Table 2 A comparison of the estimated kinetic rates with those from previous studies.

From: Quantitative analysis reveals reciprocal regulations underlying recovery dynamics of thymocytes and thymic environment in mice

Term

Value

CI

Previous study

Inflow rate to DN [cells day−1] (estimated by the coarse-grained model)

3.3 × 104

[3.3 × 103, 6.6 × 104]

2.0 × 104 (19), 1.3 × 104 (43)

Inflow rate to DN (cells day−1)

(estimated by the detailed model)

6.61 × 101

N/A

101 ~ 2 × 102 (36), 4.9 × 101 (20)

DN apparent proliferation rate (day−1)

1.3 × 10−1

[−2.2 × 10−2, 3.3 × 10−1]

2.3 × 10−1 (19), 6.2 × 10−4 (43)

3.6 × 10−1 (20)

DN differentiation rate (day−1)

1.4 × 10−1

[5.7 × 10−6, 3.5 × 10−1]

2.4 × 10−1 (19), 2.8 × 10−2 (43)

3.4 × 10−1 (20), 4.5 × 10−1 (42)

DN residence time (hour)

1.7 × 102

[6.9 × 101, 4.3 × 106]

4.2 × 102 (19), 3.5 × 102 (20)

DP apparent proliferation rate (day−1)

1.0 × 10−1

[5.8 × 10−2, 2.5 × 10−1]

1.5 × 10−2 (19), −3.7 × 10−1 (21)

−1.6 × 10−1 (42), −9.0 × 10−3 (43)

DP differentiation rate to SP4 (day−1)

1.1 × 10−1

[6.0 × 10−2, 2.5 × 10−1]

2.1 × 10−2 (19), 1.2 × 10−2 (21)

3.0 × 10−2 (42), 9.9 × 10−2 (43)

DP residence time (hour)

2.3 × 102

[9.5 × 101, 4.0 × 102]

9.4 × 101 (19), 7.6 × 101 (21), 1.2 × 102 (22)

Proportion of DP to SP4 in DP export (%)

10

[4.9, 30]

6.0 (19), 0.016 (21), 8.1 (42), 65 (43)

SP4 apparent export rate (day−1)

5.2 × 10−1

[2.7 × 10−1, 1.2 × 100]

2.0 × 10−2 (19), 9.0 × 10−2 (21)

1.4 × 10−1 (42), 1.7 × 10−1 (43)

  1. (CI: confidence interval) The value of each term is estimated in our model by the following equations of the parameters evaluated at the steady state \(n_i^ \ast\)
  2. Inflow rate to DN thymocytes: ϕ1
  3. DN apparent proliferation rate: \(\delta _1 - \mu _1\left( {1 - r_1} \right)n_{{\rm{cTEC}}}^ \ast\)
  4. DN differentiation rate: \(\mu _1r_1n_{{\rm{cTEC}}}^ \ast\)
  5. DN residence time: \(24/(\mu _1r_1n_{{\rm{cTEC}}}^ \ast )\)
  6. DP apparent proliferation rate: \(\theta _2(1 - n_{{\rm{DP}}}^ \ast /K_2) - \left( {1 - r_{24}} \right)\mu _2n_{{\rm{cTEC}}}^ \ast\)
  7. DP differentiation rate to SP4: \(r_{24}\mu _2n_{{\rm{cTEC}}}^ \ast\)
  8. DP residence time: \(24/(r_{24}\mu _2n_{{\rm{cTEC}}}^ \ast )\)
  9. Proportion of DP to SP4 in DP export: r24
  10. SP4 apparent export rate: \(\mu _4n_{{\rm{mTEC}}}^ \ast\)
  11. We note that our point estimate of the DP residence time 230 h may be an overestimate, although the previous estimates overlap the statistically confident range of the values obtained by our bootstrap analysis. This is because the residence time was estimated only from the output flux rate, due to the fact that the apoptosis rate cannot be estimated in our model
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