Table 1 Variables, parameters, their interpretation, and values

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

$r_{p^{\prime }}$

Maximum rate of stem cell asymmetrical division

0.001

${\Phi }_p^{\prime }\left(\right[L],[M\left]\right)$

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

${\varphi }_{p^{\prime }l}\left(l\right)$

Feedback control of fully differentiated lymphoid cells on asymmetric renewal

Eqn 11

${\varphi }_{p^{\prime }m}\left(m\right)$

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

${\alpha }_{p^{\prime }l}$

Feedback parameter in ${\varphi }_{p^{\prime }l}\left(l\right)$

20

α _sm

Feedback parameter in ϕ _sm (m)

0.1

α _pm

Feedback parameter in ϕ _pm (m)

0.001

${\alpha }_{p^{\prime }m}$

Feedback parameter in ${\varphi }_{p^{\prime }m}\left(m\right)$

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

$\mathcal{F}\left(t\right)$

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