Table 1 Overall summary of integration issues

• Added basal state levels of resting macrophages and IDC using MK latency parameter values:

• Removed “HTL” (T_H1) from activation of macrophages.

• B_M conversion to B cells has the same rate as the death of B_M.

- M_R[0] = 5 * 10⁸ cells

• Using DB value for M_A half-life.

• Antibody produced by B_P, B_A in blood, and B_A 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 T_CP and T_HP 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 M_I (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

- Volume_MI = 8*10^-9 * x₃

• Accounted for T_CP 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 (T_H1) in FACTOR to HTLP (T_HP).

- 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 M_R 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 (T_H1).

- Receptor sites have 2 states: antigen-bound and free

- T-cell induced apoptosis (v₄) releases x₅/x₃ extracellular bacteria into the system.

• Added T_H1 (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 T_CP (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 M_APC from the DB model. M_APC and its corresponding fluxes (v₅₇, v₅₈) will remain inactive and undefined. The functionality of M_APC 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 T_HP presence in the blood, created a separate variable x₁₃.

■ Used term from MK stimulation, but replaced x₄ (P_E) 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 (T_H1) 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 T_H2 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 T_H2 population was leaving the T_H2 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 M_R.

- v₈₄ → death of T_HP in the blood

• Permeation of tumor debris to blood is turned off.

IL-12[0] = 5*10⁸ (q_78a/η₇₉)

- v₈₅ → death of T_CP in the blood

- Tumor-antibody interaction lacks definition at this time

- v₈₆ → proliferation of T_H1 in the lung (removed negative term from v₂₈)

• Defined initial conditions with analytical solutions for:

- M_R, IDC, T, T_HP in the lymphoid T, T_HP in the blood, T_CP in the lymphoid T, T_CP in the blood, IL-12 in the lung