Alphavirus Particles Can Assemble with an Alternate Triangulation Number

Alphaviruses are spherical, enveloped RNA viruses primarily transmitted by mosquitoes, and cause significant arthritogenic and neurotropic disease in humans and livestock. Previous reports have shown that—in contrast to prototypical icosahedral viruses—alphaviruses incorporate frequent defects, and these may serve important functions in the viral life cycle. We confirm the genus-wide pleomorphism in live viral particles and extend our understanding of alphavirus assembly through the discovery of an alternate architecture of Eastern equine encephalitis virus (EEEV) particles. The alternate T = 3 icosahedral architecture differs in triangulation number from the classic T = 4 icosahedral organization that typifies alphaviruses, but the alternate architecture maintains the quasi-equivalence relationship of asymmetric units. The fusion spike glycoproteins are more loosely apposed in the T = 3 form with corresponding changes in the underlying capsid protein lattice. This alternate architecture could potentially be exploited in engineering alphavirus-based particles for delivery of alphaviral or other RNA.

Introduction
Viruses typically form icosahedral shells or helical tubes by repeating a capsomere (made up of one or a few protein subunits) in a structured design to protect their genome and form an active virion [1]. Each copy of the capsomere has the same shape and they tile [2] across the shell in a regular pattern. The geometric requirements of this tessellation constrain how many capsomeres can be present and how they are arranged in the shell [1,2]. For viruses obeying the classical Caspar-Klug quasi-equivalent arrangement of subunits, their architecture is described by the triangulation number T, and they have 60 × T capsomeres.
An inner nucleocapsid core containing the genome is formed by 240 capsid proteins (Cps) also arranged in T = 4 icosahedral symmetry.
During alphavirus infection, Cp auto-proteolytic cleavage from the structural polypeptide leads to genomic association and cytosolic NC assembly. Alphavirus particles assemble and bud at the plasma membrane, where envelope glycoprotein complexes transported through the secretory system bind and enwrap NCs through E2:Cp interactions. A conserved E2 sequence in the cytoplasmic tail binds to a hydrophobic Cp pocket, linking two protein layers across the membrane. Interestingly, Cps that fail to assemble into cytoplasmic NCs can form T = 4 icosahedral virions during budding, although production of such particles is inefficient [5,6]. In addition, anti-CHIKV antibodies that disrupt spike-spike interactions were shown to prevent virus budding, suggesting lateral envelope interactions drive the assembly/budding of released virions. Within released virions and in vitro-assembled cores, previous biochemical and 2D structural data indicated that Ross River virus (RRV) particles do not form complete icosahedral NC shells and incorporate defects [7]. A capsid mutant of Sindbis virus can form particles of variable, cargo-dependent size, underscoring the promiscuity of the alphavirus assembly pathway [8].
To analyze virion structures produced by alphavirus assembly/budding, we purified and imaged four different viruses from the genus. Alphaviruses are highly infectious agents and several neurotropic alphaviruses (WEEV, VEEV, EEEV) are capable of causing serious and potentially fatal infections of the central nervous system. Therefore, wildtype (WT) infectious neurotropic alphaviruses are classified as priority pathogens and Biosafety level 3 (BSL3) agents requiring increased biocontainment facilities. Wild-type arthritogenic alphaviruses such as CHIKV are classified as BSL2+ and typically require similar biocontainment and biosecurity practices. Due to the absence of these facilities and the inability to fully enclose the specimen preparation devices and electron microscopes in our facility, it was necessary to handle viruses at BSL2 or below. Therefore, we used a chimeric virus based on the insect-specific Eilat virus (EILV) that can be handled under BSL1 laboratory conditions [9]. The EILV/EEEV virus chimera contains structural proteins from EEEV (strain EEEV-FL 93-939) and nonstructural proteins from Eilat virus [10]. Similarly, an analogous chimera using chikungunya virus (CHIKV) does not differ structurally from wild-type CHIKV virus [11].
Here, we analyze the particle morphologies and 3D structures of neurotropic and arthritogenic alphaviruses and describe a wide range of assembly outcomes. Compared to a control virus known for its structural monodispersity, alphaviruses are more likely to exhibit pleomorphism including large, multi-cored particles. Furthermore, we identify a stable T = 3 viral particle as a minor component of a purified alphavirus preparation. Structural heterogeneities are an inherent feature of alphavirus particles and deviations from the theoretically predicted T = 4 perfectly icosahedral structure are plentiful.

Purification and Electron Microscopy of Alphavirus Particle Morphologies
EILV/EEEV, EILV/CHIKV, and EILV/VEEV chimeric alphaviruses were generated by replacing the structural protein open reading frame (str ORF) of EILV with that of wild-type EEEV, CHIKV and VEEV, respectively, as previously described [10,11]. Briefly, the region of the genome corresponding to the 26S subgenomic RNA (which contains the structural polyprotein but not the subgenomic promoter or 3 noncoding regions of the genome) was amplified by PCR, digested with restriction enzymes, and ligated into pEILV [12] to give rise to a full-length viral cDNA clone whose sequence was confirmed by Sanger sequencing. The PCR fragment was amplified from reverse-transcribed viral DNA in the case of CHIKV (strain CHIKV-99659) and from infectious clones in the cases of VEEV (strain TC-83) or EEEV (strain FL93-939). Each virus construct was independently amplified by infection of cultured C7/10 mosquito cells at a multiplicity (MOI) of 0.1 PFU/cell, and at 48 h post-infection (HPI), the supernatants were harvested and clarified by centrifugation for 10 min at 3000× g. To concentrate virus, clarified supernatants were mixed with polyethylene glycol (PEG) 8000 and NaCl to 7% and 2.3% (wt/vol), incubated overnight at 4 • C, and the precipitate was pelleted by centrifugation for 30 min at 3100× g. Pellets were then resuspended in PBS and titrated by C7/10 plaque assay as described below. Resuspended virus was overlaid onto a 20-70% continuous sucrose gradient and separated from contaminants by ultracentrifugation for 1.5 h at 210,000× g. The virus band was collected and applied to a 100-kDa Amicon filter (Millipore, Billerica, MA). Residual sucrose was then removed by 5 washes with PBS. The EILV/X virions (where X refers to EEEV, CHIKV or VEEV str ORF) in Tris/EDTA/NaCl (TEN) buffer (0.05 M Tris-HCl [pH 7.4], 0.1 M NaCl, 0.001 M EDTA) were diluted with an equal volume of TEN buffer to reduce particle concentration. Three µL of the diluted virion solution was applied to a Quantifoil grid (mesh size 200) and blotted with an FEI Vitrobot Mark IV for 2 s at 100% relative humidity and room temperature before plunge freezing. Preliminary imaging on a JEM-2010F cryomicroscope was used for initial model generation in EMAN2 [13]. Final imaging was performed in a JEM-3200FSC cryomicroscope with Omega-type energy filter. Micrographs of EILV/CHIKV and EILV/VEEV were recorded at 1.96 Å/pix on a DE-20 direct electron detector. 60 electrons per Å 2 were captured. Damage compensation and motion correction were performed as previously described [14]. Micrographs of EILV/EEEV were collected in the JEM-3200FSC cryomicroscope with K2 Summit electron detector operated in counted mode at 1.71 Å/pix. VEEV-TC83 vaccine strain virus was grown in baby hamster kidney cells, prepared to 80-90% confluence and inoculated with virus at a multiplicity of 0.1 PFU/cell. Infected cells were incubated at 37 • C for 2 days until cytopathic effects appeared; then the supernatant was clarified by centrifugation for 5-10 min at 1000-2000× g to remove cellular debris. The virus was concentrated by precipitation with 7% polyethylene glycol 6000 and 2.3% NaCl at 4 • C for >4 h. Then, the virus was centrifuged at ≥2500× g for 30 min and was gently resuspended in 1-2 mL TEN buffer (0.05 M Tris-HCl, pH 7.4, 0.1 M NaCl and 0.001 M EDTA). The virus suspension was purified by centrifugation through a 20-70% sucrose/TEN continuous gradient for 60 min at 35,000× g. The virus band was harvested using a plastic Pasteur pipette and centrifuged 3× g through Amicon 100 kDa filter (Ultra-4 Cat. No. UFC810024), resuspending each time to maximum load volume with TEN. The purified virus was harvested in the minimal remaining volume after final centrifugation (ca. 50-100 µL). Cryo-EM grids were prepared and micrographs collected on the JEM 3200FSC cryo-transmission electron microscope with Omega-type energy filter at a detector magnification of 141,110× (1.07 Å/pixel sampling rate) using a Gatan 4K × 4K CCD camera.
Adeno-associated virus serotype 8 (AAV8) was repurified in phosphate-buffered saline (PBS) as previously described [15]. Diluted virion solution was applied to a glowdischarged Quantifoil grid (mesh size 200) with a continuous carbon overlay with thickness between 2 and 3 nm, as measured by quartz oscillation frequency in the Leica ACE600 used to deposit the carbon on cleaved mica by e-beam deposition. Imaging was performed in a Talos Arctica cryomicroscope with Gatan Bioquantum energy filter with K2 Summit electron detector operated in counted mode at 1.04 Å/pix.

EEEV Cryo-EM Data Processing
Particles were boxed using EMAN2.1 and then motion/damage-corrected using the script DE_process_frames.py [14]. Initial, iterative image alignment and reconstruction was performed in the package MPSA [18], which aligns images by the method of common lines. This achieved pseudoconvergence in 5 iterations. This result was not utilized in further refinements. To investigate particle heterogeneity, all 23,332 accepted particles were subjected to two-class ab initio refinement in cryoSPARC v1 [19] without the use of any input model, but with enforcement of icosahedral symmetry. One of the resulting classes exhibited T = 4 quasi-equivalence and the other T = 3. To improve the resolution of these classes, each was refined independently. The particles belonging to the T = 4 class were iteratively aligned by projection-matching and averaged starting from the T = 4 ab initio model (implemented in cryoSPARC as "homogeneous refinement"), and (separately) the same was done for the T = 3 class. Refinement improved map resolution (to~10 Å in the case of the T = 3 subset) but did not alter the triangulation number. The lesspopulous T = 3 class contained 1540 out of 23,332 particles. To confirm that the difference in triangulation number was inherent to the particle subset and not a reconstruction artifact of the package, the particle subsets were isolated for reprocessing in EMAN2.1 [20]. CryoSPARC particle lists in csv format were parsed using pyem scripts (Daniel Asarnow; https://github.com/asarnow/pyem (accessed on 29 April 2020)) and then converted onward to EMAN format. The list of putative T = 3 particles was refined with icosahedral symmetry using as an initial model the cryoSPARC T = 3 reconstructed volume phaserandomized to 30 Å; the resulting map at 13.2 Å exhibited T = 3 quasi-equivalence. That list of particles was also refined in the same way against the cryoSPARC T = 4 reconstructed volume to 13.4 Å and the resulting map exhibited T = 3 quasi-equivalence. The list of putative T = 4 particles was refined against cryoSPARC T = 3 or T = 4 volumes and yielded, in either case, a map with T = 4 quasi-equivalence at subnanometer resolution.

Purified Alphavirus Particles Are Structurally Heterogeneous
To assess the pleomorphism in alphaviruses generally, we compared images of four alphaviruses. Taking advantage of the isogenic Eilat virus backbone and C6/36 expression system, we can compare micrographs of purified EILV/EEEV to EILV/CHIKV and EILV/VEEV all prepared by the same experimenter and using the same protocol ( Figure 1). We also compare the non-chimeric attenuated TC-83 vaccine strain of VEEV ( Figure 1B) [16], as well as a non-alphavirus control ( Figure 1E). The control, AAV8, is a T = 1 non-enveloped ssDNA virus with high environmental stability. We randomly selected a number of micrographs, excluded micrographs in which particle morphology is hard to detect by eye, and then counted the number of particles that appeared normal, abnormally small ( Figure 1, yellow arrows), abnormally large (green arrows), or multi-cored (i.e., having more than one core or partial core or having a dumbbell-shaped core inside the envelope; red arrows). Distinguishing larger or smaller particles was difficult because large changes in particle volume yield small changes in particle radius due to the cubic relationship, and because even normal-sized particles apparently contain discontinuities or imperfections in the protein lattice. However, multi-cored particles are easily identifiable (Figure 1, red arrows). Roughly 3% of viral particles were multi-cored in EILV/EEEV, EILV/CHIKV, and wild-type VEEV TC-83, while 1% of particles were multi-cored in EILV/VEEV (Table 1; Figure 1A-D). Multi-cored particles were stable for 120 weeks in solution (data not shown). By contrast, a control non-enveloped virus, AAV8, showed zero geminate particles and only 0.5% particles of abnormal diameter (Table 1; Figure 1E). From the prevalence and temporal stability of large, pleomorphic, multi-cored particles across alphaviruses, we conclude that such particles are likely present in vivo and reflect the frequent deviations from icosahedrality/quasi-equivalence in this genus.
Architecturally, cores within multi-cored particles had a circular or elliptical shape in projection and the particles contained areas of low density (no RNA) between cores within the same envelope. One could envision that the cores are "beads on a string" in a multi-plet configuration, where the ssRNA connecting neighboring cores is too small to observe. However, assuming a constant RNA:volume ratio within cores, a four-cored particle with just one RNA would encapsidate an RNA of over 40 kb in length, and such RNAs are exceedingly rare in the cytoplasm. Thus, we infer that a multi-cored particle contains multiple RNA molecules, each within its own nucleocapsid shell. This differs from typical cargo-driven T-number switching in viruses and may have a different etiology than the small particles discussed in the next section. Plausible non-RNA-driven mechanism for multi-cored particle formation include the presence of kinetic traps in budding or imbalance in glycoprotein/capsid ratio resulting in "starved" assembly [21]. Multi-cored particles (red arrow)-particles with two or more NCs inside the viral envelope-were frequently observed in each alphaviral preparation but not in AAV8. Particles bigger (green arrow) and smaller (yellow arrow) than normal were also observed. (F) Selected pleomorphic particles of EILV/EEEV illustrate variable spike coverage and nucleocapsid defects which are sometimes, but not always, associated with multiple cores per particle. Multi-cored particles (red arrow)-particles with two or more NCs inside the viral envelope-were frequently observed in each alphaviral preparation but not in AAV8. Particles bigger (green arrow) and smaller (yellow arrow) than normal were also observed. (F) Selected pleomorphic particles of EILV/EEEV illustrate variable spike coverage and nucleocapsid defects which are sometimes, but not always, associated with multiple cores per particle. We observed ( Figure 1F) alphaviral particles that were incompletely covered with glycoprotein spikes (i.e., they contained patches of naked membrane) as well as particles with incomplete nucleocapsids, as evinced by smaller, non-spherical nucleocapsid morphologies. Nucleocapsid was not touching the membrane in areas where no glycoprotein coated the membrane, as we might expect a priori because Cp anchoring to the membrane is via the E1/E2 endodomains.

Two Icosahedral Architectures of Eastern Equine Encephalitis Virus
We investigated the structure of the subset of EILV/EEEV particles that appeared, by eye, to have normal morphology ( Figure 1A). All particles were refined (with icosahedral symmetry enforced) to 7.5 Å resolution using the method of common lines as implemented in the software package MPSA [18], resulting in a T = 4 icosahedral reconstruction consistent with a published structure of EEEV [22] (Figure 2A; EMD-28780 main map). We suspected compositional heterogeneity might be limiting the achievable resolution, so we performed multi-model ab initio refinement in cryoSPARC v1 [19] to sort particles into classes; after, we refined each class independently by traditional projection-matching. Two structures with typical alphavirus features were obtained. Surprisingly, while the majority structure had the T = 4 architecture that is standard for all alphaviruses, a minority subset of particles yielded a T = 3 structure ( Figure 2B; EMD-28780 additional map).
To exclude algorithmic bias, we also refined the two classes of particles in EMAN2 and obtained the same result. Then, to rule out initial model bias as an explanation for the observed T = 3 architecture, we iteratively refined particles from the T = 3 class starting from a T = 4 initial model. The refinement converged to a T = 3 map despite being biased towards T = 4. In the reciprocal experiment, particles from the T = 4 class refined from a T = 3 initial model also reproduced a T = 4 map. Excluding the two most likely pathologies in computational analysis, bolsters our confidence that the T = 3 architecture is present as a subpopulation of the purified EILV/EEEV virions. Approximately 7% of particles were sorted into the T = 3 class and were further refined to produce a reconstruction at 10 Å resolution. The T = 3 particle is approximately 34% smaller in volume (3.9 × 10 4 nm 3 ) than the T = 4 particle (5.2 × 10 4 nm 3 ) and contains 180 E1/E2/Cp subunits compared to 240 in the T = 4 virion (the charged surface therefore remains proportional to the volume). To achieve a tighter radius of curvature, structural interactions within the T = 3 spike shell and core must be different than those in the T = 4 particle. We then rigid-fit the atomic model for EEEV E1•E2•Cp subunit (PDB:6MX4) into the T = 4 and T = 3 reconstructions to analyze spike-spike interactions in the outer glycoprotein shell. Organization of spike trimers in the penton was similar between T = 4 and T = 3 particles. However, in the T = 4 particle, the E1 molecules forming the hexamer assemblies were more closely packed, containing four antiparallel, flat interfaces (q3:i3 trimers, type I) with extensive contacts, and two less extensive, angled interfaces (q3:q3, type II) with a larger gap between neighboring spikes ( Figure 2C). In comparison, spikes forming the hexamer in the T = 3 virion were more loosely arranged and spaced further apart, with three flat, extensive interfaces (two q3:i3, one q3:q3) and three angled interfaces (two q3:i3, one q3:q3) ( Figure 2E). This loose organization allowed for a higher curvature of the hexamer that facilitates the smaller diameter of the T = 3 icosahedron. Cps within the NC below were linked to spikes by interactions with the E2 C-terminal tails and arranged to form correlating T = 4 and T = 3 lattices, with the T = 3 NC hexamer again more loosely packed ( Figure 2E,F). This suggests both the icosahedral spike and Cp lattices are pliable and able to accommodate different curved membrane geometries with quasi-equivalent interactions.
The interior volume that could be filled by RNA is 1.8 times larger for the native T = 4 architecture than for T = 3. However, alphavirus genomes are loosely packed: the native T = 4 virion containing a genome of 11.7 kb nt would have a Matthews coefficient (V m ) greater than 5 Å 3 /Da, which is much higher than, for example, ssRNA picornaviruses and bromoviruses [23]. Therefore, it is plausible that the T = 3 virion could contain a complete genome with V m = 3.1 Å 3 /Da. Alternatively, T = 3 particles could package a smaller RNA, such as the 26S subgenomic RNA of about 4.2kb, at even lower pressure. The T = 3 particle is approximately 34% smaller in volume (3.9 × 10 4 nm 3 ) than the T = 4 particle (5.2 × 10 4 nm 3 ) and contains 180 E1/E2/Cp subunits compared to 240 in the T = 4 virion (the charged surface therefore remains proportional to the volume). To achieve a

Discussion
The stability of T = 3 virions, the existence of defects in the icosahedral organization of envelope glycoproteins and nucleocapsid cores (Wang et al., 2015), and the heterogeneity in alphavirus morphology all underscore that alphavirus particles are best understood as "mostly icosahedral" viruses. Because virion metastability is essential to viral survival, each virus has evolved to balance order and disorder of the virion structure. As compared to other types of symmetric viruses, alphaviruses are more pleomorphic and incorporate more defects. However, it remains unclear how or if these heterogeneities offer advantages during the virus life cycle.
Despite the outer protein shell, when alphavirus particles bud they form pleomorphic virions with various sizes and morphologies. We attribute the presence of multi-cored particles (containing spikes on the envelope surface and 2-5 nucleocapsid cores) to assembly events rather than post-budding fusion of released particles for two reasons. First, virus stored at 4 • for almost two years showed no increase in multi-cored particle prevalence [10]. Second, we previously showed that NC cores docked closely at the plasma membrane could result in sharing of spikes across neighboring particle buds, forming what appears to be early intermediates of the multi-cored particles [24]. This can happen especially during infection with high MOI, where NCs are presumably delivered at high local concentration to budding sites. Such multi-cored particles, if endocytosed via spike-mediated receptor interactions, would result in high local multiplicity of infection (MOI) during entry. High MOI usually promotes virus infection by saturating host restriction factors [25,26], and contributes to modulation of viral pathogenesis by maintaining genetic diversity [27,28]. Alphavirus virions enveloping multiple cores is reminiscent of certain non-enveloped viruses that are packaged into enveloped microvesicles for dissemination, and are associated with a higher infectivity [29]. Future functional studies of these multi-cored alphaviruses, both in vitro and in vivo, are warranted. For example, does the producer cell species (e.g., Aedes albopictus vs. Homo sapiens) or cell type impact the relative abundance of T = 3 and T = 4 particles? Additionally, as cryoEM methods continue to improve, per-particle analysis (potentially by tomography) should reveal more insights into the provenance and structure of the T = 3 particles.
Alternate triangulation numbers have been observed for in vitro systems based on cowpea chlorotic mottle virus [30], brome mosaic virus [31], SV40 [32], and others. These correspond to "dead-end" assembly events reflecting the essential promiscuity of intersubunit interactions. The best-characterized systems of T-number switching are related to cargo encapsulation. It could be that T = 3 virions are not formed in natural EEEV infections: although EILV/EEEV does not differ from wild-type EEEV in the sequence of its structural proteins it may produce RNA differently; it is conceivable that EILV non-structural proteins interact differently with EEEV structural proteins or RNA cis-acting elements differently than isogenic non-structural proteins would, and this could affect RNA production (or another step leading to proper virion assembly). Regardless, we have established that unmutated EEEV structural proteins can form RNA-containing T = 3 virions under some conditions of cell infection; their properly folded spikes indicate that they can likely fuse with human cells and deliver RNA-although this has not been experimentally confirmed. Further work is necessary to determine what RNA species is packaged into T = 3 virions and whether such particles relevant to alphavirus infection in vivo.
Assembly of both T = 4 and T = 3 virions in the same preparation raises the question of what determines the achieved icosahedral architecture of a released particle. It is conceivable that packaging of smaller RNA species such as 26S RNA could result in a smaller RNA-Cp NC intermediate in accordance with the proposal that NCs assemble as Cps neutralize the negative RNA charge [33]. Based on recent reports of CHIKV assembly/budding in situ, a smaller RNA/Cp assembly would serve as a rough scaffold that indirectly guides self-assembly of a smaller icosahedral spike lattice than the potentially larger cytoplasmic NC intermediate packaging the 49S genomic RNA [24]. When Aura virus is propagated in the C6/36 cells (the same cell line we used to propagate EILV/EEEV), 52% of the packaged RNA molecules were 26S RNA [34]. Negatively-stained Aura virus contained two classes of particles with diameters comparable to those observed here (62 vs. 63 nm and 72 vs. 69 nm); it was speculated that the small particles had T = 3 geometry [34]. However, the two classes of particles could not be confirmed by cryoEM [35]. This could be because methods for in silico separation of different classes of particles occurring within the same dataset were not well-developed at that time. If the T = 3 particles in fact package non-replicative alphaviral subgenomic RNA or cellular RNA, they could be of interest as a future alphavirus vaccine or mRNA delivery platform. The relative infectivity and immunogenicity of particles differing in triangulation number remains to be assessed. The different quasi-equivalent interactions in the T = 3 virion ultimately highlights the structural plasticity of the alphavirus spike lattice self-assembly. We recently reported rare flat sheet and tubular lattices of hexagonal spike arrays in CHIKV-infected cells, further demonstrating the ability of spike assemblies to cover different underlying membrane geometries [24]. It can be expected that alphavirus spikes can form arrays with numerous different protein-protein interfaces due to their extensive lateral contact areas. In summary, we demonstrated that alphavirus particles can assemble using an alternate triangulation number. That an alternate assembly lattice should be possible has been proposed but not previously experimentally observed [7]. Here, T = 3 particles-having 180 copies each of the envelope glycoproteins and capsid protein instead of 240 copies-constituted about 1 of every 15 particles formed during cell-culture propagation of a biosafe derivative of Eastern equine encephalitis virus.


The Biomechanical Profile of an Osseo-Integrated Rectangular Block Implant: A Pilot In Vivo Strain Analysis

Aim: To load-test the osseo-integrated rectangular block implant (RBI), measure the generated cortical peri-implant strains, and relate these findings to known human physiological parameters. Materials and methods: Two RBIs were placed into the posterior mandibular saddle in a mature greyhound dog and allowed to osseo-integrate. The half mandible (implants in situ) was mounted in a servohydraulic system. Four triple-stacked rosette gauges were placed cortically (mesial, distal, buccal, and lingual). A modified ISO-14801 protocol was used (1000 N, 300, 2 Hz, 1 h) and the generated principal strains (ep, eq) and their angular orientations (F), were calculated. Results: (1) Bucco-lingual “horizontal” dimension: dominant “horizontal” compressive stresses were on the lingual aspect and “horizontal” tensile stresses on the buccal aspect. The buccal cortex was elastically tensile-stretched, while the lingual cortex was elastically compressed. (2) Bucco-lingual “vertical” dimension: dominant vertical torsional stresses were oriented buccally and apically, with an overall buccally inclined torsional effect. This was also evidenced on the lingual aspect, where there remained high torsional rotation elements (high F and e2). (3) Mesio-distal “horizontal” dimension: dominant torsional stresses oriented as a distal-lingual “counter-clockwise” rotation. Conclusions: The applied off-axial loads generated a heterogeneous pattern of bucco-lingual and mesio-distal cortical strains, both vertically and horizontally. The short dimensioned osseo-integrated RBI design appeared to biomechanically withstand the applied loads and to maintain the strains generated to levels that were within physiological limits. More studies and statistical analyses are needed to confirm these findings.

Introduction
Short implant-supported prosthodontic success for the resorbed posterior saddle has been reported as high [1]. This problem is especially evident in the mandibular posterior saddle, where occlusal loads are high [2] and where, after many years, the ridge is resorbed. The importance of implant design in addressing functional demands and reducing stress concentration has been extensively discussed [3,4]. This research project poses a novel design of dental implant, the rectangular block implant (RBI). It is specifically designed to address the needs of patients with this clinical problem. It represents a new concept in implant design and force distribution [5].
Occlusal overload has been defined as a load that exceeds the load-bearing capacity of the implant and its prosthesis, resulting in the biological failure of osseo-integration and the mechanical failure of the prosthesis [6].
Despite the suggestion that occlusal overload may serve as a major contributing factor to prosthetic failure [7][8][9], various clinical and animal studies have provided conflicting evidence regarding its negative impact on implant osseo-integration [10][11][12].
Strain gauge analysis has been extensively applied to bone [29] and the peri-implant cortical elements of osseo-integrated fixtures in an effort to characterize the impact of the loads applied to the adjacent bone [2]. The importance of these endeavors is exemplified by work [30] which has first established that bony structure adapts through remodeling processes to maximally withstand applied loads and secondly, clarified strain levels as determinants of the capacity of bone to undergo such physiological adaptation. Frost [30][31][32] defined adaptive bone physiological limits where remodeling begins at approximately 500 µε and ceases at approximately 3000 µε, beyond which a pathological state exists.
This endeavor is not designed to replace cylindrical implant designs that currently exist. It is aimed at providing a specialized implant fixture for a particular clinical application, that is, the restoration of the resorbed alveolar ridge. The RBI presents a novel approach in that its longitudinal axis is along the mesial-distal length of the remaining ridge, which is the very dimension in which nature preserves the maximal remaining bone volume, while its flat surfaces provide an even force distribution and maximizes surface area.
The aim of this article is to qualitatively analyze the biomechanical characteristics of the osseo-integrated RBI by determining the peri-implant cortical strains generated through the application of high (1000 N) unfavorably angulated loads that simulate extreme masticatory force. It is a qualitative analysis, in supplementation of the post-integration mechanical testing of the osseo-integrated RBI (mechanical push and pull tests) that has already been performed [5].

The Rectangular Block Implant
For details of design, readers are referred to patents: Europe and the United Kingdom (EP 32911759 B1; Australia (2016257149 B2). The manufacture of the RBI has been described in an earlier publication [5].

Animal Surgery and Ethics
All procedures were performed under Animal Ethics approval (see below). The approval for this in vivo animal model and its selection was based on its ability to mimic the human resorbed alveolus after creation of edentulous posterior regions.
The surgical protocol evaluation and clinical testing were achieved through the placement of 2 RBIs into a mature male greyhound dog in a prepared (left side) posterior edentulous mandibular saddle. This animal model was chosen on the basis of its thin mandibular structure and underlying inferior alveolar nerve neurovascular bundle, closely simulating that of the human structure in the edentulous state. The details of the surgical aspect of implant placement, including anesthesia, have been described elsewhere [5].
Ethical constraints in this study mitigated against the use of greater numbers of animals and mandated the use of the minimal possible number. As a result, one animal only was available for this component of the RBI's biomechanical analysis.
The animal experimentation protocol (including the research question, key design features, and analysis plan) was prepared prior to the commencement of this study and submitted for approval (and retained) by the Animal Ethics Committee at the University of Melbourne. Upon approval, the conduct and reporting of the study were executed in accordance with the principles of Enhancing the Quality and Transparency Of health Research (EQUATOR), which are embodied by [33] as applied to animal experimentation: Animal Research Reporting In Vivo Experiments (ARRIVE).

Osseo-Integration
This was assessed clinically at second-stage surgery exposure, at which time the animals were sedated, and then euthanized through administration of 20 mL of sodium pentobarbitone (325 mg/mL) into the right cephalic vein.
Resonance frequency analysis (RFA) (Osstell, W & H Pty Ltd., Sydney, Australia, Smart Peg #47) and torque tests (torque wrench: Nobel Biocare, Sydney, Australia) applied through a cylindrical healing abutment were performed. Successful clinical osseointegration was deemed to have been achieved if the implant produced Osstell readings over 80 from all directions (mesial, distal, lingual, and buccal), as well as five torque test levels of over 35 Ncm.

Embedding
After second-stage clinical testing, the mandible was carefully dissected, de-fleshed, and sectioned in two through the midline to isolate the half mandible arch into two, containing the two implants.
The left half of the mandible was embedded in acrylic material (Vertex Trayplast, Vertex-Dental BV, The Netherlands), such that it was rigidly stabilized. The acrylic was ground and sanded to produce a platform with a flat base. The mandibular section was kept as one long piece as much as practicably possible ( Figure 1). The embedment of the bone was limited so as to expose the entire implanted region. Buccal and lingual bone was left exposed to a depth (8-9 mm) such that it exceeded the depth of the implants (5.5 mm).
The mesial implant had passed both tests at the second stage and, hence, was used for this component of the study. The distal implant was left undisturbed in situ throughout the remaining course of this experiment and remained as a "spare".

Prosthetic Crown and the Force Application
A titanium (Grade V) prosthetic abutment designed to engage the unique RBI internal geometry was prepared and inserted into the mesial RBI at 35 Ncm.
A prosthetic test crown (Cobalt Chrome alloy) was designed ( Figure 2) with a central hollow shaft for abutment screw access and prepared ( Figure 2) with a grooved step placed on the lingual aspect for a buccally oriented off-axial load application. The crown was trial fitted to ensure complete and stable seating on the prosthetic abutment. After confirmation of fit, Cavit (Dentsply, Australia) temporary material was placed over the opening of the screw shaft of the prosthetic abutment and the crown was cemented into position with Fuji Plus (GC Corporation, Japan) glass ionomer luting cement. Excess material was removed and a period of at least 24 h was allowed for complete setting. Figure 3 depicts the resultant moments from the force application. It is noted that M+ > M−; hence, ΣM is positive (i.e., 2.9 F) but less than M+. This was compounded by the fact that the anti-rotational geometry of the assembly had a much more definitive vertical stop design than horizontal limitation. This was a natural physical consequence of the axial path of engagement between the prosthetic abutment and its underlying implant geometry. These calculations pertained primarily to the crestal regions and have been based on the assumption of the pivotal point being at the crestal surface (i.e., at 11 mm). It should be clarified, however, that, after factoring in the effect of the axial force component, this pivotal point would be transferred deeper into the mandible (depending on the relative stiffness of the cortico-cancellous architecture). The exact position of this remained unknown.

Strain Gauges
The gauges used were of a stacked rosette design: miniature three-element 45-degree rosettes ((WA06030WR120) Measurements Group Inc., Raleigh, NC, USA). The configuration used in the current project was that of a quarter bridge (that is, 3 precise resistors and 1 active in each gauge).
The stacked rosette gauge ensured that all three-gauge elements were above the portion of the region being examined. Each of the grids was at 45 degrees to the other. The area of overlap defined the portion of the cortex being examined.
The mesial and distal gauges were in the "horizontal-crestal" plane parallel to the "occlusal plane". The buccal and lingual gauges were, in their respective "vertical" planes, perpendicular to the crestal surface. These channels were ascribed the strain values ε1, ε2, and ε3 in the following "flat-plan" configuration ( Figure 5).
A series of secondary terminals were bonded adjacent to each of the gauges in an area not being investigated. The secondary terminal prevented any strain transferring to the gauge from accidental pulling of the wires. The lead wires were connected to the secondary terminals using fine color-coded Teflon-encased wires (Miniature PTFE Wire (H-UT 3607 T F) Habia Cable Asia Ltd., Swedish Branch, Soderfors, Sweden).

Figure 5.
Orientation of gauge leads with respect to the implant surfaces. The orientation of the mesial and distal rosettes and their leads was such that ε1 was perpendicular to the adjacent surface of the implant, ε3 was parallel to this surface, while that of the buccal and lingual gauges was such that ε3 was perpendicular to the adjacent surface of the implant and ε1 was parallel to this surface; ε2 was at 45 0 to each of these in each case.
The wires from the secondary terminals that were a larger gauge cable were used to connect to the data acquisition system (Data Logger, CPE Systems, Victoria, Australia). The strain gauges were connected to a Wheatstone signal conditioning module (SCC-SG03 National Instruments Corp., Austin, TX, USA) housed in a configurable connector unit (SC-2345 National Instruments Corp., Austin, TX, USA).
The outputs went directly to this system. The data were then processed and collated using the lab view program supplied with the acquisition system. Computer software: (Lab View 7 Express, National Instruments Corp., Austin, TX, USA). An initial measurement of 120 Ω ensured that the gauge was functional and ready to be tested.

The Mounted Set-Up
The acrylic embedding was bolted onto a brass plate attached to the base of the servohydraulic platform with an angulated face of 30 0 from the vertical ( Figure 6). The bone was kept moist with saline through the use of a paper towel wick to avoid desiccation. The first test run engaged the mesial and buccal gauges, while the second engaged the lingual and distal. Uni-axial sinusoidal cyclic loading was at a possible frequency range of 3-5 Hz for a total of up to 3 × 10 4 cycles, utilizing closed-loop servo-hydraulics (MTS 810, Materials Test Systems Corporation, Eden Praire, MN). This frequency and cycle number was chosen to expedite the test process, without deviating significantly from a low frequency-high cycle regime. The final ε value for each channel was determined through the mean difference between maximal and minimal detections of surface deflection to yield positive (tension) and negative (compression) values.

Channel Data
Schemes 1 and 2 depict the sinusoidal patterns of the gauge channels. The mean difference (and standard deviation) between maxima and minima for each of the channels was calculated. The results are depicted in Table 1.

Principal Strains
Using a "strain-transformation" relationship, the principal strains from the rosette gauge were calculated (Vishay Measurements Group, NC, USA: Technical Note-515) ( Table 2). This is expressed as the two principal strains (perpendicular to each other) and their angular orientation to the reference grid. Since the direction of the principal strain is unknown, the angle (θ) is from the direction of the principal axis εp or εq (the determination of which is given below) to a specified strain gauge reference grid (either ε1 or ε3) according to: (a) If ε1 > ε3, then φp,q = φp: the reference is from ε1 to εp. (b) If ε1 < ε3, then φp,q = φq: the reference is from ε3 to εq. (e) If ε1 = ε2 = ε3, then φp,q is indeterminate (equal bi-axial strain). Table 2. Principal strains and their orientations. It is clarified here that, although the positive and negative values of the principal strains refer to tensile and compressive strains, respectively, the overall understanding of the directions of the strains is gained when the angular orientation is factored-in. Where ε2 values are ascribed as large, this was: (i) Relative to the associated absolute ε1 and ε3 readings for that output; (ii) Indicative of a high torsional element affecting that peri-implant cortex.
The overall plan view of these principal strains with respect to their proximal implant surface is depicted in Figure 7. where, indicated in red, the value of ε2 was of a relatively large magnitude, and this has been included to be indicative of a high torsional element. The green circular arrows represent the overall "horizontal" torsional (rotatory) effect on the RBI. Horizontally: the mesial and distal gauges now combined to show an overall counter-clockwise torsion (green arrows). Vertically: there was a strong push to the buccal: the overall trend was a buccally oriented torsion (red arrow).

Observational Summary
Mesio-distally: the large ε2 values represented strong torsional elements, and the distal counter-clockwise rotation was evident (as defined in the current plan view depiction of the block).
Bucco-lingually: the compressive strains on the lingual aspect were evident, as well as large tensile strains on the buccal aspect. This was especially evident on the buccal aspect, where there was a very low Φ value, yielding essentially the buccal tensional load and the rotational element.
On the lingual aspect, however, there remained high torsion rotational elements (high Φ and ε2), giving a complex picture of lingual compression, a buccally directed torsion, and a block torsion in a counter-clockwise rotation.

Measured Cortical Strains
Although the data generated were collected in mesio-buccal and then disto-lingual pairs, the results of these experiments were analyzed, by comparing the principal strains and angular orientations of the gauge readings, as paired mesio-distal and bucco-lingual outputs. The combined effects of the resultant paired angulated tensile-compressive strains highlighted a complex array of results, where dominant patterns encompassed: (a) In the buco-lingual horizontal dimension: dominant "horizontal" compressive stresses on the lingual aspect, coupled with "horizontal" tensile stresses on the buccal aspect. (b) In the bucco-lingual "vertical" dimension: dominant vertical torsional stresses oriented buccally and apically. (c) In the mesio-distal "horizontal" dimension: dominant torsional stresses oriented as a distal-buccal "counter-clockwise" rotation.
The bucco-lingual and the mesio-distal aspects will now be discussed in turn and then as a composite picture.

Tensile and Compressive Elements in the Bucco-Lingual (Horizontal) Dimension
The ramifications of this pattern were two-fold.
(i) Horizontally. In the horizontal bucco-lingual aspect, this could be seen as an elastic deformation of the body of the mandible. The deformation of the lingual cortex would have resulted in concavity, while that of the buccal cortex would have resulted in convexity. This equated to a three-point bending configuration.
This was in congruence with the complex nature of a peri-implant cortico-cancellous bone elastic deformation buttressing effect. This effect served to limit strains to within physiological limits. This is vital to the success of this implant design, which has the combined characteristics of cornered ends (potential stress concentrations) and being intended for the posterior region, where masticatory forces are maximal.
(ii) Vertically. The second ramification of this strain pattern was in the vertical (axial) and bucco-lingual aspect, where there was an overall buccally inclined torsional effect (Figure 8). This was evidenced on the lingual aspect, where there remained high torsional rotation elements (high Φ and ε2), giving a complex picture of lingual compression and a buccally directed torsion.

Mesio-Distal Torsion
Relatively large ε2 values for both mesial and distal gauges were present. The distalbuccal rotation pattern, as evidenced by the patterns of the principal strains and their angular orientations, was dominant in this (horizontal) plane. That is, the mesial and distal gauges at 1000 N showed opposite directional characteristics, which highlighted a strong counter-clockwise rotation (Figure 9).
Although, from a bucco-lingual aspect, the 30 0 off axial load would be evident, from the mesio-distal aspect, the force applied at the ledge of the crown should be coincident with the axis of the entire implant crown complex. Figure 9. Horizontal bucco-lingual torsional effect: buccal view. The red arrow depicts the applied force, while the horizontal black arrow depicts the "horizontal" mesio-distal resultant moment generating the cortical torsional strains in this orientation. Again, it should be noted that there would also be a "vertical" apical equal and opposite reactive force evenly distributed along the flat face of the block (blue arrows). The measurement of this element was beyond the scope of this experiment, including any of its secondary effects of super-imposing further strains at the positions of the surface strain gauges.
It is posited that there were imperceptible off-axial loadings in the mesio-distal engagement of the ledge. This, in turn, would have resulted in a mesio-distal rotational moment generating (via the osseo-integration interface) localized torsional cortical stresses. Such a nonaxial load could result in rotatory cortical torsional stresses, which may be either mesially or distally oriented (clockwise or counter-clockwise).

Combined Mesio-Distal and Bucco-Lingual Torsion
Ultimately, the results of this study have highlighted horizontal and vertical cortical torsional stresses, which, although analyzed separately in the above results, were expressed simultaneously in the peri-implant cortical environment (i.e., the super-imposition of all strains).
These torsional elements were evident through high ε2 strain gauge values for the lingual, mesial, and distal gauges. It is thought that this was not reflected in the buccal gauge at 1000 N due to the dominant buccal flexure of the body of the mandible at that point ( Figure 10). The torsional elements at 1000 N were further evidenced by the complex angular orientations of the principal strains. A diagrammatic representation of the overlay of the horizontal and vertical cortical torsional stresses can be given ( Figure 11).  . The remaining gauges allowed an overall picture of torsional stresses in the body of the mandible. The horizontally (mesial-distal) oriented rotational moment caused by the inadvertent off-axial load application, as seen from the buccal aspect, has been included as a horizontally oriented torsional load (yellow arrow). In this study, this rotation has been defined as counter-clockwise.

The Complexity of the Principal Strains and their Angular Orientations
The generation of the complex patterns of principal strains and their angular orientations in the results of this study reflected the equally complex relationship between the block implant and its surrounding bony environment. Possible (and undefined) key factors underpinning this complexity included: (i) The angulation and rotation of the block in the mandible, e.g., the bucco-lingual slant.
This factor varied with respect to the differences between the crestal morphology of the alveolar ridge and the underlying cross-sectional morphology of the body of the mandible. (ii) The particular pattern of osseo-integration around the block itself. Judge [34] extensively studied the trabecular and cortical architecture of the dog mandible, depicting a high level of variation and heterogeneity in its make-up, while Monje et al. [35] have highlighted the variability in trabecular density and volume in the posterior mandible from site to site. (iii) The particular relative thicknesses of the cortical and cancellous bone, as well as the shape of the mandible at the position of the implant. These factors would have affected the critical elements of cortical flexural stress and cancellous tensile shear stress, as defined by the mathematical principles of such a bi-layered composite beam [36,37]. (iv) The inability to perfectly align the application of the force. The step on the crown and the engaging push rod would inevitably have some degree of variation in their orientations. Deviations from perfect parallelism would be expressed as a bias in force resolution, as well as the resultant axial moments, torsional stress concentrations, and strain levels.
Furthermore, internally within the cancellous bone which forms the bulk of the osseointegrative connection, the block itself will undergo rotatory influences depending on the exact angulation of the force applied to the prosthetic crown and the alignment of this force system to the implant body and its alignment, in turn, to the body of the mandible.
This complex interplay of both the bucco-lingual cortical and cancellous rotatory moments ultimately expressed influence on the mesial and distal peri-implant bone stresses, producing either compression or tension depending on the rotation experienced. The elucidation of these factors will require further analyses.
In the oral environment, bony architecture is highly variable, opposing teeth may be axially tilted, and there may be little prosthodontic latitude in directing masticatory forces axially. Indeed, it emerges that the current possible paraxial loading and non-parallelism in placement is most likely a reflection of the true clinical setting. There is little information that can clarify these factors, and further analyses beyond the scope of this endeavor are needed.

Physiological Limits
Crucially, the strains generated in the mandible here were within physiological limits [29] (<3000 µε, Frost 1987), despite the application of 1000 N of obliquely applied force. The successful ability of the osseo-integrated RBI environment to biomechanically withstand such forces points to two key factors.
(i) The importance of the role of the mandible as a single and flexible composite beam.
It was found that, at high loads, tensile strains dominated buccally, while compressive strains dominated lingually. It was posited that these strains were evidence of a buccallingual mandibular torsional flexure, both in the vertical and horizontal planes.
The differential in the moduli of elasticity between the cortical and cancellous osseous components would yield a rigid yet flexible beam. The successful osseo-integration of the block into the mandible meant that it was essentially a fixed component of this "beam", and the forces applied to the implant were transferred to the body of the mandible itself. The predominant stresses generated were buttressed through both cancellous bone shear and cortical axial bending stresses.
Despite having a higher failure rate than their longer counterparts, short implants have been extensively documented as being successful, even with crown-to-implant ratios exceeding 200%. It is postulated that the observations of this component on a more general level elucidate a fundamental factor at play, which, although present in all implants, is especially highlighted in short implants; the higher concentration of stresses per unit area of the implant is dissipated through the flexure of the mandible itself, acting as a single composite beam. What emerges is a reduction in peri-implant strain levels to within physiological limits, even when forces are applied that would be expected to produce strains beyond physiological limits. These results are in congruence with the results of: Kan et al. [2]: masticatory overloaded implant scenarios failed to yield peri-implant stresses beyond physiological limits.
Judge [34]: masticatory mechanical loading of the mandible yielded flexure and stressinduced elastic deformation of the mandible as a whole, as evidenced by a complex array of transient strains, even at sites distant to the implant.
It must be highlighted that this study has focused solely on the use of cortically placed strain gauges. Cancellous bone tensile strength is also a critical factor in mandibular composite beam analysis. Assessment of this, however, requires the trabecular assessment of strains. Although beyond the scope of this analysis, it emerges that further studies are needed using trabecular, as well as cortical bone strain gauge readings.
(ii) The rectangular design.
It is posited that the flat walls of the polygonal block design acted to reduce torsional stress concentrations by providing a large wall-like flat surface area that served to yield a more even distribution of stresses. In the buccal "vertical" torsional stress orientations, this was achieved by the flat 24 mm 2 face of the block. This is to be contrasted with the uneven stress distribution of a cylindrical counterpart, where the most buccal radial curvature must reflect the greatest burden of stress concentration.
This difference was also reflected in the mesio-distal "horizontal" torsional stress orientation. The radially symmetrical nature of a cylinder will induce higher radial torsional stresses within the investing bone at its mesial and distal tangents when subjected to a rotatory load as compared to a rectangular block of the same mesio-distal maximal dimension ( Figure 12). This is, in part, due to the anti-rotational geometry of the block resulting from its length and its corners and cornered edges. These factors will also act to reduce peri-implant torsional stresses of the osseo-integrated RBI. and a block implant of length 2X: an equal moment M, is generated through an equal force F, applied at an equal distance X from the center of each structure. It is seen that the torsional surface stresses will be more concentrated at the radial tangents of the cylinder compared to the lower, more even distribution of the torsional loads of the flat-faced block (depicted as red arrows). The corners of the block wound also act in opposing resistive directions to the applied moment (green arrows), further reducing the overall peri-implant torsional stresses.

Limitations
It is acknowledged that the results of this study must be interpreted with caution, as it is lacking statistical power. Further studies are needed, where larger samples of implant bone samples are used to yield high numbers of results. The utilization of strain gauges [19,34] in these samples would also yield data for future FEA of the osseo-integrated RBI. These limitations were underpinned by both financial and ethical approval constraints. These constraints impacted directly on the number of implants and animals used, and, hence, the lack of controls, as well as the small sample size.
It is further conceded that this study is animal-based; hence, caution should be imposed when extrapolating implications of these results to the human situation.

Conclusions
The observations of this limited qualitative analysis showed that the applied offaxial load to the osseo-integrated RBI generated a heterogeneous pattern of strains. The dominant characteristics of this pattern were: (i) Tensile and compressive strains were expressed bucco-lingually and mesio-distally. (ii) Bucco-lingually, there was a "horizontal" flexure of the body of the mandible, producing buccal tensile strains and lingual compressive strains. (iii) Bucco-lingually, there were strong "vertical" torsional stresses directed apically on the buccal aspect. (iv) Mesio-distally, there were strong horizontal torsional stresses in a disto-buccal orientation.
The short dimensioned osseo-integrated RBI design appeared to biomechanically withstand the deliberately exaggerated off-axial simulated masticatory loads and to maintain the strains generated to levels that were within physiological limits. The conclusions and ramifications of this study are provisional, as more studies and statistical analyses are needed to confirm them.