Unlike the other hybrid methods, which use a dynamic partitioning strategy based on particle numbers, Hybrid (RK-45) relies on a user-defined partitioning strategy.
It is also the only hybrid method, with support for discrete events.
Max Internal Steps:
Maximum number of internal steps. Default: 1000000.
Relative Tolerance: Desired numeric relative tolerance (default: $1.0 \cdot 10^{-6}$; best achievable is approximately $2.22 \cdot 10^{-16}$).
Absolute Tolerance: Desired absolute tolerance, applied to species concentrations. Default: $1.0 \cdot 10^{-9}$.
Deterministic Reactions: (Used only if “User specified Partition” is selected.) Specifies which reactions are simulated deterministically. The rest are treated stochastically.
Use Random Seed:
0 (default) means a random seed is used for each run; 1 will use the
user-supplied random seed for repeatable trajectories.
1. Default: 1.The Hybrid (Runge-Kutta) simulation method combines deterministic numerical integration of ordinary differential equations (ODEs) with a stochastic simulation algorithm. The entire biochemical network is internally partitioned into a deterministic subnet and a stochastic subnet.
Users can specify which particle numbers are considered “low” or “high” using the Lower Limit and Upper Limit parameters. Species with particle numbers between these limits do not change their status, resulting in a hysteresis-like behavior. This avoids unnecessary switching when particle numbers fluctuate in the middle range.
Partitioning can be recalculated dynamically during the simulation, at intervals specified by the Partitioning Interval parameter. During each run, the deterministic and stochastic subnets are simulated in parallel. The deterministic part is integrated using a 4th-order Runge-Kutta method, while the stochastic part uses the Gibson and Bruck algorithm (Gibson00). Reaction probabilities in the stochastic subnet are approximated as constant during each stochastic step, even though they may actually change due to deterministic effects.
Note: The current Hybrid Runge-Kutta implementation is inefficient for models with assignment rules, causing significantly longer calculation times.
Max Internal Steps:
Positive integer specifying the maximum number of internal steps allowed
before the next reporting time. Default: 1000000.
Lower Limit:
Double value specifying the lower particle number limit. Species below this
are considered to have a low particle number. Cannot be higher than the upper
limit. Default: 800.
Upper Limit:
Double value specifying the upper particle number limit. Species above this
are considered to have a high particle number. Cannot be lower than the
lower limit. Default: 1000.
Runge Kutta Stepsize:
Positive double specifying the step size for the Runge-Kutta integrator.
Default: 0.001.
Partitioning Interval:
Positive integer specifying after how many steps the partitioning is
recalculated. Default: 1 (i.e., every step).
Use Random Seed:
Boolean flag (0 or 1). If 0 (default), a random seed is chosen for
each run, producing different trajectories. If 1, a user-supplied random
seed is used, giving repeatable results.
Random Seed:
Unsigned integer used as the random seed if Use Random Seed is set to 1.
Default: 1.
The Hybrid (LSODA) method is similar to the Hybrid (Runge-Kutta) method but uses the LSODA algorithm for integration instead of 4th-order Runge-Kutta.
Max Internal Steps:
Maximum number of internal steps before reporting. Default: 1000000.
Lower Limit:
Double specifying lower particle limit. Default: 800.
Upper Limit:
Double specifying upper particle limit. Default: 1000.
Runge Kutta Stepsize:
Step size for deterministic (Runge-Kutta) solver. Default: 0.001.
Partitioning Interval:
Steps between partition recalculation. Default: 1.
Use Random Seed:
Flag; 0 (default) for random seed, 1 to use user-supplied seed.
Random Seed:
Random seed value (unsigned integer). Default: 1.
Integrate Reduced Model:
Boolean. 1 (default) integrates using mass conservation laws, reducing
system variables. 0 to use the full system of ODEs.
Relative Tolerance: Numeric value specifying the desired relative tolerance for the integrator. Default: $1.0 \cdot 10^{-6}$. The smallest achievable is approximately $2.22 \cdot 10^{-16}$.
Absolute Tolerance: Positive numeric value specifying the absolute tolerance. For species, this applies to the concentration. Default: $1.0 \cdot 10^{-12}$.
Max Internal Step Size:
Maximum allowed size for internal steps (positive double). Default: 0 (no
limit).