scholarly journals Stoichiometric network analysis as mathematical method for examinations of instability region and oscillatory dynamics

Author(s):  
Z. Cupic ◽  
G. Schmitz ◽  
Lj. Kolar-Anic
2003 ◽  
Vol 3 ◽  
pp. 319-341 ◽  
Author(s):  
Stefan Franzle ◽  
Bernd Markert

The biological application of stoichiometric network analysis (SNA) permits an understanding of tumour induction, carcinogenesis, and chemotherapy. Starting from the Biological System of the Elements, which provides a comprehensive treatment of the functions and distributions of chemical (trace) elements in biology, an attempt is made to interrelate the essential feature of biology and — regrettably — of tumour genesis by superimposing SNA reasoning on common features of all crucial biological processes. For this purpose, aspects, effects and drawbacks of autocatalysis (identical reproduction which can occur either under control or without control [in tumours]) are linked with the known facts about element distributions in living beings and about interference of metals with tumours (in terms of both chemotherapy and carcinogenesis). The essential role of autocatalysis in biology and the drawbacks of either controlled or spontaneous cell division can be used to understand crucial aspects of carcinogenesis and chemotherapy because SNA describes and predicts effects of autocatalysis, including phase effects that may be due to some kind of intervention. The SNA-based classifications of autocatalytic networks in cell biology are outlined here to identify new approaches to chemotherapy.


1988 ◽  
Vol 12 (1) ◽  
pp. 237-253 ◽  
Author(s):  
Bruce L. Clarke

2011 ◽  
Vol 14 (03) ◽  
pp. 451-469 ◽  
Author(s):  
QI WANG ◽  
BO LIU ◽  
SHIWEI YAN

We discuss the existence of Hopf bifurcation, the dynamical stability breaking of the molecular concentrations of two generic biochemical reaction systems and their sensitivity to the changes of the parameters incorporated in the model equations. It is found that the oscillatory dynamics can be expected for the systems due to the inclusion of time delays. The chaotic dynamics and the periodic windows in the chaotic domains can exist in the case of the system with two time delays. The proposed mathematical method may have the significance in the problems where the negative and/or positive feedback dynamics, as well as the time delays have the characteristic physical and biological background.


2008 ◽  
Vol 112 (51) ◽  
pp. 13452-13457 ◽  
Author(s):  
Guy Schmitz ◽  
Ljiljana Z. Kolar-Anić ◽  
Slobodan R. Anić ◽  
Željko D. Čupić

2018 ◽  
Vol 20 (36) ◽  
pp. 23726-23739 ◽  
Author(s):  
David Hochberg ◽  
Josep M. Ribó

SNA extreme currents allow for the evaluation and understanding of entropy production of NESS in open system reaction networks.


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