• Figure 1.
    Download figureOpen in new tabFigure 1. Cell culture systems and the basic reproduction number under cell-to-cell and cell-free infection.

    (A) Static and shaking cultures of Jurkat cells. The static and shaking cell cultures allow human immunodeficiency virus type 1 (HIV-1) to perform both cell-free and cell-to-cell infection, and only cell-free infection, respectively. (B) The basic reproduction number, R0, is defined as the number of the secondly infected cells produced from a typical infected cell during its infectious period. In the presence of the cell-to-cell and cell-free infection, the basic reproduction number consists of two sub-reproduction numbers through the cell-free infection, Rcf, and through the cell-to-cell infection, Rcc, respectively.

    DOI: http://dx.doi.org/10.7554/eLife.08150.003

    Figure 3.
    Download figureOpen in new tabFigure 3. Distribution of the basic reproduction numbers, generation time, and Malthus coefficient.

    The distribution of the basic reproduction number, R0, the number of secondary infected cells through the cell-free infection, Rcf, and the cell-to-cell infection, Rcc, calculated from all accepted Markov Chain Monte Carlo (MCMC) parameter estimates are shown in A, B, and C, respectively. The contribution of the cell-to-cell infection (i.e., Rcc/(Rcf + Rcc)) is distributed as in D. For each plot, the last 15,000 MCMC samples among the total 50,000 samples are used. a.u., arbitrary unit.

    DOI: http://dx.doi.org/10.7554/eLife.08150.009

    Figure 4.
    Download figureOpen in new tabFigure 4. Simulating cell-to-cell infection of HIV-1.

    Using our estimated parameters, the pure cell-to-cell infection is simulated in silico (solid curves). The simulated values are located between the time course of experimental data under the static conditions (closed circles) and those under the shaking conditions (open circles). The shadowed regions correspond to 95% posterior predictive intervals.

    DOI: http://dx.doi.org/10.7554/eLife.08150.011

  • Table 1.

    Parameters estimated by mathematical-experimental analysis

    DOI: http://dx.doi.org/10.7554/eLife.08150.004

    Parameter nameSymbolUnitExp. 1Exp. 2Exp. 3Ave. ± S.D.
    Parameters obtained from simultaneous fit to time-course experimental dataset
     Rate constant for cell-free infectionβ10−6 × (p24 day)−15.59* (3.54–8.41)3.27 (2.05–5.01)3.70 (2.28–5.77)4.18 ± 1.41
     Rate constant for cell-to-cell infectionω10−6 × (cell day)−10.88 (0.45–1.39)1.25 (0.70–1.97)1.13 (0.64–1.79)1.09 ± 0.33
     Production rate of total viral proteinpday−10.37 (0.22–0.59)0.59 (0.34–0.92)0.54 (0.31–0.86)0.50 ± 0.16
     Death rate of infected cellsδday−10.45 (0.32–0.64)0.54 (0.38–0.75)0.50 (0.36–0.68)0.50 ± 0.10
    Quantities derived from fitted values
     Basic reproduction number through cell-free infectionRcf2.88 (2.34–3.53)2.27 (1.98–2.66)2.43 (2.04–2.95)2.44 ± 0.23
     Basic reproduction number through cell-to-cell infectionRcc2.95 (1.48–4.70)3.65 (1.77–6.05)3.39 (1.82–5.38)3.39 ± 0.91
     Basic reproduction numberR05.83 (4.20–7.75)5.92 (3.99–8.46)5.83 (4.21–7.89)5.83 ± 0.94
     Contribution of cell-to-cell infectionRccRcf+Rcc0.50 (0.34–0.63)0.60 (0.44–0.72)0.57 (0.43–0.70)0.57 ± 0.07
    • Mean value.

    • 95% confidence interval.

    • Average and standard deviation of merged values in experiment 1, 2, and 3.

  • Table 2.

    Generation time and Malthus coefficient of virus infection

    DOI: http://dx.doi.org/10.7554/eLife.08150.010

    Cell culture systemExp. 1Exp. 2Exp. 3Ave. ± S.D.
    Generation time of HIV-1
     Static cell culture2.51* days2.08 days2.22 days(2.22 ± 0.32) days
    (1.78–3.38) days(1.54–2.78) days(1.69–2.93) days
     Shaking cell culture2.73 days2.34 days2.47 days(2.47 ± 0.32) days
    (1.99–3.59) days(1.77–3.06) days(1.91–3.18) days
    Malthus coefficient of HIV-1
     Static cell culture1.61 day−12.03 day−11.86 day−1(1.86 ± 0.37) day−1
    (1.10–2.27) day−1(1.32–3.01) day−1(1.26–2.72) day−1
     Shaking cell culture0.57 day−10.46 day−110.49 day−1(0.49 ± 0.05) day−1
    (0.47–0.67) day−1(0.38–0.56) day−1(0.39–0.61) day−1
    • Mean value.

    • 95% confidence interval.

    • Average and standard deviation of merged values in experiment 1, 2, and 3.

    • HIV-1, human immunodeficiency virus type 1.