Abstract
The concept of shape space proposed by Perelson and Oster (1979,J. Theor. Biol. 81, 645–670) has been a useful tool for theoretical immunologists, who have invoked it to model idiotypic binding, which plays a significant role in mathematical models of immune networks. The actual construction of such a space from its definition requires specialized experimental information, which is not completely available. In this article, we discuss, with illustrative examples, how graphical representations similar to the idea of shape space can be derived by analyzing real affinity matrices, and the relative merits of such representations to approximations that might be obtained by the approach of Perelson and Oster. We also give directions for future research with a view toward applications.
Similar content being viewed by others
References
Borg, I. and J. Lingoes. 1987.Multidimensional Similarity Structural Analysis. New York: Springer.
B-Rao, C. and K. C. Majumdar, 1996. Map-like representation of phylogenetic relationships: application to tilapiine fish. Unpublished manuscript.
Carneiro, J. and J. Stewart. 1994. Rethinking “shape space”: evidence from simulated docking suggests that steric shape complementarity is not limiting for antibody-antigen recognition and idiotypic interactions.J. Theor. Biol. 169, 391–402.
De Boer, R., P. Hogeweg and A. Perelson. 1992a. Growth and recruitment in the immune network. InTheoretical and Experimental Insight into Immunology, A. S. Perelson and G. Weisbuch (Eds), NATO ASI Series, Vol. H66, pp. 223–247. Berlin: Springer.
De Boer, R. J., L. A. Segel and A. S. Perelson.1992b. Pattern formation in one- and two-dimensional shape-space models of the immune system.J. Theor. Biol. 155, 295–333.
Grandien, A., Y. Modigliani, A. Freitas, J. Andersson and A. Coutinho. 1994. Positive and negative selection of antibody repertoires during B cell differentiation.Immunol. Rev. 137, 53–89.
Heiser, W. 1981. Unfolding analysis of proximity data. Doctoral thesis, Rijksuniversiteit, Leiden.
Hsu, D.-H. 1988. Doctoral thesis, University of California, Los Angeles.
Kearney, J. F., M. Vakil and N. Nicholson. 1987. Non randomV H gene expression and idiotype-anti-idiotype expression on early B cells. InEvolution and Vertebrate Immunity: The Antigen Receptor and MHC Gene Families, G. Kelsoe and D. Schulze (Eds), pp. 175–190. Austin TX: Texas University Press.
Meulman, J. 1986.A Distance Approach to Nonlinear Multivariate Analysis, Leiden: DSWO Press.
Percus, J. 1988. Polydisperity in immune networks. InTheoretical Immunology, Part Two, A. S. Perelson (Ed.)SFI Studies in the Science of Complexity, Vol III, pp. 345–358. Redwood City, CA: Addison-Wesley.
Perelson, A. S. and G. Oster. 1979. Theoretical studies of clonal selection: minimal antibody repertoire size and reliability of self-non-self discrimination.J. Theor. Biol. 81, 645–670.
Roitt, I. M. 1991.Essential Immunology. Boston, MA: Blackwell.
Seber, G. A. F. 1984.Multivariate Observations. New York: Wiley.
Segel, L. A. and A. S. Perelson. 1988. Computations in shape space: a new approach to immune network theory. InTheoretical Immunology, Part Two, A. S. Perelson (Ed),SFI Studies in the Science of Complexity, Vol III, pp. 321–343. Redwood City, CA: Addison-Wesley.
Stewart, J. and F. Varela. 1989. Exploring the meaning of connectivity in the immune network.Immunol. Rev. 110, 37–61.
Stewart, J. and F. J. Varela, 1991. Morphogenesis in shape space: elementary metadynamics of immune networks.J. Theor. Biol. 153, 477–498.
Sulzer, B., J. L. van Hemmen and U. Behn. 1994. Central immune system, the self and autoimmunity.Bull. Math. Biol. 56, 1009–1040.
Tarantola, A. 1987.Inverse Problem Theory: Methods for Data Fitting and Model Parameter Estimation. Amsterdam: Elsevier.
Weinand, R. G. 1990. Somatic mutation, affinity maturation and the antibody repertoire: a computer model.J. Theor. Biol. 143, 343–382.
Weinand, R. G. 1991. Somatic mutation and the antibody repertoire: a computational model of shape space. InMolecular Evolution on Rugged Landscapes, A. S. Perelson and S. A. Kauffman (Eds).SFI Studies in the Science of Complexity, Vol IX, pp. 215–236. Redwood City, CA: Addison-Wesley.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
B-Rao, C., Stewart, J. Inverse analysis of empirical matrices of idiotypic network interactions. Bltn Mathcal Biology 58, 1123–1153 (1996). https://doi.org/10.1007/BF02458386
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02458386