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# Viral reassortment as an information exchange between viral segments

Edited by Robert A. Lamb, Northwestern University, Evanston, IL, and approved January 10, 2012 (received for review August 17, 2011)

## Abstract

Viruses have an extraordinary ability to diversify and evolve. For segmented viruses, reassortment can introduce drastic genomic and phenotypic changes by allowing a direct exchange of genetic material between coinfecting strains. For instance, multiple influenza pandemics were caused by reassortments of viruses typically found in separate hosts. What is unclear, however, are the underlying mechanisms driving these events and the level of intrinsic bias in the diversity of strains that emerge from coinfection. To address this problem, previous experiments looked for correlations between segments of strains that coinfect cells in vitro. Here, we present an information theory approach as the natural mathematical framework for this question. We study, for influenza and other segmented viruses, the extent to which a virus’s segments can communicate strain information across an infection and among one another. Our approach goes beyond previous association studies and quantifies how much the diversity of emerging strains is altered by patterns in reassortment, whether biases are consistent across multiple strains and cell types, and if significant information is shared among more than two segments. We apply our approach to a new experiment that examines reassortment patterns between the 2009 H1N1 pandemic and seasonal H1N1 strains, contextualizing its segmental information sharing by comparison with previously reported strain reassortments. We find evolutionary patterns across classes of experiments and previously unobserved higher-level structures. Finally, we show how this approach can be combined with virulence potentials to assess pandemic threats.

Reassortment of segmented viruses is a key mechanism for rapid novel virus creation. At least two human influenza pandemics in the last century were linked to lineages where some number of genomic segments reassorted with a genome of nonhuman origin (1, 2). This fact was reinforced by the emergence of the 2009 H1N1 pandemic (2009 pdm) virus (3⇓–5). Novel reassortant strains can evade adaptive immunity by introducing antigens to a naïve host population or overly stimulate innate immunity by presenting a new host with abundant nonself molecular signals (6⇓⇓⇓–10). Moreover, both sequence database studies and in vitro experiments have shown that genome reassortment between strains happens nonrandomly: If two strains coinfect the same cell, their progeny may not sample all possible strain/segment combinations uniformly (11⇓⇓–14). These analyses focused on whether it is more likely that pairs of segments from the same strain appear together in reassortments, typically using chi-square tests to establish significance.

Because influenza has eight segments, there are 256 possible reassortant viruses when a cell is coinfected by two strains. Each strain type and host cellular environment can influence reassortment differently, so it would seem impossible to predict whether a new pandemic strain can form. However, not every possible progeny combination may occur or survive. As we show, this problem can be reformulated using information theory, determining the information content of a segment’s strain of origin distribution and the information shared among segments. Our approach uncovers new aspects of the process of reassortment, demonstrating significant combinations that occur commonly in several different crosses of viral strains. We show that virus strain and host cell-type influence outcomes. We include a novel experiment with the latest pandemic strain, 2009 pdm, and the seasonal H1N1 strain circulating prior to its introduction, expanding the number of reassortment examples analyzed to date and comparing this case to other analogous experiments within our framework.

Information theory is a general mathematical framework for quantifying the transmission and exchange of information (15, 16). Within this framework, we can separate multiple levels of information transfer and exchange within viral segment replication and reassortment. At the same time, this formalism allows us to show how these different levels constrain one another and to relate information theoretic quantities, such as entropy and mutual information, to the likely diversity of viral populations produced by a host coinfection. We further provide a nonparametric permutation test to assess the statistical significance of these quantities. We show which segments share meaningful amounts of information across all experiments, implying general segregation rules in influenza, and which segments only share significant information for particular strain pairings. Significantly, we quantify how much information they actually share—a key component in determining the diversity of progeny. Finally, we extend our method to reoviruses, a member of the reoviridae family, which includes rotavirus, the leading cause of acute childhood diarrhea worldwide (17).

In a typical experiment, a relevant cell type is coinfected with two different strains, and the repertoire of progeny viruses is explored. These experiments separate intrinsic biases from those observed in circulating strains, in refs. 11 and 12, that may have additional causes. Suppose two strains are introduced to cells in culture at equal multiplicities of infection (MOI), a typical experimental scenario. MOI is defined as the ratio of infectious agents to host targets, so each strain, ideally, is equally likely to infect a target cell. After an experiment, the output probability that a segment comes from a given parental strain may no longer be the input value of one-half. We quantify this effect as the entropy change per segment between the input probability distribution that a segment came from a given strain versus the output distribution.

If bias exists toward how pairs of segments appear together in the output virus, such as may arise from packaging effects, this will be captured by the mutual information shared between those two segments. The entropy per segment constrains this quantity: The mutual information between segments is always less than the minimum entropy per segment. For these quantities we have designed a nonparametric “channel scrambling” test for generating *p* values. Furthermore, we use the total correlation to capture structures of a higher order than pairwise, a feature not found in previous analyses. A hypothetical case is represented in Fig, 1, where segments 2, 3, and 7 have a significant total correlation. In this case the segments, taken individually, are equally likely to come from the same strain of origin. Yet, if one segment has a given strain of origin, the other two segments will also come from the same strain.

By formalizing the mathematical analysis for this process and testing that analysis on both new and existing reassortment data, we may better understand reassortment outcomes and predict limitations upon which virus will emerge, resulting in better preparedness. That is the goal of this program. While a full exploration of the true set of reassortment biases requires a large-scale exploration of all combinations of infecting strains, infected cell type, and cell-type species of origin, in a manner that faithfully reflects the likely backgrounds and cellular response states in which coinfecting strains could replicate, our approach makes the problem more quantitative and informative. In doing so, we demonstrate both how this method can be used in future experiments to assess pandemic risk and to uncover fundamental limits on the ability to communicate strain information between viral segments.

## Results

### Entropy Change per Segment in Coinfection Experiments.

In the classic coinfection experiment, first outlined in Lubeck et al., two strains of equal MOI of 1–5 PFU (plaque forming units) per cell are introduced to MDCK cell culture (11). However, the total concentration of a given segment in the progeny viruses may be far from uniform. If two strains are introduced to these cells, and each segment has an initial probability of ½ for having come from a given strain, then each segment will have an initial entropy per segment of 1 bit. We assume that there are initially *M* strains introduced to a cell with an equal probability, although this does not need to be the case, and *p*_{n}(*s*) is the probability that a given segment, *n*, from the output viruses came from strain, *s*. If the entropy of a segment, *n*, for output viruses is defined as the entropy change for that segment will be Typically, there are two equally probable coinfecting strains and the first term will then be equal to 1. The above quantity measures how much the output distribution deviates from uniformity. For a given segment, a value near zero would indicate that, in the output viruses, one is equally likely to see a segment come from either strain. If the value is close to 1, it indicates that this segment is dominantly from one of the two input strains in the output viruses. Hence, a change in entropy implies that one type of progeny virus is now more likely to appear than another, whereas previously that was not the case.

We analyze this quantity for an original experiment in which MDCK cells were coinfected at MOI of 1 PFU/cell of seasonal H1N1 (A/Hong Kong/226654/07) and 2009 pdm (A/California/4/09). MDCK cells were incubated with virus inoculums for 1 h at room temperature and then were briefly washed by acidic buffer to inactivate nonincorporated wild-type parental viruses. The virus was allowed to grow, and the supernatant was collected at 72 h post infection and used to perform standard plaque assays. Plaques were purified and their genotypes were identified by RT-PCR using segment specific primers for both strains as previously described (18). A detailed description of these procedures is available in *SI Text*, along with a full table of results.

The results of our original experiment were compared to two previous experiments in which MDCK cells were coinfected with influenza strains. MDCK cells are commonly used to measure infection of a cell by multiple possible strains of origin, given the ability of a wide variety of influenza subtypes to infect and grow productively in these cells (19). Because of this, they provide a standard context for comparison of intrinsic reassortment potential. The first comparison experiment, performed, by Li et al., cotransfected seasonal human H3N2 and equine H7N7 expression plasmids into 293T cells (20). The data in this study was derived by reverse genetics techniques, and the viral repertoire studied was generated by cotransfection of viral segments producing plasmids for H3N2 and H7N7 strains as well as the viral polymerase complex protein expressing plasmids for H1N1. The second is the aforementioned Lubeck experiment in which seasonal human H1N1 and H3N2 strains coinfect MDCK cells (11). It should be noted that these experiments used different experimental settings and time courses to generate recombinant viruses. Given that there may be different experimental biases in each of these settings, using data generated from different experimental platforms might help us to reduce the overall bias in our analysis and would make trends that are observed across experimental platforms all the more convincing. A comparison of the different approaches used by the published influenza experiments under analysis in this work is also provided in *SI Text*.

Several noteworthy features are presented in Table 1 and Fig. 2. Entropy changes of greater than ½ for our experiment correspond to segments 4 (encoding HA) and 7 (M), respectively. In comparison, the experiment of Li et al., with two strains of very different species origin compared to the other two experiments, shows four segments with changes greater than 0.4 and Lubeck et al., with two human seasonal strains, shows no changes greater than 0.1515 bits. Comparative examination of these results shows that, in our case and in the case of Li et al., HA dominantly occurs from one strain, which also happens once for PB2 in the Li et al. experiment. Presumably these HA had an advantage over another as the reassortant viruses reinfected. It is also interesting to note that segments 6 (NA) and 8 (NS) show very little change in entropy across all three experiments, implying that one strain’s version of these proteins is typically not favored. Segment 8, consisting of two nonstructural proteins (NS1/NS2) and one of the more conserved sequences in influenza, may not be expected to have divergent function across strains, implying that one strain’s proteins have no real strain specific advantage.

### Mutual Information Among Replication-Biased Segments.

Given that the entropy per segment is altered from a uniform probability, the opportunity for viral segments to communicate their strain to one another will become limited. For instance, in the case of the H3N2-H7N7 reassortment experiment of ref. 20, segment 1 has lost all entropy per segment because every progeny strain has segment 1 from the same parental strain. Hence, even if another segment would gain an advantage from pairing with a segment 1 from H7N7, such communication about strain type is not possible because segment 1 is always from H3N2. The ability of segment 1 to communicate information to another segment is closed.

In information theoretic terms, the mutual dependence between two random variables is quantified by the mutual information, applied to this problem as where *p*_{mn}(*s*_{i},*s*_{j}) is the joint probability that segments *m* and *n* come from strains *s*_{i} and *s*_{j}, respectively, and, therefore, *H*_{mn} is the entropy for the two-segment joint probability. The mutual information and entropy per segment constrain one another via the inequality due to the fact that the joint entropy is always greater than the maximum individual entropy, as summarized in *SI Text* (15).

Two issues now present themselves. The first is to determine that a quantity of mutual information between two segments should be deemed significant, as opposed to when it could have been achieved randomly. We use a nonparametric test for associating a *p* value to the mutual information shared between segments. To obtain a *p* value, we randomly permute the order of the output strains for each segment—“scrambling” the message. We count the number of times, out of the number of permutations, that the observed mutual information is greater than the empirical value (following the convention of counting those on the boundary half of the time). Our procedure is further described in *SI Text*. Second, because there are eight segments in the virus, there are multiple pairs of segments that can share information. Multiple hypothesis correction must be taken into account. To focus on the clearest associations, we use Bonferroni corrections. There are 28 possible segment pairs, so we use a *p* value of 0.05/28 = 0.00179 for significance. The results of those segment combinations that pass the Bonferroni corrections, under 10^{5} permutations, are listed in Table 2. In this table significant pairs are listed, along with their mutual information and *p* value. Also listed is the normalized mutual information: the mutual information divided by the maximum possible value given by the above inequality.

As is clear from Table 2 and Fig. 3, the most consistently significant pairing is between segments 2 and 3 (PA). In each case this pair is significant, sharing between 0.1303 and 0.1912 bits of information per segment, with the more closely related strains, seasonal H1N1 and H3N2, typically sharing the most information. Each strain also has strain specific pairings, which may indicate an association that was significant to the biology of that particular strain combination but not to others. For instance, segments 3 and 8 show significant communication for 2009 pdm and seasonal H1N1, marginal association for H1N1 and H3N2, and no association for H3N2 and H7N7. The constancy of the 2–3 pairing across strains is important. In the original experiment on the subject, ref. 11, the entire polymerase complex was significantly associated—that is, segments 1, 2, and 3. However, it is clear from this work that if, in fact, polymerase segments pair preferentially by strain, only segments 2 and 3 pair as a general rule. In H3N2—H7N7, the H7N7 PB2 is completely dominant, while for H1N1—2009 pdm segments 1 and 2 make no significant associations.

### Total Correlation For More Than Two Segments.

Our approach can be generalized for correlations between higher order complexes, such as triples of segments and so on. However, there are two drawbacks. First, there are many ways to extend the concept of mutual information to multivariate distributions (21). No one function captures all aspects of the two-dimensional mutual information for multivariate distributions. Second, looking for associations among greater combinations of segments can create more hypotheses to test, necessitating more experiments. For significant association among three segments, there are 56 possible hypotheses, and the Bonferroni correction would yield a *p* value of 0.05/56 = 0.000893.

Here we focus on the total correlation (22). This measure captures the notion that the proper measure of dependence is the Kullback–Leibler divergence between the multivariate distribution and the independent distribution. Another commonly used quantity, the multivariate mutual information, is a natural generalization of the idea that the relevant quantity in an *N*-dimensional information measure is the difference in information between an *N* - 1 dimensional subset and the probability distribution of that subset conditioned on an additional variable. This quantity, although containing useful insights, can be difficult to interpret in ambiguous cases (23). Unlike the total correlation and two-dimensional mutual information, it can be negative and, as such, is ill-suited for our significance test because there is not a monotonic interpretation of the meaningfulness of this quantity. Both quantities reduce to the mutual information in the two-dimensional case.

The total correlation is the difference between the total entropy of all single variables and the entropy of the *N* variable independent probability distribution. It is nonnegative, and one can define a nonparametric “channel scrambling” test as in the previous section. For three segments, *l*, *m*, and *n*, the total correlation is defined as This quantity has attractive qualities in terms of convergence and decomposition (22). The equivalent of the aforementioned inequality for mutual information is that as derived in *SI Text*. Significant total correlations are listed in Table 3 and all total correlations are plotted against the logarithm of their *p* values in Fig. 4. They follow the same pattern as the mutual information: More closely related strains have higher total correlations in general. While there is no completely consistent pattern, in all but one case significant total correlations contain two segments from the polymerase complex. This suggests that other segments may group with these polymerase complex pairs preferentially rather than with their individual segments. This is particularly true for the H3N2-H7N7 pairing, where the segment 2–3 pair, itself significant, appears significantly associated with every other segment. The distance between these two strains, one equine and one human, may therefore enhance the need for other segments to associate with this pair in a strain-specific manner, because the two strains evolved in comparatively different host backgrounds.

### Comparison to Other Experimental Settings and Segmented Viruses.

The above experiments deal with the important setting of equiprobable strain reassortment in MDCK cells. We now examine three variants on the previous experiments. In Octaviani et al., reassortants between H5N1 and 2009 pdm were examined in MDCK cells (24). For some strains, even when one infectious unit is provided per target cell for an infection, many cells may not be coinfected with both viruses due to a particular strain’s dominance. For example, in the pilot experiment of ref. 24 when H5N1 and 2009 pdm were recombined at equal MOI of 1 PFU/cell, the H5N1 was highly dominant, so the authors increased the MOI ratio to 5∶1. Clearly this is a significant study, because a combination of H5N1’s high case fatality rate with the 2009 pdm quick transmission ability could cause a significant public health crisis (25, 26). Because the initial probability distribution for a segment coming from a given strain is no longer (1/2, 1/2), but is now (1/6, 5/6), the full entropy formula is used for the initial distribution. The initial entropy is now 0.6836 bits per segment, rather than the previous 1 bit per segment. Because this is no longer the maximum entropy, the possibility exists that the entropy can either increase or decrease over the course of the experiment. In Table S2, we see that in most cases the entropy increased. That is, output viruses were typically more random per segment than the input viruses. For segment 5 (NP) the trend was reversed and for segment 1 it was minimal. In Varich et al., a human H1N1 virus (A/WSN/33) and an avian H4N6 virus (A/Duck/Czechoslovakia/56) coinfect chicken embryos at high, equal MOI of 5–10 PFU/cell (27). Both experiments again show the potential variability of the HA containing segment from the random distribution—in each case one particular HA is preferred. Likewise, we calculated the entropy change per segment for equal MOI of 5–10 PFU/cell reassortment experiments on two mammalian reovirus strains performed by Nibert et al. (28). Reoviruses are 10 segment dsRNA viruses, so their *p*-value cutoff is altered accordingly, showing the strongest associations between segments 3 and 7.

An interesting aspect of these variants comes when the mutual information is examined between influenza segments, as shown in Table S3. In the case of H5N1—2009 pdm, there are many unique associations that are not seen for other strains. However, some association between segments 2 and 3 continues to persist—it is just below our cutoff. For the H4N6-H1N1 chicken egg reassortment, the highest amount of mutual information in any experiment is recorded, between segments 3 and 5 and 4 and 7. Although this suggests fundamentally different interactions in avian cells, other experiments are needed before drawing such conclusions.

## Discussion

Quantifying reassortment bias is critical for understanding potential future strains and gaining insight into the environment in which segmented viruses operate. As we have shown, information theory provides a natural approach to interpreting and contextualizing experimental results across multiple settings. Our method is applicable to any segmented virus, or any system where genetic segments from multiple sources combine in progeny. From it one gains the insights that come from showing that this problem can be interpreted in an information theoretic context, biological information from experiments directly studied in this work, and a template for future studies that will assist practical and theoretical endeavors. We summarize these features below.

At the single segment level, the entropy per segment captures a change from the input probability of that segment coming from a particular strain. If input segments were all equally likely to have come from one of two strains, it would be expected that, for *N* output viruses, there are 2^{N} equally likely outputs for each segment. If the entropy, *H*, is reduced and one has a reliable estimate of its value, there will “typically” be 2^{HN} equally likely experimental outputs. For all eight segments the number of readouts will therefore change from In these cases, one needs solid estimates, rather than just ascertaining significance. Because these quantities are biased estimators, to minimize error one wants to ensure, in such a planned experiment, that all strain probabilities, *p*_{i}, satisfy *Np*_{i}≫1 (29).

Further gain comes from separating the preceding step from the mutual information between segments and beyond to total correlations. Assuming the mutual information between segments 2 and 3 is significant across strains, then, in all cases, the contribution of those terms to the diversity of strains will further change from If one assumes that enough trials have been performed, as indicated by significance under our method, one can now get a handle on which reassortants are most probable. The ratio of the likelihood of one reassortant to another would give a gross sense of relative fitness (this would not be exact because the number of generations is unclear). If the mutual information is significant, then the probability that two segments came from a given strain is to be replaced by the joint probability, and, likewise, a significant total correlation would indicate replacement of the independent probabilities of, say, three segments, with their joint probabilities.

The power of these methods can be increased when combined with approaches such as that of Li et al. (30, 31). In this work, all 256 possible output viruses were examined for their virulence potential. Because our approach gives a better handle on which reassortants are most likely to be produced, one can examine the overlap between the set of most probable viruses and a viral phenotype. We could not find a strain cross that has been assessed in the literature for both reassortment and phenotype of all strain crosses. However, the methods employed here inform future experiments, where virulence could also be combined or substituted with transmissibility or another relevant phenotype.

If a likely reassortant also has a stronger than normal phenotype, then a higher priority can be placed on preventive measures, such as vaccine preparation, surveillance, or eradication of an infected bird or pig host. When such a case exists, that strain can also be examined more closely, such as by querying its immunostimulatory potential in relevant cell types. In this way, one can attempt to characterize potentially virulent, pandemic strains before they can enter a population. This is one of the real values of our approach. Only a rare reassortant may occur with the probability and virulence to cause a dangerous pandemic. With the proper experiments one could estimate this probability, identify any viral genomic alterations that could put a population at risk, and thus respond accordingly. If, through surveillance, two strains are found in the same location, with a suitable host for mixing these strains in the wild, we could estimate the diversity of reassortant strains prior to this mixing occurring. These predictions could well provide measured responses depending upon the threat level.

Biologically, these experiments open a window into the cellular environment in which influenza replicates. The largest mutual information was associated with accessory proteins to the viral polymerase, PB1 significantly associated with PA across all similar experiments, but not consistently with PB2 as some had found. One possibility is related to the work of ref. 32, which indicates that a PB1-PA dimer is formed separately from a monomeric PB2 and assembled in the nucleus. Our results suggest that this pairing may well be the most consistently significant effect on viral progeny diversity across strains. However, it remains to be determined experimentally if this advantage comes from the favorability of dimerization or an optimization of one dimer over another for, say, more efficient polymerization. In addition to the association of segments 2 and 3 by strain, we also note that segments 6 and 8 seem to show indifference to their strain of origin. Moreover, segment 4, containing HA, is highly variable between experiments, ranging from random to almost complete dominance. In this case, because HA binds to sialic acid for viral entry, one would be inclined to attribute the change in progeny diversity to the fitness of one HA over another. Future reassortment experiments at a single cell level would make an interesting point of comparison.

Theoretically, if a sufficient quantity of strain combination experiments were studied, the maximum mutual information would give an indication of the channel capacity between strains, giving a bound on how much information can be possibly communicated between two segments in a noisy environment. If the rate of reassortment is pushed past this limit, it could disrupt viral segment communication, a possible novel defense strategy. As more consistent groupings are found, over many experiments, investigators can narrow in on these consistent sets to see whether the increase in likelihood of certain progeny being found over others in a given environment is due to factors such as the fitness of a reassortant, functional constraints on the proteins, or genome packaging sequence differences. Understanding how much these segments transfer information about their strain of origin, and to what extent this is possible, can ultimately lead to novel antiviral strategies. We provide a quantitative framework, along with specific examples of what can be discovered, giving a greater sense of how to assess preparedness and the limits of viral segment communication.

## Acknowledgments

We would like to thank Vladimir Trifonov, Hossein Khianbanian, Edo Kussell, Yoshihiro Kawaoka, and Gabriele Neumann for helpful discussions and comments. We also thank Polly Mak for her technical support. R.R. is supported by the Northeast Biodefence Center (U54-AI057158), the National Institutes of Health (U54 CA121852-05), and the National Library of Medicine (1R01LM010140-01). The laboratory work was supported by the Area of Excellence Scheme of the University Grants Committee Hong Kong (AoE/M-12/06) and the Research Fund for the Control of Infectious Disease Commissioned Project from Food and Health Bureau, Hong Kong. B.D.G. is the Eric and Wendy Schmidt Member in Biology at the Institute for Advanced Study and would like to thank them for their support.

## Footnotes

- ↵
^{1}To whom correspondence should be addressed. E-mail: beng{at}ias.edu.

Author contributions: B.D.G., O.T.W.L., L.L.P., A.J.L., and R.R. designed research; B.D.G. and O.T.W.L. performed research; B.D.G., O.T.W.L., L.L.P., A.J.L., and R.R. analyzed data; and B.D.G., O.T.W.L., L.L.P., A.J.L., and R.R. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1113300109/-/DCSupplemental.

Freely available online through the PNAS open access option.

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