2012, 9(3): 663-683. doi: 10.3934/mbe.2012.9.663

A minimal mathematical model for the initial molecular interactions of death receptor signalling

1. 

Institute of Applied Analysis and Numerical Simulation, Univ. of Stuttgart, Pfa enwaldring 57, 70569 Stuttgart, Germany

2. 

Institute of Cell Biology and Immunology, Univ. of Stuttgart, Allmandring 31, 70569 Stuttgart, Germany, Germany

3. 

Institute of Computational and Applied Mathematics, WWU Münster, Einsteinstr. 62, 48149 Münster, Germany

Received  August 2011 Revised  May 2012 Published  July 2012

Tumor necrosis factor (TNF) is the name giving member of a large cytokine family mirrored by a respective cell membrane receptor super family. TNF itself is a strong proinflammatory regulator of the innate immune system, but has been also recognized as a major factor in progression of autoimmune diseases. A subgroup of the TNF ligand family, including TNF, signals via so-called death receptors, capable to induce a major form of programmed cell death, called apoptosis. Typical for most members of the whole family, death ligands form homotrimeric proteins, capable to bind up to three of their respective receptor molecules. But also unligated receptors occur on the cell surface as homomultimers due to a homophilic interaction domain. Based on these two interaction motivs (ligand/receptor and receptor/receptor) formation of large ligand/receptor clusters can be postulated which have been also observed experimentally. We use here a mass action kinetics approach to establish an ordinary differential equations model describing the dynamics of primary ligand/receptor complex formation as a basis for further clustering on the cell membrane. Based on available experimental data we develop our model in a way that not only ligand/receptor, but also homophilic receptor interaction is encompassed. The model allows formation of two distict primary ligand/receptor complexes in a ligand concentration dependent manner. At extremely high ligand concentrations the system is dominated by ligated receptor homodimers.
Citation: Christian Winkel, Simon Neumann, Christina Surulescu, Peter Scheurich. A minimal mathematical model for the initial molecular interactions of death receptor signalling. Mathematical Biosciences & Engineering, 2012, 9 (3) : 663-683. doi: 10.3934/mbe.2012.9.663
References:
[1]

B. B. Aggarwal, Signalling pathways of the TNF superfamily: A double-edged sword,, Nature Reviews Immunology, 3 (2003), 745.  doi: 10.1038/nri1184.  Google Scholar

[2]

Hyun-Jung An, Young Jin Kim, Dong Hyun Song, Beom Suk Park, Ho Min Kim, Ju Dong Lee, Sang-Gi Paik, Jie-Oh Lee and Hayyoung Lee, Crystallographic and mutational analysis of the CD40-CD154 complex and its implications for receptor activation,, Journal of Biological Chemistry, 286 (2011), 11226.  doi: 10.1074/jbc.M110.208215.  Google Scholar

[3]

David W. Banner, Allan D'Arcy, Wolfgang Janes, Reiner Gentz, Hans-Joachim Schoenfeld, Clemens Broger, Hansruedi Loetscher and Werner Lesslauer, Crystal structure of the soluble human 55 kd TNF receptor-human TNF[beta] complex: Implications for TNF receptor activation,, Cell, 73 (1993), 431.  doi: 10.1016/0092-8674(93)90132-A.  Google Scholar

[4]

D. Berg, M. Lehne, N. Müller, D. Siegmund, S. Münkel, W. Sebald, K. Pfizenmaier and H. Wajant, Enforced covalent trimerization increases the activity of the TNF ligand family members TRAIL and CD95L,, Cell Death and Differentiation, 14 (2007), 2021.  doi: 10.1038/sj.cdd.4402213.  Google Scholar

[5]

Verena Boschert, Anja Krippner-Heidenreich, Marcus Branschädel, Jessica Tepperink, Andrew Aird and Peter Scheurich, Single chain TNF derivatives with individually mutated receptor binding sites reveal differential stoichiometry of ligand receptor complex formation for TNFR1 and TNFR2,, Cellular Signalling, 22 (2010), 1088.  doi: 10.1016/j.cellsig.2010.02.011.  Google Scholar

[6]

Marcus Branschädel, Andrew Aird, Andrea Zappe, Carsten Tietz, Anja Krippner-Heidenreich and Peter Scheurich, Dual function of cysteine rich domain (CRD) 1 of TNF receptor type 1: Conformational stabilization of CRD2 and control of receptor responsiveness,, Cellular Signalling, 22 (2010), 404.  doi: 10.1016/j.cellsig.2009.10.011.  Google Scholar

[7]

Francis Ka-Ming Chan, Hyung J. Chun, Lixin Zheng, Richard M. Siegel, Kimmie L. Bui and Michael J. Lenardo, A domain in TNF receptors that mediates ligand-independent receptor assembly and signaling,, Science, 288 (2000), 2351.  doi: 10.1126/science.288.5475.2351.  Google Scholar

[8]

Lauren Clancy, Karen Mruk, Kristina Archer, Melissa Woelfel, Juthathip Mongkolsapaya, Gavin Screaton, Michael J. Lenardo and Francis Ka-Ming Chan, Preligand assembly domain-mediated ligand-independent association between TRAIL receptor 4 (TR4) and TR2 regulates TRAIL-induced apoptosis,, Proceedings of the National Academy of Sciences of the USA, 102 (2005), 18099.  doi: 10.1073/pnas.0507329102.  Google Scholar

[9]

M. A. Degli-Esposti, M. C. Dougall, P. J. Smolak, J. Y. Waugh, C. A. Smith and R. G. Goodwin, The novel receptor TRAIL-R4 induces NF-kappaB and protects against TRAIL-mediated apoptosis, yet retains an incomplete death domain,, Immunity, 7 (1997), 813.  doi: 10.1016/S1074-7613(00)80399-4.  Google Scholar

[10]

John G. Emery, Peter McDonnell, Michael Brigham Burke, Keith C. Deen, Sally Lyn, Carol Silverman, Edward Dul, Edward R. Appelbaum, Chris Eichman, Rocco DiPrinzio, Robert A. Dodds, Ian E. James, Martin Rosenberg, John C. Lee and Peter R. Young, Osteoprotegerin is a receptor for the cytotoxic ligand TRAIL,, Journal of Biological Chemistry, 273 (1998), 14363.  doi: 10.1074/jbc.273.23.14363.  Google Scholar

[11]

Matthias Grell, Eleni Douni, Harald Wajant, Matthias Löhden, Matthias Clauss, Beate Maxeiner, Spiros Georgopoulos, Werner Lesslauer, George Kollias, Klaus Pfizenmaier and Peter Scheurich, The transmembrane form of tumor necrosis factor is the prime activating ligand of the 80 kDa tumor necrosis factor receptor,, Cell, 83 (1995), 793.  doi: 10.1016/0092-8674(95)90192-2.  Google Scholar

[12]

Matthias Grell, Harald Wajant, Gudrun Zimmermann and Peter Scheurich, The type 1 receptor (CD120a) is the high-affinity receptor for soluble tumor necrosis factor,, Proceedings of the National Academy of Sciences of the United States of America, 95 (1998), 570.  doi: 10.1073/pnas.95.2.570.  Google Scholar

[13]

F. Henkler, E. Behrle, K. M. Dennehy, A. Wicovsky, N. Peters, C. Warnke, K. Pfizenmaier and H. Wajant, The extracellular domains of Fasl and Fas are sufficient for the formation of supramolecular FasL-Fas clusters of high stability,, Journal of Cell Biology, 168 (2005), 1087.  doi: 10.1083/jcb.200501048.  Google Scholar

[14]

N. Holler, A. Tardivel, M. Kovacsovics-Bankowski, S. Hertig, O. Gaide, F. Martinon, A. Tinel, D. Deperthes, S. Calderara, T. Schulthess, J. Engel, P. Schneider and E. Tschopp, Two adjacent trimeric Fas ligands are required for Fas signaling and formation of a death-inducing signaling complex,, Molecular And Cellular Biology, 23 (2003), 1428.  doi: 10.1128/MCB.23.4.1428-1440.2003.  Google Scholar

[15]

Sarah G. Hymowitz, Hans W. Christinger, Germaine Fuh, Mark Ultsch, Mark O'Connell, Robert F. Kelley, Avi Ashkenazi and Abraham M. de Vos, Triggering cell death: The crystal structure of apo2l/TRAIL in a complex with death receptor 5,, Molecular Cell, 4 (1999), 563.  doi: 10.1016/S1097-2765(00)80207-5.  Google Scholar

[16]

Sarah G. Hymowitz, Mark P. O'Connell, Mark H. Ultsch, Amy Hurst, Klara Totpal, Avi Ashkenazi, Abraham M. de Vos and Robert F. Kelley, A unique zinc-binding site revealed by a high-resolution x-ray structure of homotrimeric Apo2L/TRAIL,, Biochemistry, 39 (2000), 633.  doi: 10.1021/bi992242l.  Google Scholar

[17]

A. Krippner-Heidenreich, F. Tübing, S. Bryde, S. Willi, G. Zimmermann and P. Scheurich, Control of receptor-induced signaling complex formation by the kinetics of ligand/receptor interaction,, Journal of Biological Chemistry, 277 (2002), 44155.  doi: 10.1074/jbc.M207399200.  Google Scholar

[18]

F. C. Kull, S. Jacobs and P. Cuatrecasas, Cellular receptor for 125I-labeled tumor necrosis factor: Specific binding, affinity labeling, and relationship to sensitivity,, Proceedings of the National Academy of Sciences of the United States of America, 82 (1985), 5756.  doi: 10.1073/pnas.82.17.5756.  Google Scholar

[19]

R. Lai and T. L. Jackson, A mathematical model of receptor-mediated apoptosis: Dying to know why FasL is a trimer,, Mathematical Biosciences and Engineering, 1 (2004), 325.   Google Scholar

[20]

H. W. Lee, S. H. Lee, Y. W. Ryu, M. H. Kwon and Y. S. Kim, Homomeric and heteromeric interactions of the extracellular domains of death receptors and death decoy receptors,, Biochemical and Biophysical Research Communications, 330 (2005), 1205.  doi: 10.1016/j.bbrc.2005.03.101.  Google Scholar

[21]

Frank Mühlenbeck, Pascal Schneider, Jean-Luc Bodmer, Ralph Schwenzer, Angelika Hauser, Gisela Schubert, Peter Scheurich, Dieter Moosmayer, Jürg Tschopp and Harald Wajant, The tumor necrosis factor-related apoptosis-inducing ligand receptors TRAIL-R1 and TRAIL-R2 have distinct cross-linking requirements for Initiation of apoptosis and are non-redundant in JNK activation,, Journal of Biological Chemistry, 275 (2000), 32208.  doi: 10.1074/jbc.M000482200.  Google Scholar

[22]

Y. Mukai, T. Nakamura, M. Yoshikawa, Y. Yoshioka, S. Tsunoda, S. Nakagawa, Y. Yamagata and Y. Tsutsumi, Solution of the structure of the TNF-TNFR2 complex,, Science Signaling, 3 (2010).  doi: 10.1126/scisignal.2000954.  Google Scholar

[23]

James H. Naismith, Tracey Q. Devine, Barbara J. Brandhuber and Stephen R. Sprang, Crystallographic evidence for dimerization of unliganded tumor necrosis factor receptor,, Journal of Biological Chemistry, 270 (1995), 13303.  doi: 10.1074/jbc.270.22.13303.  Google Scholar

[24]

James H. Naismith, Tracey Q. Devine, Tadahiko Kohno and Stephen R. Sprang, Structures of the extracellular domain of the type I tumor necrosis factor receptor,, Structure, 4 (1996), 1251.  doi: 10.1016/S0969-2126(96)00134-7.  Google Scholar

[25]

P. Schneider, J. L. Bodmer, N. Holler, C. Mattmann, P. Scuderi, A. Terskikh, M. C. Peitsch and J. Tschopp, Characterization of Fas (Apo-1, CD95)-Fas ligand interaction,, Journal of Biological Chemistry, 272 (1997), 18827.  doi: 10.1074/jbc.272.30.18827.  Google Scholar

[26]

P. Schneider, N. Holler, J. L. Bodmer, M. Hahne, K. Frei, A. Fontana and J. Tschopp, Conversion of membrane-bound Fas ligand to its soluble form is associated with down regulation of its proapoptotic activity and loss of liver toxicity,, Journal of Experimental Medicine, 187 (1998), 1205.  doi: 10.1084/jem.187.8.1205.  Google Scholar

[27]

Richard M. Siegel, John K. Frederiksen, David A. Zacharias, Francis Ka-Ming Chan, Michele Johnson, David Lynch, Roger Y. Tsien and Michael J. Lenardo, Fas preassociation required for apoptosis signaling and dominant inhibition by pathogenic mutations,, Science, 288 (2000), 2354.  doi: 10.1126/science.288.5475.2354.  Google Scholar

[28]

Richard M. Siegel, Jagan R. Muppidi, Malabika Sarker, Adrian Lobito, Melinda Jen, David Martin, Stephen E. Straus and Michael J. Lenardo, SPOTS: Signaling protein oligomeric transduction structures are early mediators of death receptor-induced apoptosis at the plasma membrane,, The Journal of Cell Biology, 167 (2004), 735.  doi: 10.1083/jcb.200406101.  Google Scholar

[29]

Steven H. Strogatz, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering,'', $1^{st}$ edition, (1994).   Google Scholar

[30]

Alemseged Truneh, Sunita Sharma, Carol Silverman, Sanjay Khandekar, Manjula P. Reddy, Keith C. Deen, Megan M. McLaughlin, Srinivasa M. Srinivasula, George P. Livi, Lisa A. Marshall, Emad S. Alnemri, William V. Williams and Michael L. Doyle, Temperature-sensitive differential affinity of TRAIL for its receptors. DR5 is the highest affinity receptor, Journal of Biological Chemistry, 275 (2000), 23319.  doi: 10.1074/jbc.M910438199.  Google Scholar

[31]

A. Waage, P. Brandtzaeg, A. Halstensen, P. Kierulf and T. Espevik, The complex pattern of cytokines in serum from patients with meningococcal septic shock. association between interleukin 6, interleukin 1, and fatal outcome,, Journal of Experimental Medicine, 169 (1989), 333.  doi: 10.1084/jem.169.1.333.  Google Scholar

[32]

Harald Wajant, Dieter Moosmayer, Thomas Wüest, Till Bartke, Elke Gerlach, Ulrike Schönherr, Nathalie Peters, Peter Scheurich and Klaus Pfizenmaier, Differential activation of TRAIL-R1 and -2 by soluble and membrane TRAIL allows selective surface antigen-directed activation of TRAIL-R2 by a soluble TRAIL derivative,, Oncogene, 20 (2001), 4101.  doi: 10.1038/sj.onc.1204558.  Google Scholar

[33]

Wolfgang Walter, "Gewöhnliche Differentialgleichungen. Eine Einführung,'', $6^{th}$ edition, (1996).   Google Scholar

[34]

Liwei Wang, Jin Kuk Yang, Venkataraman Kabaleeswaran, Amanda J. Rice, Anthony C. Cruz, Ah Young Park, Qian Yin, Ermelinda Damko, Se Bok Jang, Stefan Raunser, Carol V. Robinson, Richard M. Siegel, Thomas Walz and Hao Wu, The Fas-FADD death domain complex structure reveals the basis of DISC assembly and disease mutations,, Nature Structural & Molecular Biology, 17 (2010), 1324.  doi: 10.1038/nsmb.1920.  Google Scholar

show all references

References:
[1]

B. B. Aggarwal, Signalling pathways of the TNF superfamily: A double-edged sword,, Nature Reviews Immunology, 3 (2003), 745.  doi: 10.1038/nri1184.  Google Scholar

[2]

Hyun-Jung An, Young Jin Kim, Dong Hyun Song, Beom Suk Park, Ho Min Kim, Ju Dong Lee, Sang-Gi Paik, Jie-Oh Lee and Hayyoung Lee, Crystallographic and mutational analysis of the CD40-CD154 complex and its implications for receptor activation,, Journal of Biological Chemistry, 286 (2011), 11226.  doi: 10.1074/jbc.M110.208215.  Google Scholar

[3]

David W. Banner, Allan D'Arcy, Wolfgang Janes, Reiner Gentz, Hans-Joachim Schoenfeld, Clemens Broger, Hansruedi Loetscher and Werner Lesslauer, Crystal structure of the soluble human 55 kd TNF receptor-human TNF[beta] complex: Implications for TNF receptor activation,, Cell, 73 (1993), 431.  doi: 10.1016/0092-8674(93)90132-A.  Google Scholar

[4]

D. Berg, M. Lehne, N. Müller, D. Siegmund, S. Münkel, W. Sebald, K. Pfizenmaier and H. Wajant, Enforced covalent trimerization increases the activity of the TNF ligand family members TRAIL and CD95L,, Cell Death and Differentiation, 14 (2007), 2021.  doi: 10.1038/sj.cdd.4402213.  Google Scholar

[5]

Verena Boschert, Anja Krippner-Heidenreich, Marcus Branschädel, Jessica Tepperink, Andrew Aird and Peter Scheurich, Single chain TNF derivatives with individually mutated receptor binding sites reveal differential stoichiometry of ligand receptor complex formation for TNFR1 and TNFR2,, Cellular Signalling, 22 (2010), 1088.  doi: 10.1016/j.cellsig.2010.02.011.  Google Scholar

[6]

Marcus Branschädel, Andrew Aird, Andrea Zappe, Carsten Tietz, Anja Krippner-Heidenreich and Peter Scheurich, Dual function of cysteine rich domain (CRD) 1 of TNF receptor type 1: Conformational stabilization of CRD2 and control of receptor responsiveness,, Cellular Signalling, 22 (2010), 404.  doi: 10.1016/j.cellsig.2009.10.011.  Google Scholar

[7]

Francis Ka-Ming Chan, Hyung J. Chun, Lixin Zheng, Richard M. Siegel, Kimmie L. Bui and Michael J. Lenardo, A domain in TNF receptors that mediates ligand-independent receptor assembly and signaling,, Science, 288 (2000), 2351.  doi: 10.1126/science.288.5475.2351.  Google Scholar

[8]

Lauren Clancy, Karen Mruk, Kristina Archer, Melissa Woelfel, Juthathip Mongkolsapaya, Gavin Screaton, Michael J. Lenardo and Francis Ka-Ming Chan, Preligand assembly domain-mediated ligand-independent association between TRAIL receptor 4 (TR4) and TR2 regulates TRAIL-induced apoptosis,, Proceedings of the National Academy of Sciences of the USA, 102 (2005), 18099.  doi: 10.1073/pnas.0507329102.  Google Scholar

[9]

M. A. Degli-Esposti, M. C. Dougall, P. J. Smolak, J. Y. Waugh, C. A. Smith and R. G. Goodwin, The novel receptor TRAIL-R4 induces NF-kappaB and protects against TRAIL-mediated apoptosis, yet retains an incomplete death domain,, Immunity, 7 (1997), 813.  doi: 10.1016/S1074-7613(00)80399-4.  Google Scholar

[10]

John G. Emery, Peter McDonnell, Michael Brigham Burke, Keith C. Deen, Sally Lyn, Carol Silverman, Edward Dul, Edward R. Appelbaum, Chris Eichman, Rocco DiPrinzio, Robert A. Dodds, Ian E. James, Martin Rosenberg, John C. Lee and Peter R. Young, Osteoprotegerin is a receptor for the cytotoxic ligand TRAIL,, Journal of Biological Chemistry, 273 (1998), 14363.  doi: 10.1074/jbc.273.23.14363.  Google Scholar

[11]

Matthias Grell, Eleni Douni, Harald Wajant, Matthias Löhden, Matthias Clauss, Beate Maxeiner, Spiros Georgopoulos, Werner Lesslauer, George Kollias, Klaus Pfizenmaier and Peter Scheurich, The transmembrane form of tumor necrosis factor is the prime activating ligand of the 80 kDa tumor necrosis factor receptor,, Cell, 83 (1995), 793.  doi: 10.1016/0092-8674(95)90192-2.  Google Scholar

[12]

Matthias Grell, Harald Wajant, Gudrun Zimmermann and Peter Scheurich, The type 1 receptor (CD120a) is the high-affinity receptor for soluble tumor necrosis factor,, Proceedings of the National Academy of Sciences of the United States of America, 95 (1998), 570.  doi: 10.1073/pnas.95.2.570.  Google Scholar

[13]

F. Henkler, E. Behrle, K. M. Dennehy, A. Wicovsky, N. Peters, C. Warnke, K. Pfizenmaier and H. Wajant, The extracellular domains of Fasl and Fas are sufficient for the formation of supramolecular FasL-Fas clusters of high stability,, Journal of Cell Biology, 168 (2005), 1087.  doi: 10.1083/jcb.200501048.  Google Scholar

[14]

N. Holler, A. Tardivel, M. Kovacsovics-Bankowski, S. Hertig, O. Gaide, F. Martinon, A. Tinel, D. Deperthes, S. Calderara, T. Schulthess, J. Engel, P. Schneider and E. Tschopp, Two adjacent trimeric Fas ligands are required for Fas signaling and formation of a death-inducing signaling complex,, Molecular And Cellular Biology, 23 (2003), 1428.  doi: 10.1128/MCB.23.4.1428-1440.2003.  Google Scholar

[15]

Sarah G. Hymowitz, Hans W. Christinger, Germaine Fuh, Mark Ultsch, Mark O'Connell, Robert F. Kelley, Avi Ashkenazi and Abraham M. de Vos, Triggering cell death: The crystal structure of apo2l/TRAIL in a complex with death receptor 5,, Molecular Cell, 4 (1999), 563.  doi: 10.1016/S1097-2765(00)80207-5.  Google Scholar

[16]

Sarah G. Hymowitz, Mark P. O'Connell, Mark H. Ultsch, Amy Hurst, Klara Totpal, Avi Ashkenazi, Abraham M. de Vos and Robert F. Kelley, A unique zinc-binding site revealed by a high-resolution x-ray structure of homotrimeric Apo2L/TRAIL,, Biochemistry, 39 (2000), 633.  doi: 10.1021/bi992242l.  Google Scholar

[17]

A. Krippner-Heidenreich, F. Tübing, S. Bryde, S. Willi, G. Zimmermann and P. Scheurich, Control of receptor-induced signaling complex formation by the kinetics of ligand/receptor interaction,, Journal of Biological Chemistry, 277 (2002), 44155.  doi: 10.1074/jbc.M207399200.  Google Scholar

[18]

F. C. Kull, S. Jacobs and P. Cuatrecasas, Cellular receptor for 125I-labeled tumor necrosis factor: Specific binding, affinity labeling, and relationship to sensitivity,, Proceedings of the National Academy of Sciences of the United States of America, 82 (1985), 5756.  doi: 10.1073/pnas.82.17.5756.  Google Scholar

[19]

R. Lai and T. L. Jackson, A mathematical model of receptor-mediated apoptosis: Dying to know why FasL is a trimer,, Mathematical Biosciences and Engineering, 1 (2004), 325.   Google Scholar

[20]

H. W. Lee, S. H. Lee, Y. W. Ryu, M. H. Kwon and Y. S. Kim, Homomeric and heteromeric interactions of the extracellular domains of death receptors and death decoy receptors,, Biochemical and Biophysical Research Communications, 330 (2005), 1205.  doi: 10.1016/j.bbrc.2005.03.101.  Google Scholar

[21]

Frank Mühlenbeck, Pascal Schneider, Jean-Luc Bodmer, Ralph Schwenzer, Angelika Hauser, Gisela Schubert, Peter Scheurich, Dieter Moosmayer, Jürg Tschopp and Harald Wajant, The tumor necrosis factor-related apoptosis-inducing ligand receptors TRAIL-R1 and TRAIL-R2 have distinct cross-linking requirements for Initiation of apoptosis and are non-redundant in JNK activation,, Journal of Biological Chemistry, 275 (2000), 32208.  doi: 10.1074/jbc.M000482200.  Google Scholar

[22]

Y. Mukai, T. Nakamura, M. Yoshikawa, Y. Yoshioka, S. Tsunoda, S. Nakagawa, Y. Yamagata and Y. Tsutsumi, Solution of the structure of the TNF-TNFR2 complex,, Science Signaling, 3 (2010).  doi: 10.1126/scisignal.2000954.  Google Scholar

[23]

James H. Naismith, Tracey Q. Devine, Barbara J. Brandhuber and Stephen R. Sprang, Crystallographic evidence for dimerization of unliganded tumor necrosis factor receptor,, Journal of Biological Chemistry, 270 (1995), 13303.  doi: 10.1074/jbc.270.22.13303.  Google Scholar

[24]

James H. Naismith, Tracey Q. Devine, Tadahiko Kohno and Stephen R. Sprang, Structures of the extracellular domain of the type I tumor necrosis factor receptor,, Structure, 4 (1996), 1251.  doi: 10.1016/S0969-2126(96)00134-7.  Google Scholar

[25]

P. Schneider, J. L. Bodmer, N. Holler, C. Mattmann, P. Scuderi, A. Terskikh, M. C. Peitsch and J. Tschopp, Characterization of Fas (Apo-1, CD95)-Fas ligand interaction,, Journal of Biological Chemistry, 272 (1997), 18827.  doi: 10.1074/jbc.272.30.18827.  Google Scholar

[26]

P. Schneider, N. Holler, J. L. Bodmer, M. Hahne, K. Frei, A. Fontana and J. Tschopp, Conversion of membrane-bound Fas ligand to its soluble form is associated with down regulation of its proapoptotic activity and loss of liver toxicity,, Journal of Experimental Medicine, 187 (1998), 1205.  doi: 10.1084/jem.187.8.1205.  Google Scholar

[27]

Richard M. Siegel, John K. Frederiksen, David A. Zacharias, Francis Ka-Ming Chan, Michele Johnson, David Lynch, Roger Y. Tsien and Michael J. Lenardo, Fas preassociation required for apoptosis signaling and dominant inhibition by pathogenic mutations,, Science, 288 (2000), 2354.  doi: 10.1126/science.288.5475.2354.  Google Scholar

[28]

Richard M. Siegel, Jagan R. Muppidi, Malabika Sarker, Adrian Lobito, Melinda Jen, David Martin, Stephen E. Straus and Michael J. Lenardo, SPOTS: Signaling protein oligomeric transduction structures are early mediators of death receptor-induced apoptosis at the plasma membrane,, The Journal of Cell Biology, 167 (2004), 735.  doi: 10.1083/jcb.200406101.  Google Scholar

[29]

Steven H. Strogatz, "Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering,'', $1^{st}$ edition, (1994).   Google Scholar

[30]

Alemseged Truneh, Sunita Sharma, Carol Silverman, Sanjay Khandekar, Manjula P. Reddy, Keith C. Deen, Megan M. McLaughlin, Srinivasa M. Srinivasula, George P. Livi, Lisa A. Marshall, Emad S. Alnemri, William V. Williams and Michael L. Doyle, Temperature-sensitive differential affinity of TRAIL for its receptors. DR5 is the highest affinity receptor, Journal of Biological Chemistry, 275 (2000), 23319.  doi: 10.1074/jbc.M910438199.  Google Scholar

[31]

A. Waage, P. Brandtzaeg, A. Halstensen, P. Kierulf and T. Espevik, The complex pattern of cytokines in serum from patients with meningococcal septic shock. association between interleukin 6, interleukin 1, and fatal outcome,, Journal of Experimental Medicine, 169 (1989), 333.  doi: 10.1084/jem.169.1.333.  Google Scholar

[32]

Harald Wajant, Dieter Moosmayer, Thomas Wüest, Till Bartke, Elke Gerlach, Ulrike Schönherr, Nathalie Peters, Peter Scheurich and Klaus Pfizenmaier, Differential activation of TRAIL-R1 and -2 by soluble and membrane TRAIL allows selective surface antigen-directed activation of TRAIL-R2 by a soluble TRAIL derivative,, Oncogene, 20 (2001), 4101.  doi: 10.1038/sj.onc.1204558.  Google Scholar

[33]

Wolfgang Walter, "Gewöhnliche Differentialgleichungen. Eine Einführung,'', $6^{th}$ edition, (1996).   Google Scholar

[34]

Liwei Wang, Jin Kuk Yang, Venkataraman Kabaleeswaran, Amanda J. Rice, Anthony C. Cruz, Ah Young Park, Qian Yin, Ermelinda Damko, Se Bok Jang, Stefan Raunser, Carol V. Robinson, Richard M. Siegel, Thomas Walz and Hao Wu, The Fas-FADD death domain complex structure reveals the basis of DISC assembly and disease mutations,, Nature Structural & Molecular Biology, 17 (2010), 1324.  doi: 10.1038/nsmb.1920.  Google Scholar

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Scipio Cuccagna, Masaya Maeda. A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020450

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Xin-Guang Yang, Lu Li, Xingjie Yan, Ling Ding. The structure and stability of pullback attractors for 3D Brinkman-Forchheimer equation with delay. Electronic Research Archive, 2020, 28 (4) : 1395-1418. doi: 10.3934/era.2020074

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Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020316

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Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020317

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Shuang Chen, Jinqiao Duan, Ji Li. Effective reduction of a three-dimensional circadian oscillator model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020349

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Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020339

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Yolanda Guerrero–Sánchez, Muhammad Umar, Zulqurnain Sabir, Juan L. G. Guirao, Muhammad Asif Zahoor Raja. Solving a class of biological HIV infection model of latently infected cells using heuristic approach. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020431

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