The non-linear analysis of cybernetic models. Guidelines for model formulation

A set of guidelines are formulated, using tools from bifurcation theory, that describe the qualitative characteristics of the different forms of competition for key cellular resources present within the cybernetic framework. These guidelines establish the basis of a modular approach for the construction of abstracted cybernetic models of microbial processes. This methodology, employed in the subsequent papers of this series, affords the construction of entire classes of cybernetic models that are guaranteed to possess desired dynamic features, thus reducing the model formulation burden and yielding insight into the necessary level of metabolic pathway abstraction.

[1]  Ronald K. Pearson,et al.  Nonlinear model-based control using second-order Volterra models , 1995, Autom..

[2]  D. Ramkrishna,et al.  Metabolic Engineering from a Cybernetic Perspective. 1. Theoretical Preliminaries , 1999, Biotechnology progress.

[3]  J. Varner,et al.  Metabolic Engineering from a Cybernetic Perspective. 2. Qualitative Investigation of Nodal Architechtures and Their Response to Genetic Perturbation , 1999, Biotechnology progress.

[4]  L. Rédei.  CHAPTER I – SET-THEORETICAL PRELIMINARIES , 1967 .

[5]  Doraiswami Ramkrishna,et al.  Cybernetic Modeling and Regulation of Metabolic Pathways. Growth on Complementary Nutrients , 1994 .

[6]  R Ramakrishna,et al.  Cybernetic modeling of growth in mixed, substitutable substrate environments: Preferential and simultaneous utilization. , 1996, Biotechnology and bioengineering.

[7]  D. Sattinger,et al.  Loss of stability and bifurcation at a double eigenvalue , 1973 .

[8]  Ronald K. Pearson,et al.  Identification of structurally constrained second-order Volterra models , 1996, IEEE Trans. Signal Process..

[9]  G. Iooss,et al.  Elementary stability and bifurcation theory , 1980 .

[10]  D. Ramkrishna,et al.  Metabolic regulation in bacterial continuous cultures: I. , 1991, Biotechnology and bioengineering.

[11]  G. T. Tsao,et al.  Investigation of bacterial growth on mixed substrates: Experimental evaluation of cybernetic models , 1986, Biotechnology and bioengineering.

[12]  M. Golubitsky,et al.  Singularities and groups in bifurcation theory , 1985 .

[13]  M. J. Guardia,et al.  Cybernetic Modeling and Regulation of Metabolic Pathways in Multiple Steady States of Hybridoma Cells , 2000, Biotechnology progress.

[14]  D. Ramkrishna,et al.  Complex growth dynamics in batch cultures: Experiments and cybernetic models , 1991, Biotechnology and bioengineering.