Doubly weighted stochastic simulation algorithm (dwSSA)

The doubly weighted stochastic simulation algorithm (dwSSA) 1 solver is developed solely for estimating rare event probabilities and thus should not be used for recording time-course trajectories.

dwSSA requires a set of biasing parameters to reach the rare event of interest. If a set of biasing parameters is not provided in the .cfg configuration file, dwSSA will execute multilevel cross- entropy (CE) method prior to the dwSSA simulation to obtain optimal (minimum CE) biasing parameters. The solver then employs these biasing parameters in selecting the next reaction and the next time step, yielding a trajectory weight that is a product of likelihood ratios from importance sampling. For the successful trajectories that reach the rare event, these weights are used to compute an unbiased estimator of the rare event probability with a confidence interval 2.

Parameter

Data type

Default

Description

solver

string

NA

dwSSA is the only valid name to run this solver.

reExpressionName

string

If unspecified, the solver searches the model file for reExpression.

The name of the function that defines the rare event expression in the model file.

reValName

string

If unspecified, the solver searches the model file for ReVal.

The name of the parameter that defines the rare event value in the model file.

gammas

vector of floats

Multilevel cross entropy (CE) simulations are performed to compute optimal gamma values prior to dwSSA simulations.

The positive real numbers provided in the vector are used as importance sampling parameters in selecting the next reaction and the next time step, as well as in computing the likelihood ratio of a biased trajectory. The length of the vector is equal to the total number of reactions in the model.

crossEntropyRuns

integer

100,000

The number of trajectories simulated in each level of multilevel CE simulations (not required for dwSSA simulations). Accepts values greater than or equal to 5000. If crossEntropyRuns * crossEntropyThreshold is less than crossEntropyMinDataSize, the value of crossEntropyRuns is dynamically adjusted to be the smallest integer greater than crossEntropyMinDataSize / crossEntropyThreshold.

crossEntropyThreshold

float

0.01

The fraction of top-performing trajectories chosen to compute an intermediate rare event in multilevel CE simulations (not required for dwSSA simulations). Accepts values between 0 and 1.

Note

If slow convergence is detected during the multilevel CE simulations, the value is decreased to 80% of its previous value.

crossEntropyMinDataSize

integer

200

The minimum number of successful trajectories required to compute an intermediate rare event for multilevel CE simulations. Accepts values greater than or equal to 100.

outputFileName

string

File name in the form of <modelname>_dwSSA_1e<log>(<runs>), where the base of <log> is 10 and <modelName> is the name of the model file.

The name of the output file that includes runs, estimates for the rare event probability, 68% uncertainty, and sample variance.

Example

{
    "duration": 10,
    "runs": 1000000,
    "solver": "dwSSA",
    "dwSSA": {
        "gamma": [1.53, 0.45],
        "reValName": "reVal",
        "reExpressionName": "reExpression",
        "crossEntropyRuns": 100000,
        "crossEntropyThreshold": 0.01,
        "crossEntropyMinDataSize": 300,
        "outputFileNate": "SIR_dwSSA_1e6.txt"
    }
} 
1

Daigle, Bernie J et al. “Automated estimation of rare event probabilities in biochemical systems.” The Journal of Chemical Physics 134 4 (2011): 04410.

2

Gillespie, Dan T et al. “Refining the weighted stochastic simulation algorithm.” The Journal of Chemical Physics 130 17 (2009): 174103.