could be placed [4]. Compositional biases are directly linked to functional roles of IDRs [5,6].

However, IDRs and CBRs are not simply compositional entities. They have various types of patterning such as repeat structure, alternating compositional blocks or bands, multiple discrete compositional modules/motifs, and amino-acid runs or ‘homopeptides’. Such residue patterning in IDRs can have functional significance e.g., repeat patterns in prion-determinant domains [7]; patterning of charged residues into blocks (i.e., residue ‘blockiness’) in transcriptional regulators and nucleolar proteins [8,9]; homopeptide content in transcriptional activators [10]; compositional modularity in stress-response proteins such as the water stress sensor protein FLOE-1 in Arabidopsis [11]. Some tools have been developed in recent years to tackle characterizing such patterning. The program NARDINI was developed to analyze specific types of binary compositional patterning in IDRs [12]. Particularly for CBRs, the program LCD-Composer can be applied to analyze both compositional bias and residue dispersion, the inverse concept to ‘blockiness’ [13], and the LCT server analyses ‘low complexity’ and distance to perfect repeat structure [14]. Blockiness and homopeptide content were demonstrated to have strong functional associations for intrinsically-disordered CBRs in Saccharomyces cerevisiae [5].

To aid those venturing deeper into the dark proteomes, I have assembled a troupe of five decipherment helpers, collectively called Patterny. These are programs that each focus on one particularly feature of IDRs and CBRs, as listed above in the Abstract. They have been applied to three large data sets, and the penetrance of the analysed phenomena are discussed. Some illustrative examples are probed in more detail.

2. Materials and Methods

2.1. Data Sets

The DISPROT database of intrinsically-disordered regions was downloaded in FASTA format in July 2025 [15]. This was reduced for sequence redundancy using an algorithm previously described [16], yielding a set of 6,643 sequences. The proteome of budding yeast Saccharomyces cerevisiae (strain 288c) was obtained at the same time from UniProt [17]. For comparative purposes, the ASTRALSCOP40 data set of protein domain sequences (version 2.08) was also analyzed [18]. Orthologs of the illustrative example Chromogranin-A were taken from the OrthoDB database [19], and from previously calculated fungal ortholog sets by the author for the other example MSA2 [20].

2.2. Annotation of Compositional Bias Using fLPS2

The fLPS2 algorithm was used to label compositional biases and low-complexity regions [21,22]. It was updated to include a FASTA format output (-f option), and an option (-b) to allow minimum window sizes down to 3, which is used for analysis of banding (see below).

2.3. Patterny Flow Design

The Patterny flow is drawn in Figure 1A. Submitted sequence data is assessed by each program individually, however output of the Moduley program is further fed into the Blocky, Repeaty and Runny programs. Bandy operates separately. The individual programs/scripts are described below.

2.4. Moduley: Labelling Compositional Modules (CModules) and Other Possible Compositional Boundaries

Compositional modules (CModules) are defined as regions of compositional bias, optimized over a range of possible parameter sets. Moduley performs this definition task (Figure 1B). For this, a list of twelve fLPS2 parameter sets that were applied to thoroughly picking apart the functional associations of intrinsically-disordered compositional biases (Table 1 in ref. [4,5]), were re-applied here. All the annotated compositionally-biased regions from all the outputs are sorted on increasing P-value. Then for any one region, any other region with the same primary bias (i.e., most dominant residue type) and with overlap over most of its extent (≥0.5) is de-selected. This progressive de-selection continues until there are no more regions to assess.

In parallel, larger lists of boundary sets are formed through an analogous de-selection procedure, except the criterion for overlap is to have both ends within a small margin (=5 was found to be suitable).

There is one flag for the Patterny script (‘–cmodules yes|no’), which can be used to turn off calculation and analysis of CModules, e.g., if a set of previously calculated CModules is being digested.

2.5. Bandy: Discerning Compositional Banding

Compositional banding occurs when two or more patches of the same primary compositional bias are detected in an input sequence. Bandy has been designed to pick out sets of bands and to assess how evenly arranged these bands are. To discern band sets, a new option in the fLPS2 program was applied (‘-b’) which allows for minimum window lengths down to 3, while keeping maximum window sizes ≤20. A set of twelve parameter sets using very smaller window sizes was applied, and the resulting annotations were pooled and then segregated according to their primary residue bias, or both primary and secondary residues biases for multiple-residue biased regions (Figure 1C).

Each band set was then assessed for its distance to perfect banding (DPB). This is calculated by: (1) re-distributing the endpoints of the bands evenly over the same overall span; (2) calculating the deviation of each original endpoint to its corresponding ‘perfect’ endpoint; (3) summing these deviations to get DPB. The original DPB values are then compared to the DPB values arising from a sample of 1,000 random endpoint sets of the same number placed along the same span, to derive z-scores and P-values (Figure 1C). In doing so, for band sets with band number ≥4, outlier intervals between bands are labelled and excised if their median absolute deviation is ≥3.5. Finally, for each primary bias, the following are output: (a) the band set with the highest band number (if there is a tie, the one with the smallest P-value is picked); (b) the band set with the lowest z-score; (c) the band set with the highest z-score.

2.6. Blocky: Assessing Residue Segregation

The Blocky algorithm was described previously [5]. It calculates a blockiness score (B), which is an indicator of how segregated residue types are along an input sequence (Figure 2A). Originally, it was normalized using time-consuming calculations of minimum possible blockiness. Here, it is simplified relative to its previous treatment, so that only the raw score B is considered, but also now it is compared against values calculated for 1,000 scrambled sequences of the same composition. From the B distribution, z-scores and P-values are calculated. Residue-specific blockiness values are also determined in the same way. Where residue-specific B values are > the overall B value, this indicates that the residue is contributing to the residue segregation tendency.

2.7. Runny: Measuring Homopeptide Content

Homopeptides are defined as runs of amino acids of the same type with a minimum length of 3 residues [23]. Previously we dissected the intimate connection between homopeptide content (hpep) and the function of intrinsically-disordered compositionally-biased regions (ID-CBRs) [5]. Here, Runny calculates homopeptide content and assesses its significance relative to a population of 1,000 scrambled sequences of the same composition, as above for Blocky (Figure 2B).

2.8. Repeaty: Calculating Repetitiveness

Repeaty calculates the overall repetitiveness of a sequence using a concept of residue interval entropy (IE) drawn up here, which is given by:

$$\mathit{I}\mathit{E}=\mathit{ }\sum _{\mathit{i}\le \mathit{N}}\mathit{ }(-{\mathit{p}}_{\mathit{i}}.{\log }_2{\mathit{p}}_{\mathit{i}})$$

where there are N types of residue interval. N comprises all possible interval types of the sort x…[δ]…z, where the interval δ is in the range 0 to 100, and the residue pairs x and z are all possible pairings, including those with x=z. To make the calculation computationally tractable, only intervals between residue types that occur at least three times in the sequence are considered. As above for Runny and Blocky, the significance of the value of IE is assessed relative to a population of 1,000 scrambled sequences of the same composition (Figure 2C). IE values just for intervals with x=z (same-residue) and x≠z (different-residue) are also determined.

In addition to these overall IE values, an ‘experimental’ output of the top ten intervals contributing most to IE is provided, sorted in two different ways: (1) any significant interval, but sorted on decreasing frequency; (2) sorted on significant P-value.

2.9. The Patterny Script and the Program Implementations

Each of the components of Patterny are written in C and shell script (with one short AWK script), and executed using a shell script (patterny, either BASH or zsh, there are no shell-specific commands). The current version of fLPS2 (2.1, described above) has also been updated. The package is available from Github [https://github.com/pmharrison/patterny/], and includes some examples input and output files. The details of program execution and output format appear in the README.

3. Results & Discussion

3.1. Rationale, Test Data Sets & Performance

Patterny is a troupe of decipherment helpers designed to provide information which may guide further inquiry and hypothesis generation for protein regions whose function is encoded in a distributed manner, such as IDRs, and LCRs/CBRs more generally. Currently, there are five members in the troupe that focus on different distributed properties. Firstly, Moduley discovers optimized compositional modules (termed CModules), and also longer lists of Boundary Sets for compositionally-defined regions. The latter may be useful for picking more sensible tracts to piece together for experimental constructs, or someone might even be keen on applying them to more thorough bioinformatical analyses. Secondly, Bandy labels compositional banding, which occurs when there are at least two tracts with the same primary amino-acid compositional bias. Thirdly, Blocky assesses the overall segregation of residues by type along a sequence tract (blockiness). Fourthly, Runny highlights sequence tracts that have significant enrichments (or occasionally, lacks) of homopeptides, i.e., runs of amino-acid residues ≥3 in size [23]. Both the latter properties were demonstrated to have clear functional associations for tracts with the same primary bias in the model organism Saccharomyces cerevisiae [5]. Fifthly, Repeaty measures the overall repetitiveness of a tract using a novel conception of residue interval entropy, and provides output that highlights the most prominent residue intervals. Repeaty assesses repetitiveness without explicitly pulling predicted repeats out of the input.

Two data sets were derived for testing Patterny: (1) the DISPROT database of intrinsically-disordered regions found by experiment was reduced using a clustering procedure previously developed [16], to make it non-redundant (DISPROT_NR); (2) A set of CModules from the S. cerevisiae (budding yeast) proteome found by the Moduley program (CModules_YEAST). A third set of structural protein domain sequences, ASTRALSCOP40 takes on the role of a comparative ‘control’.

The performance of the package was checked for the DISPROT_NR set (6,643 sequence tracts) and the CModules_YEAST set (24,043 sequence tracts). The full Patterny package takes 39.1s system time to process DISPROT_NR and 103.5s for the CModules_YEAST, with ~>90% of these timings being taken up with the Repeaty program. For CModules_YEAST, derivation and assessment of Cmodules is not carried out (‘–cmodules no’). These timings were assessed on a 2020 Apple Mac Mini with an M1 chip and 16GB RAM. The package can thus analyze large databases and proteomes quite tractably.

3.2. Prevalences of Features in the DISPROT_NR Set

To gauge the penetrance of the phenomena explored, I summarized all the results for the three data sets in a big table (i.e., Table 1). CModules are a common feature of every data set, but the average –log(P-value) of the compositional bias is substantially lower for the larger abundance of them in the ASTRALSCOP40 structural domain sequences (~4.4, i.e., P-values of about 10^–4), compared to DISPROT_NR (~8.3), and CModules_YEAST (~6.4). Compositional banding occurs for about 1 in 10 of sequences regardless of origin, and there is even a handful of banding patterns ≥3 in number and ‘significantly uneven’ (0.2% in DISPROT_NR and CModules_YEAST). Significant blockiness and homopeptide content (hpep) are most common in DISPROT_NR, with significant repetitiveness actually most common in ASTRALSCOP40, but ≥9% frequency for all three data sets. Again, there are diminutive handfuls of sequences that are significantly un-blocky, un-repetitive or lacking in hpep (Table 1).

Are Blocky and Bandy redundant in utility? Maximum blockiness occurs when residues are perfectly segregated by type. Perfect banding occurs when a residue type occurs in bias bands that are perfectly spaced. However, only about 21% (90/430) of the DISPROT entries that have ‘significantly even’ bands are also ‘significantly blocky’ by the Blocky algorithm, indicating some overlap, but a substantial difference of emphasis.

3.3. Ranges of Behaviour for the Properties Explored

As a validatory exercise, extremes of modularity, blockiness, band evenness, hpep, and repetitiveness were examined. These are listed in Suppl. File S1. The output from each example for the relevant Patterny program has been isolated along with its sequence. (The description of the headers is given in detail in the README bundled with the package.) Just to highlight a few of these examples, firstly, an extreme case of modularity is the frequency clock protein from Neurospora crassa, which has 16 CModules which do not merge into a larger CModule, such as is observed in the C-terminal fragment of S/A-repeat-containing protein D from Staphylococcus aureus [24,25]. Disprot entry DP01621r005 (the C-terminal IDR of the LANA protein from Herpesvirus 8) is both extremely un-blocky and devoid of hpep [15]. To demonstrate the effectiveness of IE at ascertaining repetitiveness, the most extreme value is observed for the central disordered fragment from Nucleoporin NSP1 from S. cerevisiae (DP01077r015), with a z-score of -46.1) [26]. This protein contains several large exact repeats.

3.4. Detailed Example from DISPROT: Chromogranin-A from Domestic Cod

Two detailed random examples of no particular interest were picked from each data source. The output files for these examples are available at Github [https://github.com/pmharrison/patterny/tree/main/Examples/output]. Firstly, the protein chromogranin-A from Bos taurus (domestic cow) (entry DP00118r011 from DISPROT). Chromogranin A is a multi-functional precursor that, through its proteolytic cleavage, generates a family of biologically active peptides that collectively exert regulatory effects on diverse physiological systems in vertebrates. It is experimentally demonstrated to be ~100% intrinsically-disordered [15,27]. It was probed for a small panel of vertebrates. The CModules observed in it are drawn in Figure 3A, with other Patterny outputs summarized in 3B. Significant blockiness is a feature of chromogranin-A for several vertebrates, and any blockiness observed is centred around E, L, A and S residues chiefly. There are notable hpep enrichments in the mammalian sequences generally for E-homopeptides, and for Q-homopeptides specifically only in mouse. The sequences have a significant conserved repetitiveness across all species that stems largely from intervals between different residue types. These results are observed for both the whole sequences and the largest CModules within each sequence.

3.5. Detailed Example from CModules_YEAST: Putative Transcriptional Activator MSA2 from S. cerevisiae

The second example is MSA2 a putative transcriptional activator that along with its paralog MSA1 is a key regulator of the G1/S transition of the cell cycle. MSA2 originated after the whole-genome duplication of budding yeasts; it is sporadically conserved across Saccharomycetaceae, and originated since the last common ancestor of that clade. Alphafold predicts it as almost completely disordered, with intermittent alpha helices (for reference, please see its UniProt database record [17]). Here, we observe that MSA2 has a core CModule that tends to contain S, N and P residues (Figure 4A). There is compositional banding for N residues across most species, and conserved significant blockiness is observed in Saccharomyces (S_*) and Naumovozyma (N_*) species that is mainly caused by segregation of S, N, T, P and K residues, while significant hpep is observed in most of the species, most notably for S and N residues. Unlike the DISPROT example, there is not a conserved significant repetitiveness over the whole data set (just within the Saccharomyces genus, and in N. glabratus), either across whole orthologs or just within CModules. In a recent analysis of ID-CBRs (intrinsically-disordered compositionally-biased regions), the short Q-rich tract in MSA2 is linked to clusters with a possible function in regulation of transcription by RNA polymerase II (GO:0006357), and the N-rich tract to various categories linked more generally, or more specifically to regulation of transcription (e.g., GO:0006355, GO:0045944, GO:0001228) [5,29].

3.6. Further Examples

Some further examples (four each from DISPROT_NR and CModules_YEAST) and their outputs are bundled with the package, and available at Github [https://github.com/pmharrison/patterny/tree/main/Examples]. These demonstrate diverse traits in terms of modularity, banding, blockiness, homopeptide content and repetitiveness. For example, there is an EK-rich CModule (that was also identified as an intrinsically-disordered CBR in ref. [5]) in mannosyltransferase regulator 4, which operates in N-glycan mannosylphosphorylation (a functionality only found in fungi), that has obvious E and K banding and high hpep values.

3.7. Patterny Source Code Distribution

The Patterny source code, some executables and the example data is available at Github [https://github.com/pmharrison/patterny/]. The details of output formats can be found in the README.txt bundled with the package.

4. Conclusions

It is hoped that this package might be useful for hypothesis generation for IDRs and CBRs in proteins. The Patterny outputs could be used to guide mutations and molecular constructs in laboratory experiments. Indeed, in addition to the short-listed CModules, there are longer lists of possible compositional ‘boundary sets’, that might be useful for specifying boundaries for constructs. Also, computational biologists could graft the package into pipelines to probe large-scale data sets for the functional manifestations of IDR and CBR features.

Several further developments of the package are anticipated. Firstly, the sort of linear regression that was used in a previous study of yeast intrinsically-disordered CBRs [5], will be implemented more generally. Also, the package will gain further power through the lens of phylogeny trees, and explicit consideration of clade-specific conservation of traits. Such phylo-optical intensification of the algorithms will hopefully yield insights when cross-referenced with functional information, e.g., from Gene Ontology [29].