Some books about power-law models

Biochemical systems analysis: a study of function and design in molecular biology (Savageau, M. A., 1976. Reading, MA, Addison–Wesley). The classical book of M.A. Savageau in which the basic concepts about power-law models were introduced.

Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity (Voit, E.O. (ed), 1991. Van Nostrand Reinhold, NY). This book contains a series of chapters about advanced topics in analysis of power-law models.

Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists (Voit, E.O., 2000. Cambridge University Press, Cambridge, U.K.). This books is an updated introduction to power-law models and their application in biotechnology and biomedicine. The target audience of the book are biochemists and molecular biologists, and the basic concepts are explained in a intuitive manner.

Pathway Analysis and Optimization in Metabolic Engineering (Torres, N.V., and E.O. Voit 2002. Cambridge University Press, Cambridge, U.K.). This book is an introduction to metabolic engineering and applied biotechnology using power-law models. It contains several examples where the integration of mathematical modelling and optimisation resulted useful for the biotechnological improvement of microorganisms.

Ten basic references about power-law models

In this section we introduce some basic references about the properties and the use of power-law models. The idea is not to include a list of "classical" references ClasRef^?, but only a few recent articles with some theoretical discussions, use of power-law in state-of-the-art models, and development of new analytical tools. For the beginners, the order of the references is intentional. We start with a brief simple introduction to the topic and go more in depth into the properties and use of these models.

1. Models-of-data and models-of processes in the post-genomic era (Voit, E.O 2002. Mathematical Biosciences 180, 274).

2. Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways (Savageau, M.A 1998. Biosystems 47(1-2):9-36).

3. Simulation and validation of modelled sphingolipid metabolism in Saccharomyces cerevisiae (Alvarez-Vasquez F. et al. 2005. Nature 27;433(7024):425-30).

4. Extending the method of mathematically controlled comparison to include numerical comparisons (Alves R. and Savageau, M.A. 2000. Bioinformatics 16(9):786-98).

5. Use of physiological constraints to identify quantitative design principles for gene expression in yeast adaptation to heat shock (Vilaprinyo, E. et al. 2006. BMC Bioinformatics. 3;7:184).

6. Multicriteria Optimization Of Biochemical Systems By Linear Programming. Application To The Ethanol Production By Saccharomyces Cerevisiae (Vera, J. et al. 2003. Biotechnology and Bioengineering 83 (3):335-343).

7. Design principles for elementary gene circuits: Elements, methods, and examples (Savageau, M.A. 2001. Chaos 11(1):142-159).

8. Parameter estimation using Simulated Annealing for S-system models of biochemical networks (Gonzalez et al. 2006. Bioinformatics doi:10.1093/bioinformatics/btl522).

9. Power-Law models of signal transduction pathways (Vera, J. et al 2007, Cellular Signalling doi:10.1016/j.cellsig.2007.01.029).

10. Design of gene circuits using power-law models (Atkinson,M.R. et al 2003, Cell 113:597–607,).