Automatic selection of time interval size in implicit tau-leaping algorithm

Patent metadata

Field	Value
Publication number	US-9811640-B1
Application number	US-37431606-A
Country	US
Kind code	B1
Filing date	Mar 13, 2006
Priority date	Mar 13, 2006
Publication date	Nov 7, 2017
Grant date	Nov 7, 2017

Abstract

A modeling and simulation environment enables a user to create a model of a stiff chemical or biological system. The stiff chemical or biological system refers to a system that includes at least two or more different time scales of the chemical or biochemical reactions. The modeling and simulation environment also enables the user to solve the stiff chemical or biological system using a leaping algorithm. The leaping algorithm may leap over simulation of the reactions occurring in the time interval to accelerate the simulation of the chemical or biological system. The algorithm maximizes the size of the time interval by adjusting the size of the time interval using a bracketing algorithm.

First claim

The invention claimed is:

1. A method comprising:
determining an initial value of a time interval for execution of a model using a leaping algorithm,
the model being associated with a chemical system or a biological system, and
the determining being performed by a computing device;

adjusting the initial value of the time interval using a bracketing algorithm,
the adjusting being performed by the computing device, and
the adjusting comprising:
providing an upper limit for the time interval and a lower limit for the time interval; and
determining, a first time, if a leap condition is satisfied for the model over the time interval,
the determining if the leap condition is satisfied comprising:
 setting the lower limit for the time interval as the initial value and increasing the initial value when the leap condition is satisfied, and
 setting the upper limit for the time interval as the initial value and decreasing the initial value when the leap condition is not satisfied;

comparing a distance between the lower limit and the upper limit to a predetermined distance,
the lower limit being selected as a final time interval when the distance between the lower limit and the upper limit is less than the predetermined distance,
the determination if the leap condition is satisfied being performed a second time when the distance between the lower limit and the upper limit is greater than the predetermined distance, and
the comparing being performed by the computing device;

simulating the chemical system or the biological system using the model and using time steps corresponding to the final time interval to generate a simulation result,
the simulating being performed by the computing device; and

outputting the simulation result for analysis,
the outputting being performed by the computing device.

2. The method of claim 1 , where the leaping algorithm comprises a tau(τ)-leaping algorithm.

3. The method of claim 2 , where a state of the model at time (t+τ) is a function of a state of the model at time t and the state of the model at time (t+τ).

4. The method of claim 2 , where the initial value of the time interval is determined by an equation provided for a non-discrete τ-leaping algorithm.

5. The method of claim 2 , where a state of the model at time (t+τ) is provided as a function of a state of the model at time t.

6. The method of claim 1 , further comprising:
determining the leap condition based on a user-defined tolerance of a relative change in a state of the model.

7. The method of claim 1 , where the lower limit satisfies the leap condition and the upper limit does not satisfy the leap condition.

8. The method of claim 1 , where the initial value of the time interval is increased or decreased using a predetermined ratio.

9. The method of claim 1 , further comprising:
determining a point between the lower limit and the upper limit; and
determining whether the point satisfies the leap condition.

10. The method of claim 9 , further comprising:
updating, a first time, the lower limit with the point when the point satisfies the leap condition; or
updating, a first time, the upper limit with the point when the point does not satisfy the leap condition.

11. The method of claim 10 , further comprising:
updating the lower limit a second time;
updating the upper limit a second time; and
setting, based on updating the lower limit the second time and updating the upper limit the second time, a size of the time interval to the lower limit.

12. The method of claim 1 , where a plurality of discrete events, associated with the model, are associated with at least two different time scales.

13. A non-transitory computer-readable medium storing instructions, the instructions comprising:
one or more instructions which, when executed by at least one processor, cause the at least one processor to:
determine an initial value of a time interval for execution of a model using a leaping algorithm,
the model being associated with a chemical system or a biological system;

adjust the initial value of the time interval using a bracketing algorithm, the one or more instructions to adjust the initial value including:
one or more instructions to provide an upper limit for the time interval and a lower limit for the time interval; and
one or more instructions to determine, a first time, if a leap condition is satisfied for the model over the time interval, the one or more instructions to determine if the leap condition is satisfied including:
one or more instructions to set the lower limit for the time interval as the initial value and increase the initial value when the leap condition is satisfied, and
one or more instructions to set the upper limit for the time interval as the initial value and decrease the initial value when the leap condition is not satisfied;

compare a distance between the lower limit and the upper limit to a predetermined distance,
the lower limit being selected as a final time interval when the distance between the lower limit and the upper limit is less than the predetermined distance, and
the determination if the leap condition is satisfied being performed a second time when the distance between the lower limit and the upper limit is greater than the predetermined distance;

simulate the chemical system or the biological system using the model and using time steps corresponding to the final time interval to generate a simulation result; and
output the simulation result for analysis.

14. The non-transitory computer-readable medium of claim 13 , where the leaping algorithm comprises a tau(τ)-leaping algorithm.

15. The non-transitory computer-readable medium of claim 14 , where a state of the model at time (t+τ) is a function of a state of the model at time t and the state of the model at time (t+τ).

16. The non-transitory computer-readable medium of claim 14 , where the initial value of the time interval is determined by an equation provided for a non-discrete τ-leaping algorithm.

17. The non-transitory computer-readable medium of claim 16 , where a state of the model at time (t+τ) is a function of a state of the model at time t.

18. The non-transitory computer-readable medium of claim 13 , where the instructions further include:
one or more instructions to determine the leap condition based on a user-defined tolerance of a relative change in a state of the model.

19. The non-transitory computer-readable medium of claim 13 , where the lower limit satisfies the leap condition and the upper limit does not satisfy the leap condition.

20. The non-transitory computer-readable medium of claim 13 , where the initial value of the time interval is increased or decreased using a predetermined ratio.

21. The non-transitory computer-readable medium of claim 13 , where the instructions further include:
one or more instructions to determine a point between the lower limit and the upper limit; and
one or more instructions to determine whether the point satisfies the leap condition.

22. The non-transitory computer-readable medium of claim 21 , where the instructions further include:
one or more instructions to update, a first time, the lower limit with the point when the point satisfies the leap condition; or
one or more instructions to update, a first time, the upper limit with the point when the point does not satisfy the leap condition.

23. The non-transitory computer-readable medium of claim 22 , whe

Assignees

• Savant Shrikant Vitthal
• Mathworks Inc

Inventors

• Savant Shrikant Vitthal

Classifications

• G06F19/32

  Physics · mapped topic

• G06F19/70 Primary

  Physics · mapped topic

• G06F19/30

  Physics · mapped topic

• G16C20/10

  Analysis or design of chemical reactions, syntheses or processes · CPC title

• G16B5/20 Primary

  Probabilistic models · CPC title