Transition from stochastic to deterministic behavior in calcium oscillations.
Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism.
Kummer
Ursula
U
Bioinformatics and Computational Biochemistry Group, EML Research, D-69118 Heidelberg, Germany. ursula.kummer@eml-r.villa-bosch.de
Krajnc
Borut
B
Pahle
Jürgen
J
Green
Anne K
AK
Dixon
C Jane
CJ
Marhl
Marko
M
D000255:Adenosine Triphosphate / Q000737:chemistry; D000465:Algorithms; D000818:Animals; D001671:Biochemistry / Q000379:methods; D001703:Biophysics / Q000379:methods*; D002118:Calcium / Q000737:chemistry* / Q000378:metabolism; D020013:Calcium Signaling; D017364:Collagenases / Q000378:metabolism; D003198:Computer Simulation; D022781:Hepatocytes / Q000166:cytology; D007700:Kinetics; D008297:Male; D008954:Models, Biological; D015233:Models, Statistical; D008962:Models, Theoretical; D009991:Oscillometry; D010477:Perfusion; D051381:Rats; D017208:Rats, Wistar; D015398:Signal Transduction; D013269:Stochastic Processes; D013598:Systems Theory; D013997:Time Factors
D000255:Adenosine Triphosphate; D017364:Collagenases; D002118:Calcium