Table 1.

Overall summary of integration issues

Integration issues resolved with the mapping of the MK model [Ref.[10]] onto the FIRM network structure	Integration issues resolved with the integration of the DB model [Ref.[5]] with the MK model [Ref.[10]]	Integration issues resolved with the integration of the BL model [Ref.[8]] into the FIRM framework comprised of the DB model [Ref.[5]] and the MK model [Ref.[10]]
• Added basal state levels of resting macrophages and IDC using MK latency parameter values:	• Removed “HTL” (TH1) from activation of macrophages.	• BM conversion to B cells has the same rate as the death of BM.
- MR[0] = 5 * 108 cells	• Using DB value for MA half-life.	• Antibody produced by BP, BA in blood, and BA in lymphoid B.
- IDC [0] = 5 * 107 cells	- η13 = 1 day-1	• Expansion of the BL model due to the relaxation of equilibrium assumptions required the creation of variables x41-x52 and fluxes v87-v100.
• Combined bursting (v3) and natural death (v14) of infected macrophages into one flux (v3). The reaction rate will be the summation of the two individual reaction rates.	• Created constant recruitment of TCP and THP in the lymphoid T, in fluxes v50 and v21, respectively, analogous to I1 and I2 from the DB model.	• Created “antigen” variable in blood and Site of recognition.
• Introduced MI (Infected Macrophages) as a separate space with a variable volume:	- I1 → ρ50 , I2 → ρ21	- “Antigen” can be either a tumor debris or a bacteria cell, they become a part of the “antigen” pool once they enter the blood
- VolumeMI = 8*10-9 * x3	• Accounted for TCP presence in the blood, created a separate variable x25.	- Permeates from lung to blood, and from blood to Site
• Fixed bacteria accounting issues:	• Temporarily changed HTL (TH1) in FACTOR to HTLP (THP).
- In the MK model, half of the amount of bacteria released during bursting was required to infect one macrophage. These two amounts have been made independent, but they are currently set to 25 bacteria for infection and 50 bacteria for bursting. These are the same values used in the MK model, but they can be changed easily.	• Using DB value for MR half-life.	• Created receptor sites on select B cell populations.
- Bursting (v3) is based on the ratio of intracellular bacteria to infected macrophages (x5/x3). The bursting will occur at a greater rate as the ratio approaches a set number (the macrophage’s capacity). This capacity is currently set to 50.	- η10 = 0.05 day-1	- x16, x17, and x18 have receptor sites
- Bursting (v3) releases x5/x3 extracellular bacteria into the system, instead of a fixed number.	• Redefined FACTOR with HTL (TH1).	- Receptor sites have 2 states: antigen-bound and free
- T-cell induced apoptosis (v4) releases x5/x3 extracellular bacteria into the system.	• Added TH1 (HTL) proliferation from the DB model as a negative term to the death flux v28.	• Expanded antigen-B cell interaction to include receptor sites and binding events.
- It is important to note that x5/x3 is a time-dependent ratio.	• Modeled differentiation of naïve T cells to TCP (v50) to mirror the action of v21 from the MK model.	- All antigen-receptor binding events occur at the same rate
• Combined naïve T cell death and recirculation from the MK model into one clearance flux (v20). The reaction rate will be the summation of the two individual reaction rates.	• Modified MAPC from the DB model. MAPC and its corresponding fluxes (v57, v58) will remain inactive and undefined. The functionality of MAPC described in the DB model, using the variable INFLAM, will be merged with the dendritic cells:	- The receptor-antigen binding event is a reversible reaction
• Added basal state levels of resting macrophages and IDC using MK latency parameter values but using the new clearance flux of naïve T cells (v20):	- Added term to recruitment of IDC cells (v15) using INFLAM as a trigger.	- x20 is assumed to have the same receptor state as x18
- T[0] = 98,039 cells	■ (ρ21 + ρ50)/2 * INFLAM	• Expanded antigen-antibody interactions to include dynamic single- and double-bound states.
• Modified rate law v22. The MK formulation allowed for negative proliferation.	- Added term to migration/maturation of IDCs (v17) using INFLAM as a trigger.	- All antigen-antibody binding events occur at the same rate
• Accounted for THP presence in the blood, created a separate variable x13.	■ Used term from MK stimulation, but replaced x4 (PE) with INFLAM	- All bound antibody states are cleared at the same rate
• Used volume ratios to properly account for cell migrations across tissue space borders.	• Cut off an INFLAM feedback loop by globally redefining INFLAM without HTL (TH1) when substituting in FACTOR. Now, the only variable that determines INFLAM is tumor burden. The basic premise of the INFLAM loop is an increase in INFLAM causes dendritic cells to produce more helper T cells, and the creation of these helper T cells caused FACTOR to increase, which in turn caused INFLAM to increase.	- Binding events occur in both the blood (with “antigen”) and the lung (with extracellular bacteria)
• Eliminated flux v30. The migration flux of TH2 to the blood (v31) that was to be added with the B cell response will take its place. v31 will take the death rate of v30 (0.3333 day-1) as its reaction rate. Having two fluxes drain the TH2 population was leaving the TH2 levels in the lung much too low and ineffective.	• Added new fluxes to FIRM structure:	• Defined initial conditions with analytical solutions for B cells and B cell free receptors sites.
• Added basal state levels of IL-12 in the lung, produced by the basal levels of MR.	- v84 → death of THP in the blood	• Permeation of tumor debris to blood is turned off.
IL-12[0] = 5*108 (q78a/η79)	- v85 → death of TCP in the blood	- Tumor-antibody interaction lacks definition at this time
	- v86 → proliferation of TH1 in the lung (removed negative term from v28)
	• Defined initial conditions with analytical solutions for:
	- MR, IDC, T, THP in the lymphoid T, THP in the blood, TCP in the lymphoid T, TCP in the blood, IL-12 in the lung