Abstract
We study the evolution of genetic sequences by means of a coupled map lattice model. Mutations generate short range interactions while ecological constraints define a network with long range interactions. Experimental information and trends from the statistical analysis of the sequence composition are incorporated in the modelling allowing for evolution fitness criteria. Concepts such as quasi-species and error threshold emerge in a natural way. The model gives qualitative predictions regarding the stability under mutations of AIDS RNA sequences which are corroborated experimentally. The relation of the model with other formalisms used in the study of biological networks such as neural nets is pointed out.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bunimovich, L.A., Lambert, A. and Lima, R.: 1990, ‘The emergence of coherent structures in coupled map lattices’ J. Stat. Phys., 61, 253.
Cocho, G. and Martinez-Mekler, G.: 1991, ‘On a coupled map lattice formulation of the evolution of genetic sequences’ Physica D, 51, 119.
Cocho, G. and Rius, J.L.: 1989, ‘Discrete aspects of morphogenesis and gene dynamics’, Theoretical Biology, B. Goodwin and P. Saunders (eds.), Edinburgh University Press, 177.
Cocho, G., Rius, J.L., Medrano, L. and Miramontes, P.: 1990, ‘Structural constraints, DNA periodicities, and gene dynamics’, Quasicrystals and Incommensurate Structures in Condensed Matter, M. José Yacamán, D. Romeu, V. Castaño and A. Gómez (eds.) World Scientific, page 465.
Cocho, G. and Miramontes, P.: 1990, ‘Physico-chemical constraints in the modelling of gene dynamics’, Proceedings of Workshop on Complexity and Evolution, Les Houches, March 1990, N. Boccara, R. Livi, J.P. Nadal and N. Packard (eds), in press.
Crutchfield, J.P. and Kaneko, K.: 1988, ‘Are attractors relevant to turbulence’, Phys. Rev. Lett., 60, 2715.
Eigen, M. and Schuster, P.: 1977, ‘The hypercycle, a principle of natural self-organization’ Naturwissenschaften, 64, 541.
Eigen, M.: 1986, ‘The physics of molecular evolution’ Chemical Scripta, 26 B, 10.
Schuster, P.: 1986, The physical basis of molecular evolution’ Chemical Scripta, 26B, 27.
Kaneko, K.: 1984, ‘Period doubling of kink-antikink patterns, quasi-periodicity in antiferro-like structures and spatial intermittency in coupled logistic lattice’, Prog. Theor. Phys., 72, 480.
Kaneko, K.: 1986, ‘Lyapunov analysis and information flow in coupled map lattices’, Physica, D23, 436.
Kaneko, K.: 1989, ‘Pattern dynamics in spatio-temporal chaos’, Physica, D34, 1.
Kaneko, K.: 1990, ‘Clustering, coding, switching, hierarchical ordering and control in network of chaotic elements’, Physica, D41, 137.
Kaneko, K. (ed.): 1992, ‘Chaos focus issue on coupled map lattices’, Chaos, 2, 279.
Kauffman, S.: 1989, ‘Adaptation on rugged fitness landscapes’, Lectures in the Sciences of Complexity, SFI Studies in the Sciences of Complexity, Lectures Vol. I, D. Stein (ed.) Addison-Weseley, Redwood City, California, 527.
Kauffman, S. and Johnsen, S.: 1990, ‘Coevolution to the edge of chaos: coupled fitness landscapes, poised states, and coevolutionary avalanches’, Santa Fe Institute, preprint.
Kauffman, S.: 1991, ‘Antichaos and Adaptation’, Scientific American. 265(2), 64.
Livi, R., Martinez-Mekler, G. and Ruffo, S.: 1990, ‘Periodic orbits and long transients in coupled map lattices’, Physica D, 45, 452.
Bunimovich, L.A., Livi, R., Martinez-Mekler, G. and Ruffo, S.: 1992, ‘Coupled trivial maps’, Chaos, 2, 283.
Martínez-Mekler, G., Cocho, G., Gelover A. and Bulajich, R.: 1992, ‘Modelling genetic volution with coupled map lattices’, Rev. Mex. Fis., 38, Suplemento 1, 127.
May, R.: 1976, ‘Simple mathematical models with very complicated dynamics’, Nature, 261, 459.
Miramontes, P.: 1992, Un Esquema de Autómata Celular como Modelo Matemético de la Evolución de los Acidos Nucleicos, Ph.D. thesis, Facultad de Ciencias, UNAM.
Schuster, P.: 1991a, ‘Optimization of RNA structure and properties’, Molecular Evolution on Rugged Landscapes: Proteins, RNA and the Immune System, SFI Studies in the Sciences of Complexity, Proceedings Vol. 9, A.S. Perelson and S.A. Kauffman (eds.) Addison-Wesley, Redwood City, California, 47.
Schuster, P.: 1991b, ‘New scenarios for evolution’, Bulletin of the Santa Fe Institute, 6, 4.
Solé, R.V. and Vails, J.: 1991, ‘Order and chas in a 2D Lotka — Volterra coupled map lattice’, Phys. Lett., 153, 330.
Sole, R.V. and Vails, J.: 1992, ‘Nonequilibrium dynamics in lattice ecosystems: chaotic stability and dissapative structures’, Chaos, 2, 387.
Starcich, R.B., Hahn, B.H., Shaw, G.M., McNeely, P.D., Modrow, S., Wolf, H., Parks, E.S., Parks, W.P., Josephs, S.F., Gallo, R.C., et. al.: 1986, ‘Identification and characterization of conserved and variable regions in the envelop gene of HTLV-III/LAV, the retrovirus of AIDS’, Cell, 45, 637.
Stryer, L.: 1989, Molecular Design of Life, W.H. Freeman and Company, New York.
Waller, I. and Kapral, R.: 1984, ‘Spatial and temporal structure in systems of coupled nonlinear oscillatorors’, Phys. Rev., A30, 2047.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Cocho, G., Santiago, A.G., Martínez-Mekler, G. (1993). An Interplay Between Local and Global Dynamics in Biological Networks: The Case of Genetic Sequences. In: Boccara, N., Goles, E., Martinez, S., Picco, P. (eds) Cellular Automata and Cooperative Systems. NATO ASI Series, vol 396. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1691-6_8
Download citation
DOI: https://doi.org/10.1007/978-94-011-1691-6_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4740-1
Online ISBN: 978-94-011-1691-6
eBook Packages: Springer Book Archive