Abstract
The linearization of the dynamic equations governing biochemical systems is an inadequate approximation procedure, since the dynamic range of the variables is known to produce highly non-linear operation. A power-law approximation technique based on the non-linear nature of these reactions is presented in this paper. The range of validity is considerably greater than in the linear case, while the effort necessary to obtain steady-state solutions is about the same. The approximation procedure is applied to a general n-pool system; the nature and number of the steady-state solutions are derived. An example is also given to illustrate the different types of solutions and their physical interpretation.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 370-379 |
| Number of pages | 10 |
| Journal | Journal of Theoretical Biology |
| Volume | 25 |
| Issue number | 3 |
| State | Published - Dec 1969 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Medicine(all)
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics
- Immunology and Microbiology(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Agricultural and Biological Sciences(all)
Cite this
Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. / Savageau, Michael A.
In: Journal of Theoretical Biology, Vol. 25, No. 3, 12.1969, p. 370-379.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation
AU - Savageau, Michael A.
PY - 1969/12
Y1 - 1969/12
N2 - The linearization of the dynamic equations governing biochemical systems is an inadequate approximation procedure, since the dynamic range of the variables is known to produce highly non-linear operation. A power-law approximation technique based on the non-linear nature of these reactions is presented in this paper. The range of validity is considerably greater than in the linear case, while the effort necessary to obtain steady-state solutions is about the same. The approximation procedure is applied to a general n-pool system; the nature and number of the steady-state solutions are derived. An example is also given to illustrate the different types of solutions and their physical interpretation.
AB - The linearization of the dynamic equations governing biochemical systems is an inadequate approximation procedure, since the dynamic range of the variables is known to produce highly non-linear operation. A power-law approximation technique based on the non-linear nature of these reactions is presented in this paper. The range of validity is considerably greater than in the linear case, while the effort necessary to obtain steady-state solutions is about the same. The approximation procedure is applied to a general n-pool system; the nature and number of the steady-state solutions are derived. An example is also given to illustrate the different types of solutions and their physical interpretation.
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UR - http://www.scopus.com/inward/citedby.url?scp=0014658880&partnerID=8YFLogxK
M3 - Article
C2 - 5387047
AN - SCOPUS:0014658880
VL - 25
SP - 370
EP - 379
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
IS - 3
ER -