Changes in the level of poly(Phe) synthesis in Escherichia coli ribosomes containing mutants of L4 ribosomal protein from Thermus thermophilus can be explained by structural changes in the peptidyltransferase center: a molecular dynamics simulation analysis

Abstract

Data from polyphenylalanine [poly(Phe)] synthesis determination in the presence and in the absence of erythromycin have been used in conjunction with Molecular Dynamics Simulation analysis, in order to localize the functional sites affected by mutations of Thermus thermophilus ribosomal protein L4 incorporated in Escherichia coli ribosomes. We observed that alterations in ribosome capability to synthesize poly(Phe) in the absence of erythromycin were mainly correlated to shifts of A2062 and C2612 of 23S rRNA, while in the presence of erythromycin they were correlated to shifts of A2060 and U2584 of 23S rRNA. Our results suggest a means of understanding the role of the extended loop of L4 ribosomal protein in ribosomal peptidyltransferase center.

Appendix

In this section, a justification is given for the application of a linear regression analysis to identify distant groups affected by the mutations. First, we start with a simplification of the complex process of the protein elongation step, by assuming that the binding of the aminoacyl-tRNA to the A-site pocket is the rate limiting step. According to the transition state theory,

$$ {\text{Kinetic scheme 1: L }} + {\text{ S }} \rightleftarrows {\text{ }}({\text{LS}})^{{ \ne {\text{ }}}} \to {\text{ LS}} $$

where L is the ligand (aminoacyl-tRNA), S is the acceptor molecule (mRNA-programmed ribosome, containing peptidyl-tRNA at the P-site), and LS is the encounter complex prior to peptide bond formation.

The rate constant k of the overall reaction is given by

$$ k = \frac{{k_{{\text{B}}} T}} {h}{\text{e}}^{{ - \Delta G^{{ \ne {\text{ }}}} {\text{/ }}RT}} , $$

(3)

where $\Delta G^{{ \ne}} = G^{ \ne }_{{{\text{LS}}}} {\text{ }} - {\text{ }}(G_{{\text{L}}} {\text{ }} + {\text{ }}G_{{\text{S}}} ).$

In the latter relationship, ΔG ^≠ is the activation energy, G ^≠_LS is the free energy of the activated complex, and G _L, G _S are the free energies of the ligand and the acceptor molecule, respectively. The symbols T, k _B and h have their usual meaning. It might be expected that the activation energy depends on the conformation of the binding pocket and that of the ligand (aminoacyl-tRNA). Also, it might be expected that some conformations of the binding pocket favor binding (smaller ΔG ^≠) while others prevent it (higher ΔG ^≠). It is reasonable to assume that the major contribution to the dependence of ΔG ^≠ on conformational changes comes from G ^≠_LS . This is because aminoacyl-tRNA is not disturbed by the mutations and because the changes of G _S are small compared with changes of the interaction energy between n groups at the (LS)^≠ interface. Lets denote by δ _i the distance of an individual residue i of S at the interface with L from its counterpart at L. The interaction potential between these individual groups is assumed to be of the Lennard-Jones type. For small changes in δ _i , leaving the system on the same side of the potential well, we can roughly adopt a linear dependence of the interaction potential on δ _i . Other factors contributing to the activation energy do not significantly depend on δ _i and therefore,

$$ \frac{{\partial \Delta G^{ \ne}}} {{\partial \delta _{i}}} \sim {\left\langle {\frac{{\partial U}} {{\partial \delta _{i} }}} \right\rangle} \sim\gamma _{i}. $$

(4)

In Eq. 4, U is the total interaction potential of all trans-interacting groups at the interface, and γ _i are constants. The symbols “∼” and “ ${\left\langle {} \right\rangle}$” denote proportionality and ensemble averaging correspondingly.

After mutating an amino acid at the extended loop of L4, the disturbed system adopts a new equilibrium for residue positions (near the original), leading to a change dδ _i in δ _i . In turns, this leads to a change in the rate constant,

$$ {\text{d}}k = - k\frac{{\partial \Delta G^{ \ne } }} {{RT\partial \delta _{1} }}{\text{d}}\delta _{1} - k\frac{{\partial \Delta G^{ \ne } }} {{RT\partial \delta _{2} }}{\text{d}}\delta _{2} - \cdots - k\frac{{\partial \Delta G^{ \ne } }} {{RT\partial \delta _{n} }}{\text{d}}\delta _{n} . $$

(5)

Equation 5 combines with 4 to give the relationship

$$ {\text{d}}k = {\sum\limits_{i = 1}^n {\beta _{i} {\text{d}}\delta _{i} } }, $$

(6)

where $\beta _{i} \approx -\frac{{k_{{{\text{wt}}}} \gamma _{i} }} {{RT}},$ and k _wt is the rate constant for the wild type.

We can use similar considerations to generalize the above analysis to include all N interacting groups in the ribosome and express the overall change of the experimentally measured level of poly(Phe) synthesis in 60 min, R, as a linear function of dδ _i . We use as a measure of dδ _i what we call here shifts, s _i , given by the relationship

$$ s_{i} = {\sqrt {(x^{{\text{m}}}_{i} - x^{{{\text{wt}}}}_{i} )^{2} + (y^{{\text{m}}}_{i} - y^{{{\text{wt}}}}_{i} )^{2} + (z^{{\text{m}}}_{i} - z^{{{\text{wt}}}}_{i} )^{2} } }, $$

(7)

where x ^m ,y ^m ,z ^m and x ^wt ,y ^wt ,z ^wt are the equilibrium coordinates of the residues’ mass centres. Hence:

$$ {\text{d}}R = {\sum\limits_{i = 1}^N {\alpha _{i} s_{i} } }{\text{ or }}R_{{m }} = R_{{wt}} + {\sum\limits_{i = 1}^N {\alpha _{i} s_{i} } }. $$

(8)

Coefficients α _i summarize all parameters affecting R, which do not depend on mutations.

Concerning the sum in Eq. 8, we notice that most of its terms contribute very little because of relatively small s _i or/and small α _i . Moreover, since α _i can be positive or negative, they can cancel each other in many cases. On the other hand there must be some regions of the 50S subunit, like the PTase center, that are expected to contribute largely. In the frame of this analysis, we tried to identify the residues that exhibit the largest contributions in the sum of Eq. 8, keeping only two variables in the regression analysis. Of course this is not a rigorous analysis. Nevertheless, it is operationally a useful one, since a posteriori the results of the regression analysis are meaningful.