Delayed continuous time Markov chains for genetic regulatory circuits Conference Paper

Author(s): Guet, Calin; Gupta, Ashutosh; Henzinger, Thomas A; Mateescu, Maria; Sezgin, Ali
Title: Delayed continuous time Markov chains for genetic regulatory circuits
Title Series: LNCS
Affiliation IST Austria
Abstract: Continuous-time Markov chains (CTMC) with their rich theory and efficient simulation algorithms have been successfully used in modeling stochastic processes in diverse areas such as computer science, physics, and biology. However, systems that comprise non-instantaneous events cannot be accurately and efficiently modeled with CTMCs. In this paper we define delayed CTMCs, an extension of CTMCs that allows for the specification of a lower bound on the time interval between an event's initiation and its completion, and we propose an algorithm for the computation of their behavior. Our algorithm effectively decomposes the computation into two stages: a pure CTMC governs event initiations while a deterministic process guarantees lower bounds on event completion times. Furthermore, from the nature of delayed CTMCs, we obtain a parallelized version of our algorithm. We use our formalism to model genetic regulatory circuits (biological systems where delayed events are common) and report on the results of our numerical algorithm as run on a cluster. We compare performance and accuracy of our results with results obtained by using pure CTMCs. © 2012 Springer-Verlag.
Conference Title: CAV: Computer Aided Verification
Volume: 7358
Conference Dates: July 7-13, 2012
Conference Location: Berkeley, CA, USA
Publisher: Springer  
Date Published: 2012-01-01
Start Page: 294
End Page: 309
Sponsor: This work was supported by the ERC Advanced Investigator grant on Quantitative Reactive Modeling (QUAREM) and by the Swiss National Science Foundation.
DOI: 10.1007/978-3-642-31424-7_24
Open access: no
IST Austria Authors
  1. Thomas A. Henzinger
    415 Henzinger
  2. Călin Guet
    31 Guet
  3.  Ali Sezgin
    5 Sezgin
  4. Ashutosh Gupta
    16 Gupta
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