Background
Defective interfering (DI) particles are virus-like byproducts of infections that are unable to infect cells on their own because they carry mutations, typically large deletions, in essential viral genes. However, when DI particles and standard virus particles co-infect the same cell the DI particles compete for resources that ultimately enable them to reproduce at the expense of virus particles. DI particles were discovered more than 60 years ago [
1,
2], and their generation by diverse DNA and RNA viruses has been widely documented [
3‐
5], but it is not yet known what role DI particles may play in the behavior of natural infections. Defective viral genomes have been isolated from natural infections [
5‐
8], but their potential for interference and their broader roles in viral pathogenesis remain open.
The unique biological properties of DI particles make them interesting and important for several reasons. First, their ability to interfere with standard virus infections highlights their potential use as therapeutic agents [
9]. Moreover, the use of site-specific mutagenesis or reverse genetics to precisely create desired genomic defects, or introduce new functions, opens applications for DI particles as vaccines or prophylactics [
10,
11]. Second, their ability to activate innate immunity can alter the susceptibility of host cells to infection by standard virus [
12,
13]. Here, advances in the understanding of DI particle interactions with cells may suggest new ways to modulate how viruses grow and spread within a host. Third, mixtures of different DI particles can complement their own defects and thereby productively infect cells in the absence of standard virus [
14‐
16]. This example provides an intriguing mechanism for viral infections to spread and persist in the absence of a single agent that can be isolated and cultured. Such mixtures may also offer advantages as a vaccines [
17]. Finally, the ability of DI particles to adapt their degree of interference in response to mutation and selection of their co-infecting virus [
18] may provide insights for the design of anti-viral strategies that resist escape [
19,
20].
A characteristic feature of DI particles is their emergence and outgrowth during high multiplicities of infection (MOI), where numerous copies of the standard virus infect each host cell. Under such conditions "predator" DI particles can productively interact with "prey" cells infected with standard virus. Ecological models of predator-prey behavior have been proposed to describe the dynamics of virus and DI particle populations [
21‐
26], where the models have been loosely based on diverse measures of virus and DI particles, reviewed elsewhere [
27]. However, the development of population dynamic models of virus and their DI particles have yet to be fully integrated with quantitative experiments. Recently, we used a yield-reduction assay to quantify how DI particles of vesicular stomatitis virus (VSV) impact the production of virus and DI particles in BHK cells, where we interpreted these measures using a mathematical model. The model enabled us to estimate parameters that describe how input levels of virus, DI particles and host cells interact to define outputs, specifically the production of virus and DI particles in a single passage [
28]. Here we extend this data-driven modeling approach to better understand how virus and DI particle interactions impact their population behavior over multiple passages.
Discussion
By maintaining a fixed multiplicity of infection (MOI) across serial virus passages we observed a regular pattern of population behavior: average yields of virus declined more rapidly for passages performed at higher MOIs (Fig.
1b). The earlier and faster decline in virus level at higher MOI's could be attributed most simply to smaller dilution effects. At higher MOI more virus and more DI particles are transferred from one generation to the next, enabling more rapid accumulation of DI particles and greater inhibitory effects on virus growth. Alternatively, high MOI infections in the absence of DI particles could be associated with intrinsically higher rates of
de novo DI particle production. To test this possibility we allowed for
de novo DI particle generation in our model and found that declines in virus yields for passages at MOI 100 and MOI 10 could be reasonably accounted for by assuming a fixed intrinsic rate of
de novo DI particle generation (g = 0.01 IE/cell), as shown in Fig.
3a. In contrast, the model failed to capture the extent of observed yield reduction for passages performed at MOI 5 and MOI 1. For these lower MOI a better agreement between the model and the data could be obtained by incorporating a significantly higher rate of DI particle generation into the model (g = 20 IE/cell, not shown). A higher DI particle generation rate for conditions of lower MOI may initially seem paradoxical, because the generation of DI particles should depend on the number of replication events, which would be reduced at lower MOI. However, it should be noted that the DI particle generation rates are expressed as IE generated per
infected cell. Other mechanisms may also play a role in the mismatch between model and data at low MOI. For example, DI particle populations may evolve to more potently inhibit amplification of virus in cells co-infected with both virus and DI particles, or
de novo generated DI particles may emerge and displace existing DI particles [
18,
33,
34]. Further studies on isolated DI particle sub-populations will be needed to elucidate mechanisms responsible for the differences between the model and data at low MOI.
What causes the chaotic population dynamics that is a hallmark of fixed-volume serial virus cultures? Mathematical models of passage behavior have previously suggested how chaotic behavior can arise during fixed-volume passages [
21], but these models have been based on assumptions that cells co-infected with standard and DI particles produce only DI particles. They have also assumed constant yields of DI particles are produced from co-infected cells. These assumptions are not generally valid based on our recent experimental and modeling studies of VSV growth on BHK cells [
28]. Specifically, co-infected cells produce both virus and DI particles rather than only DI particles. Moreover, average yields of virus and DI particles determined from co-infected cells were not constant; instead, they depended on DI particle dose. These experimental results were used here to develop new mathematical models and simulate the behavior of virus and DI particle populations in fixed-volume passages. The simulated populations exhibited no chaotic behavior. Instead, initial transients spanning up to six passages settled into either steady-state or regular oscillatory behaviors (Fig.
4a-d). Experimental measures of standard and DI particle behavior over fixed-volume VSV passages have shown cyclic behavior [
32], but the observed six passages were too few to establish whether regular oscillations were feasible. We carried out fixed-volume passages in the laboratory and observed irregular changes in the virus productivity from one passage to the next, most notably between passages 6 and 10 (Fig.
1a). When we expanded the model to incorporate experimentally measured host-cell levels at each passage then the predicted virus levels exhibited significant fluctuations, especially beyond passage 6, with a greater than 100-fold drop between passages 8 and 9, as observed in experiments (Fig.
3b and Fig.
4e/
4f). Relatively small changes in cell levels can give rise to large changes in virus production from infected and co-infected cells, owing to the non-linear relationship between virus production(
V
N+1
) and cell level(
C
N
) shown in Eq.
1. A testable prediction of the model is that by controlling experiments to reduce fluctuations in cell levels one should observe more regular behavior of virus levels (e.g., steady-state or regular oscillations) during constant-volume passages, as reflected in Fig.
4a-d. More broadly, these results show that passage-to-passage changes in the virus level can arise from competition between virus and DI particles for host-cell resources, as well as from fluctuations in the level of host cells. From an ecological perspective, fluctuations in host cells may be viewed as periodic mortality events that can significantly impact the predator-prey dynamics [
35].
To run our model one must provide an initial condition that specifies not only the concentration of virus particles, but also the concentration of DI particles in the initial passage. In the laboratory, the concentration of DI particles in the initial passage will depend on the history of the stock solution. For example, if the stock is amplified from an isolated plaque at low MOI or serially passaged at high MOI it may contain negligible or high levels of DI particles, respectively. In our model this input was found to have no effect on the steady-state dynamics of the virus and DI particle populations (Fig.
4g/
4h). Even in the absence of initial DI particles the
de novo generation of DI particles produced interference activity that was rapidly amplified in co-infections with wild-type virus. It appears that once DI particles are available they will tend to dominate subsequent co-infections. While new or different DI particles could, in principle, be generated by
de novo processes, the low productivity of such processes prevents
de novo DI particles from being competitive with existing DI particles. This dominance of initial DI particles has been found experimentally by observing how parallel cultures initiated from a common stock preserve DI particles present in the stock [
36].
Some cells can make nearly a million-fold more DI particles than other cells, depending on how they are infected. When a cell is infected with viable virus, in the absence of any DI particles, few if any DI particles will be made, reflecting the small de novo rate of DI particle generation. This rate was estimated for VSV at 0.001 IE/cell. However, when a cell is co-infected with viable virus and DI particles, then many DI particles can be made, reflecting their ability to divert resources from virus to DI particle production.
Experiments suggest that more than 500 IE per cell can be produced under optimal conditions for DI particle production [
28]. If we assume a single DI particle corresponds to a single interference unit (IU), then we may estimate that optimal condition for DI particle production make (500 IE/cell × 200 IU/IE × 1 DI particle/IU) or 100,000 DI particles per cell. At the other end of the spectrum, the least productive or
de novo rate of DI particle generation is (0.001 IE/cell × 200 IU/IE × 1 DI particle/IU) or 1 DI particle from every five infected cells. Thus, a 500,000-fold difference in DI particle yields separates the most productive from the least productive cells. A more expanded view of productivity, which includes the production of both DI and viable particles, may be concisely expressed in terms of a particle-to-PFU ratio. Such a ratio can be experimentally determined by estimating the number of virus-sized particles in a sample by electron microscopy and dividing by the number of viable virus particles measured by the plaque assay. If we assume that only DI and viable particles are produced by a co-infected cell, then we estimate a particle-to-PFU ratio of 38 (or 102,670 particles/2670 PFU) based on maximal production of DI and viable particles. This estimate is consistent with the observed range for VSV from 10 to 50 particle-to-PFU [
37].
Although spontaneous curing of virus infections by DI particles has not been experimentally observed, the possibility has been explored in previous models [
21,
22]. Our data-driven model indicates VSV infections cannot be spontaneously cured because infected cells produce viable virus under all conditions, even when DI particles most potently interfere with virus production. If desired, our model could be adapted to simulate a curing effect by setting the parameter
q to zero, so cells co-infected with virus and a high level of DI particles would produce only DI particles. Others have found that individual cells isolated from a co-infected cell population produced no detectable virus, suggesting a curing effect, but other cells drawn from the same population did produce virus [
38]. The absence of experimental support to date for spontaneous curing of infections by DI particles should not detract from advancing their applications. DI particles have potentially therapeutic applications as enabling tools for vaccination [
39,
40], as prophylactics, or as therapeutics [
41]. In an infected patient, we expect that virus and DI particles would grow and spread continuously on susceptible host cells, so our current model would have limited application owing to its focus on discrete population passages. Our data-driven modeling approach could, however, be extended to develop a continuous rather than discrete model. We envision that such a data-driven continuous model would be based on experiments of growth kinetics that explicitly accounted for the dynamic interactions between cells, virus and DI particles.
We are seeking to develop experimental measures and theoretical methods to better understand how viruses grow and how their infections spread. Our main contribution here has been to better link quantitative experiments of virus and DI particle populations with quantitative models. This approach will be enhanced in the future by incorporating additional measures, beyond plaque counting, including electron microscopy (particle counting), quantitative PCR, and next-generation sequencing. Ultimately, our approach aims to provide a predictive capability that will enable the long-term control of virus infections.
Competing interests
The authors declare that they have no competing interests.
Authors' contributions
KT and JY conceived of the study, and KT performed all experiments. KT and JY analyzed the data and wrote the manuscript.