Method Editor

In this panel you edit the simulation method. (See the Solvers section for a description of each available solver.) First select the time dependence category:

• Time Homogeneous - For time homogeneous problems, the reaction rates may depend upon the species populations, but do not explicitly depend on time. Most of Cain's solvers belong to this category. Use may choose between exact methods (direct, next reaction, etc.) and approximate methods (tau-leaping, hybrid, etc.).
• Time Inhomogeneous - Although time inhomogeneous problems are not much more conceptually difficult, they are more costly to simulate. Sources of inhomogeneity may include time-varying volume or temperature (both affect reaction rates). Note that although Gillespie's direct method is used, the solution is not exact. We use the approximation that the reaction propensities are assumed to be constant between reaction events.
• Use Events - One must use this category if the model has events. Simulating models with events is more costly. Additionally, the solvers in this category are implemented in Python, instead of C++. Thus, these solvers are significantly slower than solvers in the other categories. Note that time inhomogeneities are allowed; the reaction propensities, parameters, and compartment volumes may be functions of time. However, the solutions for time inhomogeneous problems are approximate because, again, we make the assumption that reaction propensities are constant between reaction events.

Next select the output category. Simulations may generate several types of output:

• Time Series, Uniform - Generate stochastic trajectories. Record the populations and reaction counts at uniformly spaced intervals in time.
• Time Series, All Reactions - Generate stochastic trajectories. Record every reaction event. Use this output choice when you want a detailed view of a small number of trajectories. Choose the time interval so the number of reactions is not too large.
• Time Series, Deterministic - Generate a single, deterministic trajectory by numerically integrating a set of ordinary differential equations. Record the populations and reaction counts at uniformly spaced intervals in time. Note that in this case the populations and reaction counts are real numbers instead of integers.
• Histograms, Transient Behavior - Generate stochastic trajectories. Record the populations in histograms at uniformly spaced intervals in time. Recording the species populations in histograms gives you more quantitative information about a system than recording and plotting trajectories.
• Histograms, Steady State - Record the average population values in histograms. You may choose to start each simulation by letting the system equilibrate for a specified time interval. This does not affect the time during which the state is recorded. Average value histograms are useful for determining the steady state probability distributions for the species populations.
• Statistics, Transient Behavior - Record the mean and standard deviation of the species population at each frame. There is no solver in Cain that only records statistics. The Cain solvers for transient behavior either record trajectories, or they record both statistics and histograms of species populations. Thus, this acts as a placeholder for some external solver. If one generates a solution with another application (or records an analytical solution), then one may import it in a text file. Each line in the file records the statistics for a single time frame. The mean and standard deviation for each recorded species are listed. See the DSMTS chapter for examples.
• Histograms, Steady State - Record the mean and standard deviation of the time-averaged species populations. This is a placeholder that is used for importing externally-generated steady state solutions. The imported text file lists the mean and standard deviation for the recorded species on a single line.

In the third field select the algorithm to generate the desired output. For each method there is a choice of options which may affect the performance or accuracy.

In the right column, one sets the simulation parameters. Three values control the simulation time interval: start time, equilibration time, and recording time. The start time, as the name suggests, is the point in time at which the simulation starts. For time homogeneous problems one would typically choose zero. For time inhomogeneous problems one might want to choose a nonzero value. The equilibration time is the length of time that the simulation is advanced before recording results. One would choose a nonzero value if one were studying the steady state behavior of a system. For instance, a system may exhibit oscillatory behavior, but may take a certain amount of time to establish these oscillations. The recording time is the length of time to simulate and record the state.

Next you can select the maximum number of allowed steps when generating a trajectory. Usually one would leave this field blank to indicate that there is no set limit. However, this field may be useful if you don't know the appropriate time scale for your simulation. Then you can set a limit on the number of steps. If any of the trajectories reach this limit, the simulation will abort with an error message.

If you have elected to record the state at frames, you choose the number of frames to record. If not, the frames field is disabled. The first frame is at the beginning of the recording time, and the last is at the end. If you are only interested in the the final populations or the final reaction counts, choose the number of frames to be one. For this special case, the state will be recorded only at the end time. If you are recording the output in histograms, you select the number of bins to use in each. A histogram is an empirical probability distribution for a species population. The computational cost of converging these probablity distributions is related to the number of bins. Choose a number of bins that is appropriate for the amount of time you are willing to spend generating trajectories. Next select the histogram multiplicity. The state is recorded in multiple histogram arrays. This allows one to estimate the error in the resulting distributions. Increasing the histogram multiplicity allows one to more accurately estimate this error. However this also increases the memory requirements for the solvers. The default value of four is usually a reasonable compromise. If you are not interested in estimating the error in the probability distributions, you may set the histogram multiplicity to unity. Some simulation methods require a parameter such as allowed error or step size. This quantity is entered in the final box.