Table 1.

List of parameter values

Parameter	Value	Units	Source
r1	1.2924	per day	[16]
C1	0.1	Oxygen concentration	[16]
r2	0.001	per Tumor cell density per day	[16]
σ	1.0029	dimensionless	[16]
C2	0.054	Oxygen concentration	[16]
Cm	0.2	Oxygen concentration	[16]
k	16.0	# Microvessels per mm3	1
μa	12.8810	# HDMECs per pg of Da per day	[11]2
μl	806.9190	# HDMECs per pg of Cl per day	[11]2
ad	3.8780×10−6	per day	[11], [21]3
bd	1.7329	per Bad concentration	[11], [21]3
α1	30.0	# HDMECs per Microvessel	[16]
M0	17×103	# HDMECs per mm3	[16]
α2	0.2984	# Microvessels per pg of Da per day	[22]2
α3	6.5757	# Microvessels per pg of Cl per day	[22]2
${\eta }_1^a$	0.2250	pg VEGF per pg Ra	[16]
${\eta }_2^a$	0.1837	pg VEGF per pg Ca	[16]
${\eta }_3^a$	0.8163	pg Ra per pg Ca	[16]
${\eta }_4^a$	0.4494	pg Ra per pg Da	[16]
${\eta }_5^a$	1.2250	pg Ca per pg Ra	[16]
${\eta }_6^a$	0.5506	pg Ca per pg Da	[16]
${\eta }_7^a$	2.2250	pg Da per pg Ra	[16]
λa	15.5958	per day	[16]
r3	0.1507	pg VEGF per Tumor cell per day	[12]4
$k_{f1}^a$	1.6232	per VEGF concentration per day	[16]
$k_{r1}^a$	49.3025	per day	[16]
$k_{f2}^a$	162.32	per Ca concentration per day	[16]
$k_{r2}^a$	0.493025	per day	[16]
$k_p^a$	16.0	per day	[16]
Vchar	55.0	# Microvessels per mm3	[16]
V0	2.0	# Microvessels per mm3	[16]
∊	1.0	# Microvessels per mm3	[16]
$k_f^l$	6.7587	per CXCL8 concentration per day	[16]
$k_r^l$	43.2557	per day	[16]
$k_p^l$	24.0	per day	[16]
${\eta }_1^l$	0.1311	pg CXCL8 per pg Rl	[16]
${\eta }_2^l$	0.1159	pg CXCL8 per pg Cl	[16]
${\eta }_3^l$	0.8841	pg Rl per pg Cl	[16]
${\eta }_4^l$	1.1311	pg Cl per pg Rl	[16]
λl	15.5958	per day	[16]
βm	8.1139×10−4	pg of CXCL8 per HDMEC per day	[11] [16]2,5
ap	6.9620×10−4	pg of CXCL8 per HDMEC per day	[11] [16]2,5
bp	1.6185	per Bcl-2 concentration	[11] [16]2,5
α4	0.24845	# Microvessels per HDMEC	[16]
$k_f^b$	4	per Bad concentration per day	1
$k_r^b$	8.832	per day	[3]
$k_f^i$	40	per BL193 concentration per day	[3]6
$k_r^i$	2.56	per day	[3]6
βa	40	fg of Bcl-2 per pg Da	[12]
Di	3.4650	per day	1

¹In the absence of experimental data, biologically realistic values for these parameters were chosen so that the solution profiles best fit experimental observations.

²The parameters associated with CXCL8 production, and CXCL8 and VEGF effect on HDMEC proliferation, and microvessel formation were estimated using least squares fits of experimental data in [11, 22].

³We know that the normal death rate of HDMECs is 0.12 per day [21]. Further, in the presence of 50 ng per ml VEGF, Bcl-2 is up-regulated 3.1 fold, and consequently the level of Bad falls by a factor of 0.77. We assume a very low HDMEC death rate corresponding to this low level of Bad. From these two observations, the constants a_d and b_d may be determined.

⁴Keeping all other parameter values fixed, VEGF production rate by tumor cells was determined by fitting the microvessel density after 21 days with that observed experimentally in a (control) tumor that was allowed to grow without the application of any anti-cancer therapy [12].

⁵A relation between the constants β_m, a_p and b_p may be found by observing that at constitutive Bcl-2 levels, the production rate of CXCL8 is 0.0358 pg of CXCL8 per HDMEC per day [16]. Note that at constitutive levels of Bcl-2 and Bad, the cell death rate is taken to be 0.12 per day [21] and HDMEC CXCL8 production rate is fit to experiments in [12]

⁶It was assumed that rate of forward reaction of BL193 with Bcl-2 was higher than that of Bad binding to Bcl-2, due to the much smaller size of BL193.