TOP-IDP-Scale: A New Amino Acid Scale Measuring Propensity for Intrinsic Disorder

Databases

The creation and evaluation of sequence attributes to discriminate between order and disorder requires a database containing a balanced set of both ordered and disordered residues. Disordered regions identified by NMR, circular dichroism, or protease digestion were found by keyword searches of PubMed (http://www.ncbi.nlm.nih.gov). Additionally, starting from a subset of the Protein Data Bank (PDB) called PDB_Select_25, disordered regions in X-ray crystal structures were identified by searching for residues having backbone atoms that are absent from the ATOMS lists in their PDB files. These differently characterized disordered regions were grouped together in into a set called dis_ALL. In total, dis_ALL contains 154 proteins and 92,735 residues. An ordered set of proteins was created using the non-redundant subset of PDB called PDB_Select_25. Proteins without missing atom coordinated were selected and in total, the ordered set contains 290 proteins and 67,548 residues.

Amino acid sequence attributes

The values for various amino properties such as hydrophobicity, polarity, volume, etc., were compiled by database and literature searches. The AAIndex database (http://www.genome.jp/aaindex/) provided 494 distinct numerical property scales. In addition, three compositional attributes, and the frequency of each single amino acid were also included in the complete list. Disregarding high correlation between certain scales, all 517 distinct property scales were examined.

Scoring function for order / disorder discrimination

In this study, a method for determining how well one property scale discriminates between order/disorder versus another property scale was needed. For this evaluation, we used the sequence attributes area ratio method, which was described in detail previously [24, 30].

The first step in the evaluation method was to balance disordered windows of 21 residues from the disordered database with an equal number of ordered windows of the same size taken from the ordered dataset. Next, given a balanced number of ordered and disordered windows, the attribute values for each window were calculated as averages over the window and the windows were then binned by their attribute values. From the proportion of ordered and disordered windows in each bin, the conditional probability curves of order and disorder, P(s_o | x) and P(s_d | x) respectively, were estimated. The conditional probability curves were then plotted versus the attribute values associated with each bin. Next, the relative degree of separation of the two probability curves was determined by calculating the area between the order and disorder curves and dividing by the area of the graph, giving the area ratio value (ARV). The ARV falls between zero and one with the larger the ARV, the better the discrimination between order and disorder.

Algorithms to optimize a scale for order / disorder discrimination

Due to the large size of the attribute space, we used two different genetic algorithms to efficiently find an optimal scale for order/disorder discrimination. Genetic algorithms are a particular class of evolutionary algorithms that include techniques inspired by evolutionary biology such as inheritance, mutation, selection, and crossover/recombination. For our study, each attribute property scale is considered as an individual. As described above, we used the sequence attribute method as the fitness function meaning individuals having higher ARVs being considered of higher quality than ones with lower ARVs. The basic pseudo-code genetic algorithm looks like this:

Specifically, both a Canonical Genetic Algorithm (CGA) [31] and a Stochastic Hill Climbing Algorithm (SHCA) [32] were tested. The SHCA began with the initial set of 517 property scales as the initial population. After this population was evaluated and ranked, the top-ranked scale was selected to create the new population. The first weight value in this scale was then manipulated 99 times by adding a small random value to this initial weigh value. The new 100-scale population, including the original top-ranked scale, was again evaluated and a new top-ranked scale selected. Successive iterations manipulated the next weight value, viewed as a circular list of values, with decreasing variability to bring about convergence. The algorithm terminated when the improvement in fitness between iterations failed to change significantly.

The CGA started with population of 100 scales randomly selected from the list of 517. The scales were evaluated and ranked using the same sequence attribute method described above. The reproduction fitness of each scale is determined by rf_i = f_i / f_av , where f_i is the fitness value of the current individual and f_av is the average fitness value for all the members of the population. By using “remainder stochastic sampling” [31], an intermediate population of 100 scales was constructed. The fractional portion of the reproductive fitness value, rf_i, was used to determine the likelihood of the individual being selected for the next population while the integer portion was used to determine the number of times that individual will appear in the next population if it is selected. Scales are randomly selected based on their likelihood until the intermediate population is full.

Next, pairs of scales in the intermediate population were randomly selected for recombination with a probability of 90%. Crossover/recombination was achieved by swapping randomly selected parts of each parent scale to generate two new scales, each having a part of both parents, which were placed in the next population. The algorithm selected one random point at which to split and recombine. After crossover/recombination, mutation was applied with a probability of 5% for each weight in each scale. Mutation took place by manipulating a given weight by a random amount between 1 and -1. Once these operations were complete, a new iteration of the algorithm began until the fitness of the top-ranked scale failed to improve significantly.

Ranking previously published attributes

Using the sequence attribute method described above, ARVs were calculated for 517 previously published attributes. The ARVs for the top 10 attribute scales are listed in Table 1. The rankings of all 517 scales are available by request. The highest ranked attribute is the normalized flexibility parameters (B-values) for each residue surrounded by two rigid neighbors [33] with an ARV of 0.687. All other ARVs were lower than this, ranging as low as 0.072 for composition of amino acids in extracellular proteins (percent) [34]. Figure (1) illustrates the area ratio comparison graph for the highest value (Figure (1A). Normalized flexibility parameters (B-values) for each residue surrounded by two rigid neighbors [33]), average value (Figure (1B). Positive charge [35]), and lowest value (Figure (1C)), composition of amino acids in extracellular proteins, percent [34]). It can be seen that the area between the two curves is greater in Figure (1A) than both Figure (1B) and (1C).

TOP-IDP, an optimized scale for order / disorder discrimination

Our optimization techniques, SHCA and CGA, both resulted in scales that were essentially identical. The values of this newly optimized scale, called TOP-IDP, are compared with the best of the published scales, normalized flexibility parameters (B-values) for each residue surrounded by one rigid neighbor [33], in Table 2. Amino acids were ordered according to the scale values of the TOP-IDP scale and were divided into order-promoting and disorder-promoting categories. Note that both of these scales are over difference ranges, so comparison is difficult. When ranked according to ARV with the original 517 published attributes, TOP-IDP gave highest-ranked scale with an ARV of 0.761 as compared to 0.687 for the scale that previously ranked highest. This represents an 11% improvement in the ability to discriminate between order and disorder. Figure (1D) shows the area ratio graph for the TOP-IDP scale.

Comparing four scales

Interestingly, the only disorder propensity scale developed so far was based on the ability of amino acid residues to form a sufficient number of contacts in a globular state [36]. In this approach, the average number of contacts per residue was calculated for each residue based on a set of ordered proteins, giving rise to the FoldUnfold scale (see Table 2), and then the expected average number of contacts per residue calculated from the amino acid sequence alone (using the average number of contacts for 20 amino acid residues in globular proteins) was used as an indicator of natively unfolded proteins [36]. Another disorder propensity scale can be derived from the relative amino acid composition of IDPs. To this end, the fractional difference in composition between a set of IDPs deposited in DisProt [28, 29] and a set of ordered proteins from PDB is calculated for each amino acid residues as (C_disorder-C_order)/C_order, where C_disorder is the averaged content of a given amino acid in a set of IDPs and C_order is the corresponding averaged content in a set of ordered proteins [37]. These data can be used to derive a disorder propensity scale, DisProt scale, which is based on the statistical difference in the amino acid compositions of ordered proteins and IDPs.

The ranking of the amino acids for TOP-IDP, normalized flexibility parameters (B-values) for each residue surrounded by one rigid neighbor [33], FoldUnfold scale and DisProt scale are compared graphically in Figure (2A). To obtain this data, all the scales were normalized to have the minimal value of zero and the maximal value of 1. The order of the amino acids along the X-axis followings the ranking of TOP-IDP as can be seen from the monotonically increasing values from left to right. If the amino acid were ranked by the B-values, FoldUnfold or DisProt scales, the order of the amino acids would be very different. Figure (2A) shows that for any amino acid residues the unfoldability score assessed by Top-IDP scale is comparable with score assessed by at least one other scale, suggesting that these four scales are correlated. Figure (2B-G) represents the pair-wise comparison of these four scales and shows that they possess significant mutual correlation. Interestingly, the greatest correlation (r²= 0.785) was observed for the TOP-IDP-FoldUnfold pair. This is rather interesting finding, as four scales compared were derived using absolutely different models - normalized flexibility parameters (B-values) for each residue surrounded by one rigid neighbor [33], expected average number of contacts per residue [36], statistical difference in the amino acid compositions of intrinsically disordered and ordered proteins, and a novel amino acid attribute constructed for the discrimination between order and disorder.

TOP-IDP web-based prediction service

To apply the TOP-IDP scale to prediction of intrinsically disordered protein, a web-based prediction service has been created at http://www.disprot.org/dev/disindex.php. The page takes in a protein sequence, in either 1-letter or 3-letter code FASTA format, as input. The average global TOP-IDP value and average window-by-window TOP-IDP values are calculated based on the normalized TOP-IDP scale. Based on maximum-likelihood methods, a prediction cut-off of 0.542 was calculated giving the equation: I_Top−IDP = —(< Top — IDP > −0.542) where < Top — IDP > is the average TOP-IDP value for a protein (or window). Positive prediction values indicate proteins (or windows) that are likely to be ordered, were negative prediction values indicate proteins (or windows) what are likely to be intrinsically disordered. In order to better interpret prediction results, window prediction are plotted sequentially with the prediction value representing the center residue of the given window.

For an additional comparison, the prediction service also implements the improved algorithm of Uversky et al. [2] which used a combination of Kyte/Dolittle hydrophathy and net charge to predict intrinsic disorder [27]. These values are also plotted in the same method as the TOP-IDP value for easy comparison. All data are available for download via either tab-delimitated text or comma-separated text (csv) format.

Example of application of TOP-IDP server

Figure (3) represents an illustrative example of the Top-IDP server application. Here, the disorder propensity of the tumor suppressor protein p53 (which is at the center of a large signaling network, regulating expression of genes involved in many cellular processes such as cell cycle progression, apoptosis induction, DNA repair, and response to cellular stress [38] is estimated by Top-IDP and two well-accepted disorder predictors, PONDR® VLXT and VSL1. There are three structural domains in p53: N-terminal translational activation domain, central DNA binding domain, and C-terminal tetramerization and regulatory domain. At the transactivation region, it interacts with TFIID, TFIIH, Mdm2, RPA, CBP/p300 and CSN5/Jab1 [38]. At the C-terminal domain, it interacts with GSK3β, PARP-1, TAF1, TRRAP, hGcn5, TAF, 14-3-3, and S100B(ββ). Both N- and C-terminal domains of p53 are involved in numerous protein-protein interactions, some of which involve disorder-to-order transitions. PONDR® VLXT plot shown in Figure (3B) illustrates such a predisposition for the disorder-to-order transition as sharp dips — or short regions of predicted order — within longer regions of predicted disorder. Recently we have established that this capability of PONDR® VLXT to find the potential protein-protein interaction sites involving disorder-to-order transitions is rather unique among more than 15 predictors analyzed [46]. Intriguingly, TOP-IDP was able to reproduce many of the characteristic features observed in the PONDR® VLXT plot, suggesting that this new predictor has some interesting potential applications.