SmartCell Simulation Algorithm
SmartCell offers 3 kinds of algorithms to simulate your network, the exact stockastic algorithm, the deterministic algorithm and the approximative algorithm.
The exact stockastic algorithm
The next reaction method
The next reaction method is based on the Gillespie algorithm. It is based on a queue of events with an approximate length of Number of Event * Number of voxels.
The main steps of the algorithm are:
 Calculate the probability a_{i} for each event i
 For each i, sample a putative reaction time T_{i} from an exponential distribution with parameter a_{i}, and add it to the queue of events
 Pick the event with the lowest T from the queue
 Execute the event, recalculate a_{i}, generate a new T_{i} and add it to the queue of events
 Check dependencies and update “dirty” Ts
 If the queue is not empty, go to step 3.
The advantage of this method is that the detection of the next event is really fast as it is the first element of the queue, but the time to sort the queue can be really high on a complicated network.
The next subvolume method
The next subvolume method is based on the Elf algorithm. It is based on a queue of voxels with a length of 1 * Number of voxels.
The main steps of the algorithm are:
 Calculate the probability a_{i} for each event i
 Calculate the probability a_{v} for each voxel v, with a_{v} = sum of a_{i} of voxel v events
 For each voxel v, sample a putative reaction time T_{v} from an exponential distribution with parameter a_{v}, and add it to the queue of voxels
 Pick the voxel with the lowest T from the queue
 Select one event of voxel v, with a distribution proportional to the a_{i}
 Execute the event, recalculate a_{i}, a_{v} and T_{v} and add it to the queue of voxels
 Check dependencies and update “dirty” Ts
 If the queue is not empty, go to step 4.
The advantage of this method is that the size of the queue will be independant of the complexity of the network and as a consequence the time needed to sort the queue won't depend of the network but only the geometry. Unfortunately, an additional step will be needed in order to detect the next event as the queue will only provide the next voxel the next event will take place.
The hybrid method
The hybrid method is used in order to combine the advantage of the stochastic Next Reaction/Next Subvolume methods and the deterministic ODE method. The reaction related to species with high copy number will be simulated with ODE when the reaction related to species with low copy number will be simulated with stochastic algorithm. This will allow a speed close to the ODE but will give some stochastic results, closer to the biological reality.
The deterministic algorithm
SmartCell is offering an ODE solver in order to have a first idea of the network behavior based on ODE. This method will have the advantage of being really fast in most of the network, but won't present the stochastic behavior of the cell and can even present some wrong result in case of instable steady state of the network.
The approximative algorithm
The tauleap method
The tauleap method is an approximative algorithm based on the next reaction method and published by Gillespie in 2001.
The principle is based on:

At time t, τ is calculated considering:
 τ is a small time interval
 The events that will occur during τ have a small impact on the other events
 Jump to time t + τ
 Execution of events that occur during τ
 Calculation of new probabilities and new τ