P System Modelling Framework

Category Cross-Omics>Agent-Based Modeling/Simulation/Tools

Abstract The P System Modelling Framework is a framework for computation based on modeling with ‘P systems’ and various methodologies for executing them.

There are different approaches to evolving P systems and the framework can simulate each of these. The simulation produces output representing the state of the P system after a specific stage in computation.

The framework also incorporates model checking for verification and analysis of the P system.

Framework Description --

The framework simulates the evolution of the Multi-compartmental Gillespie algorithm over a hierarchy of compartment structures.

The kernel for the system has the following features, which aim to provide flexibility in simulation and modularization in modeling along with a model checking strategy:

1) Multi-compartments and Gillespie - The algorithm used to select a compartment and a rule in which to apply it is a variation of the stochastic Gillespie algorithm and is known as multi-compartmental Gillespie.

This creates the effect of many compartments running simultaneously under Gillespie.

2) Rule selection using probabilities and total parallelism - There are alternative mechanisms for selecting rules depending on the nature of the application.

The Gillespie algorithm assigns a ‘time’ in which each rule is applied, dependent on the availability of its reactants and a constant. Rule selection can be made in this way by applying the rule which has the shortest time.

Rule selection can also be made by ignoring the concentration of reactants and selecting a rule only by using the constant assigned to it as a probability that the rule will be applied.

There is another option to allow total parallelism, that is, once a rule is selected, it is applied the ‘maximum number’ of times that it can be applied for the number of reactants available.

3) Identify a set of rules with a value and be able to replicate them in other parts - Each compartment has a set of rules whose scope for application is the aforementioned compartment and it’s outside or inside compartment, that is, the compartment which is at the parent or a child node of the given compartment in the hierarchy tree.

The set of rules are defined and can be replicated by assigning the same set to different compartments.

4) Identify a compartment and replicate it with different initial values - A compartment or compartment hierarchy can be modulated in its ‘specification’ and then replicated many times in the model.

5) Strings in addition to objects - The species that are manipulated in the system can be Strings, in addition to objects.

6) Translation of a P system to PRISM - The specification of a P system can be translated for PRISM, (see below...) to provide model checking.


PRISM is a probabilistic model checker, a tool for formal modeling and analysis of systems which exhibit random or probabilistic behavior.

It supports three (3) types of probabilistic models: discrete-time Markov chains (DTMCs), continuous-time Markov chains (CTMCs) and Markov decision processes (MDPs), plus extensions of these models with costs and rewards.

PRISM has been used to analyze systems from a wide range of application domains, including communication and multimedia protocols, randomized distributed algorithms, security protocols, biological systems and many others.

Tools and implementations of the Framework --

A ‘P system model’ can be created in the following manner.

The P system is described in the Systems Biology Markup Language (SBML) format and a set of SBML notations is produced which describes the components of the system.

Aspects of the system that can be described separately can be specified by separate sub-systems and stored in separate files.

This is done to add comprehension of an individual system or sub-system and to allow this sub-system to be replicated in the final system that is to be simulated.

The components of the system are produced.

The SBML representations can then be transformed to construct a more specific model for simulation. The components specified can be replicated and further SBML representations can be created where the initial values of species may be changed.

For simulation, the SBML notations are transformed into the input format for the simulator. This file(s) contains the full list of compartments and the structural hierarchy and the initial amounts for their species.

This is a static view and the initial configuration of the system and it is subsequently given to the simulator to produce an evolution of the species through time.

1) Simulators --

The following simulators to evolve a P system are available:

a) An implementation of multi-compartment Gillespie, in Scilab (SL_PSimulator).

(Scilab is a scientific software package for numerical computations providing an advanced open computing environment for engineering and scientific applications).

b) An implementation of multi-compartmental Gillespie, in C - (C_PSimulator).

2) Other tools --

There are other tools to assist with the input and output of the simulator and they allow the creation of the input and graphical representation of the output.

a) Cell Designer - (see G6G Abstract Number 20159) - Cell Designer is an external software application that allows users to design P systems and save them in SBML (a XML schema).

b) SBML Converter - This tool has been developed with the simulator and allows the SBML representation of the P system to be converted into other formats suitable for simulations.

This tool takes in a set of SBML files describing parts of a P system and produces the resultant P system.

This allows a more complex system to be described in several files. The converter can then represent the system in various different formats of output and used as input for different simulators.

A compartment or compartment hierarchy can be replicated many times within the P system by specifying the number of replications and the environment to which to keep them in.

The path of the tree must be specified in the blueprint, but there can be many branches duplicated with the compartment sub-tree described, after the containing compartment node.

The output file(s) is compatible with SciLab (see above...) and spreadsheets such as OpenOffice Calc and MS Excel.

Case Studies --

Case Studies for Epidermal Growth Factor Receptor, FAS-Induced Apoptosis, and Quorum Sensing for marine bacterium Vibrio Fischeri are available on the manufacturer's web-site.

System Requirements

Contact manufacturer.


Manufacturer Web Site P System Modelling Framework

Price Contact manufacturer.

G6G Abstract Number 20595

G6G Manufacturer Number 104198