Received May 17, 1996;
Revised and Accepted July 16, 1996
ABSTRACT
A recently developed method for estimating the variability of nucleotide sites
in a sequence alignment [Van de Peer, Y., Van der Auwera, G. and De Wachter, R.
(1996) J. Mol. Evol.
42, 201-210] was applied to bacterial 16S, 5S and 23S rRNAs. In this method, the
variability of each nucleotide site is defined as its evolutionary rate
relative to the average evolutionary rate of all the nucleotide sites of the molecule. Spectra of evolutionary rates were calculated for each rRNA and show the fastest evolving sites
substituting at rates more than 1000 times that of the slowest ones.
Variability maps are presented for each rRNA, consisting of secondary structure
models where the variability of each nucleotide site is indicated by means of a
colored dot. The maps can be interpreted in terms of higher order structure,
function and evolution of the molecules and facilitate the selection of areas
suitable for the design of PCR primers and hybridization probes. Variability
measurement is also important for the precise estimation of evolutionary
distances and the inference of phylogenetic trees.
INTRODUCTION
The nucleotides in rRNAs show a considerable spread in substitution rate,
attributable to local differences in functional and structural constraints.
Detailed information about the variability or conservation of nucleotide
positions in rRNA is important for several reasons. For example, sites to which
a function can be assigned are often conserved in structure (see for example
1
,
2
). Furthermore, conserved regions are of great importance for sequence alignment
and the search for homologous regions in sequences of different organisms.
Oligonucleotides can be developed on the basis of the more conserved regions of
the molecule and used as universal primers for the amplification of the same
gene in other organisms. On the other hand, highly variable sequence regions
can be used for the development of species-specific hybridization probes or PCR primers, applicable in the detection
and identification of microorganisms. The measurement of site variability is
also important from a phylogenetic point of view. Conserved areas can be used
to unravel old relationships, while the more variable regions can be used to
study evolutionary relationships between closely related organisms. Regarding
phylogenetic tree construction, the study of site variability is gaining much
interest lately. Newly developed tree construction methods take into account
differences in nucleotide substitution rates, which leads to more consistent
tree topologies (
3
-
6
).
Quantitative estimation of the substitution rates or variabilities (both terms
will be used as synonyms throughout this paper) of nucleotide sites is not
straightforward. For example, in previous studies, variability of sites was
sometimes estimated by computing the proportion of the most common nucleotide
(see for example
7
). Manske and Chapman (
8
) pointed out that the main problem with this strategy is that it ignores the
frequencies of the other less common nucleotides. Therefore, these authors
suggested another method to measure the site variability, considering the
relative frequencies of every nucleotide at a certain alignment position.
However, this method is also not very appropriate for measuring the variability
of nucleotide positions, because it still ignores the evolutionary distance
necessary to achieve a substitution, as demonstrated by Van de Peer
et al
. (
5
).
Another way of measuring the variability of sites is by the use of maximum
parsimony. Starting from a known phylogeny, the number of changes for every
position is inferred from the reconstruction of nucleotide or amino acid states
at the internal nodes of that particular tree topology (
9
-
11
). However, since the number of changes at each site is determined by a maximum
parsimony approach (
12
), this method is biased and likely to give an underestimate of the number of
changes that have actually occurred, especially for long branches in the tree (
13
,
14
).
Recently, a new method was developed for measuring the relative substitution
rate of individual sites in a nucleotide sequence alignment on the basis of a
distance approach (
5
,
6
). The main advantage of this method is that it does not depend upon a given
tree topology and that nucleotide site variabilities can be estimated on the
basis of several hundreds of sequences. This is important, since the more
sequences taken into consideration, the more accurate the estimate.
In our research group, a database on the small and the large ribosomal subunit
RNA (respectively SSU and LSU rRNA) is maintained and made available to the
scientific community (
15
,
16
). We also used to maintain an alignment for the far smaller 5S rRNA (
17
). In this study, we determined the variability of the nucleotide sites in
bacterial 5S rRNA, SSU rRNA and LSU rRNA. Bacterial sequences were chosen for
two reasons. Firstly, the bacterial sequences form the most numerous subset of
known rRNA sequences. Secondly, bacterial rRNAs suffer less from length
heterogeneity than their eukaryotic counterparts (
16
,
18
), which makes it easier to align them properly and to deduce their complete
secondary structure.
Estimation Of Nucleotide Substitution Rates
Estimation of relative nucleotide substitution rates for bacterial 5S, 16S and
23S rRNA was as follows. For an alignment of
N
sequences,
N
(
N
- 1)/2 pairwise evolutionary distances
d
are computed according to the equation of Jukes and Cantor (
19
)
d = - {3 over 4} 1 n {left ( {1 ^ - ^ {4 over 3} f} right )}
1
where
f
is the dissimilarity between two sequences, defined as the fraction of
substitutions observed when the sequences are aligned. When all pairwise
distances are computed, they are classified into a number of distance
intervals, e.g. distances from 0 to 0.005, distances from 0.005 to 0.010, and
so on. Next, for each alignment position and for each distance interval, the
fraction of sequence pairs possessing a different nucleotide is computed. For
each position, the fraction of sequences showing a difference is plotted as a
function of the distance between them (
5
). A curve obeying equation
{p sub i} = {3 over 4} {left [ {1 - exp {left ( {- {4 over 3} {v sub i} d} right )}} right ]}
2
is then fitted to these points by non-linear regression. Equation
2
expresses the probability
p
i
that alignment position
i
contains a different nucleotide in two sequences, as a function of the
evolutionary distance
d
separating them. The slope of the curve in the origin yields the specific
nucleotide substitution rate
v
i
for position
i
(
5
).
Actually, the estimated nucleotide substitution rates are not yet optimal,
because they are derived on the basis of a distance matrix computed by means of
equation
1
. This equation only gives a first approximation of the relation between
dissimilarity and distance, since it starts from the unrealistic assumption
that all nucleotides have the same substitution rate. Therefore, after
estimation of all
v
i
values, alignment positions are grouped into sets of similar variability. A
spectrum of relative nucleotide substitution rates is thus obtained. Such
spectra are shown for the three RNA molecules in Figure
1
. Once the shape of a spectrum is known, it is possible to derive the following
equation for the dissimilarity,
f
, as a function of the evolutionary distance
d
(
6
):
f = {3 over 4} {left { {1 - exp {left [ {- {4 over 3} p 1 n {left ( {1 + {d over p}} right )}} right ]}}
right }}
3
The value of parameter
p
depends on the shape of the substitution rate spectrum. The inverse of equation
3
d = p {left [ {{{left ( {1 - {4 over 3} f} right )} sup {- {3 over {4 p}}}} - 1} right ]}
4
gives a more accurate conversion of dissimilarity into distance than equation
1
. It is then used to obtain an improved estimate of the pairwise distances from
the observed dissimilarities. The relative substitution rate
v
i
of each alignment position is then estimated again on the basis of these new
evolutionary distances, as described above, and a new spectrum of evolutionary
rates is derived. This iterative process is repeated several times until the
nucleotide substitution rates
v
i
do not change anymore. A more detailed description of nucleotide rate
calibration is given elsewhere (
6
).
.
Number of different bacterial rRNA sequences used for nucleotide substitution
rate calibration
Taxon
a
Number of sequences used
b
16S rRNA
23S rRNA
5S rRNA
Combined
c
Chlamydiae
4
Cyanobacteria
4
1
5
Fibrobacter
3
Flavobacteria and relatives
50
2
13
2
Fusobacterium and relatives
18
3
Gram-positives and relatives, low GC
50
30
42
17
Gram-positives and relatives, high GC
50
10
27
8
Green sulfur
3
1
4
1
Green non-sulfur
4
3
Planctomyces and relatives
10
1
6
1
Proteobacteria [alpha]
50
7
46
5
Proteobacteria [beta]
50
7
13
1
Proteobacteria [gamma]
50
6
80
5
Proteobacteria [delta]
42
6
Proteobacteria [epsilon]
50
2
2
2
Radio-resistant micrococci and relatives
6
1
10
1
Spirochetes
50
2
Thermotogales
6
1
Total
500
71
260
43
a
The classification of bacteria is based on the construction of evolutionary
trees (see 22). According to the phylogenetic position observed, species are
assigned to one of the taxa described by Woese and collaborators (56,57) and
our research group (58).
b
When several sequences were available for the same species, only the most
complete was used. Regarding 23S rRNA, all available species were taken into
account. For the 5S rRNA, 260 bacterial species, represented in our sequence
alignment, were considered. In the case of 16S rRNA, the number of sequences
considered was restricted to 500, because of the computational time required.
Therefore, species belonging to taxa comprising more than 50 sequences were
selected randomly.
c
See text for details.
Evolutionary Rate Spectra Of rrna Nucleotides
Figure
1
shows the spectra of relative evolutionary rates for the nucleotide sites of
16S rRNA, 5S rRNA and 23S rRNA. The spectra, calculated as described above,
were obtained by five iterations. In the case of 16S rRNA (Fig.
1
a), variabilities were estimated from an alignment of 500 16S rRNA sequences,
randomly sampled among the main bacterial taxa. The number of species
representing each taxon is listed in Table
1
. Disregarding absolutely conserved residues, one finds that the most variable
sites have a substitution rate ~7000 times higher than the least variable ones. For 5S rRNA, variabilities
were estimated from an alignment of 260 sequences, distributed according to
Table
1
. In the 5S rRNA spectrum (Fig.
1
b), the most variable nucleotide sites have a substitution rate ~1260 times that of the least variable ones. For 23S rRNA, site
variabilities were estimated from an alignment of all available bacterial
sequences, numbering 71, distributed as listed in Table
1
. In the corresponding spectrum (Fig.
1
c) the ratio of the highest to the lowest rates in 250:1.
Variability Maps Of rrna
Color maps shown in Figures
5
and
3
, superimposed on the respective secondary structure models of 16S, 5S and 23S
rRNA, were constructed by dividing nucleotides into five variability subsets,
indicated in Figure
1
a-c as alternately white and shaded areas of the spectra. The relative rate
limits of the subsets and the corresponding colors used in the variability maps
are as follows: <10
-0.925
(blue); 10
-0.925
-10
-0.425
(green); 10
-0.425
-10
+0.075
(yellow); 10
+0.075
-10
+0.575
(orange); >10
+0.575
(red). Absolutely conserved positions (
v
i
= 0) are indicated in purple. Sites colored pink belong to areas that are very
variable, but that are deleted in too many sequences to allow a sufficiently
accurate measurement of their relative evolutionary rate. Since the
distributions are not rectangular, some colors are more abundant than others.
These color maps give a much more detailed and quantitative description of
positional variability than the crude distinction between variable and
conserved areas that is often made by visual inspection of sequence alignments.
Variability map of bacterial 16S rRNA
The models in Figures
2
-
5
are all drawn clockwise in the direction 5' -> 3'. Figure
2
shows the secondary structure model of the 16S rRNA of
Escherichia coli
. The secondary structure model adopted for eukaryotic and prokaryotic SSU rRNAs
was originally derived (
20
) by comparison of six eucaryal, one archaeal, four bacterial, two plastidial
and one mitochondrial SSU rRNA sequences available in 1984 and by surveying 13
secondary structure models proposed at that time (
20
). Gradual improvements were made to the models, as reported in subsequent
papers describing our database on SSU rRNA structure (see for example
21
,
22
), taking into account compensating substitutions observed in our sequence
alignments and the results of studies by others (reviewed in
23
). The model presently adopted for bacterial SSU rRNAs is essentially identical
to the models made available in graphic form by Gutell (
24
). Five `tertiary' interactions derived by Gutell
et al
. (
25
) on the basis of coordinated substitutions are indicated in Figure
2
. Although described as `tertiary' by the latter authors, some of these
interactions would be more aptly defined as secondary interactions consisting
of single base pairs, since they satisfy the principle of contiguity (
26
) (see also Table
2
).
In Figure
3
the variability of the nucleotide sites of bacterial 16S rRNA is mapped in the
shape of the secondary structure model. The variability map shown is largely
congruent with a bacterial map published earlier (
22
). However, in the previous map, variability measurement was less precise, since
it was based on Jukes and Cantor distances only and did not involve iterations
(see Estimation of Nucleotide Substitution Rates) and sites were divided into
five equally numerous categories of increasing variability.
Figure
3
shows that in general the two nucleotides of a base pair have the same or a
neighboring color, i.e. they are about equally variable. This is as expected,
since the substitution of a base paired nucleotide generally requires a
compensating substitution in the opposite strand. However, there are a few
exceptions. Most of these occur in sites where a particular base, usually a U
or a G, seems to be required in one strand, but the complementary base can
change more freely, which is possible due to the existence of G[middot]U pairs. If the preference is for a U in one strand, the opposite base
can be A or G. Such is the case with the base pair closing the hairpin loop of
helix 25, where a green A or G faces a purple U. If the G must be conserved in
one strand, the complementary base can be either C or U. Such a case is found
in the last base pair of helix B12 of 23S rRNA (see below). There is also an
example of a base pair, namely the penultimate pair of helix 28, where an A
seems to be required in one strand. The opposite nucleotide is either U or C.
This has been interpreted (
24
) as meaning that the two ultimate base pairs of helix 28 as drawn in Figure
3
do not actually exist, since a change of A[middot]U to A[middot]C implies the disappearance of the penultimate base pair. An
alternative interpretation could be that at certain places in the molecule A[middot]C pairs can be tolerated. The structure of the A[middot]C pair in DNA heteroduplexes has been investigated by X-ray analysis (
27
) and found to be congruent with the G[middot]T pair but containing a protonated C or possibly a rare tautomeric form
of A or C. The general rule that interacting bases have similar substitution
rates also applies to the tertiary interactions indicated in Figure
2
. The variabilities of the nucleotides participating in each interaction are
listed in Table
2
, left.
.
Tertiary
a
structure interactions in 16S and 23S rRNA as proposed by Gutell
et al
. (25) on the basis of comparative evidence and confirmed by our study
16S rRNA
23S rRNA
Number
b
Variability code
c
Number
Variability code
1
a
3-3
1
2-2
2
5-5
2
2,4-6,2
3
3-3
3
2-2
4
a
6-5
4
a
3-3
5
a
5-6
5
2,3-3,2
6
6,6,6,2-2,6,6,6
7
6,5-6,6
8
6,3-3,6
9
2-2
10
5-5
11
5-5,5
12
2-2
13
2-2
14
6-6
15
2,3-3,2
16
4-5
17
3-3
Interactions followed by (
a
) are not actually tertiary, since they satisfy the principle of contiguity
(26). On the other hand, two pseudoknots, which do not satify the principle of
contiguity and therefore contain tertiary interactions, are drawn directly in
the 16S rRNA nucleotide sequence in Figure 2.
b
Interactions are listed clockwise starting from the 5'-end and are indicated by black circles in Figures 2 (16S rRNA) and
4 (23S rRNA).
c
Variability codes are as shown in Figures 3 for 16S rRNA and 5 for 23S rRNA.
In the prokaryotic secondary structure model, nine highly variable areas can be
distinguished, formed roughly by the following helices: 6; 8-11; 18; P23-1 and 24; 28 and 29; 37-P37-2; 43; 45 and 46; 49. These areas or parts thereof
have been previously distinguished on a more intuitive basis by visual
inspection of the 16S rRNA alignment (
21
,
28
). Much more detail is visible on the variability maps and it turns out that
highly variable helices are interrupted occasionally by conserved base pairs,
as in helix 24, and, conversely, a highly variable base pair is occasionally
intercalated between more conserved ones, as in helix 14. More generally,
sequence conservation of the 16S rRNA is found mainly in single-stranded regions. The importance of several highly conserved single-stranded regions for the structure or function of the 16S rRNA
molecule is supported by a large number of studies describing specific rRNA-protein interactions or functional sites (for example
28
-
32
). For example, it has been demonstrated that several bases in the highly
conserved hairpin loop of helix 27, where eight out of nine bases are
completely conserved among the 500 16S rRNA sequences, are directly involved in
ribosomal subunit association (
33
) and initiation of protein synthesis (
34
). Another highly conserved region is the pseudoknot structure formed by helices
19-21. This tertiary interaction, originally proposed by Woese and Gutell (
35
), has been shown to be essential for ribosomal function and mild perturbations
of the structure generate resistance to streptomycin, an antibiotic known to
interfere with the decoding process, i.e. A-site tRNA-ribosome interaction (
36
).
Variability maps of bacterial 5S and 23S rRNA
Figure
4
shows secondary structure models for 23S rRNA and 5S rRNA (bottom left) of
E.coli.
The shape and the helix numbering system of the 23S rRNA model are according to
De Rijk
et al
. (
16
,
37
). It conforms largely to the models developed in earlier studies (
38
,
39
).
The 5S rRNA model is slightly different from those previously published. Helices
are numbered 1-3 in order to comply with the principle used for the large rRNAs, to wit
that helices are given different numbers only when separated by a multibranched
loop, a pseudoknot loop or a single-stranded area that does not form a loop. Helices 2 and 3 each consist of
two segments separated by an internal loop. The two single base bulges on the 5'-strand of helix 2 and flanking the internal loop in this helix are
absent in most 5S rRNA secondary structure models (see for example
40
). The existence of the bulge on the 5'-strand upstream of the internal loop was proposed by Van den Eynde
and De Wachter (
41
) and that on the 5'-strand downstream of the internal loop was proposed by Egebjerg
et al
. (
42
). Figure
5
shows the variability maps of 23S and 5S rRNA superimposed upon the secondary
structure models.
Two variable double-stranded areas, namely the segment of helix 2 adjoining the bifurcation
loop and the helix 3 segment adjoining the hairpin loop, can be distinguished
in the 5S rRNA. The high variability of these helices was also noticed
previously (see
8
,
40
,
43
). In the alignment of 260 bacterial sequences, only two positions are
absolutely conserved, namely G
44
A
45
situated in the hairpin loop of helix 2. A tertiary interaction formed by a
Watson-Crick pair between G
44
and C
28
, the second bulge on the 5'-strand of helix 2, was proposed by Egebjerg
et al
. (
42
). However, contrary to the statement of these authors, the bulge corresponding
to position 28 in
E.coli
is not always a C. It is substituted by a U, A or G in several species
belonging to the Proteobacteria [alpha] subdivision, whereas the G
44
is absolutely conserved among the Bacteria. On the other hand, the existence of
the two single base bulges on the 5'-strand of helix 2 is corroborated by compensating substitutions in
the single base pairs separating each of these bulges from the internal loop
half way along helix 2. This is reflected in the fact that each of these base
pairs is formed by two nucleotides of similar variability (orange).
In 23S rRNA, as in 16S and 5S rRNAs, there is a general correspondence in the
variabilities of nucleotides forming base pairs. The tertiary interactions
identified in the former two molecules (Figs
2
and
4
) also link nucleotides of corresponding varariability. This can be seen clearly
in Table
2
. In the case of 23S rRNA, some of these interactions consist of antiparallel
base pairing between sequences of several nucleotides.
Ten highly variable areas (red and orange) can be distinguished in 23S rRNA
(Fig.
5
). They are formed by the following helices: B8 and B9; B14-B16; D2; D13 and D14; D20; D22; E11-E15, E20; G4 and G5; H1-1. These variable areas were also distinguishable in the
Pseudomonas cepacia
sequence conservation plot of Höpfl
et al
. (
44
), constructed by comparison of 20 prokaryotic and two chloroplast sequences,
and in the
E.coli
sequence conservation plot of Egebjerg
et al
. (
1
), based on 42 sequences, of which 24 were bacterial/plastid, 11 eukaryotic and
seven archaeal. Certain variable helices, such as D14 and E12, are interrupted
by conservative internal loops. As in the case of 16S rRNA, the map of Figure
5
improves on previous descriptions in being based on a larger dataset and
quantitative measurements and in being more easily surveyable.
Many of the variable areas are characterized by major size variations. The
hairpin loop of C1, a helix which itself is only moderately variable, is also a
hot-spot for extremely variable insertions in eukaryotic LSU rRNAs. To our
knowledge, these insertions were first described by Hassouna
et al
. (
45
), who referred to them as D(ivergent)-domains. Some areas subject to intense substitution show little or no
length heterogeneity, though. This is the case for helices B14-B16, D2 and E11-E13. As a rule, strong length heterogeneity seems to be most
common in apical helices, i.e. those ending in a hairpin loop. Helices formed
by long distance interactions, i.e. those bounded by multibranched loops, have
less freedom to change in length. It should be noted that the molecule contains
a number of potential branching points which bear additional helices in a
limited set of species. These branching points are not visible in Figures
4
and
5
since they do not exist in
E.coli
. As an example, helices B14 and B15, though apparently forming a continuous
helix, were numbered differently because they are separated by a potential
branching point. Helix B14-1 branching there in some species does show length heterogeneity.
Similarly potential branching points to variable helices exist between helices
D13 and D14, as well as E11 and E12. Multibranched loops such as those
separating D2-D5 and G3-G5 also bear additional helices subject to sequence and length
heterogeneity in certain species.
Applications Of Substitution Rate Calibration
In the above paragraphs, the bacterial rRNA variability maps have been
interpreted mainly in the context of structural interactions within the
molecule, functional interactions with other molecules and evolutionary aspects
of insertion hot-spots. As stated in the Introduction, the maps can also be used, more
efficiently than previously published maps constructed on a more intuitive
basis, for the design of primers and hybridization probes.
Perhaps the most important application of substitution rate calibration is in
the construction of phylogenetic trees. Once the spectrum of relative
evolutionary rates of an rRNA has been measured, this information can be used
to improve the precision of tree construction by distance methods. Two
approaches can be used. One is to divide alignment positions into a number of
sets of increasing relative substitution rate. The conversion of sequence
dissimilarity into distance can then be carried out on each set separately,
taking into account the fact that substitutions in conservative areas carry
more weight than those in variable ones. The final distance, found by averaging
the distances computed from each set, is used for tree construction. This
approach has been followed in a study of eukaryotic evolution (
5
). In the other approach, sequence dissimilarity is converted into distance for
the entire alignment, but the conversion takes into account that dissimilarity
rises more slowly as a function of distance for a set of nucleotides mutating
with variable rates than for a randomly mutating set. This is achieved by using
equation
4
with an appropriate parameter
p
adapted to the shape of the rate spectrum. The latter approach, used to study
the evolution of eukaryotic SSU rRNA sequences of different groups of protists,
yielded some significant improvements in tree topology (
6
,
53
). In particular, tree distortions due to the presence of species with an
exceptionally high evolutionary rate are eliminated to a large extent by these
methods. These distortions are caused by an underestimation of large distances
with respect to small ones if distances are computed assuming equal variability
of all nucleotides in a sequence.
In bacteria too, some taxa are characterized by an exceptionally high
evolutionary rate. A well known example are the mycoplasmas, which, on the
basis of oligonucleotide signatures, have been assigned earlier to the cluster
of Gram-positives with low GC content (
54
). Construction of bacterial SSU rRNA and LSU rRNA evolutionary trees on the
basis of Jukes and Cantor (
19
) or Kimura (
55
) distances regularly show the mycoplasmas as either an independent evolutionary
lineage or as diverging at the base of the aforementioned cluster. In contrast,
application of rate calibration to SSU and LSU rRNA sequences consistently
shows mycoplasmas originating from within the cluster of Gram-positives with low GC content, as expected (
54
,
56
), and this location is supported at a high bootstrap level. This result will be
discussed into more detail elsewhere.
Substitution rate calibration is a general method applicable to all genes for
which a dependable alignment comprising a considerable number of species is
available. It is to be expected that distance trees taking into account the
shape of the evolutionary rate spectrum of the molecules used as a molecular
clock will significantly improve the trustworthiness of the evolutionary trees
obtained. Conceivably, parsimony methods for tree construction that take into
account the shape of the evolutionary rate spectrum of genes can also be
developed in the future.
ACKNOWLEDGEMENTS
Our research was supported by the Programme on Interuniversity Poles of
Attraction (contract 23) of the Federal Office for Scientific, Cultural and
Technical Affairs of the Belgian State and by the National Fund for Scientific
Research. Yves Van de Peer is a Research Assistant of the National Fund for
Scientific Research. We thank Peter De Rijk for comments on the secondary
structure of the 23S rRNA.
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