Spatially heterogeneous stochastic petri-net modeling

• US 20070050147A1
• Filed: 08/30/2005
• Published: 03/01/2007
• Est. Priority Date: 08/30/2005
• Status: Active Grant

• Current Assignee: International Business Machines Corporation
• Original Assignee: International Business Machines Corporation
• Inventors: Abdeen Hussan, Jagir
• Granted Patent: US 8,103,454 B2
• Time in Patent Office: Days
• US Class Current: 702/19
• CPC Class Codes: G16B 5/00 ICT specially adapted for modelling or simulations in systems biology, e.g. gene-regulatory networks, protein interaction networks or metabolic networks
• CPC Class Codes: G16B 5/30 Dynamic-time models
• CPC Class Codes: G16C 20/10 Analysis or design of chemical reactions, syntheses or processes

Abstract

Modeling of biochemical reactions of a system is accomplished using spatially heterogeneous stochastic Petri-net modeling. The biochemical reactions of the system to be modeled are defined. A spatial decomposition of the system is defined by defining regions of a space in which the system is to be modeled and by assigning each biochemical reaction to a region, such that the system is spatially heterogeneous. Relationships for inter-region movement of reactants of the biochemical reactions are defined as flux, advection, convection, and/or diffusion-based molecular movements. The system of the biochemical reactions is then modeled by modeling the biochemical reactions of each region as a spatially homogenous stochastic Petri-net and by modeling the inter-region movement of the reactants based on the relationships as defined.

Claims

1. A method comprising:

defining one or more biochemical reactions of a system to be modeled, each biochemical reaction having one or more reactants;

defining a spatial decomposition of the system by defining a plurality of regions of a space in which the system is to be modeled and by assigning each biochemical reaction to one of the regions, such that the system is spatially heterogeneous;

defining relationships for inter-region movement of the reactants of the biochemical reactions; and

,

modeling the system of the biochemical reactions by modeling the biochemical reactions of each region as a spatially homogenous stochastic Petri-net and by modeling the inter-region movement of the reactants based on the relationships defined.

2. The method of claim 1, wherein each of at least one of the reactants comprises a molecule.

3. The method of claim 1, wherein defining the biochemical reactions of the system to be modeled comprises, for each biochemical reaction:

defining a plurality of places of a stochastic Petri-net for the biochemical reaction;

defining a plurality of tokens for the biochemical reaction, each token corresponding to a reactant of the biochemical reaction and located in one of the places of the stochastic Petri-net for the biochemical reaction; and

,

defining one or more transitions of the stochastic Petri-net for the biochemical reaction, each transition corresponding to a reaction.

4. The method of claim 3, wherein each transition has one or more of the input/output functions each leading from a place and leading to the transition, the transition being enabled when each place leading to the transition via an input/output function has a number of tokens located therein greater than or equal to the weight of the input/output function.

5. The method of claim 3, wherein at least one of the places is each an output place having one or more of the input/output functions each leading to the output place and leading from another place or a transition, such that occurrence of each input/output function of the output place results in transfer of tokens from the other place or the transition leading from the input/output function to the output place.

6. The method of claim 3, wherein a global marking at a given time is defined for each biochemical reaction as a vector representing a number of tokens in each place at the given time.

7. The method of claim 1, wherein defining the spatial decomposition of the system comprises defining a quad-tree decomposition of the space in which the system is to be modeled.

8. The method of claim 1, wherein defining the spatial decomposition of the system comprises defining the spatial decomposition of the system with a degree of precision corresponding to a desired accuracy of modeling of the system.

9. The method of claim 1, wherein defining the plurality of regions of the space in which the system is to be modeled comprises defining each region as a unique three-dimensional sub-space of a three-dimensional space.

10. The method of claim 1, wherein defining the relationships for inter-region movement of the reactants of the biochemical reactions comprises defining at least one of flux-based molecular movement, advection-based molecular movement, convection-based molecular movement, and diffusion-based movement.

11. The method of claim 1, wherein modeling the system of the biochemical reactions comprises running the biochemical reactions of each region as a spatially homogenous stochastic Petri-net, such that the biochemical reactions of the regions interact with one another via the inter-region movement of the reactants.

12. The method of claim 1, further comprising performing one or more actions based on modeling of the system of the biochemical reactions.

13. The method of claim 12, wherein the actions performed comprise at least one of:

analyzing results of the modeling of the system of the biochemical reactions; and

,

adjusting the system of the biochemical reactions based on the results of the modeling of the system.

14. A system comprising:

one or more processors;

one or more computer-readable media storing data representing;

one or more biochemical reactions; and

,

a plurality of regions of a space, each biochemical reaction assigned to one of the regions, such that the biochemical reactions are spatially heterogeneous; and

,

a computer program executed by the processors to model the biochemical reactions of each region as a spatially homogenous stochastic Petri-net.

15. The system of claim 14, wherein the computer-readable media further store data representing one or more relationships for inter-region movement of the reactants, each of the relationships being one of flux-based molecular movement, advection-based molecular movement, convection-based molecular movement, and diffusion-based molecular movement, the computer program further to model inter-region movement of the reactants based on the relationships.

16. The system of claim 14, wherein the computer-readable media further store data representing, for each biochemical reaction:

a plurality of places of a stochastic Petri-net for the biochemical reaction;

a plurality of tokens for the biochemical reaction, each token corresponding to a reactant of the biochemical reaction and located in one of the places of the stochastic Petri-net for the biochemical reaction;

one or more transitions of the stochastic Petri-net for the biochemical reaction, each transition corresponding to a reaction;

a label for each transition of the stochastic Petri-net for the biochemical reaction, the label corresponding to a number of time steps that are to occur between successive firings of the transition;

one or more input/output functions of the stochastic Petri-net for the biochemical reaction, each input/output function linking an input place or transition to an output place or transition as a directed arc; and

,

a weight for each input/output function of the stochastic Petri-net for the biochemical reaction, each weight corresponding to a number of tokens required for the input/output function to occur.

17. The system of claim 16, wherein

each transition has one or more of the input/output functions each leading from a place and leading to the transition, the transition being enabled when each place leading to the transition via an input/output function has a number of tokens located therein greater than or equal to the weight of the input/output function, and

at least one of the places is each an output place having one or more of the input/output functions each leading to the output place and leading from another place or a transition, such that occurrence of each input/output function of the output place results in transfer of tokens from the other place or the transition leading from the input/output function to the output place.

18. An article of manufacture comprising:

a computer-readable medium; and

,

means for modeling a system of one or more biochemical reactions as a spatially heterogeneous stochastic Petri-net.

19. The article of manufacture of claim 18, wherein the means is to model each biochemical reaction as a spatially homogeneous stochastic Petri-net within a region of a space into which the system has been spatially heterogeneously decomposed.

20. The article of manufacture of claim 19, wherein the means is to model inter-region movement of reactants of the biochemical reactions based on at least one of advection-based molecular movement, convection-based molecular movement, and diffusion-based molecular.