Modelling Viral Spread

things to fix

• Use (lastname year) citations, easier to follow and edit later. We can ultimately switch to ordinal
• Wall of text! Break up with subheadings, use bolded text to highlight important sections, use bullets where appropriate
• Should be better now!

###Overview

Most of the existing work on infection spread has focused on the cellular and population levels; the middle ground of within-host spread is relatively unexplored. However, the mechanisms discussed above, of both short- and long-range viral transport discussed above provide a basis for understanding, which has been mathematized by several papers from Santiago Elena’s lab.

###Time to systemic infection

Rodrigo and colleagues (Rodrigo et al. 2014) explicitly consider within-host dynamics as governed by short- and long-term dynamics. In this model, the infection expands outward from the primary infection site, becoming systemic once it reaches the vasculature (and after an additional latency period for vascular movement). The area of local spread required before reaching the vascular system follows a normal distribution, which yields variable times to systemic infection. This model also accounts for multiple sites of initial infection, which operate independently. The crucial virus-dependent parameters influencing time to systemic infection are the two latency periods (for the initial infected cell and for vascular transport) and the diffusion rate for cell-to-cell viral infection. These models were validated by experimental trials with two variants (low and high diffusion constants) of Turnip Mosaic Virus in nicotiana benthamiana. Their parameters cannot directly translate to adabidopsis, but it is a useful framework for predicting variable times to systemic infection.

Tracking infection spread in individual leaves

Tromas and colleagues (Tromas et al. 2014) take a different theoretical model: individual leaves are considered as each having their own internal dynamics given by a susceptible-infectious model. Beyond the need to find different transmission parameters for each leaf, there are a few modifications to the standard SI model: a spatial aggregation parameter (accounting for the fact that plant cells are not subject to random mixing) and transmission from leaves further down the phloem.

The real strength of this work, however, is in the data. By using flow cytometry to measure the viral load of large numbers of plant cells, tracking over both time and space (although only at the scale of leaves). These experiments used Tobacco Etch Virus in nicotiana tabacum, and measured 50 000 cells per leaf for each sample, with 5 replicates. This allowed for the measurement of important parameters, such as the viral multiplicity of infection (which we know to be higher for CaMV (Gutierrez et al. 2010)) and the cellular contagion rate – the number of secondary infections per infected cell per day. The cellular contagion rate is an informative parameter, giving a detailed portrayal of the dynamics of the infection over time. In this case, it was found to be small: it decreased from an already-low value of 1.342 cells/cell/day 3 days post-infection down to 0.196 cells/cell/day 7 days post-infection. These low values may, however, be characteristic of plant RNA viruses (Tromas et al. 2014) -- meaning we might see something different for CaMV.

Summary

These two different modeling approaches both tackle the difficult issue of within-host virus spread. They are quite different, since each focuses on a different unit of spatial analysis. Neither incorporates mechanistic modeling of plant defenses – the first model only investigates up to the point of systemic infection (and includes no variable defenses against local spread), while the second model incorporates defense only indirectly via reductions in the cellular contagion rate (which could also be due to exhaustion of susceptibles, changing viral strategies, or other factors). We will have to pick our unit of spatial analysis based on the measurements we can take and the research questions we wish to pursue. It might be interesting to incorporate modeling of the plant adaptive immune response into the viral spread model – beyond simply being useful, this could be new research.

Differences compared to CaMV and arabidopsis

(This section is more a compilation of rough notes, but it's important to track these differences. These quotes are all direct from Tromas et al. 2014.)

“Moreover, this array of plant immune mechanisms probably contributes to the relatively low between-host variation typically found in experimental settings (Zwart et al. 2012)”.

“For Cauliflower mosaic virus (CaMV), MOI was reported to vary from 2 to 13 over time, and most cells were infected (Gutierrez 2010). Furthermore, for CaMV virion concentrations in vascular tissue are correlated to MOI (Gutierrez et al. 2012)”

“On the other hand, in a similar model-selection-based analysis for TMV and CaMV MOI, two viruses that also move by cell-to-cell movement, spatial aggregation only marginally improved model fit for both datasets (Zwart et al. 2013).”

References

Rodrigo, Guillermo, Mark P. Zwart, and Santiago F. Elena. 2014. “Onset of Virus Systemic Infection in Plants Is Determined by Speed of Cell-to-Cell Movement and Number of Primary Infection Foci.” J. R. Soc. Interface 11 (June). doi:10.1098/rsif.2014.0555.

Tromas, Nicolas, Mark P. Zwart, Guillaume Lafforgue, and Santiago F. Elena. 2014. “Within-Host Spatiotemporal Dynamics of Plant Virus Infection at the Cellular Level.” PLoS Genetics 10 (2). doi:e1004186.

Gutiérrez, Serafín, Michel Yvon, Gaël Thébaud, Baptiste Monsion, Yannis Michalakis, and Stéphane Blanc. 2010. "Dynamics of the multiplicity of cellular infection in a plant virus." PLoS Pathog 6, no. 9 (2010): e1001113-e1001113.

Zwart MP, Daròs JA, Elena SF. 2012. "Effects of potyvirus effective population size in inoculated leaves on viral accumulation and the onset of symptoms." J. Virol. 86, 9737–9747. (doi:10.1128/JVI.00909-12)

Gutierrez S, Yvon M, Pirolles E, Garzo E, Fereres A, et al. 2012. "Circulating virus load determines the size of bottlenecks in viral populations progressing within a host." PLoS Pathog 8: e1003009.

Zwart MP, Tromas N, Elena SF. 2013. "Model-selection-based approach for calculating cellular multiplicity of infection during virus colonization of multicellular hosts." PLoS ONE 8: e64657.

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