Detecting Compensatory Covariation Signals in Protein Evolution Using Reconstructed Ancestral ...

15 Pages·2002·0.71 MB·English

B
doi:10.1016/S0022-2836(02)00239-5availableonlineathttp://www.idealibrary.comon w J.Mol.Biol.(2002)319,729–743
Detecting Compensatory Covariation Signals in
Protein Evolution Using Reconstructed
Ancestral Sequences
K. Fukami-Kobayashi1, D. R. Schreiber2 and S. A. Benner2,3*
1Center forInformation Biology When protein sequences divergently evolve under functional constraints,
and DNA Data Bank of Japan some individual amino acid replacements that reverse the charge (e.g.
National Institute of Genetics Lys to Asp) may be compensated by a replacement at a second position
Mishima 411-8540, Japan that reverses the charge in the opposite direction (e.g. Glu to Arg). When
these side-chains are near in space (proximal), such double replacements
2Departments of Chemistry
might be driven by natural selection, if either is selectively disadvanta-
and Anatomy and Cell Biology
geous, but both together restore fully the ability of the protein to contri-
andthe NASA Astrobiology
bute to fitness (are together “neutral”). Accordingly, many have sought
Institute, Universityof Florida
to identify pairs of positions in a protein sequence that suffer compensa-
Gainesville, FL, USA
tory replacements, often as a way to identify positions near in space in
3Foundation for Scientific the folded structure. A “charge compensatory signal” might manifest
Inquiry, P.O.Box 13174 itself in two ways. First, proximal charge compensatory replacements
Gainesvilla, FL 32604, USA mayoccur morefrequentlythanpredictedfromtheproductoftheproba-
bilities of individual positions suffering charge reversing replacements
independently. Conversely, charge compensatory pairs of changes may
be observed to occur more frequently in proximal pairs of sites than in
the average pair. Normally, charge compensatory covariation is detected
by comparing the sequences of extant proteins at the “leaves” of phylo-
genetic trees. We show here that the charge compensatory signal is more
evident when it is sought by examining individual branches in the tree
between reconstructed ancestral sequences at nodes in the tree. Here, we
find that the signal is especially strong when the positions pairs are in a
single secondary structural unit (e.g. a helix or b strand) that brings the
side-chains suffering charge compensatory covariation near in space, and
may be useful in secondary structure prediction. Also, “node–node” and
“node–leaf” compensatory covariation may be useful to identify the
better of two equally parsimonious trees, in a way that is independent of
the mathematical formalism used to construct the tree itself. Further,
compensatory covariation may provide a signal that indicates whether
an episode of sequence evolution contains more or less divergence in
functional behavior. Compensatory covariation analysis on reconstructed
evolutionary trees may become a valuable tool to analyze genome
sequences, and use these analyses to extract biomedically useful infor-
mationfromproteomedatabases.
q2002ElsevierScienceLtd.Allrightsreserved
Keywords: functional genomics;molecularevolution; structural biology;
*Correspondingauthor compensatory covariation;mutation; natural selection
Introduction
The evolution of protein sequences is nearly
always described using one of several stochastic
models for the accumulation of amino acid
Abbreviationsused:ASA,accessiblesurfacearea;
replacements.1 These are captured in algorithms
PAM,pointacceptedmutations;PDB,ProteinDataBank.
known by widely recognized names (e.g. the
E-mailaddressofthecorrespondingauthor:
[email protected]fl.edu Needleman–Wunsch,2 Smith–Waterman,3 and
0022-2836/02/$-seefrontmatter q2002ElsevierScienceLtd.Allrightsreserved
730 DetectingCompensatoryCovariationSignals
Felsenstein maximum likelihood4 tools). These replacement set within the context of a folded
tools have become more sophisticated in recent structure. Therefore, it has proven to be useful, in
years as mathematicians have “inched towards particular, for predicting the three-dimensional
reality”4 in their mathematical modelling well structureof proteinfolds.1
supported by a rich background in statistics, Position pairs distant in the sequence but near
theorems,and proof. space in the three-dimensional fold might also
Nevertheless, patterns of replacement predicted be expected to suffer replacement in a correlated
by these mathematical models remain quite dif- fashion.12,13 Many classes of these can be
ferent from the patterns that are actually observed envisioned.Forexample,a“big-for-small”replace-
in proteins diverging under functional con- ment at position i might be compensated by a
straints.1,5 The reason for these differences is well coincident “small-for-big” replacement at position
understood. Briefly, simple stochastic models treat j, to conserve overall size in the packed core of the
proteins as if they were linear strings of letters. In fold, and therefore conserve a functional behavior
reality, proteins have three-dimensional structures related to packing (the stability of the fold).
that support behaviors that areimportant for them Alternatively, a “positive-for-negative” charge
to contribute to the fitness of the host (“function”). replacement at position i might be compensated
These behaviours arenot a linear sum of the beha- by a “negative-for-positive” charge replacement at
viors of their parts. Amino acid replacement is position j to conserve overall charge, and therefore
therefore constrained in a way unanticipated for a conserveafunctionalbehaviorrelatedtonetcharge.
linear string of letters. Behindthisexpectationstandsamodelbasedon
The differences between mathematically con- theneutraltheoryofevolution.14Underthismodel,
venientmodelsandtherealityoforganicchemistry aminoacidreplacementsthatdramaticallyalterthe
need not be paralyzing, however. First-order sto- physical property of the side-chain (e.g. its size or
chastictreatmentsofproteinsequencescanprovide charge) will disrupt the performance of a protein
“null” hypotheses, statements about how proteins already optimized to contribute to the fitness of
would behave if they were formless, functionless the host organism. The fitness value of the protein
strings of letters. The difference between how pro- can be restored only by a second change that
teins actually divergently evolve and how first- compensates for the first alteration in physical
order treatments model their divergent evolution, properties. In the language of neutral theory, we
thereforecontainsasignalaboutfoldandfunction.1 would say that the first replacement was selec-
Analyses of this signal have been remarkably tively disadvantageous, the second was positively
productive. They provide practical tools for pre- selected (in the context of the first), and both
dicting the folded conformation of proteins from together lead to aresultthat is neutral.
sequences,1,6 and many useful approaches for Analyses of compensatory replacement have
extracting functional information from genomic found practical application. For example, a pair of
sequence data.7–9 Accordingly, one goal of con- compensatorychangesintheproteinkinasefamily
temporary computational biology is to extend the underlay the successful prediction of the anti-
concepts and tools needed to extract signals parallel sheet in the first kinase domain,15 contra-
concerning structure and function from features dicting a prediction of a parallel sheet based on
of divergent evolution that do not meet the motif analysis.16 This example represents the first
expectations ofsimple stochastic models. example where compensatory covariation analysis
Perhaps the most serious approximation made was a key to a bona fide prediction of protein
by first-order stochastic models is their treatment structure.Morerecently,Cohenandhisco-workers
of individual positions in a protein sequence as presented an elegant example of compensatory
independently evolving entities. Virtually all of replacement in phosphoglycerate kinase,17 sup-
these tools analyze sequence divergence one porting the suggestion that correlated change in
position at a time under a model where position i the evolutionary history of two protein families
in a sequence suffers independent replacement of might be taken as evidence that the two proteins
position j. Even models that recognize that differ- operate together. More generally, several labora-
ent sites may have different mutability (gamma tories have suggested that compensatory covaria-
models) treat sites as being independently tion might be used to detect incorrect folds in a
evolving.10 This is, of course, extremely convenient structureprediction environment.18–20
for any statistical model for protein sequence Unfortunately,comparisonofanytwosequences
divergence as it enables the probability of a diverging at n sites generates n(n21)/2 pairs of
sequence alignment overall to be calculated as the candidate sites holding coincident replacements.
product of probabilities calculated for individual These might be compensatory; they might be
positionsin the alignment. coincidental. Only a fraction of these will be truly
Even casual inspection of a multiple sequence compensatory, meaning that either replacement
alignment, however, shows that positions in a alone would have been rejected by natural
protein sequence do not suffer replacement inde- selection without the other. Most replacements are
pendently. Replacements in positions adjacent in a presumably not compensated, either because they
sequence are strongly correlated.11 The correlation are neutral (implying that no other changes are
almost certainly reflects functional constraints on needed to prevent their having a negative impact
DetectingCompensatoryCovariationSignals 731
This work suggested a general strategy to
strengthen the signal for compensatory replace-
ment. At the coreof this strategy isthe recognition
that compensatory replacements can be calculated
in two ways. In the first, two extant protein
sequences—sequences that are found in organisms
living today—are examined. As extant sequences
are at the leaves of an evolutionary tree, we call
these “leaf–leaf” comparisons (Figure 1). In the
past, virtually all compensatory substitution has
been sought via leaf–leaf comparisons.
An alternative approach is possible. Given a set
of homologous protein sequences, a multiple
sequence alignment, and an evolutionary tree
interrelating them, the sequences of ancestral
Figure1.Aleaf–leafcomparison(red)traversesmore proteins represented by nodes in the tree can be
evolutionary distance than a node–node comparison approximated using well-known heuristics. Given
(blue). reconstructed sequences of ancestral proteins at
nodes in an evolutionary tree, compensatory
covariation can be sought using “node–leaf” and
on functional behavior), or because they have a “node–node” comparisons.
positive impact on fitness (implying that no other As compensatory signals are stronger when
changes are desired to neutralize their impact on the sequences being compared are separated by
functional behavior). shorter distances19 and as the distance between
Thus, while such compensation is easily recog- two nodes in a tree must be shorter than the dis-
nized when analyzed in the context of a known tance between the leaves on the tree (Figure 1),
crystal structure (the sites suffering compensatory node–node and node–leaf compensatory signals
replacements presumably are near in space), it is must be stronger than the leaf–leaf signal that
difficult to identify the pairs of sites that might contains them. Phrased differently, the number of
suffer compensatory changes without a crystal replacements between average nodes is smaller
structure. As a consequence, the compensatory than the number between average leaves. This
covariation signal, represented by the number of means that the n(n21)/2 total number of pairs is
pairs of replacement that are causally interrelated smaller, implying that the truly compensatory
(where either alone would be rejected by natural pairs, those driven by a fitness constraint, will be
selection) relative to the n(n21)/2 pairs that arise less obscured by the background of uncompen-
whenever two protein sequences differing at n sated events, when they are identified on indi-
sites are compared, is weak, at least as it has been vidual branches of a tree.
generally calculated.21–23 Some have suggested Further, although the reconstructed ancestral
that the compensatory replacement signal may sequences are probabilistic, and cannot be proven
never be broadly useful for this reason.24 Others to be correct, even crude heuristics for reconstruct-
have suggested that the signal might have value, ing ancestral sequences localize specific changesto
especiallyif it can bestrengthened. specific regions of a tree better than if no recon-
A variety of laboratories has recently explored structions are done at all. Thus, even poor recon-
approaches to strengthen the compensatory struction heuristics permit us to focus on briefer
replacement signal.18,19 For example, the signal for episodes of time during which two compensatory
charge compensation appears to be stronger than changes might have occurred than is possible by
the signal for size compensation, suggesting that leaf–leaf comparisons.
it might be useful to analyze different types of Last, node–leaf and node–node comparisons
coincident replacement separately. Further, model the actual evolutionary events that might
compensatory covariation signals appear to be contain the compensatory signal better than leaf–
strongly dependent on the evolutionary distance leaf comparisons. The statement that “position i
between the two sequences, measured in PAM and position j should suffer replacement in a
units (the number of point accepted mutations per compensatory way” is equivalent to the statement
100 amino acids).25 For example, charge compen- that if either position i or position j suffer replace-
satory changes were found to be more prominent ment individually, the host organism is less “fit”
atPAM 25 than at PAM 100.19 (in a Darwinian sense). This, in turn, implies that
These observations are not surprising given the if position i suffersa replacement then position j is
model.Chargereversalchangesmight beexpected under “positive selective pressure” to suffer a
to be the change most in need of compensation. replacement.Conversely,thismeansthatareplace-
Likewise, at longer PAM distances, pairwise ment at position j will be fixed in a population
compensation might be obscured beneath com- faster than expected for a neutrally drifting
pensation arising from replacements at multiple position. This means that true compensatory
sites. changes will normally occur on the same
732 DetectingCompensatoryCovariationSignals
Figure 2. Attempted detection of charge compensatory covariation signal using leaf–leaf comparisons. (a) Distri-
bution of distances in 71 protein families between position pairs displaying charge compensatory substitution
(a positive-for-negative substitution at position i, and a negative-for-positive substitution at position j) (red bars),
using asa reference(green bars) the distribution ofallpairwisedistances inthe proteins. The x-axis isin angstroms;
they-axisisfrequency,witheachdistributionnormalizedtounity.Notetheabsenceofconsiderablytallerredbarsat
shortdistances.Totalobservationsinsample:13,460.(b)Asin(a),butusingasareferencecurvethedistancesbetween
allpairsofsurfaceresidues(bluebars,.50%exposure,calculatedbynormalizingitsaccessiblesurfacearea(ASA)by
thestandardASAoftheresidue.ASAwascomputedwiththeDSSPprogram.46Totalobservationsinsample:13,460.
(c)Asin(a),butconsideringonlynon-contiguouspairs,thosewhereiandjareseparatedbymorethanfourpositions,
with reference to a distribution of distances between all pairs of residues in the reference crystal structures (green
bars). Total observations in sample: 12,811. (d) As in (c), but with reference to the distribution of distance between
surfacepairs(bluebars).Totalobservationsinsample:12,811.
branch of the tree, even on a very short branch of between a node sequence and a leaf sequence.
the tree. Fractional changes were included. Each was asso-
This study examined the feasibility of detecting ciated with aparticular branch ofthe tree.
node–nodeandnode–leafcompensatorycovariation From these, pairs of replacements displaying
signals by examining reconstructed evolutionary charge compensatory behavior were collected, as
events within families ofproteins. described in Methods. A pair of replacements was
defined as being charge compensatory if they
were coincident (both occurring on the same
branch of the tree), if they each individually
Results
would reverse a charge, and taken together, if no
A total of 71 families of proteins were examined changeintheoverallchargeoftheproteinresulted
in this study. For each family, a multiple sequence from the two.
alignment and a phylogenetic tree were con- A three-dimensional crystal structure for a
structedusingClustal-W.26Reconstructedancestral member of the protein family was then extracted
sequences at nodes throughout the tree were from the PDB and an estimate was made for the
generated using the Fitch method as described in strength of the signal. In making this estimate, we
Methods.27 assumed that only proximal charge compensatory
We then sought charge reversal replacements in charges, near enough in space in the folded
these families. For each family, positions were structure that the two side-chains could interact
identified where an amino acid replacement coulombically, could be functionally correlated.
caused a charge reversal between two ancestral We therefore tabulated the distances between the
sequences (representing a replacement event that sites in pairs that suffered charge compensatory
occurred on a branch between two nodes) or replacements.
DetectingCompensatoryCovariationSignals 733
Figure 3. Detecting charge compensatory covariation signal using explicitly reconstructed ancestral sequences.
(a)Distributionofdistancesin71proteinfamiliesbetweenpositionpairsdisplayingchargecompensatorysubstitution
(a positive-for-negative substitution at position i, and a negative-for-positive substitution at position j) (red bars),
usingas a reference(greenbars) the distribution of allpairwisedistances in the proteins. The x-axis isinangstroms;
the y axis is frequency, with each distribution normalized to unity. Note the greater height of the red bars at both
shortdistancesandatlongdistances.Totalobservationsinsample:803.3(notefractionalnumberreflectingfractional
character assignments in ancestral states; precision is less than implied by the decimal). (b) As in (a), but using as a
referencecurvethedistancesbetweenallpairsofsurfaceresidues(bluebars,.50%exposure,calculatedbynormali-
zing its ASA by the standard ASA of the residue. ASA was computed with the DSSP program.46 Note the greater
heightoftheredbarsatshortdistancesonly.Thisisthecompensatorycovariationsignal.Totalobservationsinsample:
803.3. (c) As in (a), but considering only non-contiguous pairs, those where i and j are separated by more than four
positions,withreferencetoadistributionofdistancesbetweenallpairsofresiduesinthereferencecrystalstructures
(greenbars).Totalobservationsinsample:745.(d)Asin(c),butwithreferencetothedistributionofdistancebetween
surface pairs (blue bars). Total observations in sample: 745.5. (e) Distance distribution of charge compensatory pairs
whereonlyonesuchpairoccursonaspecificbranchoftheevolutionarytreebetweenreconstructedancestralnodes.
Totalobservationsinsample:57.2.Notethesmallsamplesize.(f)Sameas(e),butwherethepositionpairisseparated
bymorethanfourpositionsinthelinearsequence.Totalobservationsinsample:48.3.Notethesmallsamplesize.
Histograms were then constructed to show more in proximal positions than the average pair
the distance distribution of pairs suffering (where the square root of the number of pairs was
compensatory replacements. As a standard, a dis- a crude measure of significance), a signal was con-
tance distribution for all pairs of sites was calcu- sidered significant. As previous studies predicted,
lated for the proteins. If the number of charge leaf–leaf comparisons found an only barely per-
compensatorypairswaslocateddisproportionately ceptible charge compensatory signal (Figure 2).
734 DetectingCompensatoryCovariationSignals
Thatis,pairsofpositionssufferingchargecompen- near in the folded structure is considerably higher
satory replacement in two extant sequences were than expected (Figure 3(b)). This represents the
not much more likely to be near in space than the “signal” in the charge compensatory pattern of
average pair. The analogous analysis for each replacement.Whenaside-chainchangesitscharge,
evolutionarybranchinthetree,however,identified that charge is more likely to be accompanied by a
a signal that was clearly perceptible (Figure 3), compensatory change in the charge of another
even by eye. This signal wasthen analyzed. side-chain near inspaceto the first.
Charge compensation and the surface of the Charge compensation in both contiguous and
folded protein non-contiguous position pairs
Surprisingly, the initial analysis (Figure 3(a)) We then explored several features of this signal.
showed that position pairs suffering node–node First, we asked whether the signal arises only in
or node–leaf compensatory charge replacement positions that were also nearby in the polypeptide
weremorelikelytoliebothproximallyanddistally sequence (contiguous pairs), or whether it was
in the fold, when compared with the average dis- alsoobservedinresiduepairs.4positionsdistant
tance between all position pairs in the proteins. (those of i, iþq relationship, where q.4) in the
Thatis,pairsofpositionsnearinthefolddisplayed sequence (non-contiguous pairs). A strong signal
charge compensatory covariation more frequently wasalsoobservedfornon-contiguouspairs(Figure
than the average pair, as expected should charge 3(c) and (d)) as well as for contiguous pairs. This
compensatory replacement be functionally corre- implies that a charge compensatory replacement
lated. But pairs of positions distant in the fold also signal arises when two residues are near in space
displayed charge compensatory covariation more as a consequence of the tertiary fold, as well as if
than the average pair. they are near in space because they are near in the
Distal charge compensatory replacement sequence.
suggested two explanations. First, overall net
charge might be a selected trait in a protein. It is
Enhancing the charge compensation signal
conceivable,forexample,thataconstantisoelectric
point is desired by natural selection. If so, rever- These results showed that node–node and
sing a charge at one position would require an node–leaf analyses generated a more perceptible
adaptive replacement leading to the opposite charge compensatory covariation signal than leaf–
reversal somewhere (anywhere), even at a second leaf analyses. Nevertheless, the signal remained
positiondistant in the fold from the first. small.
Alternatively, charge changes are more likely to Weconsideredseveralexplanationsforthesmall
be tolerated by natural selection, and therefore are sizeofthesignal.First,weconsideredacasewhere
more likely to be observed, if they occur on the four sites suffer charge reversal replacements in a
surface of the protein. The mean distance between single evolutionary episode. Site a suffers a (þ to
a pair of surface residues is greater than the mean 2) replacement compensated by a (2 to þ)
distance between the average pair of residues. replacement at site b. Site c suffers a (þ to 2)
Therefore, charge changes are more likely by replacement compensated by a (2 to þ) replace-
chance to occur in pairs more distant than the ment at site d. Sites a and b are proximal; Sites c
average pair if they occur predominantly in and d are proximal. Compensatory changes at
positions on the surface, whether the pair is under sites b and d are required to maintain a functional
direct selection or not (i.e. if the replacement is protein given changes at sites a and c, respectively.
neutral). Two pairs that do not represent adaptively signifi-
These considerations suggested that thedistance cant compensation (a;d and b;c) arise in addition
between the average position pair might not be to the two pairs that do (a;b and c;d). This is
the most informative reference distribution for simply another way of saying that changes that
these studies. Instead, an alternative reference dis- need compensation are more noticeable when the
tribution was calculated (blue bars, Figure 3(b)) total numberof changesissmall.
for the distance between pairs of surface residues Therefore, we asked whether the signal was
in the model proteins. This new distribution fit stronger if the only branches examined were those
nicely the distal portion of the distribution of dis- holding exactly one pair of charge compensatory
tances between position pairs displaying charge replacements (Figure 3(e) and (f), for all pairs and
compensatory replacement. The result implies that non-contiguous pairs, respectively). The likelihood
the apparently high occurrence of charge compen- that two positions undergoing charge compen-
satory replacement in distal pairs of residues satory replacement are near in space was indeed
reflects simply the greater likelihood that charge more perceptible after we excluded all of the
reversal replacements occur on the surface of the events occurring on branches where more than
protein. This surface pair reference distribution two positions suffered charge reversal. The num-
does not, however, fit the proximal portion of the ber of cases was small, however (57 for all pairs,
distribution.Theprobabilitythatapairofpositions and 48 for non-contiguous pairs, respectively),
displaying charge compensatory replacement is and the plots accordingly displayed substantial
DetectingCompensatoryCovariationSignals 735
Charge compensation in specific secondary
structural elements
We then examined more closely the contiguous
position pairs (i, iþ4 or nearer) displaying charge
compensatory covariation. The most striking
feature of the charge compensatory signal within
contiguouspairswasits dependenceonthenature
ofthesecondarystructural elementthatheldthose
positions (Figure 4). In 98% of the cases where the
positions showing compensatory replacement had
an i;iþ4 relationship, one or both of the residues
was found in an a helix. In only 1.6% of these
cases was one of the residues found in a b strand,
and in none of the cases were both found in a
strand. This was significantly larger than the 47%
of the position pairs with an i;iþ4 relationship
having one or both residues in a helix found in
the dataset as a whole (Table 1). Conversely, in
49% of the cases where the position pair showing
compensatory substitution had an i;iþ2 relation-
ship, one or both of the residues was found in a b
strand.
Figure 4. Predicting secondary structure using con- Two alternative explanations can be proposed
tiguouspairsofcompensatorychanges.Therelativesizes
to account for the secondary structure bias. First,
of the “pies” indicates the relative numbers of examples
surface helices present residues to solvent (water)
ofeachpair.Wherepositionpairsareseparatedby1–5,or
once every 3.6 turns. Surface residues areexpected
6 positions, the likelihood that residue pairs are both
to be less constrained by function from diverging
foundinhelices(red),bothfoundinstrands(darkgreen),
oneinahelixandtheotherinacoil(pink),oneinastrand (that is, single replacements are more likely to be
andtheotherinacoil(lightgreen),oneinahelixandthe neutral), and aremorelikely than the average resi-
otherinastrand(violet),andbothfoundincoils.Notean due to suffer charge reversal substitutions. There-
observationthatiftwochargecompensatorysubstitutions fore, the abundance of compensatory changes
are observed with a i;iþ4 relationship, one or both are occuring with i;iþ3 or i;iþ4 relationship in the
98% likely to lie in a helix. The total number of obser- sequence might simply reflect unconstrained (i.e.
vations; i;iþ1¼12:82; i;iþ2¼6:47; i;iþ3¼11:38;
neutral) chargereversal at surface positions.
i;iþ4¼23:37; i;iþ5¼4:79; i;iþ6¼6:48: Note frac-
Alternatively, loss of a coulombic interaction
tionalvaluesandthesmallsizeofthesesamples.
between residues i and iþ3 or iþ4 might lead to
a protein less able to contribute to the fitness of
variances.Asthenumberofsequencesinthedata- the host. This view implies that once a charge
base grows, trees will become more articulated, reversal substitution occurs at position i, position
individual compensatory events will be more iþ4 is under sufficient positive selection
likely to be isolated fromothers on a single branch to acquire a compensating charge reversal
of thetree,and the signal shouldstrengthen. substitution.
Table1.Frequenciesoftheaveragecontiguouspositionpairsparticipatinginahelixversusstrand
Relationshipbetweenthepairintheproteinsequence
Pair i;iþ1 i;iþ2 i;iþ3 i;iþ4 i;iþ5 i;iþ6
EE 0.185 0.146 0.119 0.099 0.087 0.079
EC 0.077 0.148 0.192 0.219 0.234 0.239
Strand 0.262 0.294 0.311 0.318 0.321 0.318
HE 0.003 0.011 0.022 0.033 0.044 0.055
HH 0.307 0.274 0.243 0.223 0.208 0.194
HC 0.072 0.132 0.184 0.214 0.233 0.249
Helix 0.382 0.417 0.449 0.470 0.485 0.498
CC 0.356 0.289 0.241 0.212 0.195 0.185
Total 1.00 1.00 1.00 1.00 1.00 1.00
Totalsample 12.8 6.5 11.4 23.4 4.8 6.5
EE,bothpositionsinvolvedinachargecompensatoryeventfoundinstrands;EC,oneinastrandandtheotherinacoil;Strand:
HE,oneinahelixandtheotherinastrand;HH,bothinhelices;HC,oneinahelixandtheotherinacoil;Helix:CC,bothincoils.
CalculatedfromthetestsetofreferencecrystalstructuresusingDSSP.46Notethesmallnumberofobservationsineachsample,and
thefractionalnumberofchangesarisingfromparsimonyreconstructions.
736 DetectingCompensatoryCovariationSignals
Figure 5. Distribution of distances between charge anti-compensatory pairs (red bars) (a) relative to all pairwise
distances (green bars) and (b) relative to pairwise distances between all pairs of surface residues (blue bars, .50%
exposure). Notable is the absence of the increased probability of proximal anti-compensatory pairs (compare with
Figure3).Thetotalnumberofobservationsinbothdistributionsis793.3.
To explore these alternatives, we sought surprisingly, most buried charged residues do not
examples of anti-compensatory charge reversals, suffer charge reversal within the test set. Compen-
where a charge reversal (þ to 2, for example) satory changes near in space (Figure 6(b)) were
was accompanied by another charge reversal sub- slightly more likely to be found in positions that
stitution in the same direction (þ to 2) (Figure 5). were more buried, a modest signal that suggests
The histogram showing the distance distribution that compensation is more necessary in partly
in pairs suffering compensatory covariation is buried sites shielded from the high dielectric
shown in Figure 5. Here, the distribution of dis- constant presented by the solvent water. This is
tances between position pairs carrying charge the case for those residue pairs in protein kinase15
anti-compensatory substitution was not noticeably and phosphoglycerate kinase17 where charge com-
different from the distribution of distances pensatory substitution hashad predictive value.
between all surface position pairs (Figure 3(b)).
Notable is the absence of an increased probability
of proximal anti-compensatory pairs (compare Discussion
with Figure3).
Explicit reconstruction of ancestral proteins has
As a predictive tool, this enhanced charge
been shown to provide insight into the structure
compensatory signal may prove to be most
and function of protein families, both when done
valuable in secondary structure prediction. The
in silico,27–29 and when recombinant DNA tech-
accuracy of a prediction made on the relative
nology is used to resurrect ancestral proteins from
positions of a compensatory pair is extremely
extinct organisms so they can be studied in the
high. The “coverage” is low, however. Only a few
laboratory.30–33
dozen examples were observed; only 6.8% of the
The work reported here applies ancestral recon-
helices contained within the 71 test families have
structions towards a new goal. We suggest several
one or more charge compensatory position pair.
conclusions. First, node–node and node–leaf
This number will, of course, grow as the size of
comparisons between reconstructed ancestral
the protein families grows with the increasing size
sequences provide a stronger compensatory
of thegenomic database (Table2).
covariation signal than the leaf–leaf comparisons
that have been used previously in the search for a
compensatory covariationsignal.
Charge compensation in buried residues
These results are consistent with the model out-
Thehighdielectricconstantofwaterisknownto lined in Introduction, which holds that amino acid
weaken coulombic interactions between charged replacements that dramatically alter the physical
species. We therefore asked whether a stronger property of the side-chain will disrupt the per-
signal might be found in position pairs where one formance of a protein to an extent that requires a
or more of the side-chains was buried. Figure 6(a) compensatory change elsewhere in the protein
shows the distribution of surface accessibility structurea significant numberof times. The fitness
calculated for all charged amino acids (DEKR, or value of the protein can be restored only by a
Asp, Glu, Lys, and Arg) (blue), those that partici- secondchangethatcompensatesforthefirstaltera-
pate in a position pair suffering charge com- tion in physical properties. In the language of
pensatory substitution (red), and those that neutral theory, we would say that the first replace-
participate in a position pair suffering charge ment was selectively advantageous, the second
anti-compensatory substitution (green). Not was positively selected (in the context of the first),
DetectingCompensatoryCovariationSignals 737
Table2.Listof71proteinfamiliesusedinthisanalysis
ID L N Proteinname
121P 166 60 H-RasP21protein
193L 129 43 Lysozyme
1AAF 55 38 Hiv-1nucleocapsidprotein
1AAK 152 20 Ubiquitinconjugatingenzyme
1ARS 396 28 Aspartateaminotransferase
1ATP(E) 350 20 c-AMP-dependentproteinkinase
1BET 107 14 Beta-nervegrowthfactor
1BP2 123 64 PhospholipaseA2
1CCR 112 93 Cytochromec
1CPC(B) 172 44 C-Phycocyanin
1CYO 93 17 CytochromeB5(oxidized)
1DLH(A) 180 28 Hla-Dr1(Dra,Drb10101)humanclassIIhistocompatibilityprotein(extracellulardomain)
1DLH(B) 188 45 Hla-Dr1(Dra,Drb10101)humanclassIIhistocompatibilityprotein(extracellulardomain)
1EFT 405 57 ElongationfactorTu(Ef-Tu)
1FRP(A) 335 18 Fructose-1,6-bisphosphatase(D-fructose-1,6-bisphosphate1-phosphohydrolase)
1FVL 70 29 Flavoridin
1FXI(A) 96 69 FerredoxinI
1GDD 353 51 Gauninenucleotide-bindingproteinG(I)
1GP1(A) 198 16 Glutathioneperoxidase
1HAR 216 36 Hiv-1reversetranscripts(amino-terminalhalf)
1HCN(A) 92 26 Humanchorionicgonadotropin
1HDG(O) 332 109 Holo-D-glyceraldehyde-3-phosphatedehyrogenase
1HGE(A) 328 70 Hemagglutinin
1HLE(A) 345 14 Horseleukocyteelastaseinhibitor
1HMT 132 16 Fattyacidbindingprotein
1HPM 386 128 44KAtpasefragment(Nterminal)of70kDaheat-shockcognateprotein
1HRA 80 42 Retinoicacidreceptor
1HRY(A) 76 43 Humansry
1HTB(A) 374 56 Beta-3alcoholdehydrogenase
1HTM(D) 138 92 Hemagglutininectodomain(solublefragment,Tbha2)
1HUR(A) 180 35 HumanAdp-ribosylationfactor1
1HUW 166 31 Humangrowthhormone
1HVD 319 23 AnnexinV
1IRK 306 17 Insulinreceptor(tyrosinekinasedomain)
1ITG 166 42 Hiv-1integrase(catalyticdomain)
1IVD 388 23 InfluenzaAsubtypeN2neuraminidase(sialidase)
1LDM 329 27 M4lactatedehydrogenase
1MHC(A) 282 143 MhcclassIantigenH2-M3
1MLS 154 74 Myoglobin
1NDH 272 27 CytochromeB5reductase
1NHK(L) 144 26 Nucleosidediphosphatekinase
1NIP(A) 289 35 Nitrogenaseironprotein
1OCT(C) 156 33 Oct-1(Poudomain)
1OSA 148 64 Calmodulin
1PBX(A) 143 56 Hemoglobin
1PDN(C) 128 28 Prdpaireddomain
1PLQ 258 13 Proliferatingcellnuclearantigen
1PVC(2) 271 24 Poliovirustype3,Sabinstrain
1REC 201 21 Recoverin
1SXC(A) 151 51 Superoxidedismutase
1TGX(A) 60 51 Toxingamma
1TIV 86 24 Hiv-1transactivatorprotein
1TPH(1) 247 35 Triosephosphateisomerase
1YTB(A) 180 18 TATA-boxbindingprotein
1ZAA(C) 87 18 Zif268immediateearlygene
2BTF(A) 375 121 Beta-actin-profilincomplex
2CPL 165 35 CyclophilinA
2GDM 153 23 Leghemoglobin
2HMX 133 40 Humanimmunodeficiencyvirustype1matrixprotein
2HPE(A) 99 36 Hiv-2protease
2REB 352 58 RecAprotein
2TGI 112 18 Transforminggrowthfactor-b2
3RUB(S) 123 79 Ribulose1,5-bisphosphatecarboxylase/oxygenase(formIII)
4ENL 436 35 Enolase
4FGF 146 16 Basicfibroblastgrowthfactor
4GCR 174 31 Gamma-Bcrystallin
4MT2 62 50 MetallothioneinisoformII
4RHV(1) 289 24 Rhinovirus14
4RHV(3) 236 24 Rhinovirus14
7RSA 124 48 RibonucleaseA
8CAT(A) 506 34 Catalase
ID, Protein Data Bank identifier, protein subunit in parentheses; L, chain length; N, number of sequences in multiple sequence
alignment.
738 DetectingCompensatoryCovariationSignals
Figure 6. Surface accessibility of
charged residues, and charged
residues participating in a charge
compensatoryevent.(a)Afrequency
versus accessibility distribution for
all Asp, Glu, Lys, and Arg (DEKR)
residues (blue), those participating
inachargecompensatory(red)and
anti-compensatory (green) events.
Bars of each color sum to unity.
Buried DEKR residues are less
likely than average to suffercharge
reversal substitution. Compensated
charge reversal substitutions are
slightly more likely than anti-
compensated charge reversal sub-
stitutions. The total number of
observations in sample: anti,
2812.4;comp,2792.2;DEKR,3530.0.
(b) A frequency versus accessibility
distribution showing the frequency
of compensated charge reversals
for proximal pairs near in space
(less than 12A˚ distant, red) in the
folded structure, and distal pairs
distant in the folded structure
(more than 12A˚ distant, green).
A pair of charged compensatory
substitutions is slightly more likely
tobenearinspaceiftheside-chains
involvedaremoreburied.Thetotal
number of observations in sample:
near,367.1;far,795.7.
and both together are neutral. Thus, while the two believe, sufficient explanation for this effect.
compensatory substitutions taken together might Shorter branches implies a smaller n, the total
be regarded as collectively neutral, the second number of differences between the two protein
mutation in a truly compensatory pair is viewed sequences being compared, diminishing the
as positivelyadaptive in this model. number of n(n21)/2 pairs behind which the
These results also suggest that as the database compensatory signal might beobscured.
grows, the charge compensatory signal will While it is possible in principle to construct a
become more perceptible as more sequences are statistical model that permits double replacements
added to each family. More sequences mean more to be evaluated, this requires a high degree of
highly articulated evolutionary trees. This, in turn, empirical parameterization. For example, nearly a
means that compensatory events will become decade ago, we collected the parameters needed
better isolated on specific branches, preventing the to build a statistical model that concerned double
“spurious” signals that arise when more than one replacements at adjacent sites.11 Some 220 para-
pairofcompensatoryeventsoccursalongaspecific meters are formally required in this exercise, a
branch on atree. largenumberby most measures.
The stronger signal will undoubtedly find use. For the purpose of this work, a signal is
Predicting secondary structure using contiguous considered to be significant if it lies two standard
pairs of compensatory changes is one. It remains deviations outside of the fluctuation expected for
to be seen, however, how much data in a family is nsitesataspecifieddistance.Thiscanbeestimated
required for the signal to be useful to support de by the square root of the number of sites. By this
novo assembly of a protein fold in a prediction measure, all of the results reported here are
setting. strongly significant, with the exception of those
reported inFigures 3(e),(f),and 4.
Accounting for the stronger signal from node–
node comparison A model-independent method to evaluate an
evolutionary tree
The tools that we have presented make the
compensatory covariation signal more perceptible. The strength of the compensatory covariation
Isolation of truly compensatory pairs on shorter signal undoubtedly depends on the degree to
branches of a tree away from other changes is, we which the trees and the reconstructed ancestral