Simulation of Radical Chains in Multiple Small Droplets Using Stochastic Method
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Riccardo Amorati
3:24 AM (17 hours ago) 3:24 AM
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Hello,
I am a chemist working in the field of radical reactions. I would like to simulate an oxidative radical-chain process occurring in many small lipid droplets (emulsion system). The droplets are so small that each droplet contains one or two radical species at a given time (often none).
I am able to simulate a single droplet using the stochastic method by defining a very small compartment volume. However, I would like to scale up the simulation to a large number of identical droplets. When I try to increase the number of droplets by duplicating the compartment or species (for example to simuate radical transfer among droplets) , the total number of species becomes too large for COPASI to handle.
Is there a recommended strategy or modeling workflow in COPASI to simulate a large number of independent, identical micro-compartments?
Thank you in advance for your guidance.
Best regards,
Riccardo Amorati
Pedro Mendes
4:33 PM (4 hours ago) 4:33 PM
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Hi Riccardo,
From your description I think you have two alternative ways out:
1 - using parameter scan task with repeat feature
2- using stochastic differential equations
1- since you say that the droplets are independent, then you can simulate each one independently as well. This means that you just need to repeat the Gillespie simulation of one droplet many times, which can be easily done in the parameter scan task. All you need to do is to select "Repeat" and add the number of droplets as the number of repeats. COPASI uses a random seed each time it simulates so each simulation will be independent (as far as pseudo-random numbers can be). You would also have to create a report file to capture all the simulations and then do some statistics on that output. This would be my preferred option.
2- COPASI can also use stochastic differential equations. For that you need two things: add noise to each of the reactions (in the reaction widget there is a check-box to add noise and then an expression to enter the noise function; the default noise function is the same that is used in Langevin approaches, so you most likely would want that). Then in the time course widget you have to select the method "SDE Solver (RI5)". Of course, SDEs of mass action rate laws are only approximations (eg Langevin), but the numerical analysis works for larger numbers of molecules (the simulation is carried out with 64-bit floats, while the normal Gillespie approach uses 64-bit integers)
There could be a third option, the "Linear noise approximation", but that only works to determine the co-variances at the steady state (ie not a trajectory). They also work well with macroscopic systems but you get no dynamics that way.
I hope that one of these options works for you; from your description I would go with option 1.
Pedro
From your description I think you have two alternative ways out:
1 - using parameter scan task with repeat feature
2- using stochastic differential equations
1- since you say that the droplets are independent, then you can simulate each one independently as well. This means that you just need to repeat the Gillespie simulation of one droplet many times, which can be easily done in the parameter scan task. All you need to do is to select "Repeat" and add the number of droplets as the number of repeats. COPASI uses a random seed each time it simulates so each simulation will be independent (as far as pseudo-random numbers can be). You would also have to create a report file to capture all the simulations and then do some statistics on that output. This would be my preferred option.
2- COPASI can also use stochastic differential equations. For that you need two things: add noise to each of the reactions (in the reaction widget there is a check-box to add noise and then an expression to enter the noise function; the default noise function is the same that is used in Langevin approaches, so you most likely would want that). Then in the time course widget you have to select the method "SDE Solver (RI5)". Of course, SDEs of mass action rate laws are only approximations (eg Langevin), but the numerical analysis works for larger numbers of molecules (the simulation is carried out with 64-bit floats, while the normal Gillespie approach uses 64-bit integers)
There could be a third option, the "Linear noise approximation", but that only works to determine the co-variances at the steady state (ie not a trajectory). They also work well with macroscopic systems but you get no dynamics that way.
I hope that one of these options works for you; from your description I would go with option 1.
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
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