Symbol | Interpretation | Value |
---|---|---|
t | Non-dimensional time | 1-3500 |
[S] | Concentration of stem cells at time t | Eqn 1 |
[MPP] | Concentration of Multipotent Progenitor (MPP) cells at time t | Eqn 2 |
[CLP] | Concentration of Common Lymphoid Progenitor (CLP) cells at time t | Eqn 3 |
[CMP] | Concentration of Common Myeloid Progenitor (CMP) cells at time t | Eqn 4 |
[L] | Concentration of fully differentiated Lymphoid (L) cells at time t | Eqn 5 |
[M] | Concentration of fully differentiated Myeloid (M) cells at time t | Eqn 6 |
K | Maximum number of stem cells in a niche | 10 |
r s | Maximum rate of stem cell self-renewal | 2.5 |
| Maximum rate of stem cell asymmetrical division | 0.001 |
| Feedback control from fully differentiated cells to asymmetric division | Eqn 9 |
Φ s ([L],[M]) | Feedback control from fully differentiated cells to stem cell self-reneval | Eqn 7 |
Φ p ([L],[M]) | Feedback control from fully differentiated cells to symmetric division | Eqn 8 |
μ s | Rate of stem cell death | 0.004 |
λ | Rate of MPP multiplication | 0.25 |
μ p | Rate of MPP cell death | 0.02 |
Ω N | Combination of intermediate multipotent progenitor rate constants | 1.0 |
r CLP | Rate of division of CLP into fully differentiated lymphoid cells | 0.01 |
μ CLP | Rate of CLP cell death | 0.001 |
r l | Rate of multiplication of lymphoid cells | 0.025 |
μ l | Rate of lymphoid cell death when immune system is not activated | 0.028 |
μ l∗ | Additional rate of lymphoid cell death when immune system is activated | 0.01 |
I a>b | Indicator function for the inequality | =1 if a>b, 0 otherwise |
v th | Threshold concentration for pathogens to activate the immune system | 0.025 |
r CMP | Rate of division of CMP into fully differentiated myeloid cells | 0.01 |
μ CMP | Rate of CMP cell death | 0.001 |
r m | Rate of multiplication of myeloid cells | 0.0 |
μ m | Rate of myeloid cell death | 0.01 |
l | Value of [L] | varies |
m | Value of [M] | varies |
ϕ sl (l) | Feedback control of fully differentiated lymphoid cells on stem cell activity | Eqn 10 |
ϕ sm (m) | Feedback control of fully differentiated myeloid cells on stem cell activity | Similar to Eqn 10 |
ϕ pl (l) | Feedback control of fully differentiated lymphoid cells on symmetric renewal | Eqn 11 |
ϕ pm (m) | Feedback control of fully differentiated myeloid cells on symmetric renewal | Similar to Eqn 10 |
| Feedback control of fully differentiated lymphoid cells on asymmetric renewal | Eqn 11 |
| Feedback control of fully differentiated myeloid cells on asymmetric renewal | Similar to Eqn 10 |
α sl | Feedback parameter in ϕ sl (l) | 10 |
α pl | Feedback parameter in ϕ pl (l) | 100 |
| Feedback parameter in | 20 |
α sm | Feedback parameter in ϕ sm (m) | 0.1 |
α pm | Feedback parameter in ϕ pm (m) | 0.001 |
| Feedback parameter in | 0.2 |
α | Coefficient in MPP Commitment Response (MPCR) | Varies |
γ | Exponent in MPCR | Varies |
κ l | Density of lymphoid cells in homeostasis | 30 |
κ m | Density of myeloid cells in homeostasis | 30,000 |
ρ h | Fraction of lymphoid cells in homeostasis | Eqn 15 |
Δf([M] | Rate of accumulation of fitness when myeloid cell concentration is [M] | Eqn 17 |
| Fitness accumulated to time t | Eqn 18 |
ε | Ratio of organismal to cellular time scale | 0.05 |
S(t) | Survival to time t | Eqn 21 |
μ e ([M]) | Total rate of mortality when myeloid cell concentration is [M] | Eqn 20 |
μ e0 | Myeloid independent rate of mortality | 0.05 |
μ e1 | Myeloid dependent rate of mortality | 5.0 |
μ i ([V]) | Additional rate of mortality when concentration of infectious agents is [V] | Eqn 20 |
μ i0 | Coefficient of [V] in additional mortality | 0.02 |
μ i1 | Coefficient of [V]2 in additional mortality | 0.002 |
r v | Replication rate of infectious agents | 0.05 |
c l | Clearance rate of infectious agents by lymphoid cells | 0.05 |
c m | Clearance rate of infectious agents by myeloid cells | 0 |
v 0 | Concentration of infectious agents at the start of an infection | 1 |
v th | Concentration of infectious agents below which additional lymphoid mortality does not occur | 0.025 |