Mathematical modeling suggests cooperation of plant-infecting viruses

Viruses are major pathogens of agricultural crops. Viral infections often start after the virus enters the outer layer of a tissue or surface and many successful viruses, after local replication in the infected tissue, are able to spread systemically. Quantitative details of virus dynamics in plants, however, have been poorly understood, in part, because of the lack of experimental methods allowing to accurately measure the degree of infection in individual plant tissues. Recently, by using flow cytometry and two different flourescently-labeled strains of the Tobacco etch virus (TEV), Venus and BFP, kinetics of viral infection of individual cells in leaves of Nicotiana tabacum plants was followed over time [[1][1]]. A simple mathematical model, assuming that viral spread occurs from lower to upper leaves, was fitted to these data. While the the original model could accurately describe the kinetics of viral spread locally and systemically, we also found that many alternative versions of the model, for example, if viral spread starts at upper leaves and progresses to lower leaves or when virus dissemination is stopped due to an immune response, provided fits of the data with reasonable quality, and yet with different parameter estimates. These results strongly suggest that experimental measurements of the virus infection in individual leaves may not be sufficient to identify the pathways of viral dissemination between different leaves and reasons for viral control; we propose experiments that may allow discrimination between the alternatives. By analyzing the kinetics of coinfection of individual cells by Venus and BFP strains of TEV we found a strong deviation from the random infection model, suggesting cooperation between the two strains when infecting plant cells. Importantly, we showed that many mathematical models on the kinetics of coinfection of cells with two strains could not adequately describe the data, and the best fit model needed to assume i) different susceptibility of uninfected cells to infection by two viruses locally in the leaf vs. systemically from other leaves, and ii) decrease in the infection rate depending on the fraction of uninfected cells which could be due to a systemic immune response. Our results thus demonstrate the difficulty in reaching definite conclusions from extensive and yet limited experimental data and provide evidence of potential cooperation between different viral variants infecting individual cells in plants. ### Competing Interest Statement The authors have declared no competing interest. * ODE : ordinary differential equations TEV : Tobacco etch virus N. tabacum : Nicotiana tabacum nll : negative log-likelihood LS : least squares LOD : limit of detection AIC : Akaike Information Criterion SSR : sum of squared residuals OR : odds ratio [1]: #ref-1