INTRODUCTION

The ribosome is a molecular machine responsible for the translation process (protein synthesis from amino acids based on the mRNA matrix) in all living organisms. Over the past decades, the structure of the ribosome has been studied quite well [1], and its large-scale changes during translation have been revealed [2–5]. However, the physical processes responsible for the operation of this molecular machine are still a matter of debate. In particular, experimental data indicate that the relative movement and change in the conformation of the participants in the translation process—ribosomes, tRNA, and mRNA—are correlated with each other [4–7]. For example, the movement of tRNA through the ribosome is synchronized with the movement of mRNA [3, 6, 8], large-scale changes in the conformation of tRNA [9] and the ribosome [4, 5, 10, 11], as well as such chemical reactions as hydrolysis of GTP in translation factors [9] and the attachment of an amino acid to a growing peptide chain [12]. In addition, complementary binding of the mRNA codon to the tRNA anticodon in the tRNA decoding center changes its shape (tRNA accommodation occurs) [13], and the arm of the small ribosomal subunit shifts, triggering the process of GTP hydrolysis in the translation factor EF-Tu [13, 14]. In this case, the functionally active centers of the ribosome and tRNA, in which the aforementioned processes occur (including the decoding center, catalytic center, areas of significant conformational changes), are located at a considerable distance from each other (up to 9 nm).

The coordinated work of various parts of the ribosome suggests the existence of a process that coordinates their actions [6, 15, 16], but this is still unknown. Several hypotheses have been put forward regarding it, mainly of a mechanistic nature [6, 15, 16]. We recently suggested that the coordinated action of ribosome elements may be due to the transport of charges (holes) along rRNA and tRNA molecules, which leads to localization of charges in certain regions and subsequent conformational changes in the latter [17]. Electron/hole (nonionic) charge transport along RNA is possible due to π-stacking of nitrogenous bases, which can lead to a significant overlap of π-electronic systems of nucleotides. The adequacy of the hypothesis put forward was confirmed using computer modeling: it was shown that efficient hole transport is possible along the tRNA molecule, as well as along the rRNA region connecting the iron–sulfur cluster Fe4S4 and decoding center. However, the possibility of charge transport along other regions of the ribosome (the structural basis of which is rRNA molecules), and, consequently, the possibility of “electronic” coordination of their work, have not been investigated.

The ribosome consists of two subunits, large and small, into the space between which tRNA and mRNA molecules enter and move along it. One of the important elements of the small subunit of the ribosome is the h44 helix, located in the center of the subunit from the side of the intersubunit space (Fig. 1). This helix is directly involved in the decoding process: in particular, the conservative nucleotides A1492 and A1493 included in it (hereinafter, the numbering of nucleotides corresponds to that adopted for the bacterial ribosome Escherichia coli) detect the complementarity of the anticodon to the codon [2]. The h44 helix also plays an important role in the initiation of translation [18]. Finally, the nucleotides of the h44 helix are included in a number of intersubunit bridges (e.g., B2, B3, B5, B6) required to maintain the structural integrity of the ribosome [1, 19] and/or modulate the relative movement of subunits [5, 20]. The important role of the h44 helix in the translation process is emphasized by the fact that mutations in it [21] and the binding of antibiotics to it [22] critically affect the functioning of the ribosome.

Fig. 1.
figure 1

The position of the h44 helix relative to other elements of the small subunit of the ribosome, tRNA and mRNA. The h44 helix is shown in red, tRNA in the A site is shown in green, mRNA is shown in crimson, and rRNA (except for h44) is shown in blue. The intersubunit bridges formed with the participation of h44 are designated B2a–B6.

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The purpose of this work is to demonstrate the possibility of hole transport along the h44 helix using computer simulations, namely, density functional theory (DFT) calculations and the kinetic Monte Carlo method.

RESULTS AND DISCUSSION

To simulate charge transport along the h44 helix, we used the hopping transport model, which qualitatively describes the motion of a localized charge carrier in the presence of energy disorder [23, 24]. Nitrogenous bases—π-conjugated parts of nucleotides through which electron and hole transport are possible [25] (the nonconjugated sugar–phosphate backbone was considered not involved in transport)—were considered as sites between which hopping of charge carriers occurs. The rates of transitions between sites were described using the Marcus formula [26]:

$${{k}_{{ab}}} = \frac{{2\pi }}{\hbar }\frac{{J_{{ab}}^{2}}}{{\sqrt {2\pi {{\lambda }_{{ab}}}{{k}_{{\text{B}}}}T} }}\exp \left( { - \frac{{{{{\left( {\Delta {{E}_{{ab}}} - {{\lambda }_{{ab}}}} \right)}}^{2}}}}{{4{{\lambda }_{{ab}}}{{k}_{{\text{B}}}}T}}} \right),$$
(1)

where ℏ is the reduced Planck constant, kB is the Boltzmann constant, T is the absolute temperature, Jab is the integral transfer between sites a and b, λab is the energy of reorganization during charge transfer between bases, and ΔEab is the difference between the energies of the charge carrier of neighboring sites (ΔEab = Ea – Eb).

DFT calculated base energies Ea found in the studied RNA fragment are shown in Fig. 2a. Guanine has the highest energy of HOMO, and uracil has the lowest energy of LUMO; these results are in agreement with previous works [17, 27]. Methylated cytosines 5MC and 4MC have slightly higher energy levels than cytosine. Since, according to Eq. (1), charge transfer from a site with a higher energy to a site with a lower energy is more probable than the reverse transfer; the bases with the lowest low level of LUMO) can be localization centers [17]. Thus, holes should tend to localize on guanines, and electrons on uracils. It is also worth noting that the LUMO energy levels of all nitrogenous bases are above –1 eV, which prevents the efficient transport of electrons along nitrogenous bases [28]. On the contrary, the HOMO energy levels lie in the range favorable for hole transport [28]. In this regard, in this work, only hole transport is considered. The reorganization energies during hole transfer shown in Fig. 2b, are large for all nitrogenous bases, except for cytosine, and exceed 500 meV. This reduces the probability of charge transfer to the base with higher energy and, accordingly, promotes the localization of holes on guanines. The energy of reorganization for methylated cytosines is slightly higher than that for cytosine.

Fig. 2.
figure 2

Energies HOMO, LUMO (a) and reorganization energy (b) various nitrogenous bases with a methyl group in the 1-position. In addition to the values for standard nitrogenous bases of RNA (G, A, C, U), the figure shows the values for modified cytosines, 5-methylcytosine (5MC) and 4-methylcytosine (4MC), present in the fragment under study.

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The hole transfer integrals between different nitrogenous bases of the h44 helix are shown in Fig. 3. It can be seen from this figure that nearly all neighboring nitrogenous bases have significant transfer integrals exceeding 25 meV, the characteristic energy of thermal fluctuations at room temperature. The presence of significant transfer integrals provides the fundamental possibility of charge transport along h44. Many of the transfer integrals exceed 100 meV (the typical value of J in organic semiconductors with high charge mobility [29]), and the maximum values of J reach 180 meV. Since the rate of transition of a charge carrier between bases increases with increasing Jab (see Eq. 1), there is every reason to believe that the hole can move along the h44 helix. This observation is consistent with the results of our previous work [17], in which, using computer simulations, the possibility of hole transport along tRNA and an rRNA region was shown, as well as theoretical [27, 30, 31] and experimental [32, 33] works on charge transport in a molecule similar in structure, DNA. Finally, it should be noted that some nucleotides of the h44 helix have nonzero transfer integrals (up to 15 meV) with the nucleotides of the h13 and h18 helices, which makes it possible for a hole to pass from the h44 helix to neighboring elements of the ribosome and/or vice versa.

Fig. 3.
figure 3

Hole transfer integrals between different nitrogenous bases of the h44 helix. The thickness of the cylinders reflects the value of the transfer integrals; the transfer integrals <5 meV are not shown.

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The probability distribution obtained as a result of the simulation of charge transport by the Monte Carlo method hole detection on various sites, depending on its initial position, is shown in Fig. 4a. The diagonal passing through the point (0.0) in this figure corresponds to the case when the holes do not leave the initial sites. The presence of a large number of points outside this diagonal indicates the movement of the hole along the RNA. In this case, the presence of vertical stripes indicates a tendency of holes to localize on certain bases, and these stripes themselves correspond to sites that “collect” holes from their surroundings (i.e., hole localization sites). In Fig. 4b, the total probabilities of detecting a hole at various sites are shown (provided that its initial position is equally probable), which makes it possible to more clearly identify potential localization sites. It follows from this figure that such sites are, first of all, nucleotides G1405, G1475, and G1496; in addition, there is a high probability of localization at G1416, G1432, and G1454. As expected (see above), they are all guanines. Note that this work did not take into account the fact that the presence of other guanines next to guanine promotes hole localization with a large transfer integral, since such a sequence has a higher HOMO energy [34], taking this fact into account can enhance the tendency to hole localization on G1416, G1454 and G1475.

Fig. 4.
figure 4

Hole localization on the h44 helix. (a) The probability of detecting a hole on different bases within 10 ns, depending on its initial position. Sites are numbered starting from 1400; (b) averaged over the initial position of the hole, the probability of its detection on different bases; (c) location of hole localization sites on h44. The color of the bases corresponds to their types: green G, turquoise A, yellow C, red U, orange 5MC (5-methylcytosine), and violet 4MC (4-methylcytosine). The intersubunit bridges located near the localization sites are designated B2a, B3, B5, and B6.

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The location of the identified hole localization sites on the h44 helix is shown in Fig. 4c. From this figure, it can be concluded that these sites are located near functionally important regions of the ribosome—the decoding center and subunit bridges. In particular, G1405 and G1496—the sites with the highest probability of hole localization—are in close proximity to the decoding center and are part of the B2a intersubunit bridge, G1475 is part of the B5 bridge, and G1416 and G1432 are located near the B3 and B6 bridges, respectively [21, 35]. The localization of a hole on intersubunit bridges can affect the relative movement of subunits, which is an integral part of translocation, which is the movement of tRNA and mRNA during translation. In this regard, we assume that such localization can play the role of a “latch,” which ensures the coordination of translocation with other processes necessary for translation [2, 5], preventing the relative movement of subunits at certain points in time. This hypothesis is supported by the fact that replacement of guanines G1475 and G1476 with uracil suppresses protein synthesis by ribosomes under certain conditions [21]. Localization of a hole near the decoding center can lead to its transition to tRNA in the case of complementary binding of the codon and anticodon and a conformational change in the latter, which is necessary for its accommodation [17].

On the h44 helix, a number of “basins” can be distinguished, and once in each of them, the hole is localized at the corresponding site. In the framework of the model used, the hole transition between the basins does not occur, despite the presence of significant transfer integrals throughout the entire h44 helix, which determine the fundamental possibility of charge transport. However, the hopping model of charge transport used in this work is one of the simplest models used to describe charge transport through nucleic acids [27]. In particular, it does not take into account the influence of the environment on the site energies, possible charge delocalization over several sites, modulation of the charge transfer integrals and site energies by low-frequency oscillations, and other effects. The latter factor can greatly contribute to charge transitions between the basins. Indeed, it is known that for crystalline organic semiconductors thermal fluctuations in the energy of charge carriers on molecules (sites) and transfer integrals between molecules lead to “knocking out” charge carriers from traps (sites with the lowest charge carrier energy are analogous to localization sites) [36, 37]. In other words, dynamic disorder smooths out static, thereby significantly increasing the mobility of charges under certain conditions [36]. A similar effect can manifest itself for rRNA (in particular, the h44 helix), in which the standard deviation of site energies due to thermal fluctuations should be greater than in harder crystalline organic semiconductors (50–100 meV [38]). A fundamental condition for this effect is the presence of transfer integrals between sites, shown above (Fig. 3).

To test the hypothesis about the influence of thermal fluctuations on the possibility of carrier transition between localization basins, we carried out estimated calculations in which the rates of transitions between sites from Eq. (1) were multiplied by the factor exp(–dE/4kT), where the difference between the energy and the equilibrium value, dE, a random variable with a Gaussian distribution, zero mean and standard deviation σ. The addition of this factor is not a strict consequence of Eq. (1) in the presence of a Gaussian disorder of the energies of the sites, but in the zero approximation this allows one to estimate the influence of fluctuations on the transition rates at σ ~ λ (see supplementary material, Eqs. (S1) and (S2)). The resulting distribution of the probability of detecting a hole at different sites depending on its initial position, presented in supplementary materials (Fig. S1), shows that with thermal fluctuations in the energy of sites, the transfer of a charge carrier from one basin to another is indeed possible, as a result of which the sites of localization with the lowest energy collect holes from more sites. Moreover, charge carriers can be transferred from one basin to another by nonlinear localized waves of perturbation of the nucleic acid conformation, similar to breathers in DNA [39]).

Based on the foregoing, we assume that, due to dynamic disorder and/or perturbations of the conformation, transitions of a charge carrier between different basins can occur, providing the possibility of charge transport along the h44 helix over considerable distances. Such charge transport over long distances can be especially important for the “electronic control” of the ribosome. However, the simulation of charge transport taking into account the influence of thermal fluctuations in the energies of sites and perturbations of the conformation requires further research, which is significantly beyond the scope of this work.

EXPERIMENTAL

The parameters of the hopping model of charge transport (see Eq. (1)) are Eab, Jab, λ. They were calculated by the DFT method in the GAMESS package [40, 41] using the CAM-B3LYP functional (for reorganization energies) or B3LYP (in other cases) and the 6-31g (d) basis set. This approximation describes well the various properties of nucleotides [42–45], including charge-transport properties [46]. The energies of the charge carrier at the sites were approximated by the energies of the boundary orbitals—HOMO for holes and LUMO for electrons. To calculate the required parameters, nucleotides were replaced with nitrogenous bases with methyl groups instead of sugar-phosphate residues. Transfer integrals Jab were calculated using the projection method (DIPRO) [47–49]. The calculations were carried out for a vacuum; it was previously shown that taking into account the solvent (water) changes Jab no more than 20% [17]. The reorganization energy was calculated within the framework of the standard model of adiabatic potentials [50] as the sum of the relaxation energies upon loss of a charge carrier by site a, λa,dis, and when purchasing a charge carrier by the site b, λb,ch:

$${{\lambda }_{{ab}}} = {{\lambda }_{a}}_{{,{\text{dis}}}} + {{\lambda }_{b}}_{{,{\text{ch}}}} = \left( {{{E}_{{{\text{Nb}^*}}}}-{{E}_{{{\text{Nb}}}}}} \right) + \left( {{{E}_{{{\text{Ca}^*}}}}-{{E}_{{{\text{Ca}}}}}} \right),$$

where ENb and \({{E}_{{{\text{Nb}^*}}}}\) are the energy of the neutral state of the site b in the optimized geometry and in the geometry of the charged state, and ECa and ECa* are the energy of the charged state of the site a in the optimized geometry and in the geometry of the neutral state, respectively. The outer-sphere part of the reorganization energy was neglected. The initial positions of the atoms were obtained from the PDB (6qnq) structural database [51]. The simulation of the movement of holes along the h44 helix and the determination of potential sites for their localization were carried out by the Monte Carlo method. The hole was sequentially placed on different initial sites, and then the probability of its detection at different sites was analyzed for a certain time (10 ns).

CONCLUSIONS

Using computer simulations, it has been shown that there is a strong electronic interaction between the nucleotides of the central element of the small subunit of the ribosome (helix h44), i.e., significant integrals of hole transfer that facilitate hole transport along the h44 helix. Hole localization sites that “collect” holes from the surrounding nucleotides have been identified; these regions are located near important functional elements of the ribosome – the decoding center and intersubunit bridges. On the basis of the data obtained, it was suggested that the localization of the hole in the abovementioned sites can influence the relative movement of the subunits and be a “latch” that matches this movement with other processes occurring during translation. The results can make a significant contribution to the understanding of the translation process, in particular, contribute to the identification of how the work of various parts of the ribosome is coordinated.