Protein misinteraction avoidance causes highly
expressed proteins to evolve slowly
Jian-Rong Yanga,b, Ben-Yang Liaob,1, Shi-Mei Zhuanga, and Jianzhi Zhangb,2
aKey Laboratory of Gene Engineering of the Ministry of Education, State Key Laboratory of Biocontrol, School of Life Sciences, Sun Yat-sen University,
Guangzhou 510275, China; andbDepartment of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 48109
Edited by Michael Lynch, Indiana University, Bloomington, IN, and approved February 17, 2012 (received for review October 21, 2011)
The tempo and mode of protein evolution have been central
questions in biology. Genomic data have shown a strong influence
of the expression level of a protein on its rate of sequence
evolution (E-R anticorrelation), which is currently explained by
the protein misfolding avoidance hypothesis. Here, we show that
this hypothesis does not fully explain the E-R anticorrelation,
especially for protein surface residues. We propose that natural
selection against protein–protein misinteraction, which wastes
functional molecules and is potentially toxic, constrains the evolu-
tion of surface residues. Because highly expressed proteins are
under stronger pressures to avoid misinteraction, surface residues
are expected to show an E-R anticorrelation. Our molecular-level
evolutionary simulation and yeast genomic analysis confirm mul-
tiple predictions of the hypothesis. These findings show a pluralis-
tic origin of the E-R anticorrelation and reveal the role of protein
misinteraction, an inherent property of complex cellular systems,
in constraining protein evolution.
agree that the key determinant of the evolutionary rate of a
protein is its functional constraint, the exact nature of the func-
tional constraint on a protein has remained largely mysterious. In
the last decade, the advent of functional genomics has allowed
empirical examinations of correlations between the evolutionary
rate of a protein sequence and various properties of the protein
such as its expression level, expression breadth across tissues,
subcellular localization, gene structure, number of protein in-
teraction partners, and KO fitness effect (1–17). Unexpectedly,
the strongest determinant of the rate of protein sequence evolu-
tion was found to be its expression level, at least in unicellular
organisms such asbacteriaand yeast (2,3, 13,15).The reasonwhy
highly expressed proteins evolve slowly, however, is not well-un-
derstood. The prevailing explanation of the negative correlation
between the expression level of a protein and its evolutionary rate
(E-R anticorrelation) is the protein misfolding avoidance hy-
pothesis, which asserts that natural selection against cytotoxic
protein misfolding (18) is stronger for more highly expressed
proteins and constrains the evolution of these proteins (13, 19,
20). The misfolding avoidance hypothesis has been supported by a
empirical evidence (13, 20), and therefore, it has been well-
established. What is unclear, however, is whether this hypothesis
can fully explain the E-R anticorrelation. We pose this question,
because misfolding avoidance is achieved primarily by the en-
hancement ofprotein stability (20), which is mainly determinedby
the selective use of residues located in the protein core; however,
the E-R anticorrelation is not limited to the protein core. In this
on the protein surface, even when residues constrained for mis-
the E-R anticorrelation on protein surfaces, termed the protein
misinteraction avoidance hypothesis. Finally, we provide evidence
for this hypothesis using both computer simulation and empirical
lthough molecular and evolutionary biologists unanimously
Misfolding Avoidance Cannot Fully Explain the E-R Anticorrelation.
To assess whether the E-R anticorrelation is fully explainable by
the misfolding avoidance hypothesis, we first removed sites in
a protein that are constrained by misfolding avoidance and then
examined whether the anticorrelation disappears. In a recent
study (20), we derived an approximate formula for the probability
of protein misfolding (pmisfold) of a mutant gene relative to its WT
budding yeast Saccharomyces cerevisiae, we determined the rank
of the WT codon among the 61 possible sense codons in terms of
pmisfold. For example, if the WT codon has the lowest pmisfold
a gene, such top-ranked codons are expected to be under stronger
constraint for misfolding avoidance than not top-ranked codons.
Consequently, the E-R anticorrelation should be weakened when
top-ranked codons are eliminated. Evaluating the E-R anti-
correlation requires an accurate estimation of the substitution
rate. We estimated the substitution rate of each amino acid po-
sition by using sequence alignments from six yeast species that
diverged after the whole-genome duplication (WGD) that oc-
curred ∼100 Mya (21) (Materials and Methods).
We first removed all amino acid positions where the WT
codons are ranked one by pmisfold; these sites were previously
referred to as matching sites (20). For comparison, we randomly
removed the same number of amino acid sites as the number of
matching sites from each yeast protein. We then calculated the
correlation between the mRNA expression level of an S. cer-
evisiae gene and its amino acid substitution rate estimated from
the mean of the remaining amino acid sites of the protein.
Consistent with the misfolding avoidance hypothesis, removing
the top-ranked codons weakens the E-R anticorrelation signifi-
cantly more than any of the 104random removals of the same
number of sites (P < 10−4) (Fig. 1A). However, the amount of
decrease in E-R anticorrelation is small (from ρ = −0.549 to
−0.545), and the anticorrelation remains very strong after the
removal of the top-ranked codons (P < 10−292, Spearman’s rank
correlation test), which constitute 15.4% of all codons.
The genome-wide median pmisfoldrank for WT yeast protein
sequences is six. To further reduce the evolutionary constraint
imposed by misfolding avoidance, we eliminated all codons with
pmisfoldrank ≤ 6. As expected, this removal is more effective than
Author contributions: J.-R.Y., B.-Y.L., and J.Z. designed research; J.-R.Y. performed re-
search; S.-M.Z. and J.Z. contributed new reagents/analytic tools; J.-R.Y. analyzed data;
and J.-R.Y. and J.Z. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
1Present address: Division of Biostatistics and Bioinformatics, Institute of Population
Health Sciences, National Health Research Institutes, Miaoli County 350, Taiwan, Repub-
lic of China.
2To whom correspondence should be addressed. E-mail: email@example.com.
See Author Summary on page 5158 (volume 109, number 14).
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
| Published online March 13, 2012
the random removal of the same number of codons in weakening
the E-R anticorrelation (Fig. 1B); however, the anticorrelation
remains strong (ρ = −0.538, P < 10−284). We then took a third
and even more dramatic action by removing all codons with
pmisfoldranks ≤ 30 (Fig. 1C). Because each codon has 61 avail-
able choices, the remaining sites all have pmisfoldranks ≥ 31.
These sites should be equally or less stabilizing than the chance
expectation and thus, are unlikely to be subject to selection for
misfolding avoidance. Furthermore, this removal eliminated
88% of codons, resulting in a dataset that is substantially smaller
than the original one. Surprisingly, the E-R anticorrelation
remains strong (ρ = −0.496, P < 10−234). These results suggest
that the protein misfolding avoidance hypothesis does not fully
account for the E-R anticorrelation.
Misfolding Avoidance Is Especially Poor in Explaining the E-R Anticor-
relation for Protein Surfaces. Protein misfolding avoidance is ac-
complished by the reduction of both translational error-induced
and -free misfolding (20) through the use of optimal synonymous
codons, which likely increases translational accuracy (13), and the
use ofamino acid residues at key positions, which increasesprotein
stability (20). It has been reported that optimal codons are pref-
erentially used at buried sites of proteins and that this preference
intensifies with rising expression level (22). Buried sites are also
known to be more important than surface sites in determining
protein folding stability (23). Thus, natural selection against mis-
folding is expected to act primarily on the buried residues in a
residues with top-ranked pmisfoldamong exposed and buried sites.
Buried sites are defined as those sites that are accessible by fewer
than five water molecules simultaneously (Materials and Methods).
Because the genome-wide median pmisfoldrank is six for WT yeast
protein sequences, we consider residues with pmisfoldrank ≤ 6 as
stabilizing sites and compare the fraction of stabilizing sites in
buried and surface regions of yeast proteins. Indeed, in >97%
of yeast proteins examined, the fraction of buried sites that are
stabilizing is greater than the fraction of surface sites that are sta-
bilizing (Fig. 1D). The enrichment of stabilizing sites in buried
regions predicts that the removal of stabilizing sites would weaken
the E-R anticorrelation in buried regions more than in surface
Spearman’s rank correlation (ρ) between the mRNA expression level of a gene and the mean amino acid substitution rate of the gene. We used all residues
(dashed line) and removed sites with pmisfoldrank = 1 (A), pmisfoldrank ≤ 6 (B), and pmisfoldrank ≤ 30 (C). To compare with the three specific removals (indicated
by arrows), we randomly removed the same numbers of sites from each gene and repeated the random removal 1,000 times (frequency distribution indicated
by open bars). The statistical significance in the difference of ρ between the specific removals and random removals is indicated above the horizontal solid
bar. (D) Fraction of stabilizing sites in buried regions is greater than the fraction on protein surfaces for most proteins. Each dot represents a gene. Numbers of
genes below and above the diagonal line are indicated as well as the P value of the null hypothesis that these two numbers are equal. (E) Spearman’s rank
correlation (ρ) between mRNA levels and amino acid substitution rates for surface and buried residues separately after sites with pmisfoldrank less than or
equal to certain cutoffs are removed.
The protein misfolding avoidance hypothesis cannot fully explain the E-R anticorrelation in yeast, especially for sites on protein surfaces. (A–C)
| www.pnas.org/cgi/doi/10.1073/pnas.1117408109Yang et al.
regions. This prediction is indeed correct (Fig. 1E). Thus, protein
misfolding avoidance is especially poor in explaining the E-R anti-
correlation for protein surfaces. However, surface residues are not
completely irrelevant to misfolding avoidance (24), which isevident
from Fig. 1E. Furthermore, a positive correlation exists between
protein abundance and the fraction of matching sites for protein
surfaces (ρ = 0.243, P < 10−18), although the corresponding cor-
relation for protein cores is much stronger (ρ = 0.415, P < 10−55).
Estimation of pmisfoldusing protein structure information is
expected to be more accurate than using protein sequence in-
formation (20, 25). However, the above analyses were based on
protein sequence information, because most yeast proteins do
not have structure information. Nevertheless, qualitatively simi-
lar results were obtained when only those proteins with structure
information were examined. For instance, in Fig. 1D, all 26
proteins with structure information are located below the di-
agonal line. In Fig. 1E, the remaining E-R anticorrelation after
the removal of buried residues with pmisfoldranks ≤ 30 (−0.12) is
much weaker than the remaining E-R anticorrelation after the
removal of surface residues with pmisfoldranks ≤ 30 (−0.27).
Protein Misinteraction Avoidance Could Constrain the Evolution of
Protein Surfaces. What might constrain the evolution of protein
surfaces in a protein concentration-dependent manner? Protein
misinteraction could be the answer. Protein misinteraction refers
to nonfunctional and typically nonspecific protein–protein inter-
actions that occur upon random encounters between protein
molecules. For two reasons, protein misinteraction is quite fre-
quent in a cell. First, many proteins coexist at any given time in
any cellular compartment, providing ample opportunities for
misinteraction. For example, ∼1,800 proteins are coexpressed
and colocalized to the yeast cytoplasm in standard laboratory
conditions (26, 27). Because an average protein has only a few
specific partners (28), the total concentration of nonspecific
partners of a protein is much greater than the concentration of its
specificpartners.Second, althoughfunctional andspecificprotein
interactions are usually stronger than misinteractions, the dif-
ference in binding energy is moderate (29, 30). Considering these
factors, Zhang et al. (30) recently estimated that ∼22% of protein
molecules that are not engaged in specific protein interactions are
bound with nonspecific partners in yeast. Similar estimates of 23–
28% were obtained for other model organisms, including the
nematode worm, fruit fly, and human (30).
Protein misinteraction can be deleterious to an organism, be-
cause it (i) potentially leads to a higher demand for protein syn-
and (iii) initiates nonphysiological and potentially damaging cel-
lular processes. The notion that misinteraction could lead to gains
of deleterious functions is exemplified by a mutant version of the
tumor suppressor p53 that misinteracts with vitamin D3 (VD3) re-
ceptor. As a result of this misinteraction, the mutant p53 enhances
VD3-induced transcription, compromises VD3-mediated re-
pression, and converts VD3 into a harmful antiapoptotic agent
overexpression observed in yeast is largely caused by increased
protein misinteraction (32). Theoretical modeling has repeatedly
shown that, because of its deleterious effect, misinteraction con-
strains the proteome size, affects optimal protein concentrations,
and shapes the functional interaction network (30, 33, 34).
Because protein misinteraction is generally abundant and del-
eteriousand involvesproteinsurface residues, wehypothesizethat
under stronger selective pressures than lowly expressed ones to
avoid misinteraction (Fig. 2), because a misinteraction-enhancing
mutation is more harmful when it occurs in a highly expressed
gene than in a lowly expressed gene because of the presence of a
greater number of misinteracting molecules from a highly ex-
pressed protein than from a lowly expressed protein (Fig. 2).
Consequently, highly expressed proteins are less sticky on surfaces
and more constrained in surface sequence evolution than lowly
expressed ones (Fig. 2). Hence, at least in principle, protein mis-
interaction avoidance can generate an E-R anticorrelation for
Although protein misinteraction may occasionally lead to
protein aggregation, they differ in several aspects. First, although
protein misinteraction usually occurs between correctly folded
molecules, protein aggregation more often happens to mis-
folded/unfolded proteins. Second, protein misinteraction often
(but not always) involves two different proteins, whereas protein
aggregation normally involves multiple molecules of the same
protein. Third, both protein misinteraction and aggregation can
interfere with normal protein–protein interaction, but only mis-
interaction can induce potentially deleterious cellular signals
that are passed on from the involved proteins.
Misinteraction Avoidance Generates an E-R Anticorrelation: Computer
Simulation. To show that protein misinteraction avoidance can
generate an E-R anticorrelation for protein surfaces, we con-
ducted a molecular-level evolutionary simulation using a 3D
protein lattice model (Fig. 3A). In this simulation, we designed
100 pairs of proteins with specific and functional interactions.
Each of these 200 proteins consists of 27 amino acid residues
that fold into a 3 × 3 × 3 lattice and maintains at least baseline
folding stability during evolution (Materials and Methods). Using
the information in a previous study (35), for each pair of the
specifically interacting proteins, we optimized their sequences
such that the specific interaction is significantly stronger than any
misinteraction. We randomly assigned expression levels to each
pair of specific interacting partners using a power law distribu-
tion, because cellular protein concentrations are known to follow
ance hypothesis. Functional interactions between proteins are shown with
lock and key matched pairs of jigsaws, whereas misinteractions are shown
with unmatched jigsaw pairs that are also boxed.
A schematic diagram explaining the protein misinteraction avoid-
Yang et al.PNAS
| Published online March 13, 2012
simulation (details in Materials and Methods). (B) The average contact energy of misinteractions involving a particular protein decreases with rising expression
level of the protein. (C) The proportion of surface residues that are hydrophobic decreases with the rise of the protein’s expression level. (D) The probability
that a protein molecule involved in misinteraction decreases with the expression level of the protein. (E) Highly expressed proteins have high concentrations
of misinteracting molecules. (F) The number of amino acid (AA) substitutions per surface residue in 100 generations of simulation declines with rising protein
expression level. (G) The number of amino acid substitutions per buried residue in 100 generations of simulation does not decline with rising protein ex-
pression level. In B–G, each dot represents one gene, and the averaged results from 100 simulation replications are presented. The red lines are estimated
using locally weighted scatterplot smoothing. B–E are based on the observations in the 20,000th generation of the simulation, whereas F and G are based on
the period from the 19,900th generation to the 20,000th generation of simulation.
A molecular-level evolutionary simulation shows that misinteraction avoidance can create an E-R anticorrelation. (A) The general scheme of the
| www.pnas.org/cgi/doi/10.1073/pnas.1117408109Yang et al.
this distribution (36). We then calculated the probability that
each protein is bound to any other protein in the cell. For each
binary interaction, we considered all 6 × 6 × 4 = 144 possible
orientations when calculating the interaction energy. For sim-
plicity, we did not allow simultaneous interactions of three or
more molecules, which are expected to be rarer than binary
interactions. The fitness of a cell is calculated by considering two
factors: (i) the reduction in the concentrations of functional
interactions because of misinteractions and (ii) the toxicity of
misinteractions (Materials and Methods).
We constituted a population of 100 cells that evolves at the
mutation rate of 0.0005 amino acid changes per residue per
generation. After 19,900 generations of evolution, mutation se-
lection balance is reached. We then evolved the population for
another 100 generations and estimated the substitution rate
during the last 100 generations by counting only fixed amino acid
mutations. We repeated the entire simulation 100 times with
fixed expression levels but variable protein sequences.
Selection against protein misinteraction should result in lower
stickiness (37) for more abundant proteins. Indeed, our simula-
tion shows that, as the expression level of a protein increases, the
average contact energy of its misinteractions decreases (i.e.,
more positive) (Fig. 3B), which was also observed in the recent
simulation by Heo et al. (34). Hydrophobic residues are more
likely than hydrophilic residues to mediate protein misinter-
action (30), because the contact energy is greater (i.e., more
negative) for hydrophobic interactions than hydrophilic inter-
actions (38). Consistent with this prediction, we observed a re-
duced fraction of hydrophobic residues on the entire protein
surface as the protein expression level increases (Fig. 3C). As
expected, the probability for a protein to engage in misinter-
action at any time decreases with rising protein expression level
(Fig. 3D). However, this decrease in probability is slower than
the rise in expression level (Fig. 3D). Consequently, the number
of molecules involved in misinteraction is still greater for more
abundant proteins (Fig. 3E). In direct support of our hypothesis,
highly expressed proteins show lower rates of amino acid sub-
stitution on the surface (Fig. 3F) but not in the core (Fig. 3G).
It is interesting to note that all of the above results still hold
qualitatively even when misinteractions only reduce the con-
centrations of functional interactions but are not toxic (Fig. S1).
The reason is that, when a highly expressed protein increases its
stickiness, the concentrations of many functional protein com-
plexes are reduced, because highly expressed proteins misinter-
act with many proteins. The same will not happen when a lowly
expressed protein increases its stickiness by the same degree,
because it misinteracts with only a small number of proteins.
Thus, selection against stickiness is stronger in highly expressed
proteins than in lowly expressed ones, generating an E-R anti-
correlation. However, the simulation shows that the E-R anti-
correlation created by misinteraction avoidance is much weaker
when misinteraction is nontoxic (Fig. S1).
Yeast Genomic Data Support the Misinteraction Avoidance Hypothesis.
With the above simulation showing the sufficiency of misinter-
action avoidance in generating an E-R anticorrelation on protein
hypothesis makes two key predictions. First, because of stronger
the probability for each molecule to engage in misinteraction
should decrease with its concentration (34). In other words, highly
expressed proteins should be less sticky than lowly expressed ones.
Second, because of the constraint imposed by misinteraction
avoidance, nonsticky residues on protein surfaces are prohibited
from changing to sticky residues, whereas no such constraints are
imposed on sticky surface residues. Because the pressure to avoid
misinteraction increases with protein abundance, we predict that
the substitution rate of surface nonsticky residues, relative to the
substitution rate of surface sticky residues, decreases with protein
Below, we provide evidence for the first prediction using in-
formation from protein sequences and protein misinteractions. As
aforementioned, the fraction of surface residues that are hydro-
phobic can be used as a proxy for protein stickiness. Consistent
with our prediction, this fraction decreases with rising protein
abundance (Fig. 4A). We also used quantitative measures of
amino acid hydrophobicity (39) and observed a negative correla-
tion between the mean hydrophobicity of surface residues of a
protein and the abundance of the protein (Fig. 4B). By contrast,
two proxies of protein stickiness remain significantly correlated
with protein abundance after we control the fraction of matching
sites (i.e., pmisfoldrank = 1) on protein surfaces (ρ = −0.105, P <
0.05 and ρ = −0.123, P < 0.03, respectively), suggesting that the
lower stickiness of abundant proteins is not explainable by protein
misfolding avoidance. Because different amino acids have differ-
ent biosynthetic costs, it has been shown that amino acid fre-
quencies vary among proteins of different expression levels (40).
Nonetheless, the above two proxies of protein stickiness remain
significantly negatively correlated with protein abundance even
after we control the amino acid synthetic costs under either fer-
mentative or respiratory conditions (Fig. 4 A and B legend). An-
other proxy for protein stickiness is the fraction of amino acid
residueslocatedin intrinsically unstructured or disordered regions
of a protein, because these regions tend to mediate protein mis-
interaction (32). Again, we found this proxy of stickiness to de-
crease with rising protein abundance (Fig. 4C). We also
confirmed that these patterns remain qualitatively unchanged
even when proteins of the same gene ontology (41) functional
categories (e.g., enzymes or ligands/receptors) were compared
(Fig. S3). Thus, three lines of evidence from protein sequences
support the first prediction of our hypothesis.
Protein–protein interactions have been probed experimentally
by several different methods. Using the information in an earlier
study (30), we consider interactions detected by yeast two-hybrid
(Y2H) assays to include both functional interactions and mis-
interactions, because the interacting proteins are highly overex-
pressed in this assay (42). We found that the number of Y2H
interactions that a protein has is negatively correlated with its
native expression level (Fig. 4D). We consider interactions de-
tected by affinity-based methods as largely functional and specific
interactions, because in this method, proteins are expressed at
their natural levels in their natural subcellular locations (43).
Consistent with a recent report (34), the interaction number from
affinity-based methods shows a strong positive correlation with
protein abundance (Fig. 4E). A weaker positive correlation was
found when we guarded against potential false positives in affinity
data by requiring each functional interaction to have been iden-
tified at least three times (Fig. S4A). Interactions detected by
protein fragment complementation assays also reflect functional
interactions (44), and they similarly show a positive correlation
between the abundanceofa protein and itsnumber ofinteractions
(Fig. S5A). We then infer the number of misinteractions that a
protein has by the number of Y2H interactions that are not found
by affinity-based methods (or protein fragment complementation
assays). As predicted by our hypothesis, the number of inferred
misinteractions decreases with protein abundance (Fig. 4F and
Figs. S4B and S5B). Note that the inferred number of misinter-
actions can be compared among different proteins, because all
proteins are overexpressed to a similar level in Y2H that is even
higher than the expression of the most highly expressed gene in
yeast. This overexpression also ensures that false positives and
false negatives in high-throughput Y2H experiments do not dif-
ferentially affect proteins of different natural concentrations. In
affinity-based methods and protein fragment complementation
Yang et al.PNAS
| Published online March 13, 2012
than low-concentration proteins. However, our conclusion is not
dependent on the positive correlations observed in Fig. 4E (Figs.
S4A and S5A). That is, even when the numbers of functional
interactions are comparable among proteins of different concen-
trations, the Y2H data still suggest that misinteractions are fewer
for proteins of higher concentrations. Thus, the first prediction of
the misinteraction avoidance hypothesis is also supported by
protein misinteraction data.
To test the second prediction of our hypothesis, we calculated
the ratio between the substitution rate of surface hydrophilic
(i.e., nonsticky) residues and the substitution rate of surface
hydrophobic (i.e., sticky) residues in S. cerevisiae proteins using
the alignment of orthologous proteins from six post-WGD spe-
cies. Because of the large sampling error of the ratio calculated
from individual proteins, we calculated this ratio for groups of
proteins with similar levels of abundance. To increase sensitivity,
we focused on strongly hydrophobic (hydrophobicity score > 2)
and strongly hydrophilic (hydrophobicity score < −2) amino
acids (39). As predicted, this ratio decreases significantly with
rising protein abundance (Fig. 5A). As a control, we also ex-
amined the same substitution rate ratio using protein cores, but
we observed no significant relationship between the ratio and
protein abundance (Fig. 5B).
Misinteraction Avoidance Explains the Protein Surface E-R Anticorrelation
Better than Misfolding Avoidance. To assess the relative importance
of misinteraction avoidance and misfolding avoidance in gener-
ating the E-R anticorrelation for protein surfaces, we separately
removed sites under each constraint. Specifically, we progres-
sively removed surface sites constrained for misinteraction
avoidance from those sites with low hydrophobicity to those sites
with high hydrophobicity. When two sites have the same hydro-
phobicity score, we first removed the one with the larger solvent
accessibility (i.e., more exposed). As a comparison, in each pro-
tein, we separately removed the same number of surface sites
constrained most for misfolding avoidance according to the
pmisfoldrank. We found that removing sites by hydrophobicity is
more effective than removing sites by the pmisfoldrank in weak-
ening the E-R anticorrelation on protein surfaces (Fig. 6A). To
evaluate the robustness of this result, we bootstrapped all yeast
proteins 1,000 times and found that the above result is true in a
vast majority of bootstrap samples (Fig. 6B). The pmisfoldrank at a
specific site explicitly measures the misfolding probability of the
WT protein relative to the probability of the 60 possible codon
replacements at the site (20), whereas hydrophobicity is only one
specific and not site-specific; therefore, the pmisfoldrank likely
measures the misfolding probability more accurately than hy-
decreases with rising protein abundance. The correlation becomes ρ = −0.134 (P < 10−6) and −0.098 (P < 10−3) after control for amino acid synthetic costs
under fermentative and respiratory conditions, respectively. (B) The mean hydrophobicity on the surface decreases with rising protein abundance. Note that
a more positive hydrophobicity score indicates higher hydrophobicity. The correlation becomes ρ = −0.188 (P < 10−11) and −0.156 (P < 10−8), respectively, after
control for amino acid synthetic costs under fermentative and respiratory conditions, respectively. (C) The fraction of residues within disordered regions
decreases with rising protein abundance. (D) The number of interaction partners of a protein determined by Y2H assays, representing both specific and
nonspecific partners, decreases with rising protein abundance. (E) The number of interaction partners of a protein determined by affinity-based assays,
representing specific partners, increases with rising protein abundance. (F) The number of Y2H partners that are not affinity partners, representing non-
specific partners only, decreases with rising protein abundance. Genes are grouped into 10 bins of equal size based on expression levels, and each bin contains
376 genes. The error bar represents 1 SE. The protein abundance data are from ref. 27. All correlation coefficients and P values are determined from the
original data rather than the binned data.
Yeast proteins with higher abundance (number of molecules per cell) are less sticky. (A) The fraction of surface residues that are hydrophobic
| www.pnas.org/cgi/doi/10.1073/pnas.1117408109Yang et al.
drophobicity measures the misinteraction probability. Thus, the
result in Fig. 6 is expected to be conservative.
In this work, we showed that the protein misfolding avoidance
hypothesis cannot fully explain the E-R anticorrelation, especially
for protein surface residues. Instead, we propose and show that
protein misinteraction avoidance explains the E-R anticorrelation
for protein surfaces better than misfolding avoidance. The two
hypotheses have several similarities that are worth commenting
on. First, the deleterious effects from protein misfolding and
misinteraction are both protein concentration-dependent, a req-
uisite for any explanation of the E-R anticorrelation. Second,
protein misfolding and misinteraction both reduce the amount of
proteins available for performing physiological functions. Third,
both misfolding and misinteraction can lead to protein aggrega-
tion, although the causes of the aggregation may differ. Fourth,
both hypotheses can explain, at least in part, the phenomenon of
biased synonymous codon use. It has been shown that misfolding
avoidance is partially achieved by a reduction in mistranslation
through the use of optimal codons that have high translational
accuracies (13, 20, 22). In principle, the pressure to minimize
misinteraction can also result in a reduction in mistranslation
through the use of accurately translated codons. In this work, we
have chosen to focus on protein sequence evolution only, and we
will analyze the impact of misinteraction avoidance on synony-
mous codon use in a separate study.
Apart from the four similarities, the two hypotheses have three
major differences. First, selection against misfolding acts pri-
marily, albeit not exclusively, on the buried residues of a protein,
which are most important for protein stability, whereas selection
against misinteraction acts on protein surfaces, which determine
protein–protein interaction. Hence, they complement each other
in generating the E-R anticorrelation for entire protein mole-
cules. Second, protein misinteraction can generate a gain of
function effect, inducing erroneous cellular processes, which has
been documented in some mutants of p53 (31, 45). By contrast,
protein misfolding does not have such effects. Third, although
misfolding affects only the misfolded protein itself, misinter-
action affects multiple proteins. Hence, when a highly abundant
protein is sticky, it could form misinteractions with many other
proteins and affect multiple cellular processes. Thus, although
the deleterious effect of misfolding is localized and predictable,
the effect of misinteraction can be global and unpredictable.
In addition to the evidence documented here for the protein
misinteraction avoidance hypothesis of E-Ranticorrelation, there
are additional observations in the literature that are consistent
with this hypothesis. First, Plata et al. (46) found a positive cor-
relation between protein abundance and the fraction of charged
(i.e., hydrophilic) residues on solvent accessible sites in Escher-
ichia coli, which is highly consistent with our yeast observation in
Fig. 4A, suggesting the applicability of the protein misinteraction
avoidance hypothesis in prokaryotes as well. Second, it was
reported that the difference in sequence conservation between
surface residues involved in functional protein interactions (i.e.,
functional interfaces) and other surface residues decreases with
rising expression level (47). This observation is likely because of
an increasing constraint on these nonfunctional interfaces with
rising expression level caused by misinteraction avoidance com-
pared with the constraint on functional interfaces. Third, as
mentioned, Zhang et al. (30) and Heo et al. (34) studied the
biophysical properties of protein misinteraction. Their results,
from both simulation and empirical studies, strongly support
We showed that removing surface hydrophilic residues, which
are likely constrained by misinteraction avoidance, weakens the
E-R anticorrelation for protein surfaces (Fig. 6A). Nevertheless,
even when 50% of surface residues are removed, the E-R anti-
hydrophilic residues and the substitution rate of surface hydrophobic residues decreases with rising protein abundance. (B) The ratio between the substitution
rate of buried hydrophilic residues and the substitution rate of buried hydrophobic residues does not decrease with rising protein abundance. Each dot
represents ∼4,700 aa from ∼40 proteins with similar abundances (number of protein molecules per cells). The protein abundance data were from an earlier
Misinteraction avoidance constrains amino acid substitutions on protein surfaces but not cores. (A) The ratio between the substitution rate of surface
surfaces after progressive removals of surface hydrophilic residues (step size = 5%). For comparison, the same number of surface sites is removed from each
protein based on the pmisfoldrank. (B) Fraction of 1,000 bootstrap replications in which removing sites constrained by misinteraction avoidance is more ef-
fective than removing the same number of sites constrained by misfolding avoidance in weakening the E-R anticorrelation on protein surfaces.
Misinteraction avoidance explains the E-R anticorrelation for protein surfaces better than misfolding avoidance. (A) E-R anticorrelation for protein
Yang et al. PNAS
| Published online March 13, 2012
correlation is still strong (Fig. 6A). This observation has at least
two explanations. First, although hydrophobicity affects the
stickiness of a residue, it is by no means the sole determinant.
Stickiness is likely influenced by additional factors (e.g., disorder
in structure). Thus, removing hydrophilic sites may be rather in-
effective in eliminating residues constrained by misinteraction
avoidance. Second, it is possible that misfolding avoidance and
misinteraction avoidance are but two of potentially many mech-
anisms underlying the E-R anticorrelation. For example, Gout
et al. (48) and Cherry (49) recently proposed a hypothesis of se-
lection for protein function that, in principle, can also explain the
E-R anticorrelation, although it has yet to be empirically verified.
Regardless of whether their hypothesis is correct, the E-R anti-
correlation is the result of at least two factors: misfolding avoid-
ance and misinteraction avoidance. In the future, it would be
interesting to identify sites that would most effectively weaken the
E-Ranticorrelationwhendeleted andthenstudythe propertiesof
these sites to find the potential causes of the E-R anticorrelation.
Although our computer simulation focused on the role of
misinteractionavoidance inconstraining theevolution ofproteins
with presumably unchanged functions, the same constraint can
alsohinderneofunctionalization inprotein evolution; therefore,a
mutation conferring a new function may be unacceptable, be-
cause it compromises misinteraction avoidance (50). It is possible
that the E-R anticorrelation reflects reductions of both neutral
substitution rates and advantageous substitution rates in highly
expressed proteins. Our misinteraction avoidance hypothesis may
also be extended to include misinteractions between proteins and
nonprotein molecules such as DNA and RNA. Future work is
needed to evaluate the impact of such events on protein evolu-
tion. Because misinteraction may result in a gain of function, it
could occasionally be beneficial under certain conditions. Thus,
new functional protein interactions could originate from initial
misinteractions through mutation and selection (29). Because the
smaller the effective population size, the weaker the selection
against protein stickiness, one may predict that protein inter-
with smaller populations, which has been recently confirmed (51).
Misinteraction, an inevitable phenomenon in any complex sys-
tem, may, thus, both constrain and channel the evolution of
Materials and Methods
Yeast Genomic Data and Comparative Analysis. The cDNA and protein
sequences of S. cerevisiae were downloaded from the Saccharomyces Ge-
nome Database (52). Protein sequences of five other post-WGD fungi (S.
paradoxus, S. mikatae, S. bayanus, Candida glabrata, and S. castellii) and
their orthologous relationships with S. cerevisiae proteins were extracted
from the Fungal Orthogroups Repository (53). Only those genes that have
one to one orthologs in each of the six species were used. Orthologous
protein sequences from the six species were aligned using ClustalW (54), and
the substitution rate at each amino acid position of an alignment was esti-
mated by GAMMA (55). We used microarray-based measurements of S.
cerevisiae mRNA expression levels (56) and immunodetection-based meas-
urements of protein expression levels (27). Amino acid hydrophobicity scores
were previously published (39). Qualitatively, amino acids A, M, C, F, L, V,
and I were considered hydrophobic because of their positive hydrophobicity
scores (39), and the other 13 amino acids were considered hydrophilic be-
cause of their negative hydrophobicity scores. Protein–protein interaction
data of S. cerevisiae were downloaded from BioGRID v3.1.82 (57).
Estimation of pmisfold. We used a previously derived equation (20) to calculate
pmisfold, the probability of protein misfolding of a mutant gene relative to
that of the WT gene. Here, each examined mutant differs from the WT gene
by one codon replacement, and all 60 possible codon replacements are ex-
amined at each codon position of every gene. The calculation of pmisfold
considers both translational error-free and -induced misfolding and involves
the use of a computationally predicted change of protein stability (ΔΔG) due
to a codon replacement (25) and the probability of translational error (20).
Protein Structures. To determine whether a residue lies on the surface of a
protein molecule, we BLASTed yeast proteins against all protein sequences
from the Protein Data Bank (PDB) (58) using an E-value cutoff of 10−6. A yeast
protein was considered to have sufficient matches in PDB only when, in total,
over 50% of its residues were aligned to the significant hits. For each yeast
protein with sufficient PDB matches, the matched PDB entries were analyzed
by the program DSSP to obtain a solvent accessibility score for each residue
(59). Because sequence similarity usually coincides with structural similarity,
this score was used as the solvent accessibility score for the aligned yeast
protein residue. Sometimes, a multidomain yeast protein was matched to
multiple PDB entries. Because the conformations of different domains in the
same protein are relatively independent from one another and linkers be-
tween domains rarely cover surfaces, we accepted accessibility scores from
different PDB entries for different parts of a protein based on the best match
of each domain. Such a strategy was supported by the observation that use of
the best PDB hit or second best hit for solvent accessibility determination
yielded similar results: 84.3% of residues were identically categorized into
surface and buried residues. Amino acids with solvent accessibility scores
larger than 50, meaning that the residue is simultaneously accessible by at
least five water molecules (59), were considered as surface residues; other-
wise, they were considered buried. Potential errors in solvent accessibility
determination make our findings of differences between surface and buried
We used RONN to estimate the probability that a residue is natively dis-
ordered for every residue of every yeast protein, and those residues with the
probability > 0.5 were considered as disordered residues (60).
Computer Simulation of the Interactome. We built a molecular-level bio-
physical model with baseline selective constraints on protein folding to in-
evolution. First, 200 protein sequences, each with a fixed length of 27 aa,
were generated randomly. Given the sequence of a protein, we calculated its
folding energy for each possible structure in a 3 × 3 × 3 lattice by the sum of
the contact energies of spatially adjacent residues (61). A folding Z score for
structure i of a protein sequence was defined as (Eq. 1)
where Eiis the folding energy of structure i and μEand σEare the mean and
SD of the folding energies of all possible structures of the protein, re-
spectively. For each protein sequence, we randomly chose a structure with
Fi< −7 as its native structure, which ensured fast and stable folding to the
native structure (35). The native structure of a protein was fixed during the
simulation of evolution. Second, we need to define the interaction energies
for 40,000 possible pairs of folded protein cubes. To simplify the problem,
we considered only interactions mediated by the whole surface on one side
of a cube (that is, by nine intermolecule pairs of amino acids). For any two
cubes and an interaction orientation, the contact energies of the nine
intermolecule pairs of interacting amino acids were summed up as the in-
teraction energy between the two proteins for the specific orientation.
Third, we randomly divided the 200 proteins into 100 pairs of specific in-
teraction partners. We optimized the specific interaction for each protein,
and therefore, its binding Z score, defined as (Eq. 2)
was as small as possible (35). Here, protein i and protein j are specific in-
teraction partners with a specific orientation, with the interaction energy
being Eij. Additionally, μEiand σEiare the mean and SD of interactionenergies
of all other interactions involving protein i in any possible orientation, re-
spectively (including with thespecific partner in nonspecific orientations).The
−6, and Bij+ Bji< −14 (35). All interactions except those interactions between
specific partners in specific orientations are considered as misinteractions.
The genome of the progenitor cell in the in silico evolution consisted of
these 200 genes. We randomly generated 100 expression levels that follow a
power law distribution (36) and assigned them to each pair of specific
interacting partners. In other words, specific interaction partners had exactly
the same expression levels, whereas nonspecific interaction partners could
have different expression levels. We required all of the expression levels to
be integers no less than 1 μM, and the largest expression should be at least
50 μM. To have a gradient of expression levels among genes, we required
that the expression difference between two adjacent genes when ranked by
expression level should be less than 5 μM.
| www.pnas.org/cgi/doi/10.1073/pnas.1117408109Yang et al.
With the expression levels and interaction energies determined and
thermodynamic equilibrium assumed, we estimated the probability that
protein i is in a complex with protein j by solving the following quadratic
system (Eq. 3):
∀i and j;∃CiCj
∀i;∃Di¼ Ciþ ∑
Here, Ciis the concentration of free molecules of protein i (unbound to any
molecule), Cij is the concentration of the protein complex composed of
a protein i and a protein j, Diis the total concentration of protein i in the cell
(i.e., the expression level), R is the Boltzmann constant of 1.986 cal/mol per
K, T is the absolute temperature, ∀ means for any, and ∃ means there exists.
In Eq. 3, Eijis the overall binding energy between proteins i and j in all 144
orientations, and is calculated by
Eij¼ −RT ln
where Eijkis the binding energy between i and j in the kth orientation,
calculated from the contact energy between the nine amino acid pairs of i
and j that are in contact.
There are 20,300 equations with 20,300 variables to be solved in this
quadratic system. We used an iterative method to approach the solution of
this quadratic system. Specifically, we started with an arbitrary set of Civalues
and calculated Cijvalues based on the interaction energies using Eq. 3. We
then adjusted Cito be CiDi=ðCiþ ∑200
j¼1CijÞ, where Diis the assigned expres-
sion level of the protein i. We repeated this process many times until the
absolute value of the fractional adjustment in the sum of Cibetween two
consecutive iterations was smaller than 10−5. We tried multiple different sets
of initial values of Ciand found no difference in final results.
Wedefinedthefitnessofacellbyfðs;mÞ ¼ se−am,wheresistheproductof
the fractions of molecules engaged in specific interactions across 100 specific
complexes, m is the total concentration (in micromolar) of misinteraction
complexes, and a is a constant that determines the toxicity of an average
misinteraction. Without loss of generality, we assigned a = 1. The above fit-
ness function ensures that the relative fitness cost of each additional mis-
interaction is the same. We also repeated the simulation using a = 0 to
examine the outcome when misinteraction is not toxic (Fig. S1).
identical cells. Random mutations were introduced at the rate of 0.0005 per
residue per generation, with the requirement that the folding Z score of any
protein must be lower than −2. Fitness was calculated for each cell, and the
next generation of cells was generated by considering each cell’s fitness and
genetic drift. This process of mutation, selection, and drift was repeated
19,900 generations to reach theequilibrium. Wethen evolved thepopulation
for 100 additional generations and counted the number of fixed amino acid
changes from the 19,900th to the 20,000th generation. We repeated the
wholesimulation 100timeswith different protein sequences butthesame set
of expression levels.
ACKNOWLEDGMENTS. We thank Meg Bakewell, Chungoo Park, Wenfeng
Qian, the editor, and three anonymous reviewers for constructive comments.
This work was supported by a research grant from the US National Institutes
of Health (to J.Z.).
1. Hurst LD, Smith NG (1999) Do essential genes evolve slowly? Curr Biol 9:747–750.
2. Pál C, Papp B, Hurst LD (2001) Highly expressed genes in yeast evolve slowly. Genetics
3. Zhang J, He X (2005) Significant impact of protein dispensability on the instantaneous
rate of protein evolution. Mol Biol Evol 22:1147–1155.
4. Wall DP, et al. (2005) Functional genomic analysis of the rates of protein evolution.
Proc Natl Acad Sci USA 102:5483–5488.
5. Liao BY, Scott NM, Zhang J (2006) Impacts of gene essentiality, expression pattern,
and gene compactness on the evolutionary rate of mammalian proteins. Mol Biol Evol
6. Zhang L, Li WH (2004) Mammalian housekeeping genes evolve more slowly than
tissue-specific genes. Mol Biol Evol 21:236–239.
7. Drummond DA, Raval A, Wilke CO (2006) A single determinant dominates the rate of
yeast protein evolution. Mol Biol Evol 23:327–337.
8. Hirsh AE, Fraser HB (2001) Protein dispensability and rate of evolution. Nature 411:
9. Fraser HB, Hirsh AE, Steinmetz LM, Scharfe C, Feldman MW (2002) Evolutionary rate in
the protein interaction network. Science 296:750–752.
10. Jordan IK, Wolf YI, Koonin EV (2003) No simple dependence between protein
evolution rate and the number of protein-protein interactions: Only the most prolific
interactors tend to evolve slowly. BMC Evol Biol 3:1.
11. Wolf MY, Wolf YI, Koonin EV (2008) Comparable contributions of structural-
functional constraints and expression level to the rate of protein sequence evolution.
Biol Direct 3:40.
12. Wolf YI, Carmel L, Koonin EV (2006) Unifying measures of gene function and
evolution. Proc Biol Sci 273:1507–1515.
13. Drummond DA, Wilke CO (2008) Mistranslation-induced protein misfolding as
a dominant constraint on coding-sequence evolution. Cell 134:341–352.
14. Subramanian S, Kumar S (2004) Gene expression intensity shapes evolutionary rates
of the proteins encoded by the vertebrate genome. Genetics 168:373–381.
15. Rocha EP, Danchin A (2004) An analysis of determinants of amino acids substitution
rates in bacterial proteins. Mol Biol Evol 21:108–116.
16. Wang Z, Zhang J (2009) Why is the correlation between gene importance and gene
evolutionary rate so weak? PLoS Genet 5:e1000329.
17. Liao BY, Weng MP, Zhang J (2010) Impact of extracellularity on the evolutionary rate
of mammalian proteins. Genome Biol Evol 2:39–43.
18. Geiler-Samerotte KA, et al. (2011) Misfolded proteins impose a dosage-dependent
fitness cost and trigger a cytosolic unfolded protein response in yeast. Proc Natl Acad
Sci USA 108:680–685.
19. Drummond DA, Bloom JD, Adami C, Wilke CO, Arnold FH (2005) Why highly
expressed proteins evolve slowly. Proc Natl Acad Sci USA 102:14338–14343.
20. Yang JR, Zhuang SM, Zhang J (2010) Impact of translational error-induced and error-
free misfolding on the rate of protein evolution. Mol Syst Biol 6:421.
21. Wolfe KH, Shields DC (1997) Molecular evidence for an ancient duplication of the
entire yeast genome. Nature 387:708–713.
22. Zhou T, Weems M, Wilke CO (2009) Translationally optimal codons associate with
structurally sensitive sites in proteins. Mol Biol Evol 26:1571–1580.
23. Jaramillo A, Wernisch L, Héry S, Wodak SJ (2002) Folding free energy function selects
native-like protein sequences in the core but not on the surface. Proc Natl Acad Sci
24. Berezovsky IN, Zeldovich KB, Shakhnovich EI (2007) Positive and negative design in
stability and thermal adaptation of natural proteins. PLoS Comput Biol 3:e52.
25. Capriotti E, Fariselli P, Casadio R (2005) I-Mutant2.0: Predicting stability changes upon
mutation from the protein sequence or structure. Nucleic Acids Res 33:W306–W310.
26. Huh WK, et al. (2003) Global analysis of protein localization in budding yeast. Nature
27. Ghaemmaghami S, et al. (2003) Global analysis of protein expression in yeast. Nature
28. Qian W, He X, Chan E, Xu H, Zhang J (2011) Measuring the evolutionary rate of
protein-protein interaction. Proc Natl Acad Sci USA 108:8725–8730.
29. Kuriyan J, Eisenberg D (2007) The origin of protein interactions and allostery in
colocalization. Nature 450:983–990.
30. Zhang J, Maslov S, Shakhnovich EI (2008) Constraints imposed by non-functional
protein-protein interactions on gene expression and proteome size. Mol Syst Biol 4:
31. Stambolsky P, et al. (2010) Modulation of the vitamin D3 response by cancer-
associated mutant p53. Cancer Cell 17:273–285.
32. Vavouri T, Semple JI, Garcia-Verdugo R, Lehner B (2009) Intrinsic protein disorder and
interaction promiscuity are widely associated with dosage sensitivity. Cell 138:
33. Johnson ME, Hummer G (2011) Nonspecific binding limits the number of proteins in
a cell and shapes their interaction networks. Proc Natl Acad Sci USA 108:603–608.
34. Heo M, Maslov S, Shakhnovich E (2011) Topology of protein interaction network
shapes protein abundances and strengths of their functional and nonspecific
interactions. Proc Natl Acad Sci USA 108:4258–4263.
35. Deeds EJ, Ashenberg O, Gerardin J, Shakhnovich EI (2007) Robust protein protein
interactions in crowded cellular environments. Proc Natl Acad Sci USA 104:
36. Ueda HR, et al. (2004) Universality and flexibility in gene expression from bacteria to
human. Proc Natl Acad Sci USA 101:3765–3769.
37. Deeds EJ, Ashenberg O, Shakhnovich EI (2006) A simple physical model for scaling in
protein-protein interaction networks. Proc Natl Acad Sci USA 103:311–316.
38. Miyazawa S, Jernigan R (1985) Estimation of effective interresidue contact energies
from protein crystal structures: Quasi-chemical approximation. Macromolecules 18:
39. Kyte J, Doolittle RF (1982) A simple method for displaying the hydropathic character
of a protein. J Mol Biol 157:105–132.
40. Akashi H, Gojobori T (2002) Metabolic efficiency and amino acid composition in the
proteomes of Escherichia coli and Bacillus subtilis. Proc Natl Acad Sci USA 99:
41. Ashburner M, et al. (2000) Gene ontology: Tool for the unification of biology. Nat
42. Fields S, Song O (1989) A novel genetic system to detect protein-protein interactions.
43. Gavin AC, et al. (2002) Functional organization of the yeast proteome by systematic
analysis of protein complexes. Nature 415:141–147.
44. Tarassov K, et al. (2008) An in vivo map of the yeast protein interactome. Science 320:
45. Oren M, Rotter V (2010) Mutant p53 gain-of-function in cancer. Cold Spring Harb
Perspect Biol 2:a001107.
Yang et al.PNAS
| Published online March 13, 2012
46. Plata G, Gottesman ME, Vitkup D (2010) The rate of the molecular clock and the cost Download full-text
of gratuitous protein synthesis. Genome Biol 11:R98.
47. Eames M, Kortemme T (2007) Structural mapping of protein interactions reveals
differences in evolutionary pressures correlated to mRNA level and protein
abundance. Structure 15:1442–1451.
48. Gout JF, Kahn D, Duret L (2010) The relationship among gene expression, the
evolution of gene dosage, and the rate of protein evolution. PLoS Genet 6:e1000944.
49. Cherry JL (2010) Expression level, evolutionary rate, and the cost of expression.
Genome Biol Evol 2:757–769.
50. Liberles DA, Tisdell MD, Grahnen JA (2011) Binding constraints on the evolution of
enzymes and signalling proteins: The important role of negative pleiotropy. Proc Biol
51. Fernández A, Lynch M (2011) Non-adaptive origins of interactome complexity. Nature
52. Engel SR, et al. (2010) Saccharomyces Genome Database provides mutant phenotype
data. Nucleic Acids Res 38:D433–D436.
53. Wapinski I, Pfeffer A, Friedman N, Regev A (2007) Natural history and evolutionary
principles of gene duplication in fungi. Nature 449:54–61.
54. Larkin MA, et al. (2007) Clustal W and Clustal X version 2.0. Bioinformatics 23:
55. Gu X, Zhang J (1997) A simple method for estimating the parameter of substitution
rate variation among sites. Mol Biol Evol 14:1106–1113.
56. Holstege FC, et al. (1998) Dissecting the regulatory circuitry of a eukaryotic genome.
57. Stark C, et al. (2011) The BioGRID Interaction Database: 2011 update. Nucleic Acids
58. Berman HM, et al. (2000) The Protein Data Bank. Nucleic Acids Res 28:235–242.
59. Kabsch W, Sander C (1983) Dictionary of protein secondary structure: Pattern
recognition of hydrogen-bonded and geometrical features. Biopolymers 22:
60. Yang ZR, Thomson R, McNeil P, Esnouf RM (2005) RONN: The bio-basis function neural
network technique applied to the detection of natively disordered regions in
proteins. Bioinformatics 21:3369–3376.
61. Mirny LA, Shakhnovich EI (1996) How to derive a protein folding potential? A new
approach to an old problem. J Mol Biol 264:1164–1179.
| www.pnas.org/cgi/doi/10.1073/pnas.1117408109Yang et al.