Hoffman, F.; Gavaghan, D.; Osborne, J.; Barrett, I. P.; You, T.; Ghadially, H.; Sainson, R.; Wilkinson, R. W.; Byrne, Helen M. A mathematical model of antibody-dependent cellular cytotoxicity (ADCC). (English) Zbl 1394.92058 J. Theor. Biol. 436, 39-50 (2018). Summary: Immunotherapies exploit the immune system to target and kill cancer cells, while sparing healthy tissue. Antibody therapies, an important class of immunotherapies, involve the binding to specific antigens on the surface of the tumour cells of antibodies that activate natural killer (NK) cells to kill the tumour cells. Preclinical assessment of molecules that may cause antibody-dependent cellular cytotoxicity (ADCC) involves co-culturing cancer cells, NK cells and antibody in vitro for several hours and measuring subsequent levels of tumour cell lysis. Here we develop a mathematical model of such an in vitro ADCC assay, formulated as a system of time-dependent ordinary differential equations and in which NK cells kill cancer cells at a rate which depends on the amount of antibody bound to each cancer cell. Numerical simulations generated using experimentally-based parameter estimates reveal that the system evolves on two timescales: a fast timescale on which antibodies bind to receptors on the surface of the tumour cells, and NK cells form complexes with the cancer cells, and a longer time-scale on which the NK cells kill the cancer cells. We construct approximate model solutions on each timescale, and show that they are in good agreement with numerical simulations of the full system. Our results show how the processes involved in ADCC change as the initial concentration of antibody and NK-cancer cell ratio are varied. We use these results to explain what information about the tumour cell kill rate can be extracted from the cytotoxicity assays. Cited in 4 Documents MSC: 92C50 Medical applications (general) 92C60 Medical epidemiology Keywords:immunotherapy; antibody-dependent cellular cytotoxicity; ordinary differential equations; asymptotic analysis Software:Matlab; MATLAB ODE suite; Ode15s; ode23s; ode45; ode113; ode23 PDFBibTeX XMLCite \textit{F. Hoffman} et al., J. Theor. Biol. 436, 39--50 (2018; Zbl 1394.92058) Full Text: DOI Link References: [1] Almeida, C.; Ashkenazi, A.; Shahaf, G.; Kaplan, D.; Davis, D. M.; Mehr, R., Human NK cells differ more in their KIR2DL1-dependent thresholds for HLA-cw6-mediated inhibition than in their maximal killing capacity, PLoS One, 6, 9 (2011) [2] Bachireddy, P., Immunology in the clinic review series; focus on cancer: multiple roles for the immune system in oncogene addiction, Clin. Exp. Immunol., 167, 2, 188-194 (2012) [3] Bhat, R.; Watzl, C., Serial killing of tumor cells by human natural killer cells-enhancement by therapeutic antibodies, PLoS One, 2 (2007) [4] Bostrom, J.; Haber, L.; Koenig, P.; Kelley, R. F.; Fuh, G., High affinity antigen recognition of the dual specific variants of herceptin is entropy-driven in spite of structural plasticity, PLoS One, 6 (2011) [5] Callewaert, D. M.; Johnson, D. F.; Kearney, J., Spontaneous cytotoxicity of cultured human cell lines mediated by normal peripheral blood lymphocytes. III. Kinetic parameters, J. Immunol., 121, 710-717 (1978) [6] Chu, G., The kinetics of target cell lysis by cytotoxic t lymphocytes: a description by poisson statistics., J. Immunol., 120, 1261-1267 (1978) [7] Deguine, J.; Breart, B.; Lematre, F.; Bousso, P., Cutting edge: tumor targeting antibodies enhance NKG2d mediated NK cell cytotoxicity by stabilizing NK cell tumor cell interactions, J. Immunol., 189, 5493-5497 (2012) [8] Deguine, J.; Breart, B.; Lematre, F.; Santo, J. P.D.; Bousso, P., Intravital imaging reveals distinct dynamics for natural killer and CD8+ t cells during tumor regression, Immunity, 33, 632-644 (2010) [9] Douglass, E. F.; Miller, C. J.; Sparer, G.; Shapiro, H.; Spiegel, D. A., A comprehensive mathematical model for three-body binding equilibria, J. Am. Chem. Soc., 135, 16, 6092-6099 (2013) [10] Ernst, J. A.; Li, H.; Kim, H. S.; Nakamura, G. R.; Yansura, D. G.; Vandlen, R. L., Isolation and characterization of the b-cell marker CD20., Biochemistry, 44, 15150-15158 (2005) [11] Fogh, J.; Fogh, J. M.; Orfeo, T., One hundred and twenty-seven cultured human tumor cell lines producing tumors in nude mice., J. Nat. Cancer Inst., 59, 1, 221-226 (1977) [12] Garcia-Penarrubia, P.; Lorenzo, N.; Galvez, J.; Campos, A.; Ferez, X.; Rubio, G., Study of the physical meaning of the binding parameters involvedin effectortarget conjugation using monoclonal antibodies against adhesion molecules and cholera toxin., Cell. Immunol., 215, 2, 141-150 (2002) [13] Gardner, C., Stochastic methods: a handbook for the natural and social sciences. (2009), Springer [14] Hanahan, D.; Weinberg, R. A., Hallmarks of cancer: the next generation, Cell, 144, 5, 646-674 (2011) [15] Hodi, F. S.; O’Day, S. J.; McDermott, D. F.; Weber, R. W.; Sosman, J. A.; Haanen, J. B.; Gonzalez, R.; Robert, C.; Schadendorf, D.; Hassel, J. C.; Akerley, W.; van den Eertwegh, A. J.; Lutzky, J.; Lorigan, P.; Vaubel, J. M.; Linette, G. P.; Hogg, D.; Ottensmeier, C. H.; Lebb, C.; Peschel, C.; Quirt, I.; Clark, J. I.; Wolchok, J. D.; Weber, J. S.; Tian, J.; Yellin, M. J.; Nichol, G. M.; Hoos, A.; Urba, W. J., Improved survival with ipilimumab in patients with metastatic melanoma, N. Eng. J. Med., 363, 711 (2010) [16] Hudis, C. A., Trastuzumab-mechanism of action and use in clinical practice, N. Eng. J. Med., 357, 1, 39-51 (2007) [17] Iida, S.; Kuni-Kamochi, R.; Mori, K.; Misaka, H.; Inoue, M.; Okazaki, A.; Shitara, K.; Satoh, M., Two mechanisms of the enhanced antibody-dependent cellular cytotoxicity (ADCC) efficacy of non-fucosylated therapeutic antibodies in human blood., BMC Cancer, 9, 58 (2009) [18] Kute, T.; Stehle Jr, J. R.; Ornelles, D.; Walker, N.; Delbono, O.; Vaughn, J. P., Understanding key assay parameters that affect measurements of trastuzumab-mediated ADCC against her2 positive breast cancer cells, OncoImmunology, 1, 6, 810-821 (2012) [19] Lutz, C. T.; Karapetyan, A.; Al-Attar, A.; Shelton, B. J.; Holt, K. J.; Tucker, J. H.; Presnell, S. R., Human NK cells proliferate and die in vivo more rapidly than t cells in healthy young and elderly adults, J. Immunol., 186, 8, 4590-4598 (2011) [20] Mathworks, (2013). Matlab 2013a. http://www.mathworks.co.uk; Mathworks, (2013). Matlab 2013a. http://www.mathworks.co.uk [21] Matlawska-Wasowska, K.; Ward, E.; Stevens, S.; Wang, Y.; Herbst, R.; Winter, S. S.; Wilson, B. S., Macrophage and NK-mediated killing of precursor-b acute lymphoblastic leukemia cells targeted with a-fucosylated anti-CD19 humanized antibodies, Leukemia, 27, 6, 1263-1274 (2013) [22] Miller, R. G.; Dunkley, M., Quantitative analysis of the 51cr release cytotoxicity assay for cytotoxic lymphocytes, Cell Immunol., 14, 284-302 (1974) [23] Nakagawa, S.; Fujii, T.; Yokoyama, G.; Kazanietz, M. G.; Yamana, H.; Shirouzu, K., Cell growth inhibition by all-trans retinoic acid in SKBR-3 breast cancer cells: Involvement of protein kinase ca and extracellular signal-regulated kinase mitogen-activated protein kinase, Mol. Carcinogenesis, 38, 3, 106-116 (2003) [24] Ogbomo, H.; Hahn, A.; Geiler, J.; Michaelis, M.; Doerr, H. W.; Cinatl Jr, J., NK sensitivity of neuroblastoma cells determined by a highly sensitive coupled luminescent method, Biochem. Biophys. Res. Comm., 339, 1, 375-379 (2006) [25] Scott, A. M.; Wolchok, J. D.; Old, L. J., Antibody therapy of cancer, Nat. Rev. Cancer, 12, 278-287 (2012) [26] Seidel, U. J.E.; Schlegel, P.; Lang, P., Natural killer cell mediated antibody-dependent cellular cytotoxicity in tumor immunotherapy with therapeutic antibodies, Front Immunol., 4 (2013) [27] Shampine, L. F.; Reichelt, M. W., The MATLAB ODE suite, SIAM J. Sci. Comput., 18, 1-22 (1997) · Zbl 0868.65040 [28] Stewart, R.; Thom, G.; Levens, M.; Guler-Gane, G.; Holgate, R.; Rudd, P. M.; Webster, C.; Jermutus, L.; Lund, J., A variant human igg1-fc mediates improved ADCC, Protein Eng. Des. Sel., 24, 9, 671-678 (2011) [29] Thorn, R. M.; Henney, C. S., Kinetic analysis of target cell destruction by effector t cells. i. Delineation of parameters related to the frequency and lytic efficiency of killer cells, J. Immunol., 117, 2213-2219 (1976) [30] Thorn, R. M.; Henney, C. S., Kinetic analysis of target cell destruction by effector t cells. II. Changes in killer cell avidity as a function of time and antigen dose, J Immunol, 119, 1973-1978 (1977) [31] Vacchelli, E.; Pol, J.; Bloy, N.; Eggermont, A.; Cremer, I.; Fridman, W. H.; Galon, J.; Marabelle, A.; Kohrt, H.; Zitvogel, L.; Kroemer, G.; Galluzzi, L., Trial watch: tumour-targetting monoclonal antibodies for oncological indications., Oncoimmunology, 4 (2015) [32] Vanherberghen, B.; Olofsson, P. E.; Forslund, E.; Sternberg-Simon, M.; Khorshidi, M. A.; Pacouret, S.; Guldevall, K.; Enqvist, M.; Malmberg, K. J.; Mehr, R.; nfelt, B., Classification of human natural killer cells based on migration behavior and cytotoxic response, Blood, 121, 8, 1326-1334 (2013) [33] Vogel, W. H., Infusion reactions: diagnosis, assessment, and management, Clin. J. Oncol. Nurs., 14, E10-21 (2010) [34] Ward, E.; Mittereder, N.; Kuta, E.; Sims, G. P.; Bowen, M. A.; Dall’Acqua, W.; Tedder, T.; Kiener, P.; Coyle, A. J.; Wu, H.; Jallal, B.; Herbst, R., A glycoengineered anti-CD19 antibody with potent antibody-dependent cellular cytotoxicity activity in vitro and lymphoma growth inhibition in vivo, Br J Haem, 155, 4, 426-437 (2011) [35] Zeijlemaker, W. P.; Oers, R. H.J. V.; De Goede, R. E.; Schellekens, P. T., Cytotoxic activity of human lymphocytes: quantitative analysis of t cell and k cell cytotoxicity, revealing enzyme-like kinetics, J. Immunol., 119, 1507-1514 (1977) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.