---
_id: '2056'
abstract:
- lang: eng
  text: 'We consider a continuous-time Markov chain (CTMC) whose state space is partitioned
    into aggregates, and each aggregate is assigned a probability measure. A sufficient
    condition for defining a CTMC over the aggregates is presented as a variant of
    weak lumpability, which also characterizes that the measure over the original
    process can be recovered from that of the aggregated one. We show how the applicability
    of de-aggregation depends on the initial distribution. The application section
    is devoted to illustrate how the developed theory aids in reducing CTMC models
    of biochemical systems particularly in connection to protein-protein interactions.
    We assume that the model is written by a biologist in form of site-graph-rewrite
    rules. Site-graph-rewrite rules compactly express that, often, only a local context
    of a protein (instead of a full molecular species) needs to be in a certain configuration
    in order to trigger a reaction event. This observation leads to suitable aggregate
    Markov chains with smaller state spaces, thereby providing sufficient reduction
    in computational complexity. This is further exemplified in two case studies:
    simple unbounded polymerization and early EGFR/insulin crosstalk.'
acknowledgement: T. Petrov is supported by SystemsX.ch—the Swiss Inititative for Systems
  Biology.
article_processing_charge: No
arxiv: 1
author:
- first_name: Arnab
  full_name: Ganguly, Arnab
  last_name: Ganguly
- first_name: Tatjana
  full_name: Petrov, Tatjana
  id: 3D5811FC-F248-11E8-B48F-1D18A9856A87
  last_name: Petrov
  orcid: 0000-0002-9041-0905
- first_name: Heinz
  full_name: Koeppl, Heinz
  last_name: Koeppl
citation:
  ama: Ganguly A, Petrov T, Koeppl H. Markov chain aggregation and its applications
    to combinatorial reaction networks. <i>Journal of Mathematical Biology</i>. 2014;69(3):767-797.
    doi:<a href="https://doi.org/10.1007/s00285-013-0738-7">10.1007/s00285-013-0738-7</a>
  apa: Ganguly, A., Petrov, T., &#38; Koeppl, H. (2014). Markov chain aggregation
    and its applications to combinatorial reaction networks. <i>Journal of Mathematical
    Biology</i>. Springer. <a href="https://doi.org/10.1007/s00285-013-0738-7">https://doi.org/10.1007/s00285-013-0738-7</a>
  chicago: Ganguly, Arnab, Tatjana Petrov, and Heinz Koeppl. “Markov Chain Aggregation
    and Its Applications to Combinatorial Reaction Networks.” <i>Journal of Mathematical
    Biology</i>. Springer, 2014. <a href="https://doi.org/10.1007/s00285-013-0738-7">https://doi.org/10.1007/s00285-013-0738-7</a>.
  ieee: A. Ganguly, T. Petrov, and H. Koeppl, “Markov chain aggregation and its applications
    to combinatorial reaction networks,” <i>Journal of Mathematical Biology</i>, vol.
    69, no. 3. Springer, pp. 767–797, 2014.
  ista: Ganguly A, Petrov T, Koeppl H. 2014. Markov chain aggregation and its applications
    to combinatorial reaction networks. Journal of Mathematical Biology. 69(3), 767–797.
  mla: Ganguly, Arnab, et al. “Markov Chain Aggregation and Its Applications to Combinatorial
    Reaction Networks.” <i>Journal of Mathematical Biology</i>, vol. 69, no. 3, Springer,
    2014, pp. 767–97, doi:<a href="https://doi.org/10.1007/s00285-013-0738-7">10.1007/s00285-013-0738-7</a>.
  short: A. Ganguly, T. Petrov, H. Koeppl, Journal of Mathematical Biology 69 (2014)
    767–797.
date_created: 2018-12-11T11:55:28Z
date_published: 2014-11-20T00:00:00Z
date_updated: 2025-09-29T11:50:22Z
day: '20'
department:
- _id: CaGu
- _id: ToHe
doi: 10.1007/s00285-013-0738-7
external_id:
  arxiv:
  - '1303.4532'
  isi:
  - '000340588700008'
fulldoi: https://doi.org/10.1007/s00285-013-0738-7
intvolume: '        69'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: http://arxiv.org/abs/1303.4532
month: '11'
oa: 1
oa_version: Submitted Version
page: 767 - 797
publication: Journal of Mathematical Biology
publication_status: published
publisher: Springer
publist_id: '4990'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Markov chain aggregation and its applications to combinatorial reaction networks
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 69
year: '2014'
...