Modeling viral genome fitness evolution associated with serial bottleneck events: evidence of stationary states of fitness

Abstract

Evolution of fitness values upon replication of viral populations is strongly influenced by the size of the virus population that participates in the infections. While large population passages often result in fitness gains, repeated plaque-to-plaque transfers result in average fitness losses. Here we develop a numerical model that describes fitness evolution of viral clones subjected to serial bottleneck events. The model predicts a biphasic evolution of fitness values in that a period of exponential decrease is followed by a stationary state in which fitness values display large fluctuations around an average constant value. This biphasic evolution is in agreement with experimental results of serial plaque-to-plaque transfers carried out with foot-and-mouth disease virus (FMDV) in cell culture. The existence of a stationary phase of fitness values has been further documented by serial plaque-to-plaque transfers of FMDV clones that had reached very low relative fitness values. The statistical properties of the stationary state depend on several parameters of the model, such as the probability of advantageous versus deleterious mutations, initial fitness, and the number of replication rounds. In particular, the size of the bottleneck is critical for determining the trend of fitness evolution.

FIG. 1.

Numerical simulation of the evolution of the number of infectious units produced as a function of the number of plaque-to-plaque transfers. The parameters kept constant in the simulations are p = 0.01, q = 0.001, and r = 5; three different initial fitness values for the founder sequence (W₀ = 5, 10, or 15) were assayed. Each curve represents an average of five independent runs. The numerical model and computer programs used are described in Materials and Methods.

FIG. 2.

Distribution of fitness values at different plaque transfers. The probability distributions P(W) were calculated at transfers T = 10, 100, 600, and 1,000, by using the following constant values for the parameters: W₀ = 5, p = 0.01, q = 0.001, and r = 5. Each distribution has been obtained as an average of 200 independent trials. The W value in each panel is the average fitness of the genome distribution (filled boxes). The numerical model and computer programs used are described in Materials and Methods.

FIG. 3.

Evolution of fitness values during Np plaque-to-Np plaque transfers as a function of the population transmission size (Np) (A) or the initial fitness (B). In panel A the initial fitness was W₀ = 6 in all cases. In panel B the transmission size was Np = 3 in all cases, and the lines from bottom to top correspond to W = 1, 3, 5, 7, and 9, respectively. In all cases the values kept constant for the parameters were p = 0.01, q = 0.001, and r = 5. Values are the average of 200 independent trials. The numerical model and computer programs are as described in Materials and Methods.

FIG. 4.

Comparison of the infectious units produced as a function of plaque transfer number according to the numerical model and in actual experiments. (A) Time series of the number of infectious units predicted by using several combinations of parameters. (Upper left) p = 0.06, q = 0.001, r = 5, and W₀ = 6. (Upper right) p = 0.06, q = 0.001, r = 8, and W₀ = 6. (Lower left) p = q = 0, r = 5, and W₀ = 6. (Lower right) p = q = 0.02, r = 5, and W₀ = 6. (B) Number of infectious units per plaque (plaque titer) of clone as a function of plaque transfer number. (Left) Plaque titers obtained when was subjected to 100 successive plaque-to-plaque transfers (27). (Right) Plaque titers obtained with four subclones (a, b, c, and d) were isolated from plaque transfer 100 and subjected to 30 transfers; the time of plaque development was 26 to 30 h. For some plaque transfers of clone plaque transfer 100c (marked with an asterisk), the time of plaque development was increased to 46 h, since plaque transfer 27 contained less than 10 PFU after 27 h of plaque development. Note that the scale of the ordinate in the four right panels is different from that in the left panel. Simulations and experimental procedures are described in Materials and Methods.