produced is a stochastic version of the trajectory that would be
obtained by solving the corresponding stochastic differential
equations.A.11 The
Gillespie SSAs
The SSA assumes a population consisting of a finite number of
individuals distributed over a finite set of discrete states. Changes
in the number of individuals in each state occur due to reactions
between interacting states.
Given an initial time t 0 and initial population state X(t 0 ),
the SSA generates the time evolution of the state vectorX(t),
(X 1 (t),...,XN(t)) where Xi(t),i¼1,...,N, is the population
size of stateiat timetandNis the number of states. The states
interact throughMreactionsRjwherej¼1,...,Mdenotes thejth
reaction. A reaction is defined as any process that instantaneously
changes the population size of at least one state. Each reactionRjis
characterized by two quantities. The first is its state-change vector
νj¼(ν 1 j,...,νNj), whereνijis the population change in state
icaused by oneRjreaction. In other words, if the system is in
statex, assumingx¼X(t), and oneRjreaction occurs, the system
instantaneously jumps to statex+νj. The second component ofRj
is its propensity functionaj(x) which is the probability of oneRj
reaction occurring in the infinitesimal time interval [t;t+dt].Appendix B: Software Tools
Beyond personal script to manage data, we have also used and
tested several public domain softwares, based on Qt and Python.
Here we suggest those we consider more flexible and accurate.
l COPASIis a Qt software application for simulation and analysis
of biochemical networks and their dynamics. COPASI is part of
de.NBI, the “German Network for Bioinformatics Infrastruc-
ture”. It is a stand-alone program that supports models in the
SBML standard and can simulate their behavior using ODEs or
Gillespie’s stochastic simulation algorithm; arbitrary discrete
events can be included in such simulations.http://copasi.org/
l PyCoTools a COPASI based tool, in Python, for para-
meter estimation and identifiability.https://github.com/
CiaranWelsh/PyCoTools
l SloppyCellis a Python software environment for simulation and
analysis of biomolecular networks, mainly developed for sloppy
models.http://sloppycell.sourceforge.net/
l Pycelleratorprovides python libraries, a command line inter-
face, and an ipython notebook interface for Cellerator arrow
notation.https://github.com/biomathman/pycellerator92 Rodolfo Guzzi et al.