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Table 1 Model parameters. (RSE, Relative standard error)

From: Radiation and PD-(L)1 treatment combinations: immune response and dose optimization via a predictive systems model

Parameter Unit Description Value RSE (%) Comments and references
r d−1 Tumor growth rate 0.4   Taken from [41]
TVmax μL Maximal size of tumor 2500   Taken from [41]
d0 d− 1 Spontaneous death rate of tumor cells 0.01   Assumed and to preserve d0 < < r, given the proportion of apoptotic vs. proliferating cells is minor, in growing syngeneic tumors [25].
kLN cells/d Maximal influx rate of nT eff cells 279 8 Estimated based on tumor growth data
SL n/a T cell ability to infiltrate tumor tissue under systemic antigen exposure 8.89 13 Estimated based on tumor growth data
ΩSL n/a Random effects on k LN 0.696 10 Estimated based on tumor growth data
kpro d−1 nT eff proliferation rate constant 3.0   Estimated based on a minimal duration (6 h) of the cell division cycle [42]
kdif d−1 nT eff differentiation rate constant 3.2   Assumed, to preserve observed nTeff/dTeff ratio in tumor tissue [43]
kel d−1 nT eff elimination rate constant 0.2   Estimated based on half-life of primed T cells [42]
kapo d−1 dT eff apoptosis rate constant 2.0   Estimated based on activated cytotoxic T cells in tissue [42]
e d− 1• cell− 1 Rate of tumor cell kill by dT eff 0.001   Assumed based on CD8+ cell density in CT26, controlling tumor regrowth after RT [12, 25]
Kpdl cells Sensitivity of PD-L1 expression up-regulation to dT eff count 478 23 Estimated based on tumor growth data
kpdl d−1 PD-L1 up-regulation rate constant 1.0   PD-L1 response was assumed to reach a steady-state in about 1 day, as shown in vitro [44]
Ktcd d− 1 Sensitivity of DC m to TCD value 0.2   Assumed to be sufficiently high to stimulate DC maturation in the TME [17]
SR n/a Sensitivity of cellular immuno-suppression to accumulation to systemic Ag level 30.5 12 Estimated based on tumor growth data
α Gy− 1 Linear component of radiation effect 0.146 9 Estimated based on tumor growth data
δ Gy−1 DSB formation per cell per Gy 19   Taken from [45]
τ d (day) DSB repair time 0.02   Taken from [46]
μ d−1 Elimination rate of radiation-damaged tumor cells 0.1725   Calculated from the half-life value [47]
Vd L Volume of distribution for PD-L1 mAb i.p. PKPD model in mouse 0.003   Estimated from [48]
ka d−1 i.p. absorption rate 8.0   Estimated from [48]
kelmAB d−1 mAb elimination rate 0.15   Estimated from [48]
KD nM mAb PD-L1(PD-1) binding affinity 30   Taken from internal data
a μL Constant component of residual error 21.2 13 Estimated based on tumor growth data
b n/a Proportional component of residual error 0.176 10 Estimated based on tumor growth data
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