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BIOMD0000000319 - Decroly1982_Enzymatic_Oscillator

 

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Reference Publication
Publication ID: 6960354
Decroly O, Goldbeter A.
Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system.
Proc. Natl. Acad. Sci. U.S.A. 1982 Nov; 79(22): 6917-6921
  [more]
Model
Original Model: BIOMD0000000319.origin
Submitter: Kieran Smallbone
Submission ID: MODEL1102070000
Submission Date: 07 Feb 2011 13:41:30 UTC
Last Modification Date: 09 Mar 2012 15:57:51 UTC
Creation Date: 11 Aug 2010 13:53:05 UTC
Encoders:  Kieran Smallbone
set #1
bqbiol:occursIn Taxonomy cellular organisms
set #2
bqbiol:isVersionOf Gene Ontology rhythmic process
Notes

This is the scaled model described in the article:
Birhythmicity, chaos, and other patterns of temporal self-organization in a multiply regulated biochemical system
Olivier Decroly, Albert Goldbeter, Proc Natl Acad Sci USA 1982 79:6917-6921; PMID: 6960354 ;

Abstract:
We analyze on a model biochemical system the effect of a coupling between two instability-generating mechanisms. The system considered is that of two allosteric enzymes coupled in series and activated by their respective products. In addition to simple periodic oscillations, the system can exhibit a variety of new modes of dynamic behavior; coexistence between two stable periodic regimes (birhythmicity), random oscillations (chaos), and coexistence of a stable periodic regime with a stable steady state (hard excitation) or with chaos. The relationship between these patterns of temporal self-organization is analyzed as a function of the control parameters of the model. Chaos and birhythmicity appear to be rare events in comparison with simple periodic behavior. We discuss the relevance of these results with respect to the regularity of most biological rhythms.

The parameters q1 = 50 and q2 = 0.02 are explicitely included as the stoichiometric coefficients of beta and gamma in the reactions r2 and r3, respectively. Parameter values and initial conditions [ks=1.99/sec, alpha(0)=29.19988, beta(0)=188.8, gamma(0)=0.3367] are for the chaotic regime presented in the upper-curve of Figure 3b.

Model
Publication ID: 6960354 Submission Date: 07 Feb 2011 13:41:30 UTC Last Modification Date: 09 Mar 2012 15:57:51 UTC Creation Date: 11 Aug 2010 13:53:05 UTC
Mathematical expressions
Reactions
r1 r2 r3 r4
Physical entities
Compartments Species
cell alpha beta gamma
Reactions (4)
 
 r1  → [alpha];  
 
 r2 [alpha] → 50.0 × [beta];  
 
 r3 [beta] → 0.02 × [gamma];  
 
 r4 [gamma] → ;  
 
 cell Spatial dimensions: 3.0  Compartment size: 1.0
 
 alpha
Compartment: cell
Initial concentration: 29.19988
 
 beta
Compartment: cell
Initial concentration: 188.8
 
 gamma
Compartment: cell
Initial concentration: 0.3367
 
r1 (1)
 
 v_Km1
Value: 0.45   (Units: per sec)
Constant
 
r2 (2)
 
   L1
Value: 5.0E8   (Units: dimensionless)
Constant
 
 sigma1
Value: 10.0   (Units: per sec)
Constant
 
r3 (3)
 
   L2
Value: 100.0   (Units: dimensionless)
Constant
 
   d
Constant
 
 sigma2
Value: 10.0   (Units: per sec)
Constant
 
r4 (1)
 
 ks
Value: 1.99   (Units: per sec)
Constant
 
Representative curation result(s)
Representative curation result(s) of BIOMD0000000319

Curator's comment: (updated: 22 Feb 2011 00:15:16 GMT)

The upper panel shows the time course of concentration of alpha for the chaotic regime as in upper panel of fig 3B, the lower panel a bifurcation diagram of alpha against ks similar to the upper panel of fig 1 of the reference publication. The time course was calculated using Copasi v 4.6.33, the bifurcation diagram using the Oscill8 v 2.0.11 and SBW 2.7.10. In the bifurcation diagram thick lines indicate stable, thin instable solutions. The orange line stands for the steady state of alpha, the purple line for its maximal value in oscillations.

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