INTRODUCTION

At the time of writing the world is starting to emerge from its fifth global pandemic since the Spanish flu outbreak of 1918 (1). During the last decade viral epidemics have become a prevalent global health threat requiring techniques for rapid vaccine development (2). Radiation has long been used to inactivate virions (3) although the uncorrelated nature of the ionization produced by gamma rays means that the protective outer envelope of the virus is highly damaged. High-energy ion beams however produce long-thin (nanoscale) damage tracks which can be used for much more selective virion inactivation (4). Currently, in an important extension of this concept, a large-scale ion-beam facility, is using beams of heavy, high-energy ions to attempt to produce a vaccine for SARS-CoV-2 (5). As described in seminal papers by Francis et al. and Durante et al. (5, 6) and further emphasized here, fast heavy ions offer a new possibility for a general way to inactivate virions without damaging the outer structure as much as other inactivation methods. Since the ions form long straight damage tracks, each of the ions interacting with a single virion will produce many ionizations or excitations in the nucleocapsid. Each of these events has a chance to damage the RNA, rendering the virion inactive. Damage to the envelope is typically limited to one or two locations, on the ion's ‘way in’ and on its ‘way out’ (see Fig. 1), thus limiting the amount of structural damage to the surface spike proteins integral to activation of a host immune response. RNA is a highly serial structure in its biological information expression; break the RNA backbone in one critical places (i.e., within the functional parts of the sequence) and you probably render the virion inactive. In contrast the envelope proteins and phospholipid membrane are highly parallel structures so several of them can be radio-damaged without affecting the structure of the envelope significantly, leaving its function unchanged. This assertion points to an informatic aspect of the problem, one we will investigate in this paper - there are two structures involved, the structure of the virion being irradiated and the structure of the radiation tracks doing the irradiation. As we show below, the interplay between these two structural forms is a governing factor determining the predicted dose inactivation curve for any given virion.

FIG. 1

Geometry of the SARS-CoV virion and its interaction with six randomly generated 3 MeV He²⁺ ions shown from three different viewpoints, panels a and b show side-on and end-on views while panel c shows a larger perspective view of 6 ions passing through the simulation volume. The ion tracks shown here were chosen for illustrative purposes and are not necessarily representative. Tracks 1 and 6 completely miss the virion. The cores of tracks 2 and 3 pass through a spike protein whilst the core of track 4 misses but one of the secondary electrons produces an ionisation event in one of the spike proteins. Track 5 passes through the nucleocapsid causing RNA-candidate damage events (red dots), envelope damage events (green dots) and spike-damage events (magenta dots). It is necessary to include tracks such as 1 and 6 with cores far from the virion to ensure a correct weighting of the spike-damage, i.e., through tracks like those shown in here. Full details of the geometry are given in the Methods section.

If one can thus inactivate sufficient numbers of virions, they could be used as the key component for developing viral vaccines in a universal manner. The inactivation using fast ions is expected, perhaps uniquely, to produce little or no apparent change to the structure of the virions' envelopes due to the track structure the ions produce. Hence, unlike heat and chemically treated virions, fast-ion inactivated virions will present the correct, unperturbed, molecular structures and surfaces to immune cells. They can be expected to enter a host, including, in the case of SARS-CoV-2, using angiotensin-converting enzyme 2 (ACE2)mediated cellular entry (7). Upon encountering host immune cells, these inactivated antigenic virions would stimulate an immune response in the usual manner, but critically would lack reproductive capability. Hence, we call virions modified in this way Structurally Intact Radiation Inactivated Virions (SIRI-Vs).

It is worth asking the question “What would the specifications of an ion-beam facility designed to produce sufficient quantities of SIRI-Vs look like?”. High-energy, large-scale ion facilities such as the one currently being used (5) are rare and very expensive. However, we believe it is also possible to use mid-range ion facilities, such as those more traditionally associated with nuclear energy research (8). It is worth noting that the approach proposed by Francis et al. (5) and further elucidated here is a general one and it can be readily applied to other viral strains in the future. Hence, the methods and results described are of relevance to virology in general and are not limited to the SARS-CoV-2 pandemic. Together with Francis et al. (5), this work puts in place the foundations for a new subject – fast ion radiovirology.

To support development of this subject, it is important to have a set of predictive tools able to determine dose-inactivation curves reliably. Here we show rapid prediction of inactivation responses and discuss some of the barriers which must be overcome to produce reliable predictions. We believe it is currently premature to rely solely on radiation transport simulations such as those used by Francis et al. (5) or those presented here. This does not mean they are unimportant. Instead, a concerted, community effort is required to develop tools able to support calculations of this type, much has been done in the field of heavy ion cancer therapy. It is in this spirit that several new approaches are offered in this paper.

Even before the current coronavirus disease (COVID-19) pandemic, total human vaccine business was projected to be worth ∼$60 billion annually by 2024 (9) while that for animals is projected to reach ∼$11 billion by 2025 (10). Clearly then there would be commercial benefit in developing ion-irradiation facilities designed specifically for this purpose.

MATERIALS AND METHODS

A putative model of the SARS-CoV virion was developed using available structural biology information (11–14). There is important information about the tertiary structure of at least part of the RNA in the nucleocapsid (11, 12). The two virions are very similar so general conclusions reached should also apply to SARS-CoV-2 or other coronaviruses. Although the means by which genomic information is stored, varies widely among viruses, target theory (6, 15) offers a framework for relating RNA backbone breaks to inactivation. Hence, the treatment provided here is readily adaptable to other viruses.

TOPAS (16) version 3.3p01 that wraps the Geant4 10.05 patch-01 (17) was used to transport 3 MeV alpha particles through a volume of water with a density of 1.4 g/cc over a distance of 0.8 µm. These ions would have a linear energy transfer (LET) of 126 keV/µm in 1.0 g/cc water and correspondingly have an LET of 176 keV/µm. Accordingly the slowing down of the ion is negligible over the 0.8 µm distance of the simulation. The vertices for ionization by either the primary ion or any secondary electrons were recorded on an ion-by-ion basis for future simulations. One hundred such ion tracks were recorded and saved for future use. For the simulations shown in Figs. 1 and 2, one set of tracks was chosen at random and a 150 nm long section of the track was extracted. This extracted track was then shifted by a random amount in the x- and y- directions (the z-direction being the direction of propagation of the ion). The locations of the resulting ionization events were then recorded to produce the histograms shown in Figs. 2 and 3. For each of these simulations, ionizations from 200,000 independent ion tracks were recorded.

FIG. 2

RNA distribution affects propensity for ionisation interactions. The top row (panels a–c) symbolically shows sections through the virion, displaying the three cases for the RNA configuration under consideration (column by column). The second row (panels d–f) shows histograms of the probability of inflicting a number of ionising events to the virion's RNA per ion track interacting with the virion on a linear scale for the corresponding three cases. The third row (panels g–h) uses a logarithmic scale to show the long tail involving multiple hits to the RNA, again for the three cases shown in panels a-c. Panel j shows the predicted survival fractions for the three scenarios, assuming all of the RNA is the critical structure; red line case i), green line case ii) and blue line case iii).

FIG. 3

Probability of ionisation interactions with spike proteins. Histograms of (left) the probability of any selected spike protein complex being subject to an ionising event per ion track interacting with the virion and (right) the number of spikes undergoing an ionizing event per ion track interacting with the virion.

The geometry used for the virion was derived from available structural biology information (11–14). The inner and outer radii of the envelope were set to 40 and 44 nm, respectively, with the RNA being confined within a spherical region of radius 39 nm. SARS-CoV and SARS-CoV-2 virions contain a single strand of RNA (ssRNA) which codes for all of the proteins used to make the virion. However, the exact structural form of the RNA is unknown. Accordingly, various RNA configurations within this spherical region were simulated to understand the sensitivity on the actual (largely unknown) configuration taken up by the RNA within the virion. In each case the same total amount of RNA was included, as dictated by its sequence (18). A total of 75 protein spike complexes were distributed penetrating outwards through the virion's envelope. Each spike complex was represented by an 8 nm long, 1.6 nm radius cylinder starting from the inside of the envelope and pointing radially outward. The other end of the cylinder was joined to a truncated cone, exactly matching the 1.6 nm radius at the narrow end, widening 5 nm in radius at the wide end, also with its axis point away radially and also being 8 nm long. These spike complexes were positioned so that the axis of each one pointed directly away from the centre of the virion so as to be approximately equally spaced on the envelope's surface. Each of these objects are represented by a Mathematica geometrical region, using Mathematica 12.1 with the RegionMember function used to determine if an ionisation vertex was within a region of interest.

For simulation of the RNA-protein complex, again structural information was taken from (11–14). The outside of the complex was constructed as a 30 nm long, 15 nm radius cylinder. Spiralling around the axis of this cylinder is the ssRNA, with each nucleotide represented by two spheres, one of radius 0.35 nm (backbone) and one of radius 0.31 nm (base). The backbone was constructed along a 4.35 nm radius helix of pitch 14 nm with two complete revolutions of the helix included. The bases were placed so as to just touch the backbone, with the axis joining them pointing directly outwards. This geometry was used for all the Monte Carlo calculations [Geant4 (17)], with the RNA chain modelled as water spheres with densities as shown in Table 1 and immersed in a protein environment modelled as a water with density of 1.4 g/cc.

TABLE 1

Showing the Elemental Compositions of Various Biomolecules, their Densities and the Resultant Scaled Radiodensities, i.e., the Density Water Would Have to Have to Produce the Equivalent Material-Dependent Term in Eq. (1)

In this case, Geant4 DNA (19) was used to track alpha particles and all secondary particles produced down to 10 eV and all deexcitation processes were included, such as Fluorescence, Auger cascade, and PIXE. The beam consisted of a rectangular field of 30 × 30 nm² of 3 MeV mono-energetic alphas launched along an axis, perpendicular to the RNA chain. A TOPAS extension was implemented to retrieve all the pertinent information each time an ionization occurred such as position, energy deposited in the material, particle type that indicated the interaction, material where ionization took place, track ID, and event ID of the particle. Using the last two parameters it is possible to associate all secondary particles that were created in the same event.

For the volume-scaled simulations (see the Results subsection Radiodensity Scaling) the volumes of the spheres representing the backbone and bases were modified as shown in Table 1 with the scoring being done by replaying ion tracks and using Mathematica's RegionMember function as described above. 200,000 ion trajectories were considered for each simulation. For the simulation shown in Figs. 4 and 5, the same process was repeated but the ion trajectories were rotated as well as translated so the sphere shown in Fig. 3 was uniformly and isotropically irradiated. The inner cylinder shown in Fig. 4 was used to speed up the simulations by using nested region checking since only ionisation events inside this cylinder can also be inside one of the spheres representing the RNA strands. 3.5 million ion trajectories were used in this simulation.

FIG. 4

Nucleocapsid protein-RNA geometry showing three separate tracks due to 3 MeV He²+ ions (red, green and blue), showing the various volumes used to define the simulation geometry. Panel a shows the entire simulation whilst panel b shows the representation of the RNA target as a collection of spheres as is discussed in the main text.

FIG. 5

Plot showing the effect tertiary RNA structure has on coincidental ionisation of two separate parts of the RNA structure by a single ion. Although the ssRNA takes the form of a double-helix it is important to realise this is very different from the double-helix structure famously taken up by DNA. The bases in the RNA structure shown are not paired with each other – indeed they point outwards rather than inwards. The structure is stabilised by RNA-protein interactions (11, 12). Panel a shows the indexing system used to denote locations within the two helices of the RNA. The index increases from 1 to 43 running along one portion of the ssRNA. The indexes 44 to 86 correspond to a different portion of the same ssRNA also “threaded” through the same protein complex (11, 12). Pertinent differences in indexes are illustrated by the labelled double-headed arrows. Panel b shows a 2-D map of the number of times two separate ionizing events happen on the backbone/ base combination from the same ion as a function of the indexes at which the two events occur. Note this plot contains 4 quadrants, those bottom-left and top-right corresponding to two events on the same helix, those top-left and bottom-right corresponding to two events, one on each helix. The color bar shows the number of coincidence events for each pair of RNA locations. Locations receiving 10 or more coincidences were rendered as white (saturation color). Panels c and d show the projections of these plots, summing all features with a constant difference together. The dots represent the sums over the 2-D map (i.e., the Monte Carlo data), the solid lines represent predictions made using our ‘Method of Ionizing Lines’ described in the main text.

A previous study (5) has shown that among various ions, ⁶⁰Co gamma rays and electrons, the particles which produce the least protein damage per RNA damage were 3 MeV alpha ions. Therefore, in this study we concentrated only on these ions although the methods presented are applicable to beams of other ions or electrons. Due to the sparsely ionizing nature of ⁶⁰Co gamma rays, the speed-up benefits afforded by replaying ion tracks many times and using the volume-scaling is not realized. However, we are currently developing a variation of the algorithm applicable for this case to provide comparator gamma ray inactivation data.

RESULTS

Radiodensity Scaling

To differentiate between RNA and proteins, one must account for the differences in their interactions when subject to fast charged particles. Here, results of an analytical analysis of the scaling properties are presented and used to generate either scaled effective volumes or scaled effective densities for the biomolecules concerned.

Because there are not yet a good set of well curated charged-particle interaction cross sections for either proteins or RNA, one must rely on a well curated set for water. One particularly useful and reliable set are those in Geant4 DNA. One can simulate other biological materials by scaling the density of Geant4 water (19, 23) to that of the material concerned, as was done by Francis et al. (5) and in producing the data shown in Figs. 1 and 2. However, it is not a-priory clear that the mass-density is the appropriate parameter when scaling from water. The fast ions are really interacting with charge, not mass, as is evidenced by the Bethe formula (24, 25) which for non-relativistic ion velocities reduces to

Here v is the velocity of the ion, z is its change in multiples of the electron charge, n is the electron density of the material through which the ion is passing and I is the mean excitation potential. All other symbols take their usual meanings. The electron density is given by

where the material dependent parts are Z, its atomic number, ρ, its mass density and A, is its relative atoms mass. The other two symbols are N_A, the Avogadro number and M_u, the molar mass constant. One can calculate the electron density for a compound as if it was simply a mixture of the atoms, i.e., one sums over all of the atoms present, replacing the density by the density of that atom in the material.

For most light atoms the ratio Z/A ≈ ½, allowing factorization of Z/A out of the expression for the compound electron density, providing a scaling directly between charge density and mass density. However, hydrogen is a notable exception where the ratio Z/A = 1. Hence more hydrogen-rich materials will have proportionally greater electron densities and hence will interact with charged particle beams more intensely.

The other material-dependent term in Eq. (1) is ln . It has been shown that a range of biomolecules including water, proteins and RNA all have a mean excitation energy of approximately 70 eV (26). Hence, this term can be ignored in scaling from charged interactions of water to those of other biomolecules. This argument can also be applied to the secondary electrons; hence one can find a set of scaling densities which can be applied to water, so it has approximately the same interaction rate as the material of interest. Taking known elemental compositions of biomolecules, it is then possible to generate a set of radio-equivalent densities such as those shown in Table 1. These radio-equivalent densities are the density water would have to have to have the same electron density and hence the same rate of energy loss as per Eq. 1.

If the density of the biomolecule is not known in the configuration of interest, usually both its elemental composition and total mass are known, e.g., from primary sequence information. The density of the biomolecule can then be estimated from atomic volumes to generate a mass-density. Hence results like those provided in Table 1 can be generated for many biomolecules as required.

The choice to scale the densities is somewhat ad hoc, indeed there is an assumption being made about the volumes of the objects which is used to determine their mass-densities. Since these are small objects compared with the length-scales over which the ion slows down one could fix the densities of the objects representing the various biomolecules in a simulation and instead scale their volumes, i.e., instead of slightly perturbing the densities of objects in a simulation to account for their different interactions with charged particles, one could instead slightly perturb their volumes. This second approach has the operational advantage that the entire nanoscale radiation transport simulation can now be performed at a constant mass-density. A set of ion tracks can be calculated for one density and then be ‘replayed’ many times with different starting positions and angles. Because the tracks do not pass-through regions of different densities, the computationally expensive boundary-crossing checks are not required, instead one simply must consider the volumes in which the transformed ionisations occur to determine the effects of the track.

We have explored both approaches (i.e., density and volume scaling) in the next section where we present results for ions passing through the RNA-protein nucleocomplex of the SARS-CoV virion. The scaled radiodensity approach and the scaling of volumes instead of densities appear to be general heuristic procedures which can be applied in the calculation of radiation transport through nanoscale biological systems and they will be subject of a future publication.²

Simulations of the RNA-Protein Complex

To begin to assess the effect of RNA tertiary structure, we created a geometrical model of the RNA nucleocapsid complex for which there exists a putative RNA structure. The geometry of the simulation was drawn from the putative structure for the RNA-protein complex (11, 12). Of course, the structures presented in these papers are far more sophisticated than the geometry used in our simulations – our geometry was simply constructed to capture the salient radiation biology effects. The RNA forms two helices separated and held in place by a protein complex, with the sugar-phosphate backbone lying on the inside of the helix and with the RNA bases facing outwards. These two separate RNA sections are about 5 nm apart and their bases are not paired. The volumes and densities of the RNA bases were chosen in three ways. In the first set of simulations the entire volume was treated as having a density of 1.40 g/cm³, close to the asymptotic value for large proteins (27), and the volumes of the RNA bases and phosphate backbone were taken from (28). This is equivalent to transferring the assumption made by Francis et al. (5) and our simulations above that the density is the same across the entire capsid down to the scale of the RNA-protein complex – clearly this is wrong in this situation but it serves as a useful starting point.

Simulations were performed in two ways, one where a full Geant4 DNA calculation was performed, and the locations of the ionisations was recorded. In a second simulation a group of tracks were replayed many times having been translated to enter the simulations at random places. The locations of the ionisations were scored using Mathematica's geometry primitives. In both cases the density was set to 1.40 g/cm³ throughout.

In a second pair of simulations the density for the RNA was calculated using appropriate atomic volumes (28) so that the RNA backbone had a density of 1.83 g/cm³ and the bases had a density of 1.65 g/cm³. This simulation did not take account of the specific bases in the sequence as the motif being simulated is a repeating unit throughout the capsid, accounting for containment of more than half of the RNA complex (11, 14). Instead the known RNA sequence (18) was used to calculate an average volume and density for the nucleobases. These densities were used in a second Geant4 DNA simulation otherwise similar to the one described above, while the same densities were used to scale volumes in a simulation which again replayed many tracks and used Mathematica's geometry primitives to determine which ionisations occurred within the RNA backbone and base structures. Here the volumes of the bases and backbone elements were scaled by a factor of 1.65/1.40 and 1.83/1.40, respectively.

In a third set of simulations, the same procedures were carried out using scaled radiodensities taken from Table 1. Again, this was used to scale the density in a full Monte Carlo simulation and also to scale the volumes in a simulation where many tracks were replayed. The results of these simulations are presented in Table 2. These simulations were conducted with the ions only coming in from one direction. In all cases, the fraction of ionisations found in simulation was greater than expected on purely geometrical grounds, suggesting the localised structure of the RNA does play a role, i.e., the probability is 5–10% greater than would be expected if transferring an approach like case iii) for the whole virion down to the scale of the RNA-protein complex. Since this result shows it is not appropriate to apply the approximation used in case iii) to the RNA-protein complex shown in Fig. 4 and given that approximately half of the RNA is in these RNA-protein complexes, it follows that this approximation made by us in case iii) and also used by Francis et al. (5) is not completely valid. Although they are generally in close agreement, the scaled volumes approach (scored using Mathematica) produces consistently smaller values than the scaled density approach calculated using Monte Carlo radiation transport. This difference could be due to differences in the volume-scoring algorithms when applied at sub-nm scale and will be the subject of further investigation. The scaling of volumes according to their radiodensities appears to be generally applicable to nano-scale biological structures and is the subject of systematic investigation and will be reported elsewhere.²

TABLE 2

Volumes and Densities used for the Various Simulations of the RNA-Protein Complex

Unlike the virion as a whole, the protein-RNA complex does not have quasi-spherical symmetry, so a full simulation should average irradiation over all orientations although this is computationally more expensive. Using radiodensity scaling, another simulation was performed. Here the full track identification for each ionisation within any of the RNA structures was stored. The simulation geometry is shown in Fig. 4.

These were then analysed for coincident events, i.e., when a single primary ion caused ionising events in two different parts of the RNA structure. The results are shown in Fig. 5. Unsurprisingly, most of the coincidental ionisation events concern proximal backbone/base units, i.e., where the difference in index (explained in Fig. 5's legend) is < 5. However, it is interesting to note that there are persistent features in this map, even when structures are several nm apart. The most prominent features are found when the difference in indexes is 32 or 53, which corresponds to the kinds of coincident events shown by the pink arrows in Fig. 5a. However, there is not a feature found corresponding to a difference in index of 44, i.e., a pair of events on directly opposite units of the two strands. There is also a weak shoulder on the same-strand distribution corresponding to a difference in index of about 17 although there is no immediately obvious cause of this feature. If each ionizing event corresponds to a chance to break the RNA strand where the ionisation took place, it follows that, depending on details of how the RNA is ordered within the nucleocapsid, the lengths of strands produced by multiple events from a single ion will reflect features of the map shown in Fig. 5b, i.e., they will reflect the tertiary RNA structure. This idea is discussed in more detail in the Discussion section.

DISCUSSION

The histograms presented in Fig. 2 clearly show that 3D arrangement of the RNA (i.e., the RNA tertiary/quaternary structure) within the virion is important. Different assumed structures give different probabilities of delivering one or more ionisations to the RNA and hence give different probabilities of rendering a virion inactive per ion. In coronavirus most of the viral RNA lies within ∼25 nm of the inner face of the membrane (13), making the arrangement similar to case ii). However, in this region it is believed to be largely in highly ordered RNA-protein complexes such as those shown in Fig. 4 (11). More recent studies of molecular architecture of the SARS-CoV-2 virus confirm this picture (29).

As Table 2 and Fig. 5 show, the probability of hitting the RNA in this complex is roughly proportional to the fractional volume occupied by the RNA, although it is consistently higher by 5–10% – something related to the RNA's tertiary/quaternary structure. The separate RNA-protein complexes will keep RNA far apart meaning that the coincident damage probability across two of these complexes will be small. Taken together these factors suggest that for a full virion the probability of RNA strand-breaking would be close to case iii) with a 5–10% increase due to the RNA's tertiary/quaternary structure in the RNA-protein complexes. Hence, one might suggest that the actual dose inactivation curve might lie somewhere between that for cases ii) and iii) considered.

Clearly the inactivation curve is sensitive to the RNA's tertiary/quaternary structure. However, it is not possible to deduce the tertiary and/or quaternary RNA structure from the dose-inactivation curve – there could be many different tertiary structures which lead to the same dose-inactivation curve. Furthermore, there is currently significant uncertainty in radiation transport cross-sections, the probability of an RNA strand-break either per ionizing event (target theory) or the amount of energy required to make a break (energy deposition theory). These factors will need to be systematically addressed before meaningful dose-inactivation curves can be deduced, even for an assumed tertiary/quaternary RNA structure.

It is interesting to speculate if the effect of the RNA tertiary/quaternary structure has observable consequences for fast ion irradiation. The survival curves in Fig. 2j show that it would clearly be possible to distinguish between case i) and cases ii) and iii). However, the similarities of the slopes of the survival curves for cases ii) and iii), coupled with the uncertainty in the exact size of the critical target suggests that it would not be possible to distinguish between these cases.

The number of hits to the RNA per ion plots (Fig. 2h and i) however show clearer differences between cases ii) and iii). This difference could manifest itself as a difference in the distribution of RNA fragment-lengths post irradiation, something which could be measured using electrophoresis. Taking the discussion further meaningfully is hampered by a lack of knowledge of the tertiary/quaternary structure. However, part of the RNA structure is known to form a well-defined RNA-protein complex (11, 12). As is discussed below, this structure is reflected in the expected locations for coincident strand-breaks produced by a single ion, something which might be amenable to measurement.

Historically there have been broadly two approaches to relate physical radiation transport processes to biological outcome, target theory (3, 6, 15) and energy deposition (20–22). Although it is an open question and one requiring further research, we argue that a target theory-based approach is more appropriate. The energy deposition approach accounts for energy deposition by excitation (of water) as well as its ionisation. In liquid water both processes lead to the formation of reactive products which mediate biological damage. However, in biological structures such as proteins and RNA, there is a larger network of bonds through which electronic energy can be transferred to stabilise the system, hence reducing bond breaking. In contrast, ionisation will almost inevitably lead to rapid bond breaking. Indeed, the system is more complex and might need an entirely new theory altogether. For example, it is reasonable to consider a highly folded 3D biological structure to be more able to disperse energy across its network of bonds. Accordingly, a folded structure such as a protein might require more energy deposition to cause significant damage than would be required to cause an RNA strand-break, i.e., the closed/networked structure of a protein can be expected to be more robust to effects of ionizing radiation than a more open one such as an RNA strand.

Both the models presented here and by Francis et al. (5) do not consider the effects of associated hydrating waters and counterions. These will be plentiful since the RNA backbone has a high charge density. Clearly this is a major challenge since calculation of the diffusive transport of radiolytic products within a highly structured environment is difficult. Furthermore, to undertake such a calculation, one would need to know the detailed structure, the processes invoked and the reaction rates for chemical damage to a range of proteins and RNA by the radiolytic products of water. Such data is not currently available. However, this shortcoming does not invalidate either the work presented here or in (5). The biological structure containing any hydrating water will be within a “cage” of RNA and proteins. Any radiolytic chemical products able to inflict bond-breaking and created within the capsid will therefore only travel a short distance prior to causing this damage. Hence the vertexes of ionisation show, to a good approximation, where the resultant damage will occur. The effect of the surrounding medium would also need to be accounted for in a more complete model – this is dependent on the irradiation environment used for a specific experiment. For example, in the experiments described in (5), frozen cryovials are being used, limiting the diffusive motion of radicals. Other environments could include dry samples or a highly scavenged medium, again limiting the effects of radiolytic species. However, any radicals created in this way will primarily interact with the spike proteins and envelope surrounding the nucleocapsid in a nonspecific manner, so the effect is likely to be small. The specific irradiation environment will have a bearing on the transport of radicals created outside of the virion. Once again, the fact that the proteins are highly folded 3D biological structures more able to tolerate radiation damage across their network of bonds, suggesting they will be robust against such effects. Although these unknowns constitute important topics for future research, they do not invalidate the conclusions of this study and (5), that fast ions offer an exciting new way to inactivate virions. Furthermore, the newer conclusion that the structural biological information interacts with the radiation track structure information to affect the final results of the biological damage is also robust in spite of these unknowns.

We have presented some new tools for the rapid evaluation of the effects of ion beams on biological systems. The concept of volume-scaling rather than density-scaling needs further investigation although ultimately what is required is a set of cross-sections for atomic and molecular processes for RNA, DNA and proteins. The entire gamut of these biomolecules is clearly too large to study, representing the entire ‘Holy Trinity’ of structural biology. However, the charge-density scaling approach leading to Table 1 is general, only requiring primary sequence information and atomic volumes. The approach, then, could form the basis of a new way of generating the cross-section data as required.²

In Fig. 5 we showed that there are preferred differences along the sequence for locations of coincident strand-breaks produced by a single ion. This was manifest as the differences in indices which produced peaks in Fig. 5c and d. Coincident ionisation events from the same ion could lead to the RNA being broken in two places. Since full ordering of the RNA through the SARS-CoV collection of RNA-protein complexes is not known, it is impossible to say if these peaks in the differences of indices will manifest as peaks in the differences of RNA strand-lengths observable after low dose irradiation (ensuring one or less ions ionise a given RNA strand) and disassembly of the capsid. Although a single strand (ssRNA) threads through the protein complex twice and there are several of these complexes known to be in the cell (11, 12), it is not clear if there is a fixed number of RNA bases between the two portions of RNA passing through each complex or even if this is persistent from virion to virion. It would not be surprising if this number of bases was constant or nearly so given the selection advantage conferred by tightly packing the RNA into a small volume and nature's propensity for repeated use of organised structures, but it is an open question.

Naturally there has been intense research regarding the structural biology of the SARS CoV-2 virion, e.g. (29–32), including a full multiscale model of its form which includes a RNA-protein complex similar to the one simulated here (31), and models which indicate the placement of the complexes within the virion. The thread-like ssRNA appears to be untangled and appears to be mildly helical in form (32), consistent with the model for the RNA-protein complex shown in Fig. 5. Interestingly, there are long range RNA duplexes within the tightly packed virion, showing many long-range RNA-RNA interactions (32). Never-the-less it is still considered enigmatic how SARS-CoV-2 packs so much RNA into such a small volume (29).

If there were peaks in the strand-length distribution, averaged over many irradiated virions, this would then show that the number of bases between the two portions of the ssRNA threading each complex was approximately constant. As such, it would be directly informative of the RNA tertiary structure in an entirely new fashion and in turn be informative of the way the virion forms. This idea then points to the idea of using coincident RNA strand-breaks induced under single-ion hit conditions as a new means of deducing tertiary/quaternary RNA structure as a complementary technique to provide additional information, alongside the array of structural biology techniques already being applied to the problem, e.g. (29–32).

The method of ionizing lines (MoILs) presented here is completely general and allows for the rapid prediction of RNA strand-length distributions after irradiation at low doses, designed to induce either single breaks or coincident breaks from a single ion. This is of course a far more general concept and it has the potential to be applied to a wide range of RNA tertiary structures. To illustrate this concept more, we show an example of a prediction taken from the RNA-Puzzles collection (33), as is shown in Fig. 6. This result clearly shows that the ion beam induced coincident fragment pattern is able to critique the best computationally derived tertiary structure from within the RNA-Puzzles collaboration compared to the ‘golden standard’ crystallography structure. Hence ion-beam induced fragment length distributions can provide clear indications of RNA tertiary structure. Essentially, the low-entropy pattern of ionisations induced by the ion beam is able to encode the tertiary structural information in the RNA in the fragmentation pattern.

FIG. 6

Panel a: Comparison of MoILs-predicted fragment length distributions of the best predicted (but not entirely correct) structure (blue dots on the histogram) and the “gold standard” X-ray crystallographic structure (red dots on the histogram) for RNA puzzle #9 (a 71 nt RNA aptamer) from the RNA puzzles collection (33). The X-ray crystallographic structure was also used to make the space-filling model shown in the inset. Note the peak at a fragment length of ∼23 is indicative of incorrect structure prediction. Features like this in the fragment length distribution could form the basis for critiquing and predicting RNA tertiary structures. Panels b and c: The corresponding heatmaps for coincidental ionisation of two separate parts of the RNA structure by a single ion for the best predicted structure (panel b) and the ‘gold standard’ X-ray crystallographic structure (panel c).

CONCLUSION

We have shown that the interplay between radiation track structure and RNA's 3D arrangement in space (i.e., the tertiary/quaternary structure) might have an effect on predicted dose-inactivation curves for virions and that this effect can be traced back to the localised, low-entropy/ highly informatic fashion ion beams transfer energy to biological systems. Indeed, it is this localised transfer which offers the promise of structurally intact radiation inactivated virions (SIRI-Vs). This informatic transfer can potentially encode tertiary/quaternary structural information in the lengths of ion-beam induced RNA fragments, pointing to a new field of radio-structural biology. Methods such as charge-density based volume scaling of targets and MoILs have been proposed as tools to help develop this field with its promise of ab-initio RNA tertiary structure determination.