The combination of high-throughput methods of molecular biology with advanced mathematical and …

• Abstract
• Results and Discussion
• Conclusion
• Methods: Model Design
• References
• Figures

Biology Articles » Biomathematics » The intricate side of systems biology » Methods: Model Design

Methods: Model Design

- The intricate side of systems biology

Directly based on the diagram in Fig. 1, we constructed and implemented a series of fully kinetic pathway models within Biochemical Systems Theory (3, 6, 15–17) as modeling framework. Choosing the Generalized Mass Action representation, the resulting model in symbolic form is

Although setting up the equations was straightforward for most variables, ATP and P_i were problematic, because these two variables are involved in many reactions that cannot all be included in the model. ATP and P_i, therefore, were not modeled as differential equations but as "offline" input functions in the form of raw data that were locally smoothed (18–19). Similarly, glucose was represented as an offline function, because the observed glucose uptake follows a sigmoidal function that is incompatible with the structure of the pathway (18). NAD and NADH were essentially constant under the aerobic conditions modeled here (data not shown). Their concentrations therefore were subsumed into the corresponding rate constants. The production term of G6P contains G6P itself, because it could be that G6P inhibits glucose uptake and utilization (20), even though this mechanism has not been demonstrated for L. lactis.

Parameter values were obtained from the observed time course data (Fig. 2) with a combination of inverse methods, as described elsewhere in extenso (18). Pertinent numerical results and technical details of model implementation in the freely available PLAS (www.dqb.fc.ul.pt/docentes/aferreira/plas.html) are given in supporting information.

Acknowledgements 

We thank two anonymous reviewers for constructive criticism and insightful suggestions. Funding was provided by the Fundação para a Ciência e a Tecnologia Projects POCTI/BIO/48333/02 and FEDER and by the Georgia Research Alliance.

Footnotes  

Abbreviations: FBP, fructose 1,6-bisphosphate; G6P, glucose 6-phosphate; PEP, phosphoenolpyruvate; PK, pyruvate kinase; 3-PGA, 3-phosphoglycerate.

To whom correspondence should be addressed. E-mail: eberhard.voit@bme.gatech.edu

Author contributions: E.V., A.R.N., and H.S. designed research; E.V. and A.R.N. performed research; A.R.N. contributed new reagents/analytic tools; E.V., A.R.N., and H.S. analyzed data; and E.V. and H.S. wrote the paper.

Conflict of interest statement: No conflicts declared.

© 2006 by The National Academy of Sciences of the USA