The results show that the assumption — starving cells die exponentially — is true only at high cell density .

Detailed analyses show intriguing quantitative characteristics of the density-dependent and biphasic survival kinetics, including that the period of the perseverance is inversely proportional to cell density .

Here, we show that this assumption is true only at high cell density .

At low cell density , cells can persevere for extended periods of time, before dying at a constant rate.

Quantitative analyses reveal simple quantitative formulas governing the patterns, e.g., the first and second kinetics are well described by exp(-t2) and exp(-t) respectively, and the duration of the first kinetics is inversely proportional to cell density .

(The results show that the previous assumption—exponential decay of survival of starving cells—is true only at very high cell density .)

The temporal kinetics of NCFU in glycerol-exhausted cultures with 5 different cell densities is plotted in Fig.

I (see S2 Fig for the kinetics of other cell densities ).

The period of the first phase becomes more pronounced at lower cell density , prolonging cell survival.

Current WHO guidelines suggest commencing treatment at CD4+ T cell density of > 350cells/yl and < 500cells/yl [45].

The activation rate a(NM/N) increases as the total T cell density (N) falls (caused by the HIV-1 progression).

Susceptible T cells turn into quiescent T cells at a rate r. They proliferate at a variable rate p (1 — N/N M), Where p is the proliferation coefficient, N is the total T cell density, and NM is the T cell density at Which proliferation stops.

This variable proliferation rate is a reasonable approximation [29] to the real T cell proliferation process, based on evidence [2] that T cell proliferation rate is density-dependent and would slow as the T cell density becomes high.

N S is the quasi-steady CD4+ T cell density and V3 is the quasi-steady density of free Virions, which are average densities between the 100th and 800th days after initial infection.

post-exposure prophylaxis) leads to no decline in CD4+ T cell density , and no chronic infection phase.

The same treatment applied when T cell density reaches the levels (500 CD4+ T cells/1,11 and 350 CD4+ T cells/1,11) at which the World Health Organization recommends ART initiation [45] is followed by a rapid virus rebound after the treatment stops, and the disease progresses according to its normal course.

Paracrine cytokine signals depend on cell density and receptor number.

The autocrine and para-crine uptake rates Iauto and Ipara depend on the level of cytokine receptor expression on the target cells (Fig 1E), and are practically independent of the cell-to-cell distance even at high cell density (Fig IF; the low cell-density scenario is independent of the cell-to-cell distance by construction).

Interestingly, a fourth system property one might expect to have a large influence on the dynamics of the system, the cell density or cell-to-cell distance, is unimportant for the results of our simulations (Fig 4E).

Target cell density and receptor expression control paracrine cytokine signals

The effect of initial cell density on the predictive powers of recovery time.

Time curves for cell density , Bla, and antibiotic concentration.

Time curves for cell density , Bla, and antibiotic concentration.