Graph theoretic approach to the stability analysis of steady state chemical reaction networks

1974 ◽  
Vol 60 (4) ◽  
pp. 1481-1492 ◽  
Author(s):  
Bruce L. Clarke
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Theoretic Approach ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
State Chemical ◽  
The Stability

scholarly journals Insights into the relation between noise and biological complexity

2017 ◽  
Author(s):  
Fabrizio Pucci ◽  
Marianne Rooman
Keyword(s):  
Steady State ◽  
Systems Biology ◽  
Chemical Reaction ◽  
Intrinsic Noise ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
Global Level ◽  
Biological Complexity ◽  
Lower Complexity

Understanding under which conditions the increase of systems complexity is evolutionary advantageous, and how this trend is related to the modulation of the intrinsic noise, are fascinating issues of utmost importance for synthetic and systems biology. To get insights into these matters, we analyzed chemical reaction networks with different topologies and degrees of complexity, interacting or not with the environment. We showed that the global level of fluctuations at the steady state, as measured by the sum of the Fano factors of the number of molecules of all species, is directly related to the topology of the network. For systems with zero deficiency, this sum is constant and equal to the rank of the network. For higher deficiencies, we observed an increase or decrease of the fluctuation levels according to the values of the reaction fluxes that link internal species, multiplied by the associated stoichiometry. We showed that the noise is reduced when the fluxes all flow towards the species of higher complexity, whereas it is amplified when the fluxes are directed towards lower complexity species.PACS numbers: 02.50.Ey, 05.10.Gg, 05.40.Ca, 87.18.-h

scholarly journals Analytical Solution of Steady-State Equations for Chemical Reaction Networks with Bilinear Rate Laws

2013 ◽  
Vol 10 (4) ◽  
pp. 957-969 ◽  
Author(s):  
Adam M. Halasz ◽  
Hong-Jian Lai ◽  
Meghan McCabe Pryor ◽  
Krishnan Radhakrishnan ◽  
Jeremy S. Edwards
Keyword(s):  
Steady State ◽  
Analytical Solution ◽  
Chemical Reaction ◽  
Chemical Reaction Networks ◽  
Reaction Networks ◽  
State Equations ◽  
Rate Laws
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