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

Yuri Kosinsky; Simon J. Dovedi; Kirill Peskov; Veronika Voronova; Lulu Chu; Helen Tomkinson; Nidal Al-Huniti; Donald R. Stanski; Gabriel Helmlinger

doi:10.1186/s40425-018-0327-9

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]
TV_max	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].
k_LN	cells/d	Maximal influx rate of ⁿT_eff cells	279	8	Estimated based on tumor growth data
S_L	n/a	T cell ability to infiltrate tumor tissue under systemic antigen exposure	8.89	13	Estimated based on tumor growth data
Ω_SL	n/a	Random effects on k_LN	0.696	10	Estimated based on tumor growth data
k_pro	d⁻¹	ⁿT_eff proliferation rate constant	3.0		Estimated based on a minimal duration (6 h) of the cell division cycle [42]
k_dif	d⁻¹	ⁿT_eff differentiation rate constant	3.2		Assumed, to preserve observed ⁿT_eff/^dT_eff ratio in tumor tissue [43]
k_el	d⁻¹	ⁿT_eff elimination rate constant	0.2		Estimated based on half-life of primed T cells [42]
k_apo	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]
K_pdl	cells	Sensitivity of PD-L1 expression up-regulation to ^dT_eff count	478	23	Estimated based on tumor growth data
k_pdl	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]
K_tcd	d^− 1	Sensitivity of DC_m to TCD value	0.2		Assumed to be sufficiently high to stimulate DC maturation in the TME [17]
S_R	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]
V_d	L	Volume of distribution for PD-L1 mAb i.p. PKPD model in mouse	0.003		Estimated from [48]
k_a	d⁻¹	i.p. absorption rate	8.0		Estimated from [48]
kel_mAB	d⁻¹	mAb elimination rate	0.15		Estimated from [48]
K_D	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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