A Reaction Route Approach to Flux Balance Analysis
Correspondence: (Login to view email address)
- Worcester Polytechnic Institute
- Document Type:
- Manuscript
- Date:
- Received 14 January 2009 22:44 UTC; Posted 15 January 2009
- Subjects:
- Biotechnology, Chemistry, Bioinformatics
- Abstract:
Background: Flux balance and network-based pathway analyses are theoretical tools aimed to find optimal steady state flux distributions in a metabolic network subject to additional constraints on the rates of the reaction steps. Although these methods are mathematically accurate, there are several physicochemical and computational aspects that are questionable and misleading. In particular, it is well known that the flux balance analysis may result in multiple flux distributions for the same objective function.
Results: The flux balance and network-based pathway analyses are reformulated in terms of reaction routes (RRs), a theoretical framework that has been developed by Horiuti over 50 years ago. Not only does the theory of RRs provide the most general and rigorous definition of a pathway, but it also relates the steady state rates of the reaction steps with the rates along RRs or pathways. In this work, we employ the simple relation between the steady state rates of the reaction steps and the rates along RRs (fluxes) established by Horiuti to eliminate the steady state constraints.
Conclusion: The newly proposed RR approach represents a powerful tool for a deeper understanding of optimal flux distributions in metabolic reaction systems. Application of the RR approach to several typical systems from the literature surprisingly reveals that an infinite number of flux distributions for the same optimal objective function may be a rule rather than the exception
Discussion
- Votes:
-
3 votes
- Comments:
-
2 comments
qyzhao [at] bio.kyutech.ac.jp
- (Login to share with a colleague)
Additional information
- License:
- This document is licensed to the public under the Creative Commons Attribution 3.0 License
- How to cite this document:
-
Fishtik, Ilie . A Reaction Route Approach to Flux Balance Analysis. Available from Nature Precedings <http://hdl.handle.net/10101/npre.2009.2788.1> (2009)
- Version info:
-
Other versions of this document in Nature Precedings
None.
Other versions of this document elsewhere on the web
None known.
Quanyu ZHAO on 14 February 2009 14:14 UTC
An interesting method was proposed to reformulate the optimization by reaction route approach for flux balance analysis. It should be declared clearly that the optimization variables are changes from reaction flux, r, to linear independent reaction route rate so the computation is improved.
1. About Loop law (paragraph 3, page 2)
In the background section, it was considered that these considerations referred to as the “loop law” have no thermodynamic background.
The loop law is based on Kirchhoff’s current law.
2. About negative value (paragraph 3, page 4)
Just as you mentioned in section of Classical Theory of Reaction Rates, another source of confusion is that in some cases one or several rates along RRs may take negative values.
In general, the weights or coefficients of elementary modes (EMs) should be nonnegative (same condition for EPs). It is obviously the linear independent RRs are not subset of EMs so they are possible to be negative for several EMs. It is important to explain the meaning of rate of RRs, J, if it takes negative value. In example 2, there is no nonnegative constraint for J3 so it is possible to be negative.
3. I think the linear independent RR is the orthonormal basis for null space of stoichiometric matrix. I calculate them for these three examples. They are same to yours for example 1 and 3. For example 2, each element in the matrix is half of that in your matrix so the objective function is J2 and it is equal to 115 which is same to the reference.
I also found the reformulation of the linear optimization while I could not explain the meaning for J.
4. Page 13 and 14
In example 2, for the flux balance analysis, the constraints for r10 and r13 are missing (r10 >= 0 and r13 >= 0).
If RR method is used, the constraint for r2 is 2J1+J2-J4 >=0 while it is shown 2J1+J2-J3 >=0.