Unreasonable implications of reasonable idiotypic network assumptions. (English) Zbl 0668.92004
We first analyse a simple symmetric model of the idiotypic network. In the model idiotypic interactions regulate B cell proliferation. Three non-idiotypic processes are incorporated: (1) influx of newborn cells; (2) turnover of cells; (3) antigen. Antigen also regulates proliferation.
We next complicate this model by incorporating antibody production. Although this “antibody” model statically accounts for the same set of equilibrium points, it dynamically fails to account for state switching (i.e. memory). The switching behaviour is disturbed by the autonomous slow decay of the (long-lived) antibodies. After antigenic triggering the system now performs complex cyclic behaviour. Finally, it is suggested that (idiotypic) formation of antibody complexes can play only a secondary role in the network.
In conclusion, our results cast doubt on the functional role of a profound idiotypic network. The network fails to account for proliferation regulation, and if it accounts for memory phenomena, it “explodes” upon the first encounter with antigen due to extensive percolation.
We next complicate this model by incorporating antibody production. Although this “antibody” model statically accounts for the same set of equilibrium points, it dynamically fails to account for state switching (i.e. memory). The switching behaviour is disturbed by the autonomous slow decay of the (long-lived) antibodies. After antigenic triggering the system now performs complex cyclic behaviour. Finally, it is suggested that (idiotypic) formation of antibody complexes can play only a secondary role in the network.
In conclusion, our results cast doubt on the functional role of a profound idiotypic network. The network fails to account for proliferation regulation, and if it accounts for memory phenomena, it “explodes” upon the first encounter with antigen due to extensive percolation.
MSC:
| 92Cxx | Physiological, cellular and medical topics |
Keywords:
immune network; simple symmetric model; idiotypic network; idiotypic interactions; B cell proliferation; non-idiotypic processes; influx of newborn cells; turnover of cells; antigen; antibody production; state switching; antigenic triggering; cyclic behaviour; memory phenomenaReferences:
| [1] | Abbas, A. K. 1988. ”A Reassessment of the Mechanisms of Antigen-Specific T-cell-Dependent B-cell Activation.”Immunol. Today 9, 89–94. · doi:10.1016/0167-5699(88)91271-6 |
| [2] | Berek, C., G. M. Griffiths and C. Milstein. 1985. ”Molecular Events During Maturation of the Immune Response to Oxazolone.”Nature 316, 314–318. · doi:10.1038/316412a0 |
| [3] | Bernable, R. R., A. Coutinho, C. Martinez-A and P. A. Cazenave. 1981. ”Immune Networks. Frequencies of Antibody- and Idiotype-Producing B cell Clones in Various Steady States.”J. exp. Med. 154, 552–556. · doi:10.1084/jem.154.2.552 |
| [4] | Bona, C. A. and B. Pernis 1984. ”Idiotypic Networks.” InFundamental Immunology, W. E. Paul (Ed.), pp. 577–592. New York: Raven Press. |
| [5] | Cohn, M. 1986. ”The Concept of Functional Idiotypic Network for Immune Regulation Mocks all and Comforts None.”Ann. Immunol. (Inst. Pasteur) 137C, 64–76. · doi:10.1016/S0771-050X(86)80007-9 |
| [6] | De Boer, R. J. 1983. RIND: Great Integrator Differential Equations. Bioinformatics Group, University of Utrecht, The Netherlands. |
| [7] | –. 1988. ”Symmetric Idiotypic Networks: Connectance and Switching, Stability, and Suppression.” InTheoretical Immunology, A. S. Perelson (Ed.), Part Two, pp. 265–289. SFI Studies in the Science of Complexity, Vol. III. Reading, MA: Addison-Wesley. |
| [8] | –. 1989. ”Information Processing in Immune Systems: Clonal Selection versus Idiotypic Network Models.” InTheoretical Models for Cell to Cell Signalling, A. Goldbeter (Ed.). London: Academic Press. |
| [9] | – and P. Hogeweg. 1986. ”Interactions between Macrophages and T-lymphocytes: Tumor Sneaking Through Intrinsic to Helper T cell Dynamics.”J. theor. Biol. 120, 331–351. · doi:10.1016/S0022-5193(86)80205-3 |
| [10] | – and –. 1987a. ”Immunological Discrimination Between Self and Non-Self by Precursor Depletion and Memory Accumulation.”J. theor. Biol.,124, 343–369. · doi:10.1016/S0022-5193(87)80121-2 |
| [11] | – and –. 1987b. ”Self-Nonself Discrimination due to Immunological Nonlinearities: the Analysis of a Series of Models by Numerical Methods.”IMA J. Math. Appl. Med. Biol. 4, 1–32. · Zbl 0613.92008 · doi:10.1093/imammb/4.1.1 |
| [12] | – and –. 1988. ”Memory but no Suppression in Low-Dimensional Symmetric Idiotypic Networks.”Bull. math. Biol. 51, 0. |
| [13] | De Boer, R. J. and P. Hogeweg. Submitted ”Idiotypic Network Models Incorporating T-B cell Cooperation: Conditions for Percolation.” |
| [14] | Early, P., H. Huang, M. Davis, K. Calame and L. Hood. 1980. ”An Immunoglobulin Heavy Chain Variable Region Gene is Generated from Three Segments of DNA:V H,D andJ H.”Cell 19, 981–992. · doi:10.1016/0092-8674(80)90089-6 |
| [15] | Eichmann, K. 1974. ”Idiotypic Suppression–I. Influence of the Dose and of the Effector Functions of Anti-Idiotypic Antibody on the Production of an Idiotype.”Eur. J. Immunol. 4, 296–302. · doi:10.1002/eji.1830040413 |
| [16] | – and K. Rajewsky. 1975. ”Induction of T and B cell Immunity by Anti-Idiotypic Antibody.”Eur. J. Immunol. 5, 661–666. · doi:10.1002/eji.1830051002 |
| [17] | Erdos, P. and A. Renyi. 1959. ”On the Random Graphs 1, Vol. 6.” Institute of Mathematics University of DeBreceniens, Debrecar, Hungary. |
| [18] | Erdos, P. and A. Renyi, 1960. ”On the Random Graphs, Publ. No. 5.” Mathematics Institute of the Hungarian Academy of Science. |
| [19] | Farmer, J. D., N. H. Packard and A. S. Perelson. 1986. ”The Immune System, Adaptation, and Machine Learning.”Physica 22D, 187–204. |
| [20] | Goldstein, B. 1988. ”Desensitization, histamine release and the aggregation ofIgE on human basophils.” InTheoretical Immunology, A. S. Perelson (Ed.), Part One pp. 3–40. SFI Studies in the Science of Complexity, Vol. II. Reading, MA: Addison-Wesley. |
| [21] | Gottwald, B. A. and G. Wanner. 1981. ”A Reliable Rosenbrock Integrator for Stiff Differential Equations.”Computing 26, 355–360. · Zbl 0451.65056 · doi:10.1007/BF02237954 |
| [22] | Gray, D. 1988. ”Is the Survival of Memory B cells Dependent on the Oerisistence of Antigen?” InAdv. Exp. Med. Biol., in press. |
| [23] | Grossman, Z. 1982. ”Recognition of Self and Regulation of Specificity at the Level of Cell Populations.”Immunol. Rev. 79, 119–138. · doi:10.1111/j.1600-065X.1984.tb00490.x |
| [24] | Gunther, N. and G. W. Hoffmann. 1982. ”Qualitative Dynamics of a Network Model of Regulation of the Immune System: a Rationale for theIgM toIgG switch.”J. theor. Biol. 94, 815–855. · doi:10.1016/0022-5193(82)90080-7 |
| [25] | Hardt, D. A., A. L. Wang, L. L. Pawlak and A. Nisonoff. 1972. ”Suppression of Idiotypic Specificities in Adult Mice by Administration of Anti-Idiotypic Antibody.”J. exp. Med. 135, 1293–1299. · doi:10.1084/jem.135.6.1293 |
| [26] | Hebb, D. O. 1949.The Organization of Behavior. New York: Wiley. |
| [27] | Hoffmann, G. W. 1975. ”A Theory of Regulation and Self Non-Self Discrimination in an Immune Network.”Eur. J. Immunol. 5, 638–647. · doi:10.1002/eji.1830050912 |
| [28] | – 1979. ”A Mathematical Model of the Stable States of a Network Theory of Self-Regulation.” InSystems Theory in Immunology, C. Bruni, G. Doria, G. Koch and R. Strom (Eds), Vol. 32, pp. 239–257. Lecture Notes in Biomathematics. Berlin: Springer. |
| [29] | – 1980. On Network Theory and H-2 Restriction.” InComtemporary Topics Immunobiology, N. L. Warner (Ed.), Vol. 11, pp. 185–226. New York: Plenum Press. |
| [30] | – 1986. ”A Neural Network Model Based on the Analogy with the Immune System.”J. theor. Biol. 122, 33–67. · doi:10.1016/S0022-5193(86)80224-7 |
| [31] | Holland, J. H. 1986. ”Escaping Brittleness: the Possibilities of General Purpose Learning Algorithms Applied to Parallel Rule-Based Systems.” InMachine Learning: An Artificial Intelligence Approach, R. S. Michalski, J. G. Carbonell and T. M. Mitchell (Eds), Vol. II, pp. 593–623. Los Altos: Morgan Kauffman. |
| [32] | Holmberg, D., S. Forsgen, F. Ivars and A. Coutinho. 1984. ”Reactions AmongIgM Antibodies Derived from Normal Neonatal Mice.”Eur. J. Immunol. 14, 435–441. · doi:10.1002/eji.1830140510 |
| [33] | –, G. Wennerstrom, L. Andrade and A. Coutinho. 1986. ”The High Idiotypic Connectivity of ”Natural” Newborn Antibodies is not found in the Adult Mitogen-Reactive B Cell Repertoires.”Eur. J. Immunol. 16, 82–87. · doi:10.1002/eji.1830160116 |
| [34] | – 1987. ”High Connectivity, Natural Antibodies Preferentially use 7183 and QUPC 52V H Families”Eur. J. Immunol. 17, 399–403. · doi:10.1002/eji.1830170315 |
| [35] | Hopfield, J. J. and D. W. Tank. 1986. ”Computing with Neural Circuits: a Model.”Science 233, 625–633. · Zbl 1356.92005 · doi:10.1126/science.3755256 |
| [36] | Irvine, D. H. and M. A. Savageau. 1985a. ”Network Regulation of the Immune Response: Alternative Control Points for Suppressor Modulation of Effector Lymphocytes.”J. Immunol. 134, 2100–2116. |
| [37] | Jerne, N. K. 1974. ”Towards a Network Theory of the Immune System.”Ann. Immunol. (Inst. Pasteur) 125C, 373–389. |
| [38] | – 1984. ”Idiotypic Networks and Other Preconceived Ideas.”Immunol. Rev. 79, 5–24. · doi:10.1111/j.1600-065X.1984.tb00484.x |
| [39] | Kauffman, S. A. 1986. ”Autocatalytic Sets of Proteins.”J. theor. Biol. 119, 1–24. · doi:10.1016/S0022-5193(86)80047-9 |
| [40] | Langman, R. E. and M. Cohn. 1986. ”The ’Complete’ Idiotypic Network is an Absurd Immune System.”Immunol. Today 7, 100–101. · doi:10.1016/0167-5699(86)90147-7 |
| [41] | Lawler, A. M., P. Sin and P. J. Gearhart. 1987. ”Adult B-cell Repertoire is Biased Toward Two Heavy-Chain Variable-Region Genes that Rearrange Frequently in Fetal pre-B cells.”Proc. Natn. Acad. Sci. U.S.A. 84, 2454–2458. · doi:10.1073/pnas.84.8.2454 |
| [42] | Martinez-A, C., P. Pereira, M. L. Toribo, M. A. R. Marcos, A. Bandeira, A. De la Hera, C. Marquez, P-A. Cazenave and A. Coutinho. 1988. ”The Participation of B cells and Antibodies in the Selection and Maintenance of T cell Repertoires.”Immunol. Rev. 101, 191–215. · doi:10.1111/j.1600-065X.1988.tb00738.x |
| [43] | Melchers, F. and J. Anderson. 1986. ”Factors Controlling the B-cell Cycle.”Ann. Rev. Immunol. 4, 13–36. · doi:10.1146/annurev.iy.04.040186.000305 |
| [44] | NAG. 1984. Numerical Algorithms Group, Oxford, U.K. |
| [45] | Novotny, J., M. Handschumacher and R. E. Bruccoleri. 1987. ”Protein Antigenicity: a Static Surface Property.”Immunol. Today 8, 26–31. · doi:10.1016/0167-5699(87)90828-0 |
| [46] | Pereira, P., L. Forni, E. L. Larsson, M. Cooper, C. Heusser and A. Coutinho. 1986. ”Autonomous Activation of B and T cells in Antigen-Free Mice.”Eur. J. Immunol. 16, 685–688. · doi:10.1002/eji.1830160616 |
| [47] | Perelson, A. S. 1988. ”Towards a Realistic Model of the Immune Network.” InTheoretical Immunology, A. S. Perelson (Ed.), Part Two, pp. 377–401. SFI Studies in the Science of Complexity Vol. III. Reading, MA: Addison-Wesley. |
| [48] | – 1984. ”Some Mathematical Models of Receptor Clustering by Multivalent Ligands.” InCell Surface Dynamics: Concepts and Models, A. S. Perelson, C. DeLisi, and F. W. Wiegel (Eds), pp. 223–275. New York: Marcel Dekker. |
| [49] | Pollok, B. A., A. S. Bhown and J. F. Kearny. 1982. ”Structural and Biological Properties of a Monoclonal Auto-Anti-(Anti-idiotype) Antibody.”Nature 299, 447–449. · doi:10.1038/299447a0 |
| [50] | Trenker, E. and R. Riblet. 1975. ”Induction of Antiphosorylcholine Antibody Formation by Anti-Idiotypic Antibodies.”J. exp. Med. 142, 1121–1132. · doi:10.1084/jem.142.5.1121 |
| [51] | Segel, L. A. and A. S. Perelson. 1988. ”Computation in Shape Space: A New Approach to Immune Network Theory.” InTheoretical Immunology, A. S. Perelson (Ed.), Part Two, pp. 321–343. SFI Studies in the Science of Complexity, Vol. III. Reading, MA: Addison-Wesley. |
| [52] | Segel, L. A. and A. S. Perelson 1989. ”Explanation of a Paradoxical Instability Caused by Relatively Short Range Inhibition.”SIAM J. appl. Math, in press. · Zbl 0693.92011 |
| [53] | Urbain, J. 1986. ”Idiotypic Networks: a Noisy Background or a Breakthrough in Immunological Thinking? The Broken Mirror Hypothesis.”Ann. Immunol. (Inst. Pasteur),137C, 57–64. · doi:10.1016/S0771-050X(86)80006-7 |
| [54] | Vakil, M. and J. F. Kearny. 1986. ”Functional Characterization of Monoclonal Auto-Anti-Idiotype Antibodies Isolated from the Early B cell Repertorie of BALB/c Mice.”Eur. J. Immunol. 16, 1151–1158. · doi:10.1002/eji.1830160920 |
| [55] | Varela, F. J., A. Coutinho, B. Dupire and N. N. Vaz. 1988. ”Cognitive Networks: Immune, Neural, and Otherwise.” InTheoretical Immunology, A. S. Perelson (Ed.), Part Two, pp. 359–375. SFI Studies in the Science of Complexity, Vol. III. Reading, MA: Addison-Wesley. |
| [56] | Vieira, P. and K. Rajewsky. 1988. ”The Half-Lives of Serum Immunologlobulins in Adult Mice.”Eur. J. Immunol. 18, 313–316. · doi:10.1002/eji.1830180221 |
| [57] | Weisbuch, G. 1989. Proceedings of ”Theories of Immune Networks” Workshop. Jerusalem, May 1988. InLecture Notes in Biomathematics, in press. |
| [58] | Wikler, M., J-D. Franssen, C. Collignon, O. Leo, B. Mariamé, P. Van de Walle, D. De Groote and J. Urbain. 1979. ”Idioptypic Regulation of the Immune System.”J. exp. Med. 150, 184–195. · doi:10.1084/jem.150.1.184 |
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.
