Experimental and mathematical insights on the competition between poliovirus and a defective interfering genome

During replication, RNA virus populations accumulate genome alterations, such as mutations and deletions. The interactions between individual variants within the population can determine the fitness of the virus and, thus, the outcome of infection. We developed an ordinary differential equation model to infer the effect of the interaction between defective interfering (DI) replicons and wild-type (WT) poliovirus. We measure production of RNA and viral particles during a single infection cycle, and use these data to infer model parameters. We find that DI replicates faster than WT, but an equilibrium is established when both WT and DI compete for resources needed for RNA replication and genome encapsidation. In the presence of DI, the concentration of WT virions at cell lysis is suppressed by the factor of 5. Multiple generations within a single cell infection provide opportunities for significant inhibition of WT replication by competition with the faster replicating DI genomes.


Introduction
Co-infections, the simultaneous infection of a host by multiple pathogen species, are frequently 30 observed (Mideo, 2009; Read and Taylor, 2001). The interactions between these microrganisms 31 can determine the trajectories and outcomes of infection. Indeed, competition between pathogen 32 species or strains is a major force driving the composition, dynamics and evolution of such popula-33 tions (Mideo, 2009;Bashey, 2015). Three types of competition among free-living organisms have 34 been defined from an ecological point of view: exploitation, apparent and interference competition 35 (Read and Taylor, 2001;Bashey, 2015;Mideo, 2009). Exploitation competition is a passive process in 36 which pathogens compete for access to host resources. Apparent competition is competition that is 37 not due to using shared resources, but to having a predator in common (Holt, 1977), and is generally defective interference particles in the context of virus infection. 90

91
Interference of WT poliovirus production by DI genomes 92 Initially, we evaluated whether DI genomes, carrying a deletion of the entire region encoding for 93 capsid proteins, could affect progression of WT virus infection ( Figure 1A). The DI genome used 94 in this study does not produce capsid proteins and, thus, it is unable to encapsidate its genome 95 and spread to other cells. However, it retains full capacity to produce non-capsid viral proteins and 96 replicate its genomic RNA. WT poliovirus and DI genomic RNAs were transfected by electroporation 97 to HeLaS3 cells and infectious titers of WT virus were determined over time by plaque assay 98 (Material and Methods). As a control we also evaluated a replication-incompetent defective RNA 99 lacking the capsid-encoding region, a part of 3D-polymerase encoding region, and the entire 3' 100 nontranslated region (NTR). HeLaS3 cells transfected by only WT genomes produced nearly 1×10 7 101 PFU/ml WT virus 9 hours after transfection, while co-transfection of WT genomes together with DI 102 RNAs resuted in 100-fold decrease of WT titers ( Figure 1B). The non-replicating defective RNA did 103 not affect WT virus production, suggesting that replicating DI genomes are required for effective 104 interference, as previously reported (Kaplan and Racaniello, 1988). 105 Quantification of the copy number of WT and DI genomes following co-transfection 106 Next, we examined the interaction between DI and WT genomes by varying the ratio of each RNA 107 used to initiate transfection. Starting with equal RNA concentrations (5 g) DI genomes were 4 times 108 more efficiently transfected than WT (data not shown). Given that DI genomes are~2,000 nucleotide 109 shorter (~1/4 shorter) than WT genomes, the copy number of DI genomes are higher than that of WT 110 genomes and transfection of shorter genomes is also more efficient than larger RNAs. We optimized 111 our protocol to deliver equal copy number of DI and WT genomes into the transfected cells. We 112 transfected 5 g of WT to 1.25 g of DI genomes, and we collected RNA samples at given timepoints 113 (t=0, 2, 3.5, 5, 7 and 9 hours after transfection). The average number of genomes in a single cell was 114 estimated as the number of genomes divided by the number of transfected cells. Replication rates 115 of WT and DI decreased ∼7 hours after co-transfection, but this effect was not observed in the cells 116 transfected only with WT or DI ( Figure 1C). Thus, replication of WT genomes was inhibited by DI 117 genomes, and the number of accumulated DI also decreased in the presence of WT. This suggests 118 that WT and DI genomes compete for a limiting factor for replication. Nonetheless, DI genomes 119 replicated faster than WT genomes ( Figure 1C). To determine the numbers of encapsidated WT 120 and DI genomes, we also treated cell lysates with a mixture of RNase A and RNase T1. Viral RNAs 121 encapsidated in virus particles are resistant to RNase activity, while naked RNAs are degraded by 122 RNase-treatment. The decrease of encapsidated WT genomes between singly and dually infected 123 cells conditions was two-fold larger than that of WT genomes without RNase-treatment, indicating 124 that DI genomes hamper WT genome encapsidation (Figure 1C&D, compare the difference between 125 plain and dashed blue lines at 9 hours after transfection in Figure 1Di to the difference in Figure 1Ci). 126 Thus, these results are consistent with the idea that DI RNAs replicate faster than WT genomes, 127 due to their shorter genome (Holland, 1991;Chao and Elena, 2017). Interestingly, co-transfection 128 results in a net reduction in replication of both WT and DI genomes most likely due to competition 129 for some host-cell limiting factor needed for genome amplification. In addition, capsid proteins, 130 produced by WT genomes, limit DI and WT virus production as DI genomes compete for these 131 proteins and thus further inhibit WT production. To further examine the mechanism of defective 132 interference and quantitatively evaluate the effect of co-replicating DIs, we designed a simple 133 mathematical model that describes the DI/WT genome interactions.  replication. The set of ODEs is the following:  Ta 192 Model predictions fit well the experimental measurements in WT is more hindered by this competition for resources than the DI (Figure 3 A, compare red 203 and blue plain curves) thanks to the higher replication rate of DI genomes ( = 1.075, Table 1). 204 Predictions also demonstrate that DI genomes are more efficiently encapsidated than WT genomic 205 RNA ( Figure 3C, compare red and blue plain curves), thanks to the higher encapsidation rate of DI 206 genomes ( = 2.185, Table 1). Most importantly, the model is able to describe the decrease in WT Supplement 1B). Also, a strong log-to-log relationship was found between the resource production 213 to decay ratio ∕ and the replication factor (Figure 3-Figure Supplement 1E). 214 Both models feature a time-dependent virus replication rate (Figure 3-Figure Supplement 1F). 215 In the reduced model, it is given by the logistic function Λ( ) (Equation 10 in Material and Methods), 216 and in the full model by the product ( ). In both models, the best fit yields approximately the     the DI-to-WT replication ratio, , and the DI-to-WT encapsidation ratio, , as well as their second-241 order interaction, were the most influential factors for the variation of Φ , explaining 72%, 19% 242 and 7% of the variance, respectively ( Figure 4A). All the remaining factors and their second-order 243 interactions had a negligible effect (less than 1% of the variance). Hence, our model predicts that 244 only parameters associated with the DI design have a strong impact on the degree of suppression 245 of WT by DI. 246 To further examine the effect of and , we varied both parameters from their best estimated 247 value ( Figure 4B). As expected from the global sensitivity analysis, was found to be more important 248 than for the production of WT virions, the gradient of Φ being steeper along -axis than along 249 -axis. Within the tested range of parameters and , the value of Φ varied between 2% and  50%. The reference value of Φ corresponding to best-fit parameter estimates from experimental 251 data was 23%. Therefore, we can predict that a DI particle with a lower replication factor, or, to a 252 lesser extent, with a lower encapsidation rate than the DI particle used in the present work would At the optimal initial conditions maximizing WT burst size, WT must infect the cell with a larger 278 MOI than DI. On the other hand, the optimal initial conditions for maximizing DI burst size are 279 when WT is initially present in slightly larger quantity than DI. The DI needs enough WT to exploit 280 its capsids and produce virions. Because (i) the DI replicates and encapsidates faster than the WT, 281 (ii) only the WT produces free capsids and (ii) replication and capsid production result in resource 282 depletion, it is more optimal for DI virion production to have the WT infect a cell in slightly higher 283 quantity than the DI. In that case, the WT has a slight initial advantage over the DI and can use 284 resources to produce free capsids. In return, the DI can exploit those free capsids at its own 285 advantage as it replicates and encapsidates more efficiently. 286 We also examined the cross-effect of the time delay and the variation of initial MOIs (

Model parameters are summarized in
. We specifically examined the competition between WT and DI genomes during RNA replica-317 tion and the consequences of DI capsid exploitation for WT virus production (Figure 1 & Figure 4). 318 Our experiment has provided three main results. First, the number of WT and DI genomes is 319 lower in dually infected cells compared to singly infected cells (Figure 1Ci& ii), indicating a limiting 320 resource for replication. Second, in dually infected cells, DI genomes replicate faster than WT 321 genomes (Figure 1Ciii), showing the advantage of their shorter genome size (Holland, 1991;Chao 322 and Elena, 2017). Third, the decrease in WT encapsidated genomes from singly to dually infected 323 cells is two folds larger than that of WT naked genomes (Figure 1Di& Ci), indicating that DI genomes, 324 by trans-encapsidating in capsid proteins produced by the WT, further inhibit WT virions production. 325 In their experiment, Cole and Baltimore (1973) observed equivalent amounts of viral RNA 326 produced in WT singly-infected cells or in dually-infected cells. In our experiment we obtain the 327 same result, with 19,281 WT genomes in singly-infected cells at 9 hours post transfection vs. 18,153 328 WT and DI genomes in dually-infected cells (ratio of singly to dually-infected cells of 1.06). 329 We have designed a minimal mathematical model able to capture key features of the DI/WT 330 interaction during a single-cell replication cycle. We accounted explicitly for depletion of cellular 331 resources and available capsid proteins, the latter solely produced by the WT virus. This has allowed 332 us to accurately describe the reference in vitro experimental data, and to predict new data on which 333 the model had not been trained. In particular, the data fitting procedure has provided us with the 334 possibility of estimating model parameters within biologically realistic ranges. 335 We expected the DI genome to replicate faster than the WT by a factor of approximately the 336 ratio of WT to DI genome lengths, that is 7515bp∕5733bp = 1.311. However, the best optimized value 337 of the corresponding parameter was lower (1.075, Table 1). This discrepancy is most probably  418 At equal MOIs, the DI particle needs to infect a cell within approximately a 2 hours window before 419 or after the WT in order to produce DI virions, and up to approximately 30 minutes after the 420 WT in order to outcompete the WT in terms of burst sizes ( Figure 5A). When simulaneously co-421 infecting a cell, the DI particles will maximise their virion production when WT and DI initial MOIs 422 are approximately equivalent, and the WT particles will maximise their virion production when 423 WT MOI is larger than DI MOI (Figure 5B-C). At equal MOIs, the difference between DI and WT 424 virion production is maximised at approximately simultaneous co-infection of a cell. This difference 425 maximisation is shifted towards cases where the DI infects a cell before the WT when WT MOI is 426 larger than DI MOI. Conversely, it is shifted towards cases where the WT infects a cell before the DI 427 when DI MOI is larger than WT MOI (Figure 5-Figure Supplement 1). 428 These results are in agreement with those of Cole and Baltimore (1973), who found that the  assumption would need to be tested in future experimental work.  464 For example, playing on resource availability could allow to slow the evolution of resistance to 465 antimicrobial drugs (Wale et al., 2017a) (Huang and Baltimore, 1970). 470 Perspectives 471 We could take advantage of the features of DI particles to develop a new type of therapeutic antiviral 472 strategy based on defective interference particle competition (Frensing, 2015). Our model suggests 473 that parameters , the DI-to-WT replication ratio, and , the DI-to-WT encapsidation ratio, are 474 the first and second most important parameters impacting the proportion of WT virions at cell 475 lysis. Therefore, a rational strategy to strengthen interference activity of DI genomes and thus 476 reduce the production of WT virions is to modify DI genomes towards higher replication speed 477 and encapsidation efficiency. Such improvements may be realized by taking advantage of the 478 evolvability of DI genomes. Serial co-passages of WT and DI particles followed by genetic analyses 479 would allow for the screening of mutations providing higher replication or encapsidation of the DI. 480 Also, the production of shorter DI genomes could lead to its faster replication. 481 Improving the interference at the intracellular level may cause less inhibition of WT viral load at Software (Bio-Rad).

Model reduction
576 As our mathematical model (Equation 1 -Equation 4) presents a classical problem of parameter 577 identifiability, we built a lower dimensional model to solve this problem by assuming that the 578 decrease in resources due to viral uptake for replication follows a logistic decreasing function. This  In Equation 11, 616 we define: with , resp. , being either experimental ( , resp. ) or numerical ( , resp. ) naked, resp. 618 encapsidated, genomes data and for WT or DI. 619 The iterative process was applied as follows (see also   (Equation 1-Equation 6). 640 Model predictions 641 Cross-validation 642 We cross validate the results of our optimisation procedure by assessing how well the model is 643 able to predict the relative WT virus burst size for various WT to DI initial ratios (after transfection) 644 for which it has not been trained. We first obtain an optimal set of model parameters on our time 645 series experimental data ( and ) featuring initial WT:DI = 1:1. We then test five additional DI-to-WT 646 initial ratios, ranging from 0 to 3.6. Initial conditions for model simulations were set as the average 647 of experimental values for each of the five initial ratios. 648 In the cross-validation experiment, evaluation of the relative WT virus burst size was based on 649 the count of plaque-forming units (PFUs Based on parameter estimation, each parameter was approximately varied by ±50% of its 674 best estimated value. Based on these boundaries, each parameter was allocated a vector of five 675 equidistant values (except for that was not varied because it was estimated at 0, see Table 1). 676 Then, all distinct combinations of parameter values were tested according to a full factorial design.   Resource decay rate, γ Frequency D q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q q qq qq  1-Equation 6). Three experimental replicate values (black dots) of relative wild-type (WT) virus output are represented for various defective interfering (DI) to WT input (proxy of multiplicities of infection) ratios. Red dots indicate predicted relative WT output starting with the same experimental input ratios. Experimental WT output corresponds to PFU while simulated WT output corresponds to burst size (number of encapsidated genomes at 9 hours post infection). All outputs were normalized by the output value (or the mean for experimental data) of WT:DI = 1:0 input ratio. R-squared and p-value of a Pearson correlation test between experimental and predicted WT outputs are given in the graphic. Square score (eq. 11).
Obtain estimation for each parameter.