update_reactions

Short description

@author: Moritz F P Becker

pyrid.reactions.update_reactions.convert_molecule_type(System, product_id, product_name, RBs, Particles, i)

Converts a molecule to a different type.

Parameters

Systemobject

Instance of System class

product_idint64

Id of the product molecule type.

product_namestring

Name of the product molecule type.

RBsobject

Instance of RBs class

Particlesobject

Instance of Particles class

iint64

Index of the molecule whose type to convert

pyrid.reactions.update_reactions.convert_particle_type(System, product_id, Particles, i)

Converts a particle to a different type.

Parameters

Systemobject

Instance of System class

product_idint64

Id of the product particle type.

Particlesobject

Instance of Particles class

iint64

Index of the particle whose type to convert

pyrid.reactions.update_reactions.delete_molecule(System, RBs, Particles, i)

Removes a molecule and its reactions from the simulation.

Parameters

Systemobject

Instance of System class

RBsobject

Instance of RBs class

Particlesobject

Instance of Particles class

iint64

Index of the molecule which to delete

pyrid.reactions.update_reactions.delete_particles(System, RBs, Particles, i)

Removes all particle belonging to a molecule and its reactions and bonds from the simulation.

Parameters

Systemobject

Instance of System class

RBsobject

Instance of RBs class

Particlesobject

Instance of Particles class

iint64

Index of the molecule whose particles to delete

pyrid.reactions.update_reactions.delete_reactions(System, i, type_id, educt_is_particle)

Removes all reactions of an educt i scheduled for this time step.

Parameters

Systemobject

Instance of System class

iint64

Index of the particle for which to delete all reactions

pyrid.reactions.update_reactions.update_reactions(System, Particles, RBs)

Evaluates the bimolecular and unimolecular reactions.

Parameters

Systemobj

Instance of System class.

Particlesobj

Instance of Particle class.

RBsobj

Instance of RBs (Rigid Bodies) class.

Notes

Reaction handler

We use a Gillespie reaction handler scheme, similar to the one used in ReaDDy:

1. All reactions events occuring within a time step are gathered in lists (a seperate list for each reaction that has been defined).

2. A reaction type is picked randomly, weighted by the its total reaction rate times the total number of reactions that are in the list of that type (the total reaction rate is the sum of the individual reaction path rates. Different reaction paths allow for the same educts to undergo, e.g., different fusion reactions or for a single molecule to convert to different products).

3. A random reaction event is picked from the list.

4. If the reaction is bimolecular, the reaction probability Eq. (28) is tested against a random number between 0 and 1.

   1. If the reaction was successfull, we pick a random reaction path, weighted by the path’s reaction rates. After the execution of the reaction, it is deleted from the list together with all the other reactions the educts participated in.

   2. If the reaction was not successful, the reaction is deleted from the list.

5. If the reaction is unimolecular, it is always successful, since, for unimolecular reactions, we draw the time point of the next reaction event from the corresponding distribution (Gillespie SSA). As such, we pick a random reaction path, weighted by the individual path’s reaction rates. After the execution of the reaction, it is deleted from the list together with all the other reactions the educt participated in.

6. Go back to 2. until no reactions are left.

(28)\[p = 1-exp\Big(-\sum_{i \in paths} \lambda_i \cdot \Delta t \Big)\]

Doi bimolecular reaction scheme

There exist different methods of how to model bimolecular reactions. PyRID, just as ReaDDy [23], uses the Doi scheme [24]. In this scheme, two molecules can react to a single product moelcule if their distance is less than some reaction radius R. In this case the reaction may occur with a microscopic reaction rate \(\lambda\).