Dependency Map of Proteins in the Small
Ribosomal Subunit
Kay Hamacher
1,2*
, Joanna Trylska
1,2,3
, J. Andrew McCammon
1,2,4
1 Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California, United States of America, 2 Center for Theoretical Biological Physics,
University of California San Diego, La Jolla, California, United States of America, 3 Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University,
Warsaw, Poland, 4 Howard Hughes Medical Institute and Department of Pharmacology, University of California San Diego, La Jolla, California, United States of America
The assembly of the ribosome has recently become an interesting target for antibiotics in several bacteria. In this work,
we extended an analytical procedure to determine native state fluctuations and contact breaking to investigate the
protein stability dependence in the 30S small ribosomal subunit of Thermus thermophilus. We determined the causal
influence of the presence and absence of proteins in the 30S complex on the binding free energies of other proteins.
The predicted dependencies are in overall agreement with the experimentally determined assembly map for another
organism, Escherichia coli. We found that the causal influences result from two distinct mechanisms: one is pure
internal energy change, the other originates from the entropy change. We discuss the implications on how to target
the ribosomal assembly most effectively by suggesting six proteins as targets for mutations or other hindering of their
binding. Our results show that by blocking one out of this set of proteins, the association of other proteins is
eventually reduced, thus reducing the translation efficiency even more. We could additionally determine the binding
dependency of THX—a peptide not present in the ribosome of E. coli—and suggest its assembly path.
Citation: Hamacher K, Trylska J, McCammon JA (2006) Dependency map of proteins in the small ribosomal subunit. PLoS Comput Biol 2(2): e10.
Introduction
Ribosomes are large ribonucleoprotein assemblies that
conduct the process of translation of the genetic code. They
are composed of two asymmetric subunits, small and large,
which associate through a network of intermolecular inter-
actions. Many antibiotics, which are widely used in the
treatment of bacterial infections, interfere with protein
synthesis. A large number of them bind to the small ribosomal
subunit [1] and block proper ribosome function either by
hindering the decoding process or by inhibiting the func-
tional conformational changes of the ribosome [2]. The
understanding of interactions governing the assembly mech-
anism is of great importance because recently it has also been
found that the aminoglycoside antibiotics inhibit not only the
translation itself but also the formation of the small subunit
[3].
In bacteria, the small and large subunits are named,
according to their sedimentation coefficients, 30S and 50S,
respectively. The 30S subunit, which is the subject of this
study, consists of the 16S ribosomal RNA (16S rRNA), and 21
proteins which are labeled S1, S2, ... , S21. During ribosome
activity, messenger RNA and transfer RNA molecules bind to
the small subunit. The main role of the small subunit is to
maintain translation fidelity by assuring for correct decoding.
In the early 1970s, it was found that the Escherichia coli small
ribosomal subunit can reassemble in vitro from the 16S rRNA
and a mixture of the 30S proteins [4,5]. Such reassembly
produces an active 30S particle, and these experiments
revealed that subunit complexation is a sequential and
ordered process. The proteins were classified as primary,
secondary, or tertiary binders, depending on their ability to
bind alone or only in the presence of other proteins. The
experimentally derived assembly order map is presented in
Figure 1. Since then, the pathway and the mechanism of the
assembly have been of significant interest (for review see [6]),
however, many details of this process still remain unclear.
Apart from the ‘‘assembly order map’’ of Nomura and
coworkers [4,5], a ‘‘kinetic assembly map’’ was also deter-
mined [7]. The kinetics-based map classifies the proteins as
early, middle, middle-late, and late binders, and suggests that
the assembly of proteins proceeds roughly from the 59,
through central, to the 39 domain of 16S rRNA even though
in vitro this process is not coupled with the temporal order of
transcription of the proteins. These two maps (assembly
order and assembly kinetics) serve as a model of the ordered
assembly of E. coli 30S subunits. Because all the information
needed for the small subunit assembly is present in the 16S
rRNA and protein components, it should be possible to study
this process based on the crystallographic structures of the
30S ribosomal complex.
Apart from the vast amount of experimental approaches to
study the association of proteins with 16S rRNA, theoretical
modelling approaches of the 30S subunit assembly have not
been numerous. Coarse-grained Monte Carlo simulations
have been performed to assess the change in fluctuations
Editor: Luhua Lai, Peking University, China
Received July 11, 2005; Accepted December 30, 2005; Published February 17,
2006
A previous version of this article appeared as an Early Online Release on January 4,
2006 (DOI: 10.1371/journal.pcbi.0020010.eor).
DOI: 10.1371/journal.pcbi.0020010
Copyright:
2006 Hamacher et al. This is an open-access article distributed under
the terms of the Creative Commons Attribution License, which permits unrestricted
use, distribution, and reproduction in any medium, provided the original author
and source are credited.
Abbreviations: a.u., arbitrary units; SCPCP, self-consistent pair contact probability
approximation
* To whom correspondence should be addressed. E-mail: hamacher_at_ctbp.ucsd
.edu
PLoS Computational Biology | www.ploscompbiol.org February 2006 | Volume 2 | Issue 2 | e100080

upon binding of proteins in the 39 domain assembly [8] and to
predict the contributions of each of the proteins to the
organization of the binding sites for the sequential proteins
in the S7 pathway. Recently, a similar coarse-grained force
field was applied in molecular dynamics simulations of the
small subunit assembly [9]. However, these two studies focus
more on the 16S rRNA conformational changes due to the
binding events than on the energetics of the 30S assembly. To
account for the latter, we have previously applied an implicit
solvent Poisson-Boltzmann model to study the relative bind-
ing free energies of 30S proteins to 16S rRNA [10]. The
Poisson-Boltzmann all-atom investigation, even though giving
encouraging results, was performed on a single 30S subunit
configuration and was somewhat sensitive to applied param-
eters, such as the dielectric constant of the subunit and the
placement of the dielectric boundary between the 30S
molecule and implicit solvent.
The biggest drawback of all these approaches is that they
are time-consuming thus are not applicable to the several
thousands of configurations we have made for this study. This
huge set of configurations is however necessary to deduce
interdependencies in a comprehensive fashion. Therefore, we
decided to base this work on a computationally faster but still
accurate approach which can focus both on the changes in
energetics and in fluctuations. Our model is based on the self-
consistent pair contact probability approximation (SCPCP)
by Micheletti et al. [11]. The SCPCP has several advantages
over other coarse-grained and computationally fast methods:
a) while it is based on the fluctuations of residues, it can—in
contrast to elastic network models—break contacts between
residues, b) the SCPCP free energy also includes entropies
that are not accessible by methods that compute binding
energies as a sole sum of knowledge based interaction
strengths. The latter cannot provide for long-range influen-
ces, which we found to be relevant in the assembly (see
Results).
We calculated the dependencies of protein binding to 16S
rRNA for the Thermus thermophilus small ribosomal subunit
and were able to reproduce in many aspects the E. coli
assembly map as well as predict the differences of assembly
between those two bacteria. We were able to identify key
proteins most important in mutual stabilization. In addition,
we propose a mechanism of binding for the THX-peptide. In
future work, the model may be easily applied to the large
ribosomal subunit for which a detailed experimental map of
binding is not yet available.
The paper is organized as follows; the Results present the
interdependencies of protein binding for the T. thermophilus
bacterium derived from computational experiments for the
removal from the 30S complex of one or two proteins at a
time. The similarities and differences with the E. coli assembly
map are discussed. The computational model and the
parameterization are presented in the Materials and Methods
section.
Results
Benchmarking by Comparison to Experiment
The SCPCP allows for the computation of the temperature
factors which we compared to B-factors determined in the
crystal structure. We used Spearman’s ranking coefficient [12]
r
s
to quantify the agreement, and the results are shown in
Table 1. We obtained an overall good agreement except for
the S12 protein for which we obtained a significance of 92%.
The origin of this deviation remains unclear because we
cannot relate this effect to the amount of buried surface area
upon binding, protein size, or other quantities that might
influence stability. The crystal structure we used [13] was
obtained only to the resolution of 3.05 A
˚
. We can, therefore,
safely assume that all other computationally derived B-factors
are in good agreement with the experiment.
Additionally, we compared the computed binding free
energies with the available experimental data for T. thermo-
philus 30S primary binding proteins [14–16]. These experi-
ments determined the apparent dissociation constants for the
binding of a single protein to the naked 16S rRNA or its
Figure 1. The 30S Subunit In Vitro Experimental Assembly Map for E. coli
The primary, secondary and tertiary binding proteins are shown in black,
orange, and blue, respectively. Arrows indicate facilitating effect of
binding of one protein on another. Adapted from the review of Culver [6]
based on the work of the Nomura Laboratory [4,5].
DOI: 10.1371/journal.pcbi.0020010.g001
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Synopsis
The ribosome acts as the protein–production facility of the cell.
Interfering with its assembly will shut down the function of the cell.
The bacterial ribosome differs from the eukaryotic one. Both
properties together prompt for the development of antibiotics
targeting the bacterial ribosome. To target this macromolecular
complex most efficiently, one needs to understand the assembly
process. The smaller subunit consists of 21 proteins and a ’ 1500
nucleotide long RNA chain. This size makes it unfeasible to treat the
assembly process with conventional computational techniques. To
overcome this size limit, this paper introduces a new approach
which computes energetic and entropic contributions to the
binding energy of individual proteins. By systematic Gedankenexperi-
ments and an accompanying analysis procedure we were able to
deduce the binding dependencies of the proteins and the influences
of their respective absence or presence onto other proteins. From
the obtained influence map we can deduce potential target proteins
for drug development or other binding hindering experiments.
Assembly of the Small Ribosomal Subunit

fragments. The binding energies are 269 a.u. (arbitrary units)
(51.7 kJ/mole) for S4 [14], 147 a.u. (48.6 kJ/mole) for S8 [15],
and 144 a.u. (42.8 kJ/mole) for S7 [16] (with the experimental
values given in parentheses). As discussed in the Parametri-
zation section, we do not expect to obtain absolute binding
free energies from our computations. We see, however, from
the few available experimental data that the SCPCP method is
capable of giving the correct ordering of the binding strength
in energetic terms.
Influence Map
Influence of removal of one protein from the 30S complex.
First, we performed a computational experiment by remov-
ing each of the 20 proteins one at a time from the whole
complex. We then computed the binding energies for all the
remaining single 19 proteins. From these calculations, we
obtained the differences in binding energies for the 19
proteins induced by the absence of every single protein.
Therefore, we could quantify the stabilizing effect that the
presence of one protein has on the others.
As confirmed above, the SCPCP gives the correct ordering
of binding energies. Therefore, we ranked every removed
protein from the remaining proteins according to their
binding strengths. The removal of one protein can induce a
shift in the ranking, thus indicating the influence of the
removed protein on the re-ranked protein. We quantify this
influence by the difference in rank D
r
. The results are shown
in Figure 2 and the procedure in a pseudo-language in
Protocol S1. The rationale behind such analysis procedure
stems from the fact that relative association or dissociation
probabilities in the assembly map are governed by the order
of binding free energies. If the removal of protein Z changes
the relative order from X-more-strongly-bound-than-Y to Y-
more-strongly-bound-than-X, then the probabilistic assembly
order is also changed, and we attribute an influence of
protein Z on protein X.
In our approximation, we find that proteins S15, S16, S20,
and the peptide THX are neither influenced by any other
protein nor are influencing other proteins. This does not
come as a surprise as those proteins are only in contact with
16S rRNA and not with any other proteins. In some cases, we
notice, however, subtle correlation effects that can be
attributed to a non-local stabilization of proteins. This will
be discussed in the next section. All other proteins are found
to be the members of three influence clusters. These clusters
show a large overlap with the notion of previously obtained
assembly maps for E. coli (see Figure 1 for comparison).
The first one of those clusters has eight members (Figure 2,
blue shaded area). According to our calculations presented in
Figure 2, proteins S6 and S18 influence each other. This is in
agreement with the early experimental study of the assembly
of E. coli 30S proteins where it was proposed that S6 and S18
bind as a dimer [5,7]. Such dimerization of S6 and S18 was
recently proved for a hyperthermophilic bacteria Aquifex
aeolicus [17,18]. Also, the influence of S18 and S11 is in
excellent agreement with the experimental assembly map of
E. coli. The influence of S11 on S7 in Figure 2 is relatively
small, and it is not found in the E. coli assembly map.
However, in the T. thermophilus structure these proteins are in
contact, thus stabilizing each other slightly by the common
interface. We have to emphasize that we study the T.
thermophilus bacteria, therefore, we expect that our map may
differ from that of E. coli, and those differences may be
interesting to note. In the first cluster, S9 protein facilitates
slightly the binding of S10, which is similar to what happens
in the E. coli subunit. The influence of S9 on S7 is due to their
close proximity in the crystal structure. The strong cluster of
Table 1. Comparing Computed versus Experimental B-Factors
with a Ranking Measure (Spearman’s r
s
)
Chain r
s
RNA 0.556
S2 0.683
S3 0.603
S4 0.458
S5 0.328
S6 0.392
S7 0.417
S8 0.260
S9 0.611
S10 0.638
S11 0.280
S12 0.155
S13 0.339
S14 0.479
S15 0.657
S16 0.466
S17 0.670
S18 0.634
S19 0.448
S20 0.296
THX 0.403
We note that for the average protein we need to have r
s
. 0.182 to obtain a significance of 95% or better
[12].
DOI: 10.1371/journal.pcbi.0020010.t001
Figure 2. The Influence Network of the Presence of Single Proteins on
the Binding Stability of the Other Proteins
The three clusters and the four unaffected proteins are visible. The colors
of the arrows indicate D
r
(the larger the number, the stronger the
influence). The arrows point from the removed protein to the affected
protein, e.g., removal of S4 alters the binding strength of S5 with the
‘‘influence strength’’ of 3. The gray arrows indicate the interaction that is
due to very small relative energy change and involves the ‘‘suspicious’’
protein S12 (see text for details).
DOI: 10.1371/journal.pcbi.0020010.g002
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Assembly of the Small Ribosomal Subunit

S3, S10, and S14 proteins is also present in the E. coli
experimental assembly map. All of the three proteins are
tertiary binders according to the E. coli map, and it is,
therefore, not surprising that their binding may be inter-
dependent. It was proposed that these proteins form a strong
hydrophobic cluster [13]. We show that indeed proteins S3,
S10, and S14 have a strong influence upon one another.
The second cluster consists of proteins that are bound to
the 39 domain of 16S rRNA (Figure 2, gray shaded area). The
mutual relation between S13 and S19 agrees again with the E.
coli map and the proposal that these proteins bind together
[6]. The influence of protein S2 on S13 is rather weak and can
be attributed to a relative energy difference smaller than
0.01%. The same situation holds for S12 and S8 in the third
cluster, where the ranking difference is due to a relative
energy change of ;0.004% (relative figures with respect to
the overall binding energy of the complex). Additionally, we
note that the S12 protein was the one whose computed B-
factors did not agree well with the experimental ones.
Therefore, we have to treat the results obtained for S12
carefully.
The stabilizing mutual effect of S17 and S12 in the third
cluster agrees with the E. coli experimental map. The same
holds for proteins S5 and S8; in the E. coli map in Figure 1 the
binding of S5 is strongly dependent on S8. We also see the
impact of S4 on S5 which is present in the E. coli assembly
map but it is not a direct influence; instead it involves protein
S16. In our simulations of T. thermophilus, S16 is not in the
influencing clusters. We also see an additional influence of
S17 and S12 on S8 which is not suggested for E. coli. This is
due to a common interaction surface of those proteins. The
interaction of S17 and S8 is further interesting because S8 is
binding to the central domain of 16S rRNA and it is therefore
believed to be a later binder than S17. If this is the case, then
S8 is probably responsible for maintaining the proper fold of
the RNA that occurs during protein binding.
By removing one protein at a time and analyzing the effects
by means of D
r
, we were able to deduce a large fraction of the
stabilizing influences in the T. thermophilus assembly map. We
can, however, proceed further with the procedure of protein
removal to investigate the interdependencies in more detail.
This is presented in the following section.
Second-order stabilization revealed by two-protein remov-
al. We went one step further in the disassembly by removing
every pair of proteins and by computing the binding energies
of the remaining ones in the same way as above. Details on
the procedure can be found in Protocol S1. The results
represent a tensor DG
k
ij
whose values show the induced effect
of removing proteins i and j on the binding free energy of the
third protein k. We set DG
k
ii
¼ DG
i
ij
¼ DG
i
ji
¼ 0 for simplifica-
tion of notation.
For a fixed k, the resulting matrix DG
k
can be approximated
in general by a truncated sum of the form DG
k
’ R
L9
l¼1
k
l
~u
l

~u
T
l
where ~u
l
are the L ¼ 20 eigenvectors of DG
k
ij
and k
l
are the
respective eigenvalues. The eigenvectors and eigenvalues are
assumed to be ordered from the smallest to the largest
eigenvalue. The upper bound L9L defines the accuracy of
the approximation. This expansion allows us in general to
visualize the effects of the removal of two proteins in a very
concise fashion by looking mainly at the eigenvectors. The
contribution of a protein to the binding free energy is
proportional to its respective entry in the eigenvector.
We restricted our analysis to the two eigenvectors that are
most important for destabilization. Close inspection of the
resulting eigensystems prompts for a modified approxima-
tion of DG
k
as indicated above. We found the distribution of
eigenvalues k
l
for all k to be dominated by one large negative
eigenvalue of magnitude O(10
3
), and we encountered 18
positive eigenvalues ;O(10
1
)  O(10
2
). Note that there is
always an additional null-mode with k
2
¼ 0 because of our
setting DG
k
ii
¼ DG
i
ij
¼ DG
i
ji
¼ 0.
A destabilization occurs whenever the absolute value of the
released binding free energies gets smaller. In our sign
convention for the k
l
, this is equivalent to either a small entry
in the eigenvector ~u
1
for the eigenvalue k
1
0oralarge entry in
~u
20
for the eigenvalue k
20
. 0. The resulting influences are
shown in Figure 3. We would like to emphasize that the
effects of removing one protein are still present and are
found to be in the set of those influences stemming from the
smallest eigenvalue k
1
(Figure 3, crosses).
Close inspection of Figure 3 leads to a new insight beyond
the one protein removal experiment presented in the
previous section. We can distinguish two groups of destabi-
lizing effects: interactions due to direct contacts (which we
will call local) and interactions that occur between proteins
that are not in contact (non-local).
First, we present the analysis of the local effects. The
removal of protein S2 destabilizes the binding of S8, as they
are in contact in the crystallographic structure. Additionally,
the removal of S2 weakens its bond to S3 by a local
mechanism because both proteins are in proximity, too. In
the following contacts, the deletion of the first protein
induces additionally a weakening of the second one: S3!S4,
Figure 3. Color-Coded Contribution to Destabilization, Determined by
Eigenvector Analysis of the Two-Protein Removal Experiment
Red diamonds indicate contributions from the smallest and blue
diamonds from the largest eigenvalue, respectively. The symbol 3
indicates influences that were already found in the one protein removal
experiment of the previous section. The green 3 were discussed in the
previous section. The respective energy differences of those two
interdependencies are rather small and enter into the magnitude of
entries of the eigenvectors only slightly. Entries for ~u
20
were marked if
the value deviated more than 10% from their most likely value, while for
~u
1
this threshold was set to 1%, reflecting the respective order of
magnitude of k
1/20
.
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Assembly of the Small Ribosomal Subunit

S3!S2, S3!S10, S5!S4, S7!S9, S8!S2, S10!S9, S14!S9,
S17!S8, and S8!S17. All these influences are local and they
overlap with the results from the previous section where we
removed only one protein at a time. This indicates the
consistency of both our computations and of our analysis
procedure.
We also note the following dependencies: S6!S15,
S8!S15, S17!! S15, and S18!S15. As remarked in the
previous section, S15 is not in proximity to any other protein.
Therefore, its destabilization by all above proteins cannot be
caused by the change in the internal energy as this term is
local and equal to zero for all non-contacting residues, which
is obvious from Equation 1. As we are concerned with the
binding free energies, the only other contribution can be
entropic. The same argument holds for all the remaining
influences. From those subtle contributions, we deduce
additional stabilization effects. Moreover, this shows that
our procedure also incorporates the non-local effects.
Scoring by knowledge-based potentials only could not
provide us with such information. In the latter approach,
we would observe only those peaks in the eigenvectors that
were already found in the one protein removal case, and the
effects would be just additive.
The entropic non-local effect of (de)stabilization can be
explained as follows: consider a protein A that binds to either
the whole complex or to a complex that lacks protein B. If B is
bound, the RNA is more stiff, thus A encounters a more stiff
segment to bind to. In this case, A has to adjust its internal
motions and fluctuations to the more rigid binding partner
on a greater scale. But reducing the internal motion to a
greater amount is accompanied by the release of more
entropy, thus DS
B
. DS
3
. Therefore, the presence of B
stabilizes the bound form of A. It was previously determined
[8,9] that binding of the 30S proteins reduces the flexibility of
the 16S rRNA and its respective fluctuations, and the above
argument holds here, too. This effect is also present in the
binding of proteins with local interactions, but the additional
contribution from the contact energy makes it difficult to
judge which one is the dominating contribution. As the
SCPCP takes into account the entropic contributions only
from the bond fluctuations, we presumably underestimated
the real entropy change. Thus, we expect the effect we
described above to be more pronounced in the real molecule.
These influences are shown in Figure 4. We note that it is not
necessary to compute any entropy. The entropies are
naturally deducible from the eigenvalue spectrum, and the
fact that every free energy difference between non-contacting
residues can only be attributed to entropic effect, as non-
contacting residues do not contribute potential energy, as is
easily deducible from the Hamiltonian in Equation 1.
Assembly as an antibiotic target. To prevent bacteria
growth, one can think of interfering with its protein synthesis
through interfering with the assembly of the ribosomal
subunit. Recently, antibacterial agents were found to prevent
not only the translation process itself but also the assembly of
the 30S and 50S ribosomal subunits (see, e.g., [3,19–21]).
Aminoglycoside antibiotics, paromomycin and neomycin,
were shown to have an inhibitory effect on the assembly of
the 30S subunit both from E. coli [3] and from Staphylococcus
aureus [19]. Therefore, subunit formation and translation are
both targets for antibiotic inhibition. It was also found that
the small subunit assembly is hindered by mutations in
certain 30S proteins (e.g., S4, S5, S7, and S17 [6], and
references therein).
Hence, it seems to be most effective to not only inhibit the
binding of just one protein but, instead, of several at the same
time. Also, if one prevents an ‘‘influential’’ protein from
binding to the 16S rRNA, one not only decreases the
association rate of that particular protein and, therefore,
translational effectiveness but also hinders the binding of the
influenced proteins, making it even more unlikely to obtain a
functional subunit. In terms of chemical kinetics, if the
absence of a protein A increases the dissociation rate k
off
of
other proteins B
i
in its influence cluster by a factor of
expðbDG
A;B
i
Þ, then the overall equilibrium is shifted away
from the functional ribosome to partially formed pre-
products by an amount expðb
P
i
DG
A;B
i
Þ. We assume for
simplicity that the B
i
are not influencing each other. These
higher-order effects would even amplify the destabilizing
effect we are suggesting. If we assume all the DG to be
somehow distributed, this factor is in general larger than just
the factor induced by reducing the binding of another
protein C by some other value DG
C
.
Close inspection of the resulting dependencies presented
in Figures 2 and 4 point to S14 or S10, because this would also
lead to a smaller amount of bound S3, S10, and THX, or S14
and S3, respectively. Another attractive choice would be
either S8 or S5 in the left cluster of Figure 2 or S6 or S18 in
the middle group. Such a choice would also destabilize S15.
As it is known that the 30S proteins bind roughly from the 59
to the 39 domain of 16S rRNA [7], we suspect that the most
likely candidates are S14 or S10. These proteins are late
binders, and because we study herein the binding of proteins
to a perfectly folded structure of 16S rRNA, our simulation
setup is closer to an experimental situation for late binders
than for early ones. The early binders may in theory bind to
only partially folded 16S rRNA.
Figure 4. The Additional Destabilization from the Two-Protein Removal
Case Mapped onto the E. coli Map (Blue Diamonds in Figure 3)
The green proteins are not in contact with any other protein. The
peptide THX was placed close to the proteins that influence its binding
stability. All interactions are non-local, as the respective proteins are not
in proximity.
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Assembly of the Small Ribosomal Subunit

Predictions for the peptide THX. For the THX peptide, we
found an influence from S9, S13, S14, and S19 proteins
through entropic contributions. As this molecule is not
present in the E. coli ribosome, we would like to suggest
experiments in this direction to confirm our prediction that
THX and the other proteins are related in their assembly
behavior.
Discussion
In this study, we applied an analytic procedure to the
problem of the stability of proteins in the small subunit of the
ribosome of T. thermophilus. In the first step, we determined
several dependencies between the various proteins of the
macromolecular complex. We found an overall good agree-
ment with the in vitro determined assembly map of E. coli and
have shown the differences in comparison with the T.
thermophilus structure. In the second step, we developed a
procedure to investigate the effects of interdependent
removal of proteins on the stability of the remaining ones.
We found additional pathways that are in agreement with the
experimental E. coli assembly map. In addition, we have shown
that in roughly half of the cases the non-local effects were
responsible for the influences. As our model provides for the
energetic contributions only in a local fashion, we were able
to distinguish entropic contributions from the fluctuational
restrictions imposed on the 16S rRNA upon binding of
proteins. Additionally, we propose a new path in the T.
thermophilus assembly map for the THX peptide which is not
present in the E. coli 30S subunits.
We note that while the method uses a knowledge-based
potential, electrostatic interactions are implicitly taken into
account. To what extent, however, remains unknown. We
therefore could not deduce all dependencies. Additionally,
we utilized the crystal conformations for single proteins from
the 30S subunit crystal structure. This is not necessarily a
precise approach because the free proteins in solution might
undergo a structural change. On the other hand, the range of
coarse graining is large so that small deviations should not
make a difference.
In future, we plan to apply this method to study the
assembly of ribosomal proteins in the large subunit. We
believe that our studies may help in the investigation of
further antibiotics that target the ribosomal apparatus of
bacteria.
Materials and Methods
Computational approach. The self-consistent pair contact proba-
bility approximation (SCPCP) by Micheletti et al. [11] was used to
compute an approximation of the binding free energy. In this model,
we treat the building blocks of both the proteins and rRNA— namely
amino acids and nucleotides—as beads on a chain centered around
their respective C
a
– and P– positions. The potential energy of the
amino acids and nucleotides is approximated by a sum of harmonic
interactions along the backbones of proteins, and by terms which
assign a harmonic energy to contacts as long as the displacement is
smaller than some R. The Hamiltonian of the system may be written
in the form:
H ¼
T
2
X
N1
i¼1
K
i;iþ1
N
i;iþ1
~
X
2
i;iþ1

X
N
i;j¼1
D
ij
j
ij
2
½R
2

~
X
2
i;j

HðR
2

~
X
2
i;j
Þð1Þ
with
~
X
2
i;j
¼ð~r
i;j
~r
0
i;j
Þ
2
¼ðD~r
i
 D~r
j
Þ
2
ð2Þ
The contact matrix element D
ij
is 1 if the spatial distance between
the heavy atoms of the residues i and j is smaller than the predefined
contact distance which we set to R
C
¼ 3.75 A
˚
for the heavy atoms (see
[22] and the Structure Preparation section for details). N
i;iþ1
resembles the backbone connectivity and is 1 if i and i þ 1 are
covalently bound and 0 otherwise. D~r
i
¼~r
i
~r
0
i
is the displacement
vector of an amino acid or nucleotide from its native conformation
~r
0
i
. K
ij
is the strength of the pseudo-bond between beads i and j, while
j
ij
assigns a bead-specific contact energy to the beads (see the
Parametrization section for details).
One can try to integrate the Hamiltonian of Equation 1 by
molecular dynamics simulations [23]. This would be close to
simulating the system in a Go¯-like fashion [24]. Micheletti et al. [11]
proposed, however, a more efficient self-consistent recurrence that
allows for both an analytic and a fast treatment.
The contact probability is defined p
ij
:¼hHðR
2

~
X
2
i;j
Þi
H
as the
thermodynamic expectation value of the contact defining function.
We can then replace HðR
2

~
X
2
i;j
Þ in Equation 1 by p
ij
. In this mean-
field approximation, we obtain Gaussian-like integrals for the
partition function. It is then possible to derive a recurrence relation
for the p
ij
that converges very fast. The relation reads for the n þ 1
iteration
p
ðnþ1Þ
ij
¼ C
3
2
;
R
2
2G
ðnÞ
ij
0
@
1
A
ð3Þ
where
G
ðnÞ
ij
¼ M
ðnÞ
ii
þM
ðnÞ
jj
M
ðnÞ
ij
M
ðnÞ
ji
ð4Þ
and
M
1ðnÞ
ij
¼


K
ij
ðN
i;iþ1
þ N
i;i1
Þþ2
X
l
D
il
j
il
p
ðnÞ
il
=Ti¼ j
2p
ðnÞ
ij
D
ij
j
ij
=T  K
ij
ðd
i;jþ1
þ d
i;j1
Þ i 6¼ j
ð5Þ
Now we can compute the free energy most efficiently by
F=T ¼
3
2
ðNlnð2pÞþlnðdetMÞÞ 
R
2
2T
X
ij
D
ij
j
ij
p
ij
ð6Þ
The free energy arises from two different sources: a) the sum of
contact energies from knowledge-based potentials, and b) entropies
arising from fluctuations. While the last term can in principle be
Figure 5. The Angle a
s
between the Respective Eigenvectors for an
Interaction Strength j of Protein S12 and for the Full Parameter Set
The broken vertical lines indicate the average values used in the first two
validation experiments in the section Sensitivity to Parameters. The full
parameter set refers to the one in the Results section under Influence
Map, Second-order stabilization revealed by two-protein removal.
Inset: Illustration of the deviation in the~u
20
eigenvector contributions for
the two different average interaction values (shown for the worst case of
S7).
DOI: 10.1371/journal.pcbi.0020010.g005
PLoS Computational Biology | www.ploscompbiol.org February 2006 | Volume 2 | Issue 2 | e100085
Assembly of the Small Ribosomal Subunit

computed from elastic network models or estimated otherwise [25],
the SCPCP is a more detailed approach as it allows for the breaking of
contacts.
Parametrization. For the amino acid–amino acid interactions ~j
ij
we apply the values from the knowledge-based potentials of Miyazawa
and Jernigan [26]. These values were already successfully used with
the SCPCP method on a more coarse-grained level in the study of
binding of bovine pancreatic phospholipase A2 [27]. The interactions
between different proteins were weighted according to the values
reported in [28]. The intra-RNA contacts were assigned a strength of
2.51RT, the protein–RNA interactions an energy of 2.83RT [9,29,30].
For K
protein
we set 83.33RT as in [30], while for the RNA we set softer
bonds with K
RNA
¼ 5RT as in [30]. Table 2 and Table 3 show those
values in widely used units of kcal/mole.
We adjusted the j
ij
for the well depth by setting j
ij
:¼
~j
ij
R
2
so that the
contacts in the native structure retain the Miyazawa-Jernigan contact
energies in the Hamiltonian (Equation 1).
Binding energies are now computed as the difference of the free
energies between the complex and the binding partners—obtained
with three separate SCPCP computations. With this approach, we do
not expect to obtain exact binding free energies as, e.g., solvent
effects are taken into account only implicitly by the usage of
knowledge-based potentials. We have merely chosen the values above
to weight the interactions according to their strength. Therefore, we
referred to the obtained values in the preceding parts of this paper as
being measured in a.u.
Additionally, we would like to emphasize that the results are not
sensitive to the choice of the parameters (see below). They were
merely chosen to obtain reasonable energy scales. With the suggested
method, we cannot reveal mechanisms of molecular recognition, but
we can reveal the mutual influence of binding partners in larger
macromolecular complexes.
Sensitivity to parameters.We tested the stability of the results with
respect to our chosen parametrization. To this end we first
constructed two different tests: a) we averaged the respective values
of Keskin and Miyazawa-Jernigan and assigned to every protein–
protein contact an interaction energy j
intrachain
¼ 3.58RT, and for
every internal contact in a protein a value of j
intrachain
¼ 3.18RT; and
b) we assigned to every protein contact—regardless whether internal
or external—an overall average of j
uniform
¼ 3.37RT.
We repeated the two-protein removal tests and obtained the
eigenvectors ~u
j
l
and eigenvalues k
j
l
for both sets of js and for every
protein in the same fashion as described above for l2½1; 20.
Again the eigenvalues k
1
and k
20
showed the same behavior, so we
proceeded with a sensitivity analysis of the eigenvectors which reflect
the influence of proteins on each other as given by the respective
vector entries. For this analysis, we computed the angle
a
j;l
s
¼ arccosð~u
j
l

~u
MJ=K
l
Þ between the obtained eigenvectors in the
test and the ‘‘full’’ computation (using the Miyazawa-Jernigan/Keskin
interaction values) from above. j reflects the two test sets and
l2f1; 20g. The s indicates that this angle is a sensitivity parameter: if
the angle is small, the eigenvectors agree very well and the predicted
influences are the same.
For the eigenvector number 1, we found every angle to be smaller
than 38. We averaged the angles over all the proteins subject to any
influence and obtained a
j
interchain
=j
intrachain
;1
S
¼ 0:15860:038 and
a
j
unif orm
;1
S
¼ 0:08860:28, respectively.
For eigenvector number 20, we found 18 out of the 20 angles to be
smaller than 38 for both sets of j. Their averages were
a
j
interchain
=j
intrachain
;20
S
¼ 0:73860:188 and a
j
unif orm
;20
S
¼ 1:37860:278, respec-
tively. The two proteins (S7 and S9) for which the 20th eigenvector
showed a larger angle (’208) were analyzed further. We plotted the
relevant entries for S7, which showed the larger angle at ’248 (Figure
5, inset). Clearly the differences in the angle stem from the entries for
the influence of S9 and S11. Our 10% rule nevertheless does not fail
and will still assign an influence to both those proteins. The influence
of the changed parameters is too small to decrease the entries to an
amount that they would not be assigned as influential anymore.
To investigate the robustness of the method further, we took an
orthogonal approach and changed the interactions of all residues of
one particular protein (S12) systematically within a reasonable range
of possible interaction energies. We kept all the other interactions at
their original Miyazawa-Jernigan/Keskin values. We chose S12, as this
protein is subject to most one-protein and two-protein removal
influences at the same time and should therefore be most sensitive. In
addition, this protein was the one whose performance in the B-factor
comparison was the worst. We expect this protein to be most
influenced by any perturbations in the interactions. We removed all
of the other possible two-protein pairs as above and obtained the
eigenvectors of the resulting matrix. We show the angle a
s
as a
function of the S12-interaction strength j in Figure 5. The overall
dependence on j is very small and most likely has numerical reasons.
The overall offset of
a
s
’ 0:1258 is due to the averaged j in contrast to
the distributed j
ij
of the full parameter set of the original calculation.
Clearly the relevant eigenvectors 1 and 20 are only subject to a small
influence whose impact will be taken care of by the 1%/10% filter
rule. As an additional test, we computed a
s
also for the protein S12
but changed the interactions of S2 in the same way as above. S2
performed well in the B-factor benchmarking. We found only
smallest angles of deviation in both relevant eigenvectors.
In all test cases (averaged and varying j) we found the deviation in
the eigenvectors to be very small (roughly smaller than 38). With this
we have shown the robustness of our combination of model and
analysis procedure.
Structure preparation. The atom positions were taken from a T.
thermophilus crystal structure obtained for a 3.05 A
˚
resolution [13]
(PDB entry code 1j5e). This particular structure was chosen because of
its best available resolution and the fact that it was crystallized as a
native 30S complex without any bound ligands. It does not contain the
S1 protein, but the omission of S1 does not reduce the ribosome
function or prevent the 30S subunit assembly [31]. The structure
contains proteins S2 to S20, which correspond to those of E. coli, and a
small peptide, THX. The structure of T. thermophilus lacks protein S21.
For the heavy atoms of the 30S structure, we computed the contact
matrix D
ij
(see Equation 1) with a contact distance of the heavy atoms
R
C
set to 3.75 A
˚
for both the amino acids and the nucleotides. To
account for the stronger interactions in the regions where the RNA
forms a double helix and Watson-Crick base pairing takes place, we
added some intra-RNA contacts between the phosphate atoms. These
contacts were added for only those P


P pairs that could not be found
with our choice of R
C
. The numbering for the double helical regions
was taken from the secondary structure of the 16S rRNA presented in
[32]. Additionally, to avoid any long gaps in the structure, we placed
the missing phosphate atoms of nucleotides 1535–1538 of 16S rRNA
by molecular modelling and visual inspection without adding any
further contacts. Therefore, we just introduced a backbone loop for
those nucleotides.
Implementation. The SCPCP software was implemented using Cþþ ,
lex and yacc, the GNU Scientific Library, as well as the SuperLU-
library for matrix inversion [33]. A BASIC-like configuration language
steers the computation. The implementation allows for definitions of
abstract sets of contacting entities (e.g., all hydrophobic amino acids
in contact with all nucleotides) and their respective strengths.
Table 2. The Contact Interaction Strengths Applied in Our Model
j
ij
Amino Acid in
Protein a
Amino Acid in
Protein b
RNA
Amino Acid in Protein a [26] [28] 1.70
Amino Acid in Protein b [28] [26] 1.70
RNA 1.70 1.70 1.51
All values are in kcal/mol.
DOI: 10.1371/journal.pcbi.0020010.t002
Table 3. The Covalent Bond Strengths Applied in Our Model
Backbone Type KT
Protein 50
RNA 3
All values are in kcal/mol.
DOI: 10.1371/journal.pcbi.0020010.t003
PLoS Computational Biology | www.ploscompbiol.org February 2006 | Volume 2 | Issue 2 | e100086
Assembly of the Small Ribosomal Subunit

Supporting Information
Protocol S1. Details of the One- and Two-Protein–Removal Proce-
dures in a Pseudo Programming Language
Found at DOI: 10.1371/journal.pcbi.0020010.sd001 (85 KB PDF).
Acknowledgments
KH is grateful for the hospitality of Professor Bogdan Lesyng and the
Interdisciplinary Centre for Mathematical and Computational
Modelling of Warsaw University, where part of this work was done.
JT and JAM would like to thank Professor Charles L. Brooks III for
ideas on studying the small subunit assembly with theoretical implicit
solvent methods. We are grateful to unknown referees who prompted
for a detailed investigation of the protocol used towards parameter
perturbations (see the section Sensitivity to Parameters) and the
kinetic implications of protein removal.
Author contributions. KH, JT, and JAM formulated the project. KH
wrote the software, performed all the computations, and performed
the sensitivity analysis. KH and JT analyzed the results. JT prepared the
30S subunit structure for computations and designed the computa-
tional validation experiments. KH, JT, and JAM wrote the paper.
Funding. KH is supported through a Liebig-Fellowship of the
Fonds der chemischen Industrie. Other support has been provided by
NSF (MCB-0071429 for JAM), NIH (GM31749 for JAM), HHMI, CTBP,
NBCR, W. M. Keck Foundation, and Accelrys, Inc. JT was also
supported by the Ministry of Scientific Research and Information
Technology (115/E-343/ICM/BST-1076/2005) and by European CoE
MAMBA.
Competing interests. The authors have declared that no competing
interests exist.
&
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Assembly of the Small Ribosomal Subunit