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Add support for diffusion reactions and multiple volumes #30

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WilliamIX opened this issue Apr 30, 2020 · 0 comments
Open

Add support for diffusion reactions and multiple volumes #30

WilliamIX opened this issue Apr 30, 2020 · 0 comments
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Bioscrape Core Issues pertaining to core bioscrape functionality enhancement New feature or request help wanted Extra attention is needed

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@WilliamIX
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I will describe this problem with a use case:

Consider two volumes (internal i and external e) which we are simulating deterministically in bioscrape. We want to model diffusion between the two compartments Xi <--> Xe. Notice that to conserve number of particles, Vi d[Xi]/dt = - Ve d[Xe]/dt. This can be modelled with one either of two sets of reactions:

  1. Ve Xi --> Vi Xe @ rate = d1 Xi & Vi Xe --> Ve Xi @ rate = d2 Xe
    OR
  2. 1/Vi Xi --> 1/Ve Xe @ rate = d1 Xi & 1/Ve Xe --> 1/Vi Xi @ rate = d2 Xe

Which of the sets of equations (or any of the infinite set of rescaled equations) is best? What units are natural for the diffusion rates d?

In order to simulate this, we need to create multiple volumes and a special kind of propensity for these kinds of use cases. Note that the stochiometric coefficents might not be integers. In the stochastic case, the stochiometric coeficients are 1 and the rates are not rescaled at all - so this is an important example of very different behavior between stochastic and deterministic settings.

@ayush9pandey your input would be appreciated here (and we should check over the math and see if there is a nice reference for this stuff) @sclamons this is very similar to the discussions we have had around deterministic lineages.

@WilliamIX WilliamIX added enhancement New feature or request help wanted Extra attention is needed Bioscrape Core Issues pertaining to core bioscrape functionality labels Apr 30, 2020
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Labels
Bioscrape Core Issues pertaining to core bioscrape functionality enhancement New feature or request help wanted Extra attention is needed
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