The Enhanced Finite State Projection algorithm, using conditional moment closure and time-scale separation
Name
1122563666-MIT.pdf
Size
3.05 MB
Format
Adobe PDF
Checksum (MD5)
39223f30f9d6e993344143cfc243b7ec
Author(s)
Kwon, Ukjin.
Advisor(s)
Domitilla Del Vecchio.
Date Issued
2019
Publisher
Massachusetts Institute of Technology
Abstract
The Chemical Master Equation (CME) is commonly used to describe the stochastic behavior of biomolecular systems. However, in general, the CME's dimension is very large or infinite, so analytical solutions may be difficult to achieve. To handle this problem, the Finite State Projection (FSP) algorithm can be used. However, when multiple time scales exist, which is common in biomolecular systems, the FSP algorithm also suffers from the computational issue. To deal with this problem, we propose the Enhanced Finite State Projection (EFSP) algorithm, which combines the original FSP algorithm and the model reduction technique that we developed, to approximate an infinite dimensional CME with a finite dimensional CME that contains the slow species only. We quantify the approximation error between the slow-species counts' marginal probability distribution of the original CME and those of the approximated CME, and prove that this error becomes smaller as 3 (the EFSP error) or E (time-scale separation between the fast and slow species) decreases. Unlike other time-scale separation methods, which rely on the fast-species counts' stationary conditional probability distributions, our model reduction technique relies on only the first few conditional moments of the fast-species counts. This is possible because we apply conditional moment closure to close the fast-species counts' dynamics, which provides a significant computation advantage. The benefit of our algorithm is illustrated through a protein binding reaction and a toggle switch.
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2019
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 59-61).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.
Persistent DSpace Link
