How to perform SDE simulations of system (using Chemical Langevin equations)
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Torkel Loman
Nov 8, 2021, 4:22:17 PM11/8/21
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Hello,
I have a model (imported via SBML) for which I want to make stochastic simulations. I have tried discrete SSA simulations, but I want to perform continuous SDE simulations as well (using the chemical Langevin equation interpretation).
I go to time courses. I can successfully simulate the system deterministically using e.g. "Deterministic (LSODA)". However, I then try "SDE Solver (RI5)". I can successfully simulate using it, but there is no sign of randomness. For a long duration, the system reaches a steady state and do not deviate.
If I change to "Particle Numbers" (from "Concentrations") and then simulate using "Stochastic (Direct Method)", I do get a solution that fluctuates around the steady state. So randomness seems to work, just not using the SDE approach.
I have not found much documentation on SDE, e.g. it is not mentioned in http://copasi.org/Support/User_Manual/Methods/Time_Course_Calculation/
Am I missing something, or is there some reason I might be failing? Attaching the file I have used for reference.
Mendes,Pedro
Nov 8, 2021, 7:31:23 PM11/8/21
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Hi there,
when you select SDE as the simulation, you also have to add the noise terms in each reaction. If you want to run a Langevin approximation, then just enable noise in each reaction and keep the default noise term. The default noise terms were chosen to follow the Langevin approximation, basically the noise of each reaction is proportional to the square root of its (absolute) flux. Note that since the differential equations in COPASI are expressed in units of particle numbers, then the noise is also in terms of fluxes of particle numbers.
To enable noise for each reaction, go to each reaction and look for "add noise" check box. Once you check it, a edit box appears with the default noise term. If you had to change it, that is where you would do it (but in your case you should just leave it)
Unfortunately we don't yet have a quick way to add noise to all reactions, you will have to add them one by one (I hope your network is not too large!). Of course, this also allows one to simulate situations where only a few reactions are subject to intrinsic noise.
Pedro
when you select SDE as the simulation, you also have to add the noise terms in each reaction. If you want to run a Langevin approximation, then just enable noise in each reaction and keep the default noise term. The default noise terms were chosen to follow the Langevin approximation, basically the noise of each reaction is proportional to the square root of its (absolute) flux. Note that since the differential equations in COPASI are expressed in units of particle numbers, then the noise is also in terms of fluxes of particle numbers.
To enable noise for each reaction, go to each reaction and look for "add noise" check box. Once you check it, a edit box appears with the default noise term. If you had to change it, that is where you would do it (but in your case you should just leave it)
Unfortunately we don't yet have a quick way to add noise to all reactions, you will have to add them one by one (I hope your network is not too large!). Of course, this also allows one to simulate situations where only a few reactions are subject to intrinsic noise.
Pedro
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-- Pedro Mendes, PhD Professor and Director, Richard D. Berlin Center for Cell Analysis and Modeling University of Connecticut School of Medicine group website: http://www.comp-sys-bio.org
Torkel Loman
Nov 9, 2021, 4:51:55 AM11/9/21
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Thank you, that explains things very well.
Yes, I was able to tick in the noise boxes and do a CLE simulations, worked very well. Have some larger models where it might be a bit of a thing to go through all the boxes, but agree that it is really useful to be able to set the noise for each reaction independently!
thanks again,
Torkel
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