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Delays
In stochastic simulations, bioscrape supports delay. In a delay reaction, delay inputs/outputs are consumed/produced after some amount of delay. Reactions may have a mix of delay and non-delay inputs and outputs. Bioscrape innately supports a number of delay-types:
Note that delays and delay inputs/outputs will be ignored if a model with delays is simulated deterministically.
- fixed: constant delay with parameter "delay".
- Gaussian: gaussian distributed delay with parameters "mean" and "std".
- Gamma: gamma distributed delay with shape parameter "k" and scale parameter "theta".
Delays for each reaction can be specified in a Bioscrape model.
By default, all reactions are created without a delay.
The reaction below creates a product "B" from "A" with a massaction propensity after a fixed delay.
rxn = (["A"], ["A"], "massaction", {"k":2},
"fixed", [], ["T"], {"delay":"k_delay"})
If the delay is a fixed constant, then set the delay to a fixed constant specified by the parameter "k_delay" in the model.
The reaction below creates a product "T" from "G" with a proportionalhillpositive propensity after a delay that has a Gaussian distribution.
rxn = (["G"], ["G"], "proportionalhillpositive", {"d":"G", "s1":"I", "k":"ktx", "K":"KI", "n":"n"},
"gaussian", [], ["T"], {"mean":10.0, "std":1.0})
If the delay is Gaussian, then it is distributed according to a normal distribution with mean parameter mean and standard deviation parameter std.
The following line creates a reaction that forms a product "X" from "T" with a hillpositive propensity after a delay that is gamma distributed.
rxn2d = (["T"], ["T"], "hillpositive", {"s1":"T", "k":"ktl", "K":"KR", "n":1},
"gamma", [], ["X"], {"k":10.0, "theta":3.0})
If the delay is distributed with a gamma distribution as is commonly the case in biological circuits, then you can specify that the delay type is gamma with "k" and "theta" being parameters that contain the k and theta parameters of the gamma distribution.
To do simulations with delay, you may also create a delay queue object that stores reactions that have been queued up to happen in the future. This is part of the initial state because the initial state is both the current species level as well as any reactions that have been queued up to occur. Currently, the only type of delay queue object available is called an ArrayDelayQueue and one can be created with the code
q = ArrayDelayQueue.setup_queue(num_reactions, num_timepoints, dt)
This will create a delay queue that is capable of storing events up to num_timepoints*dt time units into the future with a temporal resolution of dt. Making dt smaller makes your timing more accurate, but will make your code slower. It will especially slow things down when you simulate cell division. You should select a suitable dt, and then select num_timepoints to be such that the maximum possible storeable delay is big enough for your purposes. The num_reactions parameter should be picked based on your system of reactions. If you want to add reactions to the queue, you can do so using the following code.
q.py_add_reaction(time, rxn_id, amount)
The time is the time that the reaction occurs, the reaction ID is the index of that reaction in the stoichiometric matrix, and the amount is the number of times you want that reaction to fire at the specified time. This would typically be 1.0 since the reaction would usually fire once in a stochastic simulation, but in some cases you might want it to fire multiple times. If you want to set up a delay simulation with reactions queued up as part of the initial state, you can create a queue and use py_add_reaction() to pre-queue reactions that will occur.