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 computational validation experiments. KH, JT, and JAM wrote the paper.
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.
The authors have declared that no competing interests exist.
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
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
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 interactions. 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 [
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
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 [
Apart from the “assembly order map” of Nomura and coworkers [
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 upon binding of proteins in the 3′ domain assembly [
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. [
We calculated the dependencies of protein binding to 16S rRNA for the
The paper is organized as follows; the Results present the interdependencies of protein binding for the
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 [
Comparing Computed versus Experimental B-Factors with a Ranking Measure (Spearman's
Additionally, we compared the computed binding free energies with the available experimental data for
First, we performed a computational experiment by removing 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 Δ
The three clusters and the four unaffected proteins are visible. The colors of the arrows indicate Δ
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
The first one of those clusters has eight members (
The second cluster consists of proteins that are bound to the 3′ domain of 16S rRNA (
The stabilizing mutual effect of S17 and S12 in the third cluster agrees with the
By removing one protein at a time and analyzing the effects by means of Δ
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
For a fixed
We restricted our analysis to the two eigenvectors that are most important for destabilization. Close inspection of the resulting eigensystems prompts for a modified approximation of Δ
A destabilization occurs whenever the absolute value of the released binding free energies gets
Red diamonds indicate contributions from the smallest and blue diamonds from the largest eigenvalue, respectively. The symbol × indicates influences that were already found in the one protein removal experiment of the previous section. The green × 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
Close inspection of
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, 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 Δ
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.
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., [
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
Close inspection of the resulting dependencies presented in
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
In this study, we applied an analytic procedure to the problem of the stability of proteins in the small subunit of the ribosome of
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.
The self-consistent pair contact probability approximation (SCPCP) by Micheletti et al. [
The contact matrix element Δ
One can try to integrate the Hamiltonian of Equation 1 by molecular dynamics simulations [
The contact probability is defined
Now we can compute the free energy most efficiently by
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 computed from elastic network models or estimated otherwise [
For the amino acid–amino acid interactions
The Contact Interaction Strengths Applied in Our Model
The Covalent Bond Strengths Applied in Our Model
We adjusted the
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.
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
We repeated the two-protein removal tests and obtained the eigenvectors
Again the eigenvalues λ1 and λ20 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
For the eigenvector number 1, we found every angle to be smaller than 3°. We averaged the angles over all the proteins subject to any influence and obtained
For eigenvector number 20, we found 18 out of the 20 angles to be smaller than 3° for both sets of
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
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
In all test cases (averaged and varying
The atom positions were taken from a
For the heavy atoms of the 30S structure, we computed the contact matrix
The SCPCP software was implemented using C++, lex and yacc, the GNU Scientific Library, as well as the SuperLU-library for matrix inversion [
(85 KB PDF)
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.
arbitrary units
self-consistent pair contact probability approximation