# Dimerization

The dimerisation process has two species P and P2 with initial amounts of 100 and 0, respectively. There are two reactions which both have mass-action kinetics: dimerization 2P → P2 and dissociation P2 → 2P, which have rate parameters of k1 = 0.001 and k2 = 0.01, respectively.

## dsmts-003-01

Use the open button in the tool bar to import the file `examples/sbml/dsmts31/dsmts-003-01.xml`. The model is imported correctly and the reactions are recognized as having mass-action kinetics. Open the file `examples/cain/dsmts31/dsmts-003-01.xml`. Below are plots of the mean and standard deviation of the species populations calculated from 10,000 trajectories.

## dsmts-003-02

This model is the same as dsmts-003-01, except that the initial amount of P is 1000, and the rate parameters are k1=0.0002 and k2=0.004.

## dsmts-003-03

This model is the same as dsmts-003-01, except that there is an event at time 25 with the assignments P = 100 and P2 = 0. Since Cain does not import events from SBML files, we need to enter the event in the time events editor. We generate 100 trajectories and plot the mean and standard deviation of the populations below.

## dsmts-003-04

This model is the same as dsmts-003-01, except that there is an event that is triggered when the amount of P2 exceeds 30. This event performs the assignments P = 100 and P2 = 0. For this model we must add an event in the trigger events editor. We generate 100 trajectories and plot the mean and standard deviation of the populations below.

Because of the trigger events, it is difficult to discern the actual behavior of the proces from a plot of the mean and standard deviation of the populations. We clear the output and generate 10 trajectories, which are plotted below.

## dsmts-003-05

This model is the same as dsmts-003-01, except that P has been removed from the system using the conservation law P = 100 - 2 P2. The reaction propensities are correctly imported. However, if you define a method and launch a simulation with the compile-and-launch button, you will get the following error: "P2 is used in the propensity function for a stochastic model, but is not a reactant. Add P2 as both a reactant and a product."

The problem is that Cain uses the lists of reactants and products to determine under what circumstances it must recompute the reaction propensities. The solution is to replace the reaction 0 → P2 with an equivalent reaction P2 → 2 P2. We generate 10,000 trajectories and plot the mean and standard deviation of the populations below.

## dsmts-003-06

This model is the same as dsmts-003-05, except that the rate law is written differently. The rate law is imported correctly, but we need to change the dimerization reaction to P2 → 2 P2.

## dsmts-003-07

This model is the same as dsmts-003-06, except that the rate law is written differently.