The Sequence Attribute Method for Determining
Relationships Between Sequence and Protein Disorder
Qian Xie

1

Gregory E. Arnold

qian@grover.chem.wsu.edu
Zoran Obradovic

2

zoran@eecs.wsu.edu

34

ge arnold bits@yahoo.com
Ethan Garner

1egarner@wsunix.wsu.edu

Pedro Romero

2

promero@eecs.wsu.edu
A. Keith Dunker

1dunker@mail.wsu.edu

1

Department of Biochemistry and Biophysics
School of Electrical Engineering and Computer Science Washington State University,
Pullman, WA 99164-4660, USA
3 Biological Information Technologies, P.O. Box 1403, Richland, WA 99352, USA
4 Present address: Amgen P Mail Stop 14-1-D, One Amgen Dr., Thousand Oaks, CA
91320, USA

2

Abstract
The conditional probability, P(sjx), is a statement of the probability that the event, s, will occur
given prior knowledge for the value of x. If x is given and if s is randomly distributed, then an
empirical approximation of the true conditional probability can be computed by the application ofBayes' Theorem. Here s represents one of two structural classes, either ordered, so , or disordered,sd , and x represents an attribute value calculated over a window of 21 amino acids. Plots ofP(sjx) versus x provide information about the correlation between the given sequence attributeand disorder or order. These conditional probability plots allow quantitative comparisons between
individual attributes for their ability to discriminate between order and disorder states. Usingsuch quantitative comparisons, 38 di erent sequence attributes have been rank-ordered. Attributes
based on cysteine, the aromatics, exible tendencies, and charge were found to be the best attributes
for distinguishing order and disorder among those tested so far.

1 Introduction
A region of protein is in the ordered state if it folds primarily into a single three dimensional structure,and it is in the disordered state if it remains mostly unfolded or partially folded into a locally exible
ensemble of structures. Despite the emerging interest in disordered states of proteins much of thestructural biology community has not yet recognized the biological importance of this structural
species. Recent studies demonstrate that disordered states are requisite in understanding the stabilities
of proteins, their transport across membranes, their transformation into pathogenic states, and theircell signaling and regulation functions. Based on these ndings, biochemical dogma will need to berevised, re ecting that amino acid sequence not only determines 3D structure [1], but also lack ofstructure as well [12].
Our recently reported results provide strong indication that some amino acid sequences code fordisordered regions rather that structured ones, and that such disordered regions are commonly involvedin function [12, 13, 14, 8]. Literature searches reveal more than 100 speci c examples of proteins thatare likely to be entirely disordered or contain disordered regions involved in function [16, 17, 11, 4,
12, 13, 8]. Our studies suggest that natively disordered regions have a variety of structures ranging
from random-coil-like to molten-globule-like; however, further work needs to be carried out in order
to investigate and characterize the structural properties of disordered states.
Towards this goal, our laboratory has developed neural networks capable of predicting, from primary sequence, disordered regions in proteins with 70% accuracy [12, 13]. A problem with the193neural network predictors is that they do not provide an understanding of the factors leading to theprediction. In an e ort to overcome this limitation a separate study has been initiated to explicitly
investigate the relationship between disorder and primary sequence.
Described herein is application of the \the sequence attributes method" [2] to a set of sequencesclassi ed as ordered or disordered. This method, which depends on Bayesian statistics [3, 6], wasdeveloped several years ago for understanding relationships between sequence and secondary structure.
This method uses a simple windowing procedure [15] to assign attribute values over stretches of 21
contiguous amino acid residues, and then partitions each window according to its attribute value. Plotsof conditional probabilities versus attribute values allow quantitative comparisons between individual
attributes for both their prediction potential and their ability to discriminate between order anddisorder states.

2 Materials and Methods
2.1

The data set

The evaluation and testing of sequence attributes for their potential to discriminate between ordered
and disordered requires prior construction of a database of sucient size containing a balanced set ofboth structural classes [14]. The database was constructed from 32 proteins that were identi ed byliterature searches, and their sequences obtained from the Swiss-protein, PIR, or PDB databases. A
complete list of these proteins along with the methods used to identify their regions of disorder can befound on the Internet at, http://disorder.chem.wsu.edu/attribute.htm. A random subset of NRL 3D
sequences corresponding in size and number to the identi ed disordered regions were used to generate
a balanced database [14]. The resulting database contains 2,547 disordered and an equal number ofordered windows of size 21.
2.2

Sequence attributes calculations

An attribute is a numerical value calculated from an amino acid sequence over a window of speci ed
length. In this work, two types of attributes are used: compositional and numerical. A compositional
attribute is the number of a speci ed amino acid, or the number of a set of amino acids, divided
by the length of the window. A numerical attribute is value of some amino acid parameter, such ashydropathy [10] or exibility index [18], averaged over the amino acids in a given window.
Here we have used windows of 21 amino acids. This value was selected in previous studies [12] asa reasonable compromise between the increased noisiness of smaller windows and the lower resolutionof larger ones.
A detailed description of the sequence attributes method including examples of the enumeration
procedure is presented elsewhere [2]. A summary of the method as applied to protein order/disordercan be found on the Internet at, http://disorder.chem.wsu.edu/attribute.htm.

3 Results
3.1

Conditional probability graph

The sequence attributes approach has been used to explore relationships between order/disorder amongthe 38 di erent compositional and numerical attributes. The dependence between structural class anda particular attribute is examined by plotting the conditional probability values, P(sjx), versus theattribute value x. The enumeration procedure described above is computed for both ordered (o) anddisordered (d) structural classes leading to two conditional probability curves, P(so jx) and P(sd jx),
per graph.
194

1

0.8

0.8

0.8

0.6

0.6

0.4

0.2

0

0

probability

1probability

Probability

1

0.4

0.05

0.1

F+W+Y

a

0.15

0.2

0

0.25

0

0.4

0.2

0.2

0

0.6

0

0.1

0.2

0.3

0.4

K+R+D+E+H/2

b

0.5

0.6

0

0

0

0.1

0.2

0.3

S+T+Q+H+N

0.4

0.5

0.6

c

Figure 1: Representative conditional probability plots. Following are three example plots ofP(sjx) vs. x, where the curve for ordered structure, P(so jx) is given by the dotted line and that forthe disordered curve, P(sd jx) is given by the dashed line, and where the attributes are as indicated:a, aromatics (W+F+Y); b, charged (K+R+D+E+H/2); c, small and hydrophilic (S+T+Q+H+N).
Three example conditional probability graphs are shown in Fig. 1. These graphs were selected as
typical examples demonstrating the capacity of various attributes to di erentiate between order anddisorder. The attributes in these examples are considered to have good (Fig. 1a), fair (Fig. 1b), andpoor (Fig. 1c) discriminating properties. A sequence attribute, x, is considered useful if P(so jx) andP(sd jx) vary reciprocally with x. In contrast, if P(so jx) and P(sd jx) remain essentially constant for
all values of x, then the attribute x provides no useful information and is considered a poor attribute.
The compositional attribute W+F+Y is shown in Fig 1a. Notice there is a strong negative correlation with the W+F+Y attribute and the conditional probability for disorder, whereas the conditional
probability for order exhibits the inverse relationship. This trend is concordant with the observations
made by Burley and Petsko, well over a decade ago, that aromatic residues make especially strong
contributions to protein stability [5]. Additionally, these 3 residues are among the most evolutionarily
conserved residues found amidst homologous proteins [7]. Considering this information, the observed
trend, namely that sequence windows with low aromatic content tend to be disordered while thosewith high aromatic content tend to be ordered, is entirely reasonable.
Figs. 1b presents the order/disorder conditional probability pro les as a function of total charge.
The order/disorder probability curve exhibits a reciprocal relationship over roughly half of the respective attribute domain, and no consistent mutual or reciprocal relationship over the remainder of theattribute domain. The correlation of this attribute with order and disorder is complex. Given the small
separation between the two curves, this attribute was judged to be fair in its potential to di erentiate
between order and disorder. When single amino acid attributes are subjected to feature selection, setsof charged amino acids are among the chosen [12, 13]. The large separation between the two curves
for highly charged local segments of sequence (e.g., for b, at large values of K+R+D+E+H/2) areprobably the basis for this selection.
The attribute in Fig. 1c shows little correlation with order and disorder, and as such was judged
to be poor attribute. There is no separation between the conditional probability curves throughout
their attribute domain. The residues S+T+Q+H+N are among the least evolutionarily conserved
residues [7] which may explain, in part, why these attributes exhibit virtually no relationship witheither structural class.
3.2

Quantitative comparison of attributes

A simple quantitative method to determine the potential of an attribute to di erentiate between thetwo structural types is by the degree of separation between the P(so jx) and P(sd jx) curves.
The largest possible degree of separation would occur for a pair of curves that were step functions,with values of 0,1 below some threshold and 1,0, respectively, above that threshold. Such an attributewould be a perfect predictor of order and disorder. The extent to which a given attribute approaches
195aProbability

0.8

0.6

0.4

0.2

0

0

0.05

0.1

F+W+Y

0.15

0.2

0.25

Figure 2: Evaluation of the area ratio. An example of calculating the area ratio of a P(sjx) vs. x plot
is given using the F+W+Y attribute. First, vertical lines are constructed at the end points of P(sjx)values. Next, the area of the rectangle bounded by these two lines and the upper and lower bordersof the graph is calculated, call it Ar . Finally, the area that separates the P(so jx) and P(sd jx) curves(shaded area) is determined, call it As . The area ratio is equal to As =Ar .
the \perfect predictor" can then be estimated by dividing the given area of separation by the total
possible area as described in the gure legend; we are calling this the `area ratio.' The area ratios
were determined for the 38 attributes in this study.
These attributes and their area-ratio values are given in rank-order in Table 1. The correlation
with disorder is also provided, where \+" means that the probability of disorder generally increases
as the attribute value increases, where \-" means the converse, and where C, for complex, means thatthe two curves intersect more than one time.
The attribute set in this study included the 20 individual amino acids. This allows amino acids
to be classi ed as \disorder-promoting" (\+" correlation), \order-promoting" (\-" correlation), or
complex.
Sets of amino acids were chosen as attributes to determine the relationships between disorder/orderand various classes of amino acids such as aromatic, polar, nonpolar, etc. Finally, two numericalattributes, hydropathy [10] and exibility index [18], were included because these attributes wereselected in our previous investigations as being important for predicting disorder [12].

4 Discussion
4.1

Prior Neural Network Prediction of Order and Disorder

Upon noticing that many proteins contain essential, functional regions that are disordered, it was
reasoned that amino acid sequence should determine not only structure [1] but also lack of structure
as well. To test this hypothesis, a small set of proteins with disordered regions was collected, andthen a prediction-based approach that employed simple neural networks was used [12]. The results of
those pilot studies and subsequent work provide evidence that disorder is encoded by the amino acidsequence [12, 13, 14, 8].
In the prior work supervised training of the neural networks was used, which means that inputs were196

Rank Sequence Attribute 1
Area Ratio
Correlation 2
1
W+F+Y+C (C is low in disordered regions)
0.517
2
C (cysteine)
0.484
3
W+C+F+I+Y+V+L+H+M (least exible, Vihinen)
0.464
4
A+T+R+G+Q+S+N+P+D+E (most exible, Vihinen)
0.464
+
5
V+I+Y+F+W (best sheet formers, Chou-Fasman)
0.439
6
F+W+Y (aromatic)
0.360
7
W+F+Y+C+V+I+L+M+P (all non-polar)
0.321
8Hydropathy
0.302
C
9
S+G+K+P+D+E (best sheet breakers, Chou-Fasman)
0.295
+
10
Flexibility (Vihinen scale)
0.294
+
11
W (tryptophan)
0.279
12
K+R+D+E (total charge)
0.265
C
13
A (alanine)
0.265
C
14
K+R-D-E (net charge)
0.260
C
15
F (phenylalanine)
0.257
16
E (glutamic acid)
0.246
C
17
Y (tyrosine)
0.244
18
K+R+D+E+H/2 (total charge)
0.213
C
19
K (lysine)
0.210
C
20
E+M+A+L (best helix formers, Chou-Fasman)
0.206
C
21
Z (glutamine or glutamate)
0.203
C
22
S+T+Q+H+N+D+E+R+K (all polar)
0.190
C
23
I (isoleucine)
0.164
24
Y+N+P+G (best helix breakers, Chou-Fasman)
0.149
C
25
B (asparagine or aspartate)
0.136
C
26
R (arginine)
0.130
C
27
S (serine)
0.126
+
28
P (proline)
0.122
+
29
L (leucine)
0.108
C
30
D (aspartic acid)
0.091
C
31
V (valine)
0.083
32
Q (glutamine)
0.083
+
33
N (asparagine)
0.082
34
T (threonine)
0.078
35
G (glycine)
0.059
C
36
S+T+Q+H+N (small and hydrophillic)
0.050
C
37
H (histidine)
0.042
C
38
M (methionine)
0.041
C
1 H/2 rather than H was used because the charge of H at neutral pH is typically 1=2.
2 Correlation with disorder, where + or - indicates a single intersection of the order/disorder curves (like Fig 1a)
whereas C (complex) indicates more than one intersection (like Fig. 1b, c).

Table 1: Rank ordering of attributes according to their area ratio values.
selected based on prior studies to nd attributes or features that are predictive of order and disorder.
These feature selection studies indicated some sequence attributes are important for determination oforder or disorder, but these observations need to be supplemented with other information to provide
understanding. For example, a feature selection process might indicate that tryptophan content isimportant for distinguishing order and disorder, but this observation by itself does not indicate thenature of the relationship between tryptophan content and order or disorder. Since the relationships
between amino acid sequence and disorder were relatively unexplored, this problem seemed to be an
excellent candidate for the application of conditional probability curves for the purpose of knowledge
discovery.
4.2

Correlations between amino acid sequence and order/disorder

The feature selection protocols used for neural network development operated on an initial pool of 24
attributes, which were the compositions of the 20 amino acids, hydropathy [10], exibility index [18],helix moment and sheet moment [9]. Here the list has been expanded to 38 attributes, which were197then rank-ordered as described above. Many of these new attributes contain the same amino acids
except for just one. This provides a simpli ed way of asking whether the amino acids cooperate in
the prediction of order and disorder. For example, a higher ranking occurs if the di erent amino acidacts cooperatively with the others in the set.
The conditional probability curves are, in essence, a tool to be used to better understand structure/attribute correlations. Fig. 1a shows that the probability of disorder decreases almost linearlywith increasing numbers of aromatic amino acids, whereas 1b shows a more complex relationshipbetween the charged residue attribute and order/disorder.
Although many of the relationships between order/disorder and amino acid sequence could havebeen predicted in advance, Table 1 contains some surprises. These may lead to new insights regarding
protein structure once the physical bases for the relationships are understood.
Consider the results for glycine. Given its ability to adopt many conformations, glycine might havebeen expected to correlate strongly with the disordered state, but it does not. It has a ranking of 35
out of the 38 attributes tested, with an area ratio value of just 0.059 and with a complex correlation.
A possible explanation for these results is provided by the work on the development of the exibility
index [18]. The exibility index of given amino acid does not depend on its intrinsic character, butrather on its typical location in proteins, with amino acids that are usually buried having a lower
index values and those that are usually on the surface having higher values. In these studies, glycine
was found to depend strongly on its neighbors, having low values when next to amino acids with low
values and having high values when next to amino acids with high values. The likely explanation isthat glycine occurs frequently not only in exible loops but also deep inside proteins where it allows
very close contacts to be made. From these considerations, the low ranking and complex correlation
for glycine do make sense after all.
As a nal example, compare serine and threonine. Given its small size and hydrophilicity, serine
might be expected to correlate strongly with disorder. As expected, it does exhibit a positive correlation with disorder. Furthermore, its ranking, although modest at number 27 in Table 1, is the highest
for a single amino acid correlating positively with disorder. The higher ranking single amino acids
either correlate negatively with disorder or exhibit complex correlations. Now consider threonine.
This amino acid might be expected to be quite similar to serine, but with a lower ranking due tothe increased hydrophobicity that results from the added methyl group. Threonine does have a lower
ranking as expected, number 34 in Table 1, but the surprise is that threonine correlates negatively withdisorder. Evidently the methyl group tips the balance and causes threonine to be \order-promoting"albeit with a very small overall propensity.
4.3

Applications and future developments

An obvious extension of the results presented herein would be the construction of new predictors
based on the best of the new attributes. Experiments in progress suggest that formal feature selection
takes many of the highest ranking attributes from Table 1 and that the resulting neural network
predictors using these new attributes signi cantly out-perform those developed originally. Indeed,
new neural networks that include some of these attributes are now achieving about 85our previous
neural networks [12, 13, 14], these new ones are achieving higher success while using a substantiallylarger dataset and with somewhat improved generalization to completely out-of-sample proteins.
Other experiments in progress have shown that there are other attributes, such as sequence complexity [19, 20, 21, 22], that may rank high on the list and so are likely to be important for determining
order and disorder. To date a rational approach has been followed in selecting input features. That is,
rst we identi ed a speci c collection of attributes that seemed likely in advance to be correlated withorder and disorder. Next, we tested the collection to nd the best among these, initially by formalfeature selection protocols (which provide little basis for understanding) and now by the sequence
attributes method (which can hopefully provide more understanding). This approach assumes that198

we know in advance which attributes distinguish between order and disorder. A useful alternative
to this rational approach would be to use the sequence attributes method as the basis for identifying useful attributes by a combinatorial procedure that sifts through very large numbers of possible
compositional and numerical attributes. Thus, it should be possible to carry out random generationof attributes and then test them by the area ratio method to determine which ones are important
and which ones are not. We are in the process of implementing this approach. It will be interesting
to determine whether this random generation approach will uncover any useful attributes, and, if
so, whether such attributes provide new insights about sequence/structure relationships, or provide
improved prediction accuracies.

5 Summary
The results in this paper provide additional evidence that order and disorder are determined by aminoacid sequence. In agreement with our earlier observations, a collection of sequence characteristics{including charge, tendency for exibility, absence of cysteine, and absence of aromatic groups{ arestrong indicators of the disordered state.

Acknowledgements
Partial support by the NSF research grant NSF-CSE-IIS-9711532 to Z. Obradovic and A.K. Dunker isgratefully acknowledged. Garner thanks Dr. John Paznokas for providing support via an institutional
grant for undergraduate research from the Howard Hughes Foundation.

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