Mathematical model calibrated to in vitro data predicts mechanisms of antiviral action of the influenza defective interfering particle “OP7”

Summary Defective interfering particles (DIPs) are regarded as potent broad-spectrum antivirals. We developed a mathematical model that describes intracellular co-infection dynamics of influenza standard virus (STV) and “OP7”, a new type of influenza DIP discovered recently. Based on experimental data from in vitro studies to calibrate the model and confirm its predictions, we deduce OP7’s mechanisms of interference, which were yet unknown. Simulations suggest that the “superpromoter” on OP7 genomic viral RNA enhances its replication and results in a depletion of viral proteins. This reduces STV genomic RNA replication, which appears to constitute an antiviral effect. Further, a defective viral protein (M1-OP7) likely causes the deficiency of OP7’s replication. It appears unable to bind to genomic viral RNAs to facilitate their nuclear export, a critical step in the viral life cycle. An improved understanding of OP7’s antiviral mechanism is crucial toward application in humans as a prospective antiviral treatment strategy.


INTRODUCTION
Viral infections cause millions of deaths annually and impose a large socio-economic burden across the world. 1 While vaccination is the preferred method for prevention of disease, treating acute infections via antiviral therapy is an essential countermeasure to save lives and limit the spread of infections.However, current antivirals might become ineffective due to emerging resistances, e.g., for influenza A virus (IAV). 2,3Thus, the development of broadly acting and readily available antiviral agents is essential for pandemic preparedness.1][12][13] For conventional IAV DIPs, this defect is induced by large internal deletions.During co-infection with their STV, DIPs can propagate since the STV provides the missing functions.4][15] DIPs were found for a large variety of viruses [16][17][18] and their antiviral capability, [19][20][21][22][23][24][25][26][27][28] mutual competition [29][30][31] and cell culture-based production 4,5,32 have been investigated extensively in recent studies.][42][43] Recently, we discovered a new type of IAV DIP referred to as OP7. 35OP7 does not feature internal deletions but contains 37 single-nucleotide substitutions (SNS).It has been shown that OP7 interferes strongly with IAV infection suppressing STV replication more efficiently than conventional DIPs. 4,5,42,43The SNS in OP7 occur in the promoter and coding regions as well as in the packaging signal of genome segment 7 (S7).This includes a G3A/C8U substitution that has been shown to induce a ''superpromoter'' correlated with increased viral genomic RNA (vRNA) synthesis. 44,45In a recent study, mice infected with a lethal dose of influenza STV were rescued by OP7 administration demonstrating its antiviral capabilities. 4Currently, the exact mechanism of OP7 interference, the source of its defect in replication and the impact of the SNS on the functionality of its associated proteins, i.e., matrix protein 1 and 2 (M1 and M2), remain elusive.
7][48][49][50][51][52] However, only a few of them focused on the interaction between IAV and DIPs.Previously, we developed models covering different aspects of co-infection, i.e., interference dynamics on the intracellular level, 14 the population level 53 and in continuous cultivation systems. 54,55These models almost exclusively considered DIPs with large internal deletions in one of the IAV genome segments encoding ll OPEN

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for viral RNA-dependent RNA polymerase (RdRp), i.e., segment 1, 2 or 3.In general, they disregarded the synthesis of aberrant viral proteins from the defective interfering (DI) genome, because the large internal deletions would likely render them non-functional.So far, the impact of IAV S7 containing SNS, which might result in the synthesis of a mutated protein affecting virus replication, has not been investigated by a mathematical modeling approach.
To obtain a more detailed understanding of OP7 and STV co-infection, we developed a mathematical model of intracellular virus replication during co-infection.This model was calibrated using experimental data and employed to explore potential effects of the SNS in the genome of OP7.Together, experimental data and model simulations provide a better characterization of the underlying mechanism of OP7 interference in animal cell cultures and support its development as an antiviral agent.

OP7 accumulates to high levels and suppresses STV replication in co-infection experiments
To examine how OP7 affects IAV infection dynamics and spreading, we utilized experimental co-infection data from a recent study performed by Kupke et al. 35 Furthermore, we analyzed the samples generated in this study using an improved assay for real-time reverse transcription qPCR (RT-qPCR) and a newly established mass spectrometry-based protein quantification technique 56 (see STAR Methods).These methods enabled the differentiation between genome segment 7 of the STV (S7-STV) and of OP7 (S7-OP7) on the RNA levels as well as for the M1 proteins derived from them (M1-STV and M1-OP7).
For STV infection, experimental results showed that the m-, c-and vRNA levels of different gene segments follow similar dynamics (Figures 1A-1C).In contrast, during OP7/STV co-infection, the levels of all S7-OP7 RNA species were one to two logs higher than those of S5 RNAs, which were themselves up to one log above the level of all S7-STV RNA species (Figures 1D-1F).S5 mRNA showed similar levels for STV infection and OP7/STV co-infection; yet, S5 cRNA levels were slightly and S5 vRNA levels strongly reduced.
Generally, the protein levels measured during OP7/STV co-infection were reduced, but exhibited dynamics similar to STV infection (Figures 1G-1L).M1-STV showed a decrease by one log during co-infection while M1-OP7 accumulated to significantly higher levels comparatively.Extracellular virus titers presented in Figures 1M, 1N, 1P, and 1Q were taken directly from Kupke et al. 35 and show that during OP7/STV co-infection the concentrations of total and infectious virions are reduced by one to two logs compared to STV infection.See also Data S1, Figure S2 and Table S1.
Lastly, we quantified the average vRNA levels in parental and progeny virus particles.To that end, extracellular vRNA concentrations of S5, S7-STV, S7-OP7 and S8 were measured in the seed virus and after infection at 12 h post infection (hpi).For comparison, the obtained values were normalized (see STAR Methods) to obtain a baseline of a single copy of each vRNA segment per STV particle (Figure 1O).The results of this analysis showed that S7-OP7 vRNA had already accumulated to more than one copy per virion in the OP7 seed virus and that S7-STV was only detected in about 10% of virions (Figure 1R).S5 and S8 vRNA levels were also reduced compared to the STV seed.Over the course of OP7/STV co-infection, these differences were exacerbated as S7-OP7 levels in progeny virions increased even further while the levels of the STV segments were reduced at 12 hpi.
In sum, OP7/STV co-infection led to the predominant accumulation of S7-OP7 RNAs and decreased STV RNA as well as STV protein levels.In addition, the large reduction of virus titers confirms the strong inhibitory capabilities of OP7 against IAV.

The mathematical model captures STV infection but requires additional changes to describe OP7/STV co-infection
To study the mechanisms of OP7 replication that induce its antiviral effect against IAV infection, we developed a mathematical model of OP7/ STV co-infection based on an intracellular model of DIP replication by Laske et al. 14 Since this model considered a DIP with an internal deletion on genome segment 3, we adjusted it to describe OP7/STV co-infection.To that end, we (1) introduced S7-OP7 as an additional segment in the system, (2) considered M1-STV and M1-OP7 separately and (3) differentiated between viral ribonucleoprotein complexes (vRNPs) bound by M1-STV and M1-OP7 (see Figure S1A and STAR Methods).
Typically, virus infection dynamics differ substantially depending on the cells used and on whether the virus is adapted to the specific cell line. 57,58Therefore, we adjusted relevant kinetic parameters used in the original model.To that end, we calibrated the OP7/STV co-infection model to the STV infection data considering that, in this scenario, no S7-OP7 was present in the virus seed.Thus, we obtained a baseline for kinetic parameters that were fixed for the description of OP7/STV co-infection (Table S1).Following parameter estimation, the model captured STV infection dynamics closely (Figures 1A-1C, 1G-1I, and 1M-1O).While the dynamics of M1 accumulation during STV infection could be described well, the levels of polymerase basic protein 1 (PB1) and nucleoprotein (NP) were slightly underestimated.
Next, we used the baseline parameters to describe the impact of OP7 during co-infection.To that end, we adjusted the viral input to match the values measured in the OP7 seed virus (Figure 1R).Model simulations, however, showed large deviations to the experimental data using this initial model implementation (Figure S2).Therefore, an extension of the OP7/STV co-infection model was required to fully represent the observed infection dynamics.
The complete co-infection dynamics can be described well when multiple changes to the functionality of S7-OP7 and M1-OP7 induced by the SNS are introduced simultaneously (Figure 2).Considering these changes, the final model captures viral RNA dynamics closely while M1 levels and the infectious virus titer are underestimated (Figure 1).The required changes comprise (1) a replication advantage of S7-OP7 cRNA and vRNA, (2) a reduced transcription of S7-OP7 mRNA, (3) a defect of M1-OP7 affecting the binding of vRNPs in the nucleus, and (4) a disturbed packaging process of S7-OP7 vRNPs (Figure S1B).In the following, we examine these changes individually from the perspective of the final model to show the impact of their inclusion and their effect in comparison to other hypotheses considered.
Taken together, the initial OP7 model was able to capture STV dynamics closely.Yet, to describe OP7/STV co-infection dynamics more precisely, it was required to implement changes regarding the functionality of S7-OP7.
Model predicts that the SNS found on S7-OP7 vRNA result in a replication advantage and a reduced transcription, confirmed by experimental data First, we focused on the replication of S7-OP7 vRNA.Previously, two of the specific SNS in the S7-OP7 genome sequence (G3A/C8U) were described to carry a superpromoter, which induces higher cRNA and vRNA synthesis. 44,45ithout changes in promoter activity of S7-OP7 vRNA, model simulations resulted in viral RNA dynamics similar to an STV infection (Figures 3A-3C).The accumulation of the three measured genome segments to distinct levels for all viral RNA species, i.e., S7-OP7 > S5 > S7-STV, can be explained by the initial discrepancy in the viral input (Figure 1R).However, the overall reduction of STV RNA levels and the large deviation between the vRNA levels of S7-OP7 and the other segments present in the experimental data was not captured.
To emphasize the differences between the segments, we incorporated a replication advantage for S7-OP7 in our model.However, it is unclear which step of S7-OP7 replication is improved. 44,45The dynamics of cRNA and vRNA were captured by increasing the synthesis rate of either RNA by 100% or both rates at specific ratios (Figure 3D).We decided to employ the same increase for the synthesis rates of both, cRNA and vRNA, since the superpromoter configuration may affect the promoter regions of both RNAs.Due to the replication advantage, the differences of two to three logs between the vRNAs of S7-OP7 and the other segments could be captured (Figures 3E-3G).Further, the dynamics of S5 and S7-STV mRNA were represented well.However, S7-OP7 mRNA showed elevated levels compared to the experimental data.
To improve the description of S7-OP7 mRNA dynamics, we explored the hypothesis that the SNS on S7-OP7 reduce the transcription of S7-OP7 mRNA.Two previous studies reported contradicting findings regarding the impact of the superpromoter mutation on mRNA levels.Investigating the impact of the superpromoter, Vreede et al. reported substantially inhibited mRNA synthesis 44 while Belicha-Villanueva et al. observed an enrichment of mRNA compared to STV experiments. 45Estimating an optimal rate of S7-OP7 mRNA transcription for the scenario shown in Figures 3E-3G suggested a large reduction (over 90%) compared to the rate of STV mRNA transcription (Figure 3H).The implementation of such a reduction improved the description of S7-OP7 mRNA dynamics (Figure 3I) as indicated by lower values for the Akaike information criterion (AIC, Table S2), 59 which can be employed to estimate the relative quality of mathematical models regarding specified datasets.
To validate this model prediction, we performed infection experiments using cycloheximide (CHX) and quantified the rate of mRNA accumulation during in vitro OP7/STV co-infection directly.CHX prevents the formation of progeny vRNA by inhibiting viral protein synthesis and subsequent replication.Thus, only the parental vRNAs can be utilized as templates for mRNA synthesis, which enables a more accurate determination of mRNA accumulation rates since the bias induced by progeny vRNA synthesis is removed.Based on the CHX experiments (Figure S3), we determined the rate of mRNA accumulation per available vRNA (Figure 3L).Indeed, the experimentally determined mRNA accumulation rates showed that S7-OP7 mRNA was transcribed significantly slower than S5 mRNA, confirming the model prediction.
In sum, model-based analysis predicted that the SNS on S7-OP7 vRNA enhances replication and reduces transcription, which is supported by experimental data.

The enhanced replication of S7-OP7 vRNA appears to deplete viral proteins and to limit STV vRNA accumulation
The replication advantage for S7-OP7 introduced in Figure 3 provides an explanation for the high S7-OP7 vRNA levels observed during OP7/ STV co-infection.However, the finding that STV vRNA levels were strongly reduced (Figure 4D) suggested a suppression of STV replication by an unknown mechanism.Previous studies discussed the hypothesis that conventional DI vRNAs compete with STV vRNAs for viral resources, e.g., the viral polymerase complex RdRp and NP, during virus replication. 13,14,60,61To examine this hypothesis in relation to OP7, we simulated the number of these viral proteins utilized for the formation of vRNAs.Then, we compared these numbers for different segments during an STV infection and an OP7/STV co-infection (Figure 4).
For STV infection, RdRp was equally distributed between the segments (Figure 4B).NP distribution showed a trend toward longer segments, because they require the binding of more NP for stabilization (Figure 4C).For OP7/STV co-infection, the distributions of both proteins were shifted toward S7-OP7, which consumed over 90% of all RdRp and over 80% of all NP available (Figures 4E and 4F).Thus, only low amounts of RdRp and NP could be utilized by other segments reducing their ability to form cRNAs and vRNAs strongly.
Based on these results, we infer that an enhanced S7-OP7 vRNA replication results in the exhaustion of viral proteins required for STV replication, similar to theories postulated for conventional DIPs.ee also Figure S1.
Model simulations indicate that the deficiency in virus replication of OP7 is induced by a defective M1-OP7 that appears unable to bind vRNPs Next, we focused on M1-OP7, which accumulates to over-proportional levels during OP7/STV co-infection, exceeding the level of any other viral protein measured in our experiments (Figures 1G-1L).These enhanced levels could have a strong impact on co-infection dynamics as M1  OP7, (E-G) a replication advantage of S7-OP7 and (I-K) the further addition of a reduced transcription of S7-OP7.For all simulations, it was assumed that M1-OP7 does not bind vRNPs in the nucleus (as elaborated in Figure 5).(D) The sum of squared residuals (SSR) for different combinations of S7-OP7 cRNA and vRNA replication advantages is presented.The red circle represents the best model fit assuming both synthesis reactions are subject to the same advantage.(H) SSR values for the application of reduced S7-OP7 mRNA synthesis rates assuming an existing replication advantage.The red circle represents the best model fit obtained.(L) Experimental data demonstrating differences in mRNA accumulation rates of S5 and S7-OP7 for an OP7/STV co-infection of MDCK cells treated with cycloheximide.Bars depict the calculated mRNA accumulation rates per available vRNA.Error bars represent the standard deviation of three independent experiments.See also Figure S3.
is an important regulatory protein during virus replication.Initial model simulations of an OP7/STV co-infection considering a fully functional M1-OP7 resulted in the underestimation of all viral RNAs and protein levels (Figures 5A-5C, 5J, and 5K).
Subsequently, we considered that the functionality of M1-OP7 might be affected by the SNS in the S7-OP7 genome sequence.We focused on the main functions of M1, i.e., (1) the nuclear export of vRNPs in conjunction with the nuclear export protein (NEP), (2) its involvement during the packaging of progeny virus particles, and (3) the binding of vRNPs in the nucleus.Disabling the nuclear export of vRNPs by M1-OP7 or its involvement during progeny virion release induced viral RNA and protein dynamics similar to a fully functional M1-OP7 (Figures 5D-5F, 5J, and 5K).To investigate experimentally whether M1-OP7 is indeed packaged and released in virus particles, we analyzed viral protein concentrations in the supernatant at 8 hpi.Following OP7/STV co-infection, the majority of released M1 consisted of M1-OP7 (Figure 5L).This result supports the prediction that M1-OP7 is involved during the packaging and release of virus particles.
Finally, when we considered a defect in the binding of vRNPs in the nucleus, we achieved a close representation of the measured OP7/STV co-infection dynamics (Figures 5G-5K) and the lowest AIC value overall (Table S2).In this scenario, the replication advantage induced to S7-OP7 leads to high S7-OP7 mRNA and M1-OP7 levels.However, if M1-OP7 does not bind or only weakly binds vRNPs to inhibit their replication, they can continue to multiply and achieve the levels observed during OP7/STV co-infection.Without this inhibition, M1-STV levels also increase to higher levels ultimately facilitating the binding and nuclear export of vRNPs.This could also explain why the previous scenarios resulted in overall low RNA levels, as large amounts of an M1-OP7 capable of binding vRNPs would shut down virus replication early.A disrupted binding of M1-OP7 to vRNPs could also provide an explanation on why OP7 is defective in virus replication, typically observed upon OP7 infection without complementation by STV.
Based on the model-based analysis of different hypotheses for the functionality of M1-OP7, we conclude that it likely cannot bind or only weakly binds vRNPs in the nucleus.iScience Article A significant fraction of virus particles produced during OP7/STV co-infection appears to be polyploid with respect to S7-OP7 Our experimental data suggested that the average vRNA levels per progeny virion were unequally distributed among the genome segments after an OP7/STV co-infection (Figure 1R).Thus, we tested different hypotheses of virus particle composition that could induce such an imbalance.For STV infection, progeny virions typically contain one vRNA per segment at 12 hpi (Figure 6A).Yet, for OP7/STV co-infection, experimental data showed significantly increased levels for S7-OP7 vRNA (Figure 6B).Moreover, average levels of S5 and S8 vRNAs in virions were decreased by one log and S7-STV was reduced even further.In previous DIP models, it was assumed that two types of virions can be formed, i.e., STV particles containing the eight STV vRNAs (S1-S8) and DIPs containing seven STV vRNAs and a DI vRNA that replaces its corresponding STV segment (''7 + 1'' formation). 14,53Implementing this approach in the model resulted in a reduction of average S7-STV vRNA content; yet, it did not result in an increase of S7-OP7 vRNA or a decrease of S5 and S8 vRNAs per virion (Figure 6C).
Since we observed that S7-OP7 accumulated to approximately ten vRNAs per virion at 12 hpi, we next considered the hypothesis that virions containing exclusively S7-OP7 vRNAs are released during OP7/STV co-infection (in addition to STV particles).A similar scenario was already subject of speculation in previous studies. 35This approach enabled the description of the increased average S7-OP7 vRNA content and reduced STV vRNA levels in virus particles (Figure 6D).However, a large reduction of S7-STV vRNA levels was not achieved.
In sum, model simulations indicate that progeny virus particles that are polyploid with respect to S7-OP7 vRNA are formed during OP7/ STV co-infection besides STVs.To describe the specific reduction of the average S7-STV vRNA levels in progeny virions, the formation and release of conventional ''7 + 1'' DIPs is necessary.

Model predictions describe S7-OP7 vRNA accumulation and STV suppression of serial infection experiments
Lastly, we tested the predictive power of the OP7 model by challenging it with additional experimental data obtained from serial OP7/STV coinfection experiments.To that end, we started co-infections with seed viruses showing different average S7-OP7 vRNA contents in virus particles (Figures 7A-7D).At 12 hpi, vRNA levels in progeny virions (Figures 7E-7H) and virus titers were quantified.Subsequently, further co-infections were performed using the virus material obtained in these infections (Figures 7I-7L).
For model simulation, we applied the vRNA levels measured in the corresponding seed viruses (Figures 7A-7D) as initial conditions for the first passage.To simulate further passages, the respective vRNA levels predicted at 12 hpi of the corresponding previous passage were used to adjust the initial conditions.We tested the hypotheses of virion release shown in Figures 6C-6E for model prediction to decide which is suited best for the final version of the model.Initially, a release of STV and conventional ''7 + 1'' DIPs resulted in the worst model fit (Table S2).This was confirmed by the model prediction for multiple passages, which did not induce the accumulation of S7-OP7 vRNAs observed for all tested conditions.Employing a release of STV and OP7 particles, but no conventional ''7 + 1'' DIPs, did not enable the description of the reduction of S7-STV vRNA observed in the passaging experiments (Figure S4).In contrast, model simulations assuming the release of all three particle types predicted the average vRNA levels in progeny virions well for passage 1-3 for all four initial conditions (Figures 7E-7L).Further, the reduction of virus titers during serial infections was described closely (Figures 7M-7P).The related AIC values also show a clear trend toward the three-particle hypothesis (Table S2), making it preferable for the final OP7/STV co-infection model.
Taken together, the OP7/STV co-infection model predicted the accumulation of S7-OP7 vRNA, the suppression of the STV segments and the reduction of virus titers induced by OP7 in serial infection experiments for up to three passages and varying initial conditions.

DISCUSSION
In this study, we utilized experimental data to develop a mathematical model of OP7/STV co-infection.The model was employed to investigate the mechanisms of OP7 interference with the STV and the source of its defect in replication, which were yet unknown.
The replication of S7-OP7 vRNA appears to be strongly increased by the SNS in its sequence.In particular, it contains the well-characterized superpromoter substitution (G3A/C8U) that is related to increased cRNA and vRNA synthesis. 44,45For conventional DIPs, a similar replication advantage has been proposed.However, it is based on the significantly shorter length of their viral genome leading to faster replication. 11,13,14,62Therefore, OP7 and conventional DIPs both show a similar phenotype, i.e., an enhanced replication of the DI vRNA.But interestingly, this appears to be based on different genotypes.In a previous modeling study, we estimated the replication advantage of a well-characterized conventional DIP ''DI244'', 33,63 which resulted in a cRNA synthesis rate increased by 32% compared to STV segments. 53pplying a similar implementation to our OP7/STV co-infection model, S7-OP7 would be subject to a higher increase in cRNA synthesis, i.e., by 100% (Figure 3D).This result is in line with our observation that OP7 shows a higher interfering efficacy than conventional DIPs in vitro and in vivo. 4,5,42,43Together, our findings support the hypothesis that the replication advantage of OP7 constitutes at least a part of its antiviral effect, as elaborated in the following.
The implementation of a replication advantage for S7-OP7 vRNA did not lead to an increase of its levels, but rather induced a decrease of STV vRNA levels by one to two logs during OP7/STV co-infection (Figures 3A-3G).To identify the underlying mechanisms, we evaluated if a competition for viral proteins could induce such an effect, as previously suggested for conventional DI vRNAs. 13,60,61Model simulations estimating the number of proteins utilized showed that S7-OP7 consumes a large portion, i.e., more than 80%, of available RdRp and NP (Figures 4E and 4F).Thus, by replicating faster, S7-OP7 cRNA and vRNA likely accumulates early capturing viral proteins before the STV segments generate enough templates to amplify their replication.Therefore, the depletion of available viral proteins by S7-OP7 could provide an explanation for the suppressed replication of STV vRNAs.This could constitute the inhibitory effect of OP7 during STV co-infection.In line with this, model-based analysis of the replication of a conventional DIP with a deletion in segment 3 showed that the competition for viral resources induces a similar suppression of STV replication. 14Interestingly, OP7 seems to establish such a DI-like behavior via the superpromoter on S7-OP7 instead of a large internal deletion.
Based on our model simulations, we found clear indications that M1-OP7 is defective and cannot bind (or only weakly binds) to vRNPs in the nucleus (Figure 5).5][66] If M1-OP7 does not bind to vRNPs, viral genomes are not exported to the cytoplasm for packaging or release.A deficient M1-OP7 could, therefore, explain the defect of OP7 particles in virus propagation, typically observed in our experiments. 4,35Accordingly, OP7 likely requires a supplementation of M1-STV to produce progeny virions as in the OP7/STV co-infections experiments performed previously 4,35 and in this work.This is similar to conventional DIPs, which cannot produce certain viral proteins due to deletions in their genome sequence and which also require complementation by STV co-infection for their propagation. 63orresponding experiments aiming to confirm the defect of M1-OP7 are the subject of future studies.
The average vRNA levels in progeny virions calculated for OP7/STV co-infection showed a strong increase of S7-OP7 vRNAs, i.e., around ten copies per particle (Figures 1R and 6B), as already observed in our previous studies. 4,35Thus, we suspect that, besides the existence of STV particles and ''7 + 1'' DIPs, some progeny virions might exclusively contain copies of S7-OP7 vRNA (Figure 6).In general, S7 vRNPs are considered to play a key role during the assembly of IAV particles, because mutations to the S7 genome sequence were shown to disrupt the organized packaging of all eight genome segments. 67,68The SNS on S7-OP7 may also impact the organized assembly of virus particles.A potential result of such a disruption is that the available vRNAs are packaged into virions randomly 67 according to their intracellular ratio (Figure 1F), which coincides with their extracellular ratio after co-infection (Figure 1R).This could lead to a diverse spectrum of genome compositions in progeny virions.Nevertheless, due to the sheer numbers involved (10 vRNAs/virion), it is highly likely that multiple copies of S7-OP7 vRNP accumulate in virus particles leading to virions being polyploid regarding S7-OP7 vRNA, as suggested previously. 35odel simulations were in good agreement with the average vRNA levels in virions and virus titers quantified during serial OP7/STV coinfection experiments demonstrating the predictive power of our OP7 model (Figure 7).These infections were mostly performed at a high multiplicity of infection (MOI), i.e., MOI 10.In this instance, nearly all cells are infected at the same time and it can be assumed that this involves at least one STV and one OP7 particle.This scenario can be described well by the single-cell model of OP7/STV co-infection we developed in this study.However, model predictions would likely be less reliable for low MOI conditions.In a low MOI infection, a mixture of STV infections, OP7 infections and OP7/STV co-infections would occur leading to a heterogeneous infection profile that cannot be captured by a single-cell model. 69In such a setting, a multiscale model would be required to describe the different infection scenarios. 53valuating the credible intervals of the estimated model parameters, we observed that some model parameters are correlated (Figure S5).These correlations are based on the underlying biological mechanisms of virus replication and are part of the basic structure of the model, e.g., the rate of M1 binding to vRNPs ðk Bind M1 Þ, which disables viral mRNA synthesis, is correlated to the mRNA synthesis rate ðk Syn M Þ.However, due to the considerable amount of quantitative experimental data used for estimation, these correlations do not induce large credible intervals in the respective parameter distributions.
Overall, the model of OP7/STV co-infection closely captured virus infection dynamics induced by the mutated genomic S7-OP7 and allowed us to infer the impact of the SNS introduced to its sequence.1][72] Furthermore, it could be extended toward simulation of in vivo infections in tissues and organs.To that end, an expansion to the second or third spatial dimension is required. 73,74[41][42][43] Ultimately, the co-infection model developed here is well calibrated for the prediction of IAV infections subject to OP7 interference. Thus,it provides a solid basis for the evaluation of application strategies to prevent or treat virus infections using OP7 as a novel antiviral treatment modality.

Limitations of the study
The packaging and release of virus particles is described as a single step in our model.For this process, various interactions of cellular and viral proteins with the viral genomes are required.However, the exact mechanisms involved in this intricate process are still largely elusive.Depending on improvements to the way we understand and quantify virus release during IAV infection, these mechanisms could be described more closely in the model to evaluate the impact of the SNS on S7-OP7 packaging and release.This could also improve the description of progeny virion composition after OP7/STV co-infection.By implementing the assumption that, in addition to STV particles and regular ''7 + 1'' DIPs, a third kind of virus particle that contains eight copies of S7-OP7 vRNA is released, we were able to reproduce our experimental data.However, our hypothesis is only a simplifying assumption, which could be reevaluated based on further knowledge regarding virus particle release during OP7/STV co-infection.
Due to the correlations observed between some kinetic parameters, it is difficult to identify one unique parameter set from the available data.Multiple parameter combinations can describe the experimental data, which leads to the uncertainties in model prediction shown in Figure 1.However, most parameters are well constrained and are distributed similarly to previously estimated results. 53,71Thus, the mechanistic relationships identified in this study are strongly supported by our model-based analysis and should be evaluated experimentally in follow-up studies.

STAR+METHODS
Detailed methods are provided in the online version of this paper and include the following:

Intracellular model of OP7/STV co-infection
The intracellular replication during OP7/STV co-infection is based on a model that was developed in our group previously. 14In short, this model uses a set of ordinary differential equations to describe virus binding and viral genome entry, viral RNA transcription and replication, viral protein synthesis, assembly and release of progeny virus particles for STVs and DIPs.This model was altered to describe OP7 instead of a regular DIPs with internal deletions by modifying Equations 20-24, 26-34, 38, 40-42, and 44-53.Therefore, we introduced S7-OP7 as the ninth genome segment considering that it has the same length as S7-STV, i.e., L 9 = L 7 and L V,9 = L V,7 .S7-OP7 follows the same replication process as the STV segments.A detailed description of the equations and parameters representing OP7/STV co-infection is provided at the end of the STAR Methods section and in Table S3, respectively.We introduced a reduction of mRNA transcription for S1-3, which was observed experimentally in previous studies [79][80][81] and used to model STV and DIP co-infection successfully. 53To that end, we changed mRNA dynamics to    3)  6) where k Exp and k Deg Rnp denote the rates of export and degradation of vRNP-M1 complexes, respectively.Furthermore, we adjusted the viral RNA replication concerning the function of RdRp.In the original DIP model, nascent vRNA and cRNA were synthesized from complementary ribonucleoprotein complexes (cRNPs) and vRNPs, respectively. 14These nascent RNAs were then stabilized by the binding of RdRp and, in a next step, NP to form progeny vRNPs and cRNPs.For our model of OP7/STV co-infection, we excluded the intermediate binding step mediated by RdRp.While cRNA synthesis can be catalyzed by the resident RdRp, a second RdRp likely binds to the newly synthesized cRNA right after the first nucleotides are generated. 82On the other hand, vRNA synthesis requires a non-resident RdRp in addition to the resident RdRp. 82,83 (Equation 53) The packaging of vRNPs in the cytoplasm is represented by a segment-specific mechanism.Cytoplasmic vRNPs form complexes including one copy of each genome segment.STV and ''7+1'' DIP complexes (V Cyt Cplx , D Cyt Cplx ) both contain STV S1-6 and S8.In addition, they carry either a S7-STV or a S7-OP7 vRNP.Complex formation occurs with rate k Cplx and degradation with rate k Deg Rnp .In total, we consider the release of three different virus particles, i.e., STV particles, ''7+1'' DIPs and particles that only contain S7-OP7.Their release is described by the rates r Rel STV , r Rel DIP and r Rel OP7 , respectively.These rates are calculated considering the maximum release rate k Rel , the available vRNP complexes and the abundance of viral proteins.Furthermore, we use V Rel Inf and V Rel Tot to represent the generated amount of infectious STV particles and the total amount of virions, respectively.The percentage of fully functional STVs is determined by the parameter F Par , which assumes that only a fraction of produced STV particles is infectious. 71To calculate the absolute amount of released OP7 particles, r Rel OP7 is divided by the amount of S7-OP7 vRNPs included in one OP7 particle, i.e., N Par OP7 .Here, we assume that N Par OP7 = 8 molecules, analogous to the number of vRNPs in a STV particle.

Figure 1 .
Figure 1.OP7/STV co-infection data and model simulations capturing the virus dynamics Simulations of the final OP7/STV co-infection model fitted to experimental data and 95% prediction bands generated by sampling from the estimated parameter distributions.(A-F) Cell-specific viral RNAs, (G-L) cell-specific viral proteins and (M-N, P-Q) extracellular virus titers for MDCK cells infected with (A-C, G-I, M-O) STV seed (influenza A/PR/8/34, H1N1) or (D-F, J-L, P-R) OP7 seed virus. 35Error bars represent the standard deviation of three independent experiments.Individual data points indicate data from a single or two independent experiments.(O and R) Normalized data (see STAR Methods) showing the average vRNA levels of virus particles for the seed virus and after infection compared to model simulations (sim).See also Data S1, Figure S2 and TableS1.

Figure 2 .
Figure 2. Schematic depiction of the OP7/STV co-infection model Virus entry, nuclear import, viral RNA and protein synthesis, nuclear export, virion assembly and progeny virus particle release during OP7/STV co-infection.The model differentiates between RNA species of individual STV segments and S7-OP7.Different forms of the viral protein M1 can be synthesized from S7-STV or S7-OP7.The model considers a reduced transcription of S7-OP7 mRNA, an increased replication of S7-OP7 cRNA and vRNA, a defect of M1-OP7 affecting the binding of viral genomes in the nucleus, and the existence of three different types of progeny virions (as elaborated in Figures 3, 5, and 6, respectively).Figure adapted from. 53ee also Figure S1.
Figure 2. Schematic depiction of the OP7/STV co-infection model Virus entry, nuclear import, viral RNA and protein synthesis, nuclear export, virion assembly and progeny virus particle release during OP7/STV co-infection.The model differentiates between RNA species of individual STV segments and S7-OP7.Different forms of the viral protein M1 can be synthesized from S7-STV or S7-OP7.The model considers a reduced transcription of S7-OP7 mRNA, an increased replication of S7-OP7 cRNA and vRNA, a defect of M1-OP7 affecting the binding of viral genomes in the nucleus, and the existence of three different types of progeny virions (as elaborated in Figures 3, 5, and 6, respectively).Figure adapted from. 53ee also Figure S1.

Figure 3 .
Figure 3.The combination of an increased replication and a reduced transcription of S7-OP7 enabled the description of OP7/STV co-infection dynamics Simulation results of a model describing (A-C) unchanged promoter activity of S7-OP7, (E-G) a replication advantage of S7-OP7 and (I-K) the further addition of a reduced transcription of S7-OP7.For all simulations, it was assumed that M1-OP7 does not bind vRNPs in the nucleus (as elaborated in Figure5).(D) The sum of squared residuals (SSR) for different combinations of S7-OP7 cRNA and vRNA replication advantages is presented.The red circle represents the best model fit assuming both synthesis reactions are subject to the same advantage.(H) SSR values for the application of reduced S7-OP7 mRNA synthesis rates assuming an existing replication advantage.The red circle represents the best model fit obtained.(L) Experimental data demonstrating differences in mRNA accumulation rates of S5 and S7-OP7 for an OP7/STV co-infection of MDCK cells treated with cycloheximide.Bars depict the calculated mRNA accumulation rates per available vRNA.Error bars represent the standard deviation of three independent experiments.See also FigureS3.

Figure 4 .
Figure 4. S7-OP7 vRNA replication suppresses the accumulation of STV segments by consuming the majority of viral polymerase and NP Model simulations for (A) an STV infection and (D) an OP7/STV co-infection considering a replication advantage and a defect of M1-OP7 affecting the binding of vRNPs in the nucleus (as shown in Figures 3 and 5, respectively).The black dashed lines represent the maximum vRNA level achieved in an STV infection.Error bars represent the standard deviation of three independent experiments.The stacked bar plots show the simulated utilization of (B, E) polymerase complex RdRp and (C, F) NP for the formation of progeny cRNA and vRNA of the different genome segments for the two scenarios, respectively.

Figure 5 .
Figure 5. Model simulations suggest that M1-OP7 is defective and cannot bind or only weakly binds vRNPs in the nucleus Simulation results of RNA dynamics for OP7/STV co-infection models describing an M1-OP7 that is (A-C) fully functional, (D-F) cannot be utilized for the assembly of progeny virus particles or prevents nuclear export of bound vRNPs and (G-I) does not bind to vRNPs in the nucleus.(J and K) Comparison of viral protein accumulation in the tested scenarios.For model simulations, it was assumed that S7-OP7 exhibits a replication advantage and a reduced transcription (Figure 3).(L) Experimental data showing concentrations of M1-STV and M1-OP7 in the supernatant at 8 hpi following an STV infection or OP7/STV co-infection.Error bars represent the standard deviation of three independent experiments.

Figure 6 .
Figure 6.Three different virus particle types are required to describe vRNA levels in progeny virions Normalized experimental data showing the average vRNA levels in progeny virions measured for four different segments at 12 hpi following the infection of MDCK cells with (A) STV seed (influenza A/PR/8/34, H1N1) or (B) OP7 seed virus (see STAR Methods).Error bars represent the standard deviation of three independent experiments.(C-E) Simulations show the average vRNA levels in progeny virions considering the existence of different virus particle types, indicated in the schemes above.

Figure 7 .
Figure 7. Model predictions describe the accumulation of S7-OP7 vRNA and the suppression of the STV over multiple in vitro co-infection passages (A-D) Average vRNAs per virion measured for four segments of different OP7 seed viruses (passage 0).(E-L) Comparison of experimental data and predictions of the final version of the model (sim) following the infection of MDCK cells at 12 hpi after up to three passages.For model simulations, either the original seed virus (passage 0) or the prediction of the previous virus passage was used as an initial condition.Measured vRNA levels were normalized (see STAR Methods).(M-P) Symbols represent experimental data of total and infectious virus particle concentrations determined in the seed virus and after serial OP7/STV co-infection passaging at 12 hpi.Curves depict the corresponding model predictions.See also Figure S4.
i and the length of the corresponding mRNA L i .The degradation of mRNA occurs with the rate k Deg M .The transcription of S1-3 is reduced by the factor F RdRp M .In contrast to the original intracellular DIP model, we included the synthesis of a viral protein encoded by the mutated segment.Thus, we consider two different versions of M1, i.e., M1-STV and M1-OP7, which are synthesized with the rate k Syn P from their corresponding mRNAs R M 7 and R M 9 , respectively.In the initial model implementation, both M1s can bind to vRNPs in the nucleus with the rate k Bind M1 .Additionally, they are required for progeny virion release.Moreover, we differentiated which type of M1 is binding to vRNPs in the nucleus, resulting indVp Nuc M1 À STV;i dt = k Bind M1 P M1 À STV Vp Nuc i À k Exp P NEP + k

TABLE
d RESOURCE AVAILABILITY B Lead contact B Materials availability B Data and code availability d METHOD DETAILS B Intracellular model of OP7/STV co-infection B Model extension B Simulation approach and parameter estimation B Model prediction B Cells and viruses B Determination of viral mRNA accumulation rates B Real-time RT-qPCR to quantify viral RNAs B Quantification of influenza virus proteins B Full model of OP7/STV co-infection Thus, we removed nascent vRNA and cRNA from the model by simplifying the dynamics of viral RNA replication to Syn V P RdRp Cp i À k Bind NP P NP + k Deg