# Directional translocation resistance of Zika xrRNA

Jul 27, 2020

### Structure of Zika xrRNA

Figure 1a shows the structure of the Zika xrRNA, a 71-nucleotide long noncoding subgenomic RNA that can resists degradation by Xrn1 and other ({5}^{prime}to {3}^{prime}) ribonucleases3. Its canonical and noncanonical base pairings are summarized in Fig. 1b. Heavy atoms contacts, including those of sugar and phosphate moieties, are shown in the native contact map of Fig. 1c. The secondary and tertiary organization is articulated over four helices (P1–P4), and multiple pseudoknot-like elements (Pk1–Pk5).

### Response to pore translocation

We integrated atomistic modeling, molecular dynamics (MD) simulations, force-spectroscopy analysis, and thermodynamic sampling techniques to understand how exactly the molecular architecture of the Zika xrRNA underpins its resistance to being driven through the lumen of exonucleases from the ({5}^{prime}) end, while still allowing to be processed and unwound by enzymes, such as polymerases and reverse transcriptases, which work from the ({3}^{prime}) end.

Inspired by force-spectroscopy approaches17,18, we adopted a force-ramping protocol where the Zika xrRNA is driven through a cylindrical pore. The pore is 11.7 Å wide and runs perpendicularly through a parallelepiped slab that is 19.5 Å thick, Fig. 2a. The pore geometry approximates the Xrn1 nuclease lumen19 and allows the passage of only a single RNA strand at a time. Mimicking an electrophoretic setup11,20, the driving force was applied exclusively to the xrRNA P atoms inside the pore, whose longitudinal axis we take as the vertical or z axis of a Cartesian coordinate system, with the xy plane coinciding with the cis surface of the slab.

The xrRNA structure was represented with SMOG. The model retains the full atomistic details and has been validated for various molecular systems, including nucleic acids21,22,23,24. SMOG employs a native-centric force field that allows us to highlight structure-dependent properties while filtering out details more related to sequence or specific RNA–protein interactions.

We carried out hundreds of ramped translocation simulations of the molecule after priming it at the pore entrance from both ends, Fig. 2a. A representative set of translocation trajectories from ({5}^{prime}) and ({3}^{prime}) ends is shown in Fig. 2b. The curves show the temporal trace of the translocated fraction of the molecule at the reference temperature T = 300 K and force-ramping rate r0 = 270 pN/μs. Translocation initiates only after a long loading stage, after which it proceeds precipitously. Major differences in translocation resistance emerge between the ({5}^{prime}) and ({3}^{prime}) ends.

The unlocking, or triggering of translocation, occurs when the vertical position of the leading P atom, measured relative to the cis plane, falls below z = −19.5 Å or z = −15 Å for ({5}^{prime}) or ({3}^{prime}) entries, respectively, and is followed by a cascade of ruptured contacts without significant pauses between the breaking of various secondary elements (Supplementary Figs. 2, 3). The typical order of rupture is given Fig. 2c. For the inherent stochasticity of the process, the triggering force is not unique but varies in a range, following a unimodal probability distribution as shown in Fig. 2b. Compared with the ({3}^{prime}) case, the most probable triggering force at the ({5}^{prime}) end is more than double; it is also much larger than the standard deviation of the triggering forces at the same end, 8 pN, or at the opposite one, 17 pN.

### Comparison with xrRNA stretching response

The unusually high resistance at the ({5}^{prime}) end is further highlighted by contrasting the translocation forces at this end with those required to unfold the xrRNA by pulling the two termini apart, as in force spectroscopy. As shown in Fig. 2b, unfolding by stretching, which occurs when the longitudinal end-to-end distance, ({R}_{ee}^{| | }) exceeds 16 nm, requires forces three times smaller than those needed to initiate ({5}^{prime}) translocations. Interestingly, the typical sequence of secondary elements rupture by stretching is similar to the case of ({3}^{prime}) translocations. The main difference is that the P4 helix, which yields when ({R}_{ee}^{| | } ,sim) 9 nm, now unfolds well before the rest of the structure (Fig. 2b and Supplementary Fig. 2).

In summary, at similar conditions, the characteristic force needed to initiate xrRNA translocation from the ({5}^{prime}) end, which resists exonuclease degradation, is distinctly higher than the forces that causes unfolding by stretching or by translocation from the ({3}^{prime}), which is processable by replicases. The same results are seen for the several hundreds of trajectories gathered over 19 combinations of T and r, from lower to higher temperatures and faster or slower ramping protocols than the reference values, see Supplementary Figs. 4, 7.

### Bell–Evans analysis

The extensive set of translocations at all explored (Tr) combinations can be recapitulated by the Bell–Evans (BE) analysis. In force-spectroscopy contexts it is customary to resort to the following BE expression for the most probable rupture force17,18,25:

$${F}^{* },=,frac{{K}_{B} T}{Delta }cdot {mathrm{ln}},left(frac{rcdot Delta }{nu cdot {K}_{B} T}right),+,frac{{E}_{T}}{Delta },$$

(1)

where ν is a kinetic coefficient and ET and Δ, the key quantities of interest, are the effective height and width of the thermodynamic barrier associated to the rupture event at zero force.

Figure 3a shows that expression (1) provides a good fit of the most probable translocation forces, yielding a χ2 ~ 3, hence of order unity, for both the ({5}^{prime}) and ({3}^{prime}) ends when all 19 (Tr) combinations are considered simultaneously. For clarity, only a subset of the considered datapoints are shown in Fig. 3—see Supplementary Fig. 7 for the complete set—and the best fit to the BE expression is shown for T = 300 K only.

The best-fit parameters are ({E}_{T}^{{rm{BE}}},=,36,pm, 2) kcal mol−1 and ΔBE = 4.4 ± 0.4 Å for ({5}^{prime}) entries and ({E}_{T}^{{rm{BE}}},=,24,pm, 1) kcal mol−1 and ΔBE = 2.0 ± 0.1 Å for ({3}^{prime}) ones. At room temperature, T = 300 K, these barriers are approximately equal to 60 KBT and 41 KBT for the ({5}^{prime}) and ({3}^{prime}) ends, respectively.

These barriers describe the system in the absence of a driving force and reflect that translocation is very unlikely to be activated by thermal fluctuations only, especially at the ({5}^{prime}) end. In the presence of a constant driving force, an estimate of the activation time can be obtained via the so-called Bell–Evans lifetimes18 and the best-fit parameterization of Eq. (1), see “Methods”. For constant driving forces of 50–100 pN, a range accessible to molecular motors26, the estimated activation time from the ({5}^{prime}) end exceeds by more than two orders of magnitude the one at the ({3}^{prime}) end.

### Directional resistance and stress redistribution

The precipitous unlocking of translocation occurs when the P atom at the ({5}^{prime}) end is just about at the trans edge of the pore, z ~ −19.5 Å (Supplementary Fig. 3). This triggering event is preceded by a long loading phase during which the driving force, which is exclusively imparted to the P atoms inside the pore, propagates an increasing tensile disturbance to the xrRNA that is still on the cis side.

The ensuing effects are best discussed by considering how the network of native contacts is distorted during the loading stage. The latter can be quantified in terms of the strain, s, of the native interactions for each nucleotide. Negative or positive values of s indicate that contacting atoms are respectively drawn closer or further apart than in the unstrained xrRNA structure, see “Methods”. Kymoplots of the s profile, during the loading stage of translocation from both ends, are shown in Fig. 4a and Supplementary Fig. 6.

The data and accompanying structures of Fig. 4 clarify that, as the initial transmission of tension along the RNA backbone draws the first nucleotides closer to or into the pore, their network of interacting nucleotides is increasingly distorted. In fact, regions G21-U28 and G38-A45 wrap more tightly around the ({5}^{prime}) end, particularly nucleotide G3 (Fig. 4b). Thanks to this tightening, which has no analog at the ({3}^{prime}) end, the increasing load is distributed over a broad portion of the molecule, which can hence better withstand the dragging force.

Increasing the load at the ({5}^{prime}) end eventually weakens the native interactions in several regions. These include xrRNA portions directly exposed to the traction of the ({5}^{prime}) end (U4-G14) and their partner strands (A17-C22 and C47-A52), see Fig. 4c. Note that the distal region A45-C48 is further disrupted by being pressed against the outer surface of the pore (Fig. 4c and Supplementary Fig. 5). At the ({3}^{prime}) end, instead, no noticeable tightening occurs around the pulled portion. The terminal tract of the P4 helix and their interacting partners in Pk4 and P4 (G31 and C58-C60) are, instead, directly exposed to the unmitigated pulling into the pore. (Fig. 4a, d). The lack of a mechanism for distributing and dissipating stress is what causes the ({3}^{prime}) end, the one processed by replicases, to yield at much lower forces than the ({5}^{prime}) end, the one resisting to exonucleases.

The tightened portion at the ({5}^{prime}) end, highlighted in blue in Fig. 4, is disconnected along the sequence, but is structurally compact. The emergence of a tightened structural element in response to a pulling force, is a distinctive feature of systems with mechanical tensegrity. In these systems, mechanical resistance results from an equilibrium between elements put under tension (positive strain) and other elements that are put under compression (negative strain) by the same applied force. Thus, the ({5}^{prime}) architecture provides a heretofore rare example of intra-molecular tensegrity, where the very pulling of the ({5}^{prime}) end is what boosts resistance to translocation and consequently to degradation.

### Native contacts network and ({5}^{prime}) resistance

We next investigated which set of native contacts and structural elements at the ({5}^{prime}) end are most conducive to the redistribution of tensile stress and translocation resistance. Our model allows for directly pinpointing these critical contributors, namely by switching off selected combinations of native secondary contacts from the interaction potential. In experiments this is not possible, and similar information can be obtained by performing mutation scans where the identity of nucleotides is affected.

Our analysis indicates that the observed resistance is virtually ascribable to the sole contacts in pseudoknots Pk1 and Pk2. These, we recall, include contacts formed by sugar and phosphate moieties, Fig. 1c. The results are illustrated in Fig. 3b as box–whisker plots for the critical translocation forces of the native xrRNA chain, and three variants lacking the native contacts in either of the two pseudoknots, ΔPk1 and ΔPk2, or both, ΔPk1–Pk2.

In variant ΔPk1 the critical force is appreciably lowered, but it still is almost twice as large as for the ({3}^{prime}) end. A stronger variation is seen for ΔPk2, whose critical force is reduced so much that it overlaps with the critical forces for the ({3}^{prime}) end. A complete loss of directional resistance is found for ΔPk1–Pk2, which yields practically the same forces encountered at the ({3}^{prime}) end. This implies a fallback to a baseline hindrance once Pk1 and Pk2 are disrupted. Of the two sets of pseudoknotted contacts, those in Pk2 are noticeably the most important ones.

### ({5}^{prime}) resistance, free-energy profile and transition state

We finally used the metadynamics framework27 to characterize ({5}^{prime}) resistance in more detail and beyond the BE analysis of out-of-equilibrium trajectories. In metadynamics, reversible transitions across significant barriers are achieved with an affordable computational expenditure by using history-dependent biases on multiple order parameters at the same time. Building on the centrality of Pk1 and Pk2 contacts on translocation resistance (Fig. 3b) we used the corresponding fraction of native contacts, QPk1 and QPk2, as natural order parameters, together with the amount of pore insertion of the ({5}^{prime}) P atom, z. To avoid effects related to the refolding of the RNA portion that has passed to the trans side, we extended the length of the pore and profiled the free energy up to z = −22Å.

A first result of the metadynamics analysis is the dominant translocation pathway shown in Fig. 5a. The pathway projections in the (QPk1z) and (QPk2z) planes clarify that during the initial stages of translocation, z from 0 to −10 Å, contacts in Pk1 and Pk2 are only modestly disrupted. Further insertion into the pore, z from −10 Å to  −15 Å, causes an appreciable loss of Pk2 contacts. The final insertion tract, z from  −15 Å to  −19.5 Å, produces a concurrent loss of contacts in both Pk1 and Pk2. Representative structures along the pathway to the force-induced transition state are shown next to the pathway, along with two-dimensional projections of the free-energy profile at the same z values, Fig. 5b–d.

The results clarify that Pk2 interactions yield at z ~ −14 Å, when the contacts involving the sugar and phosphate moieties of nucleotides G3-C22 are sheared and disrupted by the drawing of G3 into the pore while C22 is sustained and held in place by the elaborate secondary and tertiary architecture surrounding the ({5}^{prime}) end. The disruption of the nonlocal contact G3-C22 opens the way for the disruption of other contacts in Pk2 and also Pk1, such as G3 with C44 and A45, for z ~ −18 Å.

We note that the dominant pathway established from metadynamics analysis has direct bearings on out-of-equilibrium, force-ramped translocations too. This is clarified by the scattered datapoints in Fig. 5a which represent the same order parameters for conformations sampled from the force-ramped translocation trajectories at T = 300 K and r = r0. The agreement between the dominant pathway and the trajectories has three implications: it corroborates both methods, it indicates that translocation-induced unfolding occurs via a single pathway, and shows that the latter is the same in and out-of-equilibrium. The results thus cover slower ramping rates than considered in Fig. 3, including those accessible experimentally.

The salient thermodynamics of the process is aptly conveyed by the one-dimensional free-energy profile of Fig. 5e, obtained by thermodynamic integration of the metadynamics free-energy at fixed z. The free-energy increase up to z ≈ −10 Å reflects the loss of conformational entropy and native contacts during the loading stage. The steeper rise beyond z ≈ −10 Å reflects the progressive disruption of Pk2 and Pk1 contacts. The free-energy cost for reaching the depth z = −19.5 Å, the triggering condition in force-ramped simulations, is about 46 kcal mol−1.

Applying constant translocation forces tilts the free-energy profile as shown in Fig. 5e. One notes that at sufficiently high force the slope of the free-energy changes sign at about z ~ −20 Å. This value of z pleasingly matches the aforementioned triggering insertion depth obtained in force-ramp translocations (Supplementary Fig. 3). The pore insertion depth z ~ −20 Å can be interpreted as an effective transition state, embodying the rate-limiting step for force-induced translocations.

In summary, the metadynamics results aptly complement those from force-ramped translocations, giving detailed indications of the free-energy barrier associated with the triggering of translocation from the ({5}^{prime}) end, and of the associated pathway. The combined analysis shows that, in the loading stage, regions G21-U28 and G38-A45, which surround the ({5}^{prime}) end, become more tightly wrapped around it. This mechanism, that has no analog at the ({3}^{prime}) end, stabilizes the network of long-range native contacts around nucleotide G3, hindering their entrance into pore until contacts in Pk1 and Pk2, including G3-C22, are eventually disrupted.