Fig 1.
Overview of the main HBV kinetic patterns determined based on analysis of 42 humanized mice from inoculation to steady state.
HBV kinetic phases from mice after inoculation with 108 copies HBV DNA: Phase 1, rapid decline; Phase 2, lower viral plateau; Phase 3, rapid increase; Phase 4, extremely slow increase or plateau; Phase 5, prolonged amplification; Phase 6, steady state. Modified from (9); two initial clearance phases have been combined into one, now jointly termed Phase 1.
Fig 2.
(A) The human hepatocytes can be only in one of the following three phases at a given time; T = uninfected cells which are termed as target or susceptible cells, IE = HBV-Infected cells in eclipse phase (i.e., not yet releasing virions), IP = productively HBV-infected cells (i.e., actively releasing virions). The free virus in blood, V, is composed of infectious and non-infections virions. The parameter ρ represents the fraction of virions that are infectious, β represents the infection rate constant, Ω represents eclipse phase duration, c, represents viral clearance from blood and P(τ) (Eq 1) represents virion secretion from IP. (B) Schematic diagram of viral production cycle for an individual infected human hepatocyte. P(τ) is the number of virions produced by an infected cell, and l(τ)) is the time interval between production cycle (h). The virions were initially released by IP starting with a long production cycle of 1 virion per cell (Stage 1: ~0–2.5 days) that gradually reaches a production of 2 virions per cell with a shorten production cycle (Stage 2: ~2.5–3 days) and then proceeds to 3 virions per cell (Stage 3: ~3–4 days) before virion production increases to reach to a steady state production rate of 4 virions per hour per cell (Stage 4: ~ 4 days onwards).
Fig 3.
Model best fit (solid curves) with measured HBV DNA kinetics in blood (circles) in four mice M1 (A), M2 (B), M3 (C) and M4 (D) inoculated with 108 HBV genome equivalents. Estimated parameters are shown in Table 1.
Fig 4.
Simulated human hepatocytes infection kinetics post simulated inoculation.
(A) Uninfected cells (T, black line), Infected non-productive cells (IE, yellow line), and productively infected cells (IP, red line) kinetics. The bold lines of each simulation curve represent the average of 1,000 independent runs with different random seeds and the shaded areas denote 95% confidence interval of those 1,000 runs. (B) Cell states observed from a representative run in the 2D lattice at 1, 2, 3, and 6 weeks post simulated inoculation. Uninfected cells (T, black cells), Infected non-productive cells (IE, yellow cells), and productively infected cells (IP, red cells). The ABM results shown represent the best fit of mouse M1 (Fig 3A and Table 1). The spatial structure on the 2D lattice was not considered in the ABM to affect viral infection spread.
Table 1.
Best estimated ABM parameters for calibrated mice and their estimated space (J<0.7).
Parameters are defined in Eqs 1 and 2; GE, genome equivalent; J-score, represents the objective function (Eq 3) score of the genetic algorithm (GA) fits where the min J-score is the best fit curves shown in Figs 3 and 7. Parameter estimates shown in () represent the min and max of all GA fits with J-score < 0.7 shown in Figs A-G in S1 Text with their statistics in Table C in S1 Text. Parameter pair plots and their correlation plots are shown in Figs H-N in S1 Text and Figs O-U in S1 Text, respectively.
Fig 5.
HBV virion production (circles) and viral production cycles (triangles) in representative mouse (M1) inoculated with 108 HBV genome equivalents shown in Fig 3A. (A and B) represent infected cells with minimum eclipse phase of 9 hr (black-shaded “E”). (C and D) infected cells with maximum eclipse phase of 48hr. Similar predictions for mice M2, M3 and M4 are shown in Fig V in S1 Text.
Fig 6.
Model parameter estimates for representative mouse M1.
(A and B) Simulated serum viral load. (C and D) The number of total cells in eclipse phase (solid gold line), productively infected cells (solid red line) and the average virion production (or secretion) per productively infected cells (solid green line) per time post inoculation. Graphs are divided according to the kinetic phases of HBV serum DNA amplification observed experimentally in Fig 1. Phases 5 and 6 are graphed separately to accommodate the larger y-axis scale required later in infection. Dashed vertical lines and black-shaded numbers indicating kinetic Phases 1–4 in (A) and (C) and Phases 5 and 6 in (B) and (D).
Fig 7.
Model best fit curves (solid lines) with measured HBV DNA kinetics (circles) in representative mice M5, M6 and M7 inoculated with and 107 (A), 106 (B), and 104 (C) HBV genome equivalents, respectively. Estimated model parameters are shown in Table 1.
Fig 8.
Varying the eclipse phase length (Ω) and initial production cycle length (δ).
Model simulations were run from time of inoculation until day 56 post inoculation (p.i.). Days 0–14 are shown here; days 0–56 are shown in Fig W in S1 Text. Parameters equal to that estimated for mouse 1 (M1) were used except for the indicated changes. (A) The parameter range of the eclipse phase was shortened to Ω = [0,5] hr (dashed green line) or extended to Ω = [36–72] hr (dotted red line). (B) The parameter range for the production cycle was reduced to δ = 1 hr (i.e., faster production, dashed green line) or increased to δ = 36 hr (i.e., slower production, dotted red line). (C) The short eclipse parameter range of Ω = [0,5] hr was combined with the fast (dashed green line) or slow (dotted red line) production parameter ranges used in (B). (D) same as (C) assuming extended eclipse phase to Ω = [36–72] hr. The model simulations for M1, Ω = [9,48] hr and to δ = 26 hr, is shown for comparison using solid black lines.