Abstract
The current status of mathematical models of biological systems is reviewed. Advances in supercomputer hardware allows more complex models to be constructed. The new generation of microcomputers are quite adequate for many computer simulations of biological systems. A theory of modeling is being developed to improve the relationship between the real biological system and the model. Deterministic models, stochastic models and applications of control theory and optimization methods are discussed. Examples given include models of molecular structure, of experimental techniques, and of biochemical reactions. It is recommended that experimental biologists consider the use of microcomputers to model the system under study as a part of their research program.
Similar content being viewed by others
References
Sampson JR: Biological Information Processing: Current Theory and Computer Simulation. Wiley-Interscience, New York, 1984.
Segel LA: Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, Cambridge, 1980.
Crecine JP: The next generation of personal computers. Science 231:931–943, 1986.
Zeigler BP: Theory of Modelling and Simulation. Wiley-Interscience, New York, 1976.
Lumb JR, MacFarland B: A computer simulation of the production of lymphocytes in the thymus: A preliminary report. J Reticuloendo Soc 12:80–89, 1972.
Lumb JR: A regenerating computer model of the thymus. Comput Biomed Res 8:379–392, 1975.
Zeigler BP: Structuring the organization of partial models. Int J Gen Systems 4:81–88, 1978.
Zeigler BP: Multi-level multi-formalism modeling, an ecosystem example. In: Halfon E (ed). Theoretical Ecosystems. Academic Press, New York, 1979, pp 17–54.
Zeigler BP: Simplification of biochemical reaction systems. In: Segel LA (ed). Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, Cambridge, 1980, pp 112–145.
Zeigler BP: Multifacetted Modeling and Discrete Event Simulation. Academic Press, New York, 1984.
Bell GI: Mathematical model of clonal selection and antibody production. J Theoret Biol 29:191–232, 1970.
Bell GI: Mathematical model of clonal selection and antibody production, II. J Theoret Biol 33:339–378, 1971.
Bell GI: Mathematical model of clonal selection and antibody production, III. The cellular basis of immunological paralysis. J Theoret Biol 33:379–398, 1974.
Lumb JR, Morrison LM: A computer simulation of the cellular kinetics of the thymus-independent humoral immune response. Comput Biomed Res 14:220–231, 1981.
Perlson AM: Chaos. In: Segel LA (ed). Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, Cambridge, 1980, pp 349–364.
DeLisi C, Hiernaux JRJ: Regulation of Immune Response Dynamics. CRC Press, Boca Raton, FL, 1982.
Levinthal C: Molecular model-building by computer. Sci Am 214(6):42–52, 1966.
Namba K, Caspar DAD, Stubbs GJ: Computer graphics representation of levels of organization in tobacco mosaic virus structure. Science 227:773–776, 1985.
Thiebaux HJ, Pattee HH: Statistical studies of protein sequences: Pair and triplet analysis in helical conformations. J Theoret Biol 17:121–135, 1967.
Valiquette G, Zimmermann EA, Roberts JL: mRNA sequence predictions from homologous protein sequences. J Theoret Biol 112:445–458, 1985.
Klopman G, Rosenkranz H: Structural requirements for the mutagenicity of environmental nitroarenes. Mut Res 126:227–238, 1984.
Klopman G, Contreras R: Use of artificial intelligence in structure-activity correlations of anticonvulsant drugs. Mol Pharm 27:86–93, 1985.
Klopman G, Macina OT: Use of the computer automated structure evaluation program in determining quantitative structure-activity relationships within hallucinogenic phenylalkylamines. J Theoret Biol 113:637–648, 1985.
Bier M, Palusinski OA, Mosher RA, Saville DA: Electrophoresis: Mathematical modeling and computer simulation. Science 219:1281–1287, 1983.
Perlson AM: Theory of immunoassays. In: Segel LA (ed). Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, Cambridge, 1980, pp 423–439.
Priban I: Models in medicine. Science J 1968(6):61–67, 1968.
Grodins FS: General applicability of control theory to biological systems with some exemplification in the respiratory system. Fed Proc 28:47–51, 1969.
Rapp PE: Biological application of control theory. In: Segel LA (ed). Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, Cambridge, 1980, pp 146–247.
Perlson AM: Applications of control theory in immunology. In: Segel LA (ed). Mathematical Models in Molecular and Cellular Biology. Cambridge University Press, Cambridge, 1980, pp 404–422.
Brady RM: Optimization strategies gleaned from biological evolution. Nature 317:804–806, 1985.
Garfinkel D, Garfinkel L, Pring M, Green S, Chance B: Computer application to biochemical kinetics. Ann Rev Biochem 39:473–498, 1970.
Garfinkel D, Kohn MC: In: Jacobus WE, Ingwall JS (eds). Heart Creatine Kinase. Williams and Wilkins, Baltimore, 1980.
Palsson BO, Lightfoot EN: Mathematical modeling of dynamics and control in metabolic networks. I. On MichaelisMenten kinetics. J Theoret Biol 111:273–302, 1984.
Palsson BO, Jamier R, Lightfoot EN: Mathematical modeling of dynamics and control in metabolic networks. II. Simple dimeric enzymes. J Theoret Biol 111:303–321, 1984.
Palsson BO, Lightfoot EN: Mathematical modeling of dynamics and control in metabolic networks. IV. Local stability analysis of single biochemical control loops. J Theoret Biol 113:261–277, 1985.
Palsson BO, Lightfoot EN: Mathematical modeling of dynamics and control in metabolic networks. V. Static bifurcations in single biochemical control loops. J Theoret Biol 113:279–298, 1985.
Teasdale RD, Carr AR, Read RSD: Substrate aggregation and cooperation enzyme kinetics: Consideration of enzyme access with large aggregates. J Theoret Biol 114:375–382, 1985.
Eyring H, Lin SH, Lin SM: In: Basic Chemical Kinetics, Chapter 1. Wiley and Sons, New York, 1980.
Delville A, Laszlo P, Nelson DJ: Calmodulin, calcium, potassium, and magnesium ion multiple equilibria and kinetics for interconversion, including the effect of repeated stimulation. J Theoret Biol 112:157–175, 1985.
Johnson HA: Information theory in biology after 18 years. Science 168:1545–1550, 1970.
Lumb JR: The value of theoretical models in immunological research. Immunol Today 4:209–210, 1983.
Maddox J: Aggregation by very large numbers. Nature 318:229, 1985.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lumb, J.R. Computer simulation of biological systems. Mol Cell Biochem 73, 91–98 (1987). https://doi.org/10.1007/BF00219423
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00219423