Cancer Immunotherapy by Interleukin-21: Potential Treatment Strategies Evaluated in a Mathematical Model Antonio Cappuccio, Moran Elishmereni and Zvia Agur Presented by N9720001

Lineage of Immune Cells

Natural Killer Cells ()

How Does NK Cell Kill?

CD8+ T Cells (CD8+ T)T stands for thymus ()

Cluster of Differentiation (CD)

Synergic Stimulate of CD8+ T CellCancer Cell

Mouse DataNature 2001RMA: T-cell lymphoma

Chromium 51Cr () Release Assay

Human DataScience 2002Melanoma:

Assumptions for the ModelThe tumor cells grow logistically in the absence of an immune response. Both NK cells and CD8+ T cells can kill tumor cellsTumor cells have the potential to engender cytocidal activity in previously naive and noncytotoxic cells.As part of innate immunity, NK cells are always present and active in the system, even in the absence of tumor cells.As part of specific immunity, tumor-specific CD8+ T cells are recruited once tumor cells are present.Each NK cell and CD8+ T cell will eventually become inactivated after some number of encounters with tumor cells.

Logistic FunctionThe tumor cells grow logistically in the absence of an immune response.

Model Equation BasicsRate of change of tumor cell population = (growth and death rate) (cell-cell kill rate) and rate of change of active effector cell populations = (growth and death rate) + (recruitment rate) - (inactivation rate).

Equation for Tumor CellsT: Tumor cell population a: Tumor growth rate b: Carrying capacity N: Natural killer cell population L: CD8+ T cell population D: CD8+ T cell-tumor killing term c: effectiveness of NK cell d: effectiveness of CD8+ T cell

Equation for NK CellsN: Natural killer cell population : Background source rate for NK cell f: Death rate of NK cell g: Maximum NK cell recruitment rate h: Steepness coefficient of NK cell recruitment curve p: NK cell inactivation rate by tumor cells

Equation for CD8+ T CellsL: CD8+ T cell population m: Death rate for CD8+ T cell j: Maximum CD8+ T cell recruitment rate k: Steepness coefficient of CD8+ T cell recruitment curve q: CD8+ T cell inactivation rate by tumor cells r: Rate of cross activation of CD8+ T cells by tumor cells killed by NK cells

Data Fitting via Least Squares Fit ()(Power Law vs. Rational Law)Power Function

Rational Function

Fractional Cell Kill Function (D)Describing the interaction of effector cells (NK and CD8+ T cells) and tumor cells.Simplest form: -cNT (NK vs. Tumor) (O) -dLT (CD8+ vs. Tumor) (x )2nd try: -cNT(O, at =1) -dNT(x )d: Maximum lysis rate s: Steepness of the curve : Exponent

NK Cell Fit the Power FunctionFig. 1aRMA: T-cell lymphoma

CD8+ T Cell Does Not Fit Power Functionnn: 1st prime will control 2nd challenged with control

ll: 1st prime will ligand tranduction 2nd challenged with ligand tranduction Note: Ligand transduction by virus

Least Squares Fit Errors

Model Validation Using Human Sample ( CD8+ T Cell) Patient #9 Patient #10Melanoma: Cell Lysis indirectly estimated (INF-)

Sensitivity Analysis (1%)a: aggressiveness of tumor (): effectiveness of T cells (T)

Model Simulation: Effect of Vaccination ()Vaccination (Control)

Vaccination (Real)Consistent with data in Nature, 2001

Model Simulation:Threshold for Immune EfficacyNo CD8+ T Cell: 104 :105 :106 Tumor cell challenged

No NK Cell: 104 :105 :106 Tumor cell challenged

w NK Cell & T cell: 104 :105 :106 Tumor cell challenged

ReferencesThomas J. Kindt, Barbara A. Osborne and Barbara A. Osborne, Immunology, 6th ed. W. H. Freeman: 2006Diefenbach A, Jensen E, Jamieson A, Raulet D. Rae1 and H60 ligands of the NKG2D receptor stimulate tumor immunity. Nature 2001;413:16571 Dudley ME, Wunderlich JR, Robbins PF, et al. Cancer regression and autoimmunity in patients after clonal repopulation with antitumor lymphocytes. Science 2002;298:8504.

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