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. 2014 Jan 15;11(92):20131083.
doi: 10.1098/rsif.2013.1083. Print 2014 Mar 6.

How sticky should a virus be? The impact of virus binding and release on transmission fitness using influenza as an example

Andreas Handel  1 , Victoria Akin, Sergei S Pilyugin, Veronika Zarnitsyna, Rustom Antia
Affiliations

How sticky should a virus be? The impact of virus binding and release on transmission fitness using influenza as an example

Andreas Handel et al. J R Soc Interface. .

Abstract

Budding viruses face a trade-off: virions need to efficiently attach to and enter uninfected cells while newly generated virions need to efficiently detach from infected cells. The right balance between attachment and detachment-the right amount of stickiness-is needed for maximum fitness. Here, we design and analyse a mathematical model to study in detail the impact of attachment and detachment rates on virus fitness. We apply our model to influenza, where stickiness is determined by a balance of the haemagglutinin (HA) and neuraminidase (NA) proteins. We investigate how drugs, the adaptive immune response and vaccines impact influenza stickiness and fitness. Our model suggests that the location in the 'stickiness landscape' of the virus determines how well interventions such as drugs or vaccines are expected to work. We discuss why hypothetical NA enhancer drugs might occasionally perform better than the currently available NA inhibitors in reducing virus fitness. We show that an increased antibody or T-cell-mediated immune response leads to maximum fitness at higher stickiness. We further show that antibody-based vaccines targeting mainly HA or NA, which leads to a shift in stickiness, might reduce virus fitness above what can be achieved by the direct immunological action of the vaccine. Overall, our findings provide potentially useful conceptual insights for future vaccine and drug development and can be applied to other budding viruses beyond influenza.

Keywords: drug treatment; influenza; vaccines; within-host model.

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Figures

Figure 1.
Figure 1.
Schematic of the model. The quantities being tracked are virus V, uninfected and infected cells with n virions bound to the surface, Un and In, and an immune response X, all expressed in particles per millilitre. Free virions (black) attach to uninfected cells at rate formula image or infected cells at rate formula image The attachment is reversible, and detachment can occur at rates formula image and formula image (the extra factors of n or n+1 in the flow rates account for multiple bound virions). Bound virions (white) are internalized into uninfected or infected cells at rates gu and gi. If an internalized virion (grey) enters an already infected cell, it does not alter the state of the infected cell. A fraction f of virions internalized into uninfected cells turn those cells into productively infected cells. Infected cells produce progeny virions at rate p, which are initially bound to the infected cell membrane (not drawn in the figure). The virions bound to infected cells can detach from the infected cells at rate formula image to become free virions. Infected cells die and virions are cleared at fixed rates d and c, respectively. Also modelled is an adaptive immune response, which we consider a simplified representation of either a B cell/antibody or CD8+ CTL response. The immune response is described by a simple exponential growth term at rate r, corresponding to clonal expansion of T cells/B cells. The immune response is assumed to either clear free virions at a rate w1 (antibody/B-cell response) or kill infected cells at rate w2 (CTL response).
Figure 2.
Figure 2.
Virus fitness (equation (2.1)) as a function of the attachment and detachment rates k− and k+ (with k− in units of inverse days and k+ in units of millilitre over days). The three rectangles indicate ranges reported in three different experimental studies (see text). The inset shows a slice along the dotted high-fitness ridge line: for varying levels of k−, the level of stickiness (S = k+/k−) that optimizes fitness, and the level of fitness are plotted. In this scenario, no immune response is present (w1 = w2 = 0), we assumed all virions are infectious (f = 1) and attachment, detachment and internalization rates are the same for uninfected and infected cells formula image Other parameter values are as given in table 1. For plotting purposes, any values with fitness, F, below 0 were set to zero. (Online version in colour.)
Figure 3.
Figure 3.
Comparison of model results (lines) with experimental data (symbols) from an in vitro experiment [69]. The solid line and circles show virus production for a virus with a relatively high NA activity, the dashed line and squares show virus levels for a virus strain that has around a sixfold reduction in NA activity [69], which we equate to a sixfold reduction of the detachment rate k−. Since the experiment and the model express virus in different units, and the number of uninfected cells in the experiment is not known, we normalized the data such that the maximum virus titre for both experiment and model is 1. We start the simulation with no free virus and I(0) = U(0)/1000, in accordance with the experimental set-up. The values for k− were set to 6 and 1 for the strong and weak NA virus, respectively, and the value for k+ was set to 10−6. Those values are in the range of values obtained from the in vitro experiments as discussed in the text. Viral clearance rate was set to 0 to match the fact that HA does not decay significantly over the duration of the experiment. Remaining values for the parameters are as described for figure 2.
Figure 4.
Figure 4.
Illustration of the effect of anti-influenza drugs. The fitness landscape is replotted from figure 2, with arrows added to explain the functioning of different anti-influenza drugs. NA inhibitors reduce k−, illustrated by the solid (strong reduction) and dashed (weak reduction) black arrows. Influenza can evolve resistance and regain fitness by mutating the NA protein, such that the drug does not bind well anymore. This leads to an effective restoration of NA function and increase in k−. Another way to restore fitness is by mutating HA to reduce its binding activity (dotted black arrow). The solid and dashed white arrows illustrate hypothetical drugs that increase NA or decrease HA activity (see the text for explanation). (Online version in colour.)
Figure 5.
Figure 5.
The impact of B cell/antibody (Ab) or CTL immune responses on fitness and stickiness. Immune response strength is increased by increasing virus clearance, w1, for the Ab response and increasing infected cell killing, w2, for the CTL response. (a) Maximum fitness as a function of immune response strength. (b) Stickiness as a function of immune response strength. (c) Total fraction of cells or viruses killed/removed by the immune response during the infection. For every value of immune response strength, wi, we scanned across the k− and k+ parameter space to determine the maximum fitness and the level of stickiness at which this maximum fitness is achieved. Parameter values are as described for figure 2.
Figure 6.
Figure 6.
Illustration of the effect of potential vaccines targeting different influenza genes. (a) The fitness landscape in the absence of the immune response, re-plotted from figure 2. Two points with high fitness are marked (white triangle and circle). (b) The fitness landscape in the presence of a non-sterilizing antibody-based vaccine (modelled as w1 = 0.1). Overall fitness is reduced, the amount of reduction depending on the original location in the high-fitness region. In addition, a vaccine that targets HA will shift k+ to lower values, and a vaccine that mainly targets NA will shift k− to lower values. Possible HA or NA vaccines that reduce k+ or k− 10-fold are marked in the figure for two different initial locations of the virus. This can lead to additional loss of fitness, again depending on the location of the original strain on the fitness landscape. A vaccine that targets other genes, such as NP or M2, is not expected to shift stickiness. (Online version in colour.)
Figure 7.
Figure 7.
The impact of relative attachment strength of infected versus uninfected cells on fitness (triangles) and stickiness (circles). The relative attachment strength of infected versus uninfected cells, formula image, was varied. For α = 1, virions bind equally well to uninfected and infected. This corresponds to all the scenarios considered in the main text. Values of α < 1 correspond to early expression of NA by infected cells leading to a reduction in binding to infected cells. For each value of α, we scan over k− and k+, while ensuring that formula image The model contains a low-strength antibody-based immune response (w1 = 10−2, w2 = 0). Similar results are found if we instead use a CTL response (not shown). Any parameters not varied are fixed and chosen as described in the main text.
Figure 8.
Figure 8.
The impact of virion infectiousness on fitness (triangles) and stickiness (circles). The fraction of virons that lead to productive infection of cells, f, is varied. For each value of f, we scan over k+ and k− to determine optimal fitness and the level of stickiness at which this is achieved. The model contains a low-strength antibody-based immune response (w1 = 10−2, w2 = 0). Similar results are found if we instead use a CTL response (not shown). Any parameters not varied are fixed and chosen as described in the main text.
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