@inproceedings{3136,
  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.},
  author       = {Guet, Calin C and Gupta, Ashutosh and Henzinger, Thomas A and Mateescu, Maria and Sezgin, Ali},
  location     = {Berkeley, CA, USA},
  pages        = {294 -- 309},
  publisher    = {Springer},
  title        = {{Delayed continuous time Markov chains for genetic regulatory circuits}},
  doi          = {10.1007/978-3-642-31424-7_24},
  volume       = {7358 },
  year         = {2012},
}

@article{6496,
  abstract     = {We report the switching behavior of the full bacterial flagellum system that includes the filament and the motor in wild-type Escherichia coli cells. In sorting the motor behavior by the clockwise bias, we find that the distributions of the clockwise (CW) and counterclockwise (CCW) intervals are either exponential or nonexponential with long tails. At low bias, CW intervals are exponentially distributed and CCW intervals exhibit long tails. At intermediate CW bias (0.5) both CW and CCW intervals are mainly exponentially distributed. A simple model suggests that these two distinct switching behaviors are governed by the presence of signaling noise within the chemotaxis network. Low noise yields exponentially distributed intervals, whereas large noise yields nonexponential behavior with long tails. These drastically different motor statistics may play a role in optimizing bacterial behavior for a wide range of environmental conditions.},
  author       = {Park, Heungwon and Oikonomou, Panos and Guet, Calin C and Cluzel, Philippe},
  issn         = {0006-3495},
  journal      = {Biophysical Journal},
  number       = {10},
  pages        = {2336--2340},
  publisher    = {Elsevier},
  title        = {{Noise underlies switching behavior of the bacterial flagellum}},
  doi          = {10.1016/j.bpj.2011.09.040},
  volume       = {101},
  year         = {2011},
}

@inproceedings{3719,
  abstract     = {The induction of a signaling pathway is characterized by transient complex formation and mutual posttranslational modification of proteins. To faithfully capture this combinatorial process in a math- ematical model is an important challenge in systems biology. Exploiting the limited context on which most binding and modification events are conditioned, attempts have been made to reduce the com- binatorial complexity by quotienting the reachable set of molecular species, into species aggregates while preserving the deterministic semantics of the thermodynamic limit. Recently we proposed a quotienting that also preserves the stochastic semantics and that is complete in the sense that the semantics of individual species can be recovered from the aggregate semantics. In this paper we prove that this quotienting yields a sufficient condition for weak lumpability and that it gives rise to a backward Markov bisimulation between the original and aggregated transition system. We illustrate the framework on a case study of the EGF/insulin receptor crosstalk.},
  author       = {Feret, Jérôme and Henzinger, Thomas A and Koeppl, Heinz and Petrov, Tatjana},
  location     = {Jena, Germany},
  pages        = {142--161},
  publisher    = {Open Publishing Association},
  title        = {{Lumpability abstractions of rule-based systems}},
  volume       = {40},
  year         = {2010},
}

@inproceedings{3847,
  abstract     = {The importance of stochasticity within biological systems has been shown repeatedly during the last years and has raised the need for efficient stochastic tools. We present SABRE, a tool for stochastic analysis of biochemical reaction networks. SABRE implements fast adaptive uniformization (FAU), a direct numerical approximation algorithm for computing transient solutions of biochemical reaction networks. Biochemical reactions networks represent biological systems studied at a molecular level and these reactions can be modeled as transitions of a Markov chain. SABRE accepts as input the formalism of guarded commands, which it interprets either as continuous-time or as discrete-time Markov chains. Besides operating in a stochastic mode, SABRE may also perform a deterministic analysis by directly computing a mean-field approximation of the system under study. We illustrate the different functionalities of SABRE by means of biological case studies.},
  author       = {Didier, Frédéric and Henzinger, Thomas A and Mateescu, Maria and Wolf, Verena},
  location     = {Williamsburg, USA},
  pages        = {193 -- 194},
  publisher    = {IEEE},
  title        = {{SABRE: A tool for the stochastic analysis of biochemical reaction networks}},
  doi          = {10.1109/QEST.2010.33},
  year         = {2010},
}

@inproceedings{3843,
  abstract     = {Within systems biology there is an increasing interest in the stochastic behavior of biochemical reaction networks. An appropriate stochastic description is provided by the chemical master equation, which represents a continuous- time Markov chain (CTMC).
Standard Uniformization (SU) is an efficient method for the transient analysis of CTMCs. For systems with very different time scales, such as biochemical reaction networks, SU is computationally expensive. In these cases, a variant of SU, called adaptive uniformization (AU), is known to reduce the large number of iterations needed by SU. The additional difficulty of AU is that it requires the solution of a birth process.
In this paper we present an on-the-fly variant of AU, where we improve the original algorithm for AU at the cost of a small approximation error. By means of several examples, we show that our approach is particularly well-suited for biochemical reaction networks.},
  author       = {Didier, Frédéric and Henzinger, Thomas A and Mateescu, Maria and Wolf, Verena},
  location     = {Trento, Italy},
  number       = {6},
  pages        = {118 -- 127},
  publisher    = {IEEE},
  title        = {{Fast adaptive uniformization of the chemical master equation}},
  doi          = {10.1109/HiBi.2009.23},
  volume       = {4},
  year         = {2009},
}