Combined plasmid replication simulation
We built upon previous models to develop this simulation framework. It can accept parameters representing latent infections by herpesviruses, including positive and negative selective advantages, as well as identifying the most realistic parameters with which to model dually infected cells. The maintenance of plasmids was modelled as the combination of replication, in which a plasmid may be duplicated in S phase, and partitioning, when the daughter plasmids are distributed to daughter cells. Because KSHV plasmids can form clusters, we incorporated the ability of individual plasmids to come together to form clusters and for clusters to break up resulting in smaller clusters or individual plasmids. The program created to use this model, LatentPlasmidPopulation, is written for Python 3.7+.
Seven parameters describe the complexities of herpesvirus replication (some of which were found in previous work to be dispensable for EBV and KSHV but have been retained in the simulation for other replicons). S-phase duplication probability defines the per-plasmid duplication rate (0.84 for EBV, 0.98 for KSHV). Plasmid repulsion-attraction defines an axis of plasmids or clusters of plasmids binding to sister chromatids and segregating equally at a value of 0 to fully forming clusters and segregating randomly at a value of 1 (0.12 for EBV, and 1.0 for KSHV). Positive selection, that is a term for a selective advantage, applies to both EBV and KSHV and is represented as a sigmoid scaled to pass through 0 and asymptotically approach 1 (0.10 for EBV, 0.20 for KSHV). Three additional parameters are specific to KSHV: the probability of cluster breakup, the Dirichlet process CRP parameter, and a coefficient for negative selection for large-size clusters. The probability of cluster breakup defines the probability that a cluster will enter the CRP process after duplication (0.80 for KHSV). The Dirichlet process CRP alpha defines the size and number of the resulting clusters after breakup (shown in Figure 3C-D, set to 0.50). The coefficient of negative selection as a function of cluster size is modeled as an exponential decay scaled by the duplication probability (set to 0.07). Finally, an unused parameter determines the relative breakup in S-phase versus G1-phase.
Six parameters allow simulation of the differing conditions of dual infections in vitro. The initial population is set by the number of cells to simulate, which determines the number of cells with at least one plasmid that are simulated (set to 5000 for these simulations). When cells have zero plasmids, they are modeled separately for the sake of speed. This choice improves the accuracy of models with most cells containing no plasmids. The initial distribution can be set using a normal distribution by defining the mean, µ, and standard deviation, σ, or by modeling it via the multiplicity of infection, modeled as a Poisson distribution and set by the variable 𝛌 (set to 2 for EBV and 0.02 for KSHV). The population is then simulated, first for a number of “burn-in generations” to get the population to equilibrium (set to 0 except in the case of identifying the best-fit value for negative selection in KSHV that produces a mean plasmid replication rate of 0.92, in which it was set to 30), and finally simulated for a number of generations (set to 50 for the figures shown here).
The simulation contains legacy parameters unused here: a maximum number of plasmids per cell above which the simulation raises an error, and three parameters to act as a form of negative selection to exclude very high numbers of plasmids as follows: P(cell replicates|a,b,c) = c − a × x2 − b × x, where x = n_plasmids_per_cell, a = signal-selective-disadvantage-on-cell-replication-squared, b = signal-selective-disadvantage-on-cell-replication, and c = mean-cell-replication-prob.