Fig 1.
HTLV-1 infectious and mitotic spread schematic.
Left column (Infectious spread): an HTLV-1-infected cell infects an uninfected CD4+ T cell (typically by cell-to-cell contact via the virological synapse, and potentially also via cell-free spread). The HTLV-1 provirus (red) integrates in a different genomic location in the newly infected cell, so infectious spread has resulted in two clones. Right column (Mitotic spread): An HTLV-1-infected cell divides, whereupon the provirus resides in the same genomic location in each daughter cell. The figure shows a single clone with two HTLV-1-infected cells.
Fig 2.
Schematic of full simulation hybrid model.
A: Observed and estimated clone frequency distributions. From an observed sample of clones, the clone frequency distribution of the body in one host is estimated using DivE. B: Propagation of hybrid model: Estimated clone frequency distribution partitioned into deterministic and stochastic systems. Clones of frequency less than and greater than threshold F are respectively modelled stochastically and deterministically. F is chosen with respect to probability of clone extinction (S2 Text). The deterministic system is modelled using ordinary differential equations (Eq (1)). The stochastic system consists of multiple birth-death processes (one for each stochastically modelled clone) each with an absorbing state at zero (Fig 3A and 3B). The evolution of the clone probability distribution over time is governed by the chemical master equation (Eq (10), Fig 3C and 3D). New clones are created through infectious spread, i.e. the per-capita rate rI multiplied by the expected number of infected cells, in both deterministic and stochastic compartments (Eq (11)). Deterministic and stochastic systems are propagated concurrently with Strang splitting (S2 Text). C: Hybrid model diversity. The estimated number of clones S(t) (Eq (13)) at time t, given parameters θ = {π, δ, K, rI} is given by the number of clones created (Eq (11)), minus the number of clones that are expected to have died between 0 and t (Eq (12)), plus the number of clones S0 at t = 0. The number of clones is assumed to be at equilibrium in the chronic phase of infection. D: Model fitting schematic: Expected diversity at S(tDur) increases with per-capita infectious spread rate rI. Model fitted using non-linear least squares to DivE estimated diversity in the body, where the objective function is the square of the discrepancy between this value and the value of S(tDur) at equilibrium.
Fig 3.
A and B respectively show the clone state space with and without an upper limit τ. Each box denotes the potential state of a given clone, i.e. the number of cells in that clone, with the corresponding propensity of each reaction at each state. π*(t) and δ denote the per-capita rates of infected cell proliferation and death respectively. Note there is no source inflow from frequency 0 to frequency 1. C and D show clone frequency probability distributions over time. Each curve shows the distribution of the probability that the given clone i contains xi cells at time t. At successive time points the curve broadens and either shifts to the right as the expected frequency of the clone increases (C), or shifts to the left as the expected frequency of the clone decreases (D).
Fig 4.
Occupancy class model schematic.
Singletons (clones of size 1) are produced by infectious spread (red). Proliferation (orange) results in loss from clone size class nf and entry into size class nf + 1. Death of a cell (green) results in a clone moving from size class f to size class nf—1.
Table 1.
Hybrid model estimates of rate of infectious spread estimates and ratio of infectious to mitotic spread by patient.
Fig 5.
Ratio of infectious spread to mitotic spread and number of new clones per day, by patient and estimator.
A Ratio of infectious spread to mitotic spread. B Number of new clones generated per day. Values of both the ratio and number of new clones are derived from estimators of infectious spread. In each plot, red crosses and bars respectively denote point estimates and the range from the nine estimates for each subject from the hybrid model. Upper bound approximations from rI,Supremum (green triangles) are shown, together with tighter upper bounds from (coloured circles) for multiple values of fmax between 1 and 1000. Lighter colours denote higher values of fmax. Hybrid model point estimates are very close to the estimates obtained for fmax = 1 (lowest circles). Estimates plotted on logarithmic scale.
Table 2.
Parameter names and values.
Fig 6.
Comparison of estimates of ratio of infectious to mitotic spread from the hybrid model (method 1) and the occupancy class model (method 3).
(Top left) Estimate of ratio from hybrid model plotted against first estimate from occupancy class model (R1). Red line is line of best fit, black line is line of equality. (Top right) Estimate of ratio from hybrid model plotted against second estimate from occupancy class model (R2). Red line is line of best fit, black line is line of equality. (Bottom left) Estimate of ratio between hybrid model and first estimate from occupancy class model (R1). Black line denotes the median. (Bottom right) Estimate of ratio between hybrid model and second estimate from occupancy class model (R2). Black line denotes the median.