Abstract : The last couple of years has seen a flurry of research output on the topic of model reduction based on reactions evolving on disparate timescales. This minisymposium will provide the opportunity to present & discuss the state-of-the-art in this field from multiple angles spanning mathematical theory to synthetic biology and other biochemical applications, and its challenges.
Organizer(s) : Martin Wechselberger, Jae Kyoung Kim,
02541 (1/2) : 2C @G402 [Chair: Martin Wechselberger]
[04793] The relationship between deterministic and stochastic quasi-steady-state
Format : Talk at Waseda University
Author(s) :
Jae Kyoung Kim (KAIST)
Abstract : The quasi steady-state approximation (QSSA) is frequently used to reduce de- terministic models of biochemical networks. The resulting equations provide a simplified description of the network in terms of non-elementary reaction functions (e.g. Hill functions). Such deterministic reductions are frequently a basis for heuristic stochastic models in which non-elementary reaction functions are used as propensities of Gillespie algorithm. Despite the popularity of this heuristic stochastic simulations, it remains unclear when such stochastic reductions are valid. In this talk, I will present conditions under which the stochastic models with the non-elementary propensity functions accurately approximate the full stochastic models. If the validity condition is satisfied, we can perform accurate and computationally inexpensive stochastic simulation without converting the non-elementary functions to the elementary functions (e.g. mass action kinetics).
[04404] Noise attenuation and ultrasensitivity in biological oscillators utilizing the multiple transcriptional repression mechanism
Format : Talk at Waseda University
Author(s) :
Eui Min Jeong (Institute for Basic Science (IBS))
Jae Kyoung Kim (Institute for Basic Science (IBS))
Yun Min Song (KAIST)
Abstract : In many biological systems, multiple repression mechanisms are used together to inhibit transcriptional activators in many systems. This raises the question of what advantages arise from utilizing multiple repression mechanisms. Here, by deriving Fano factors and equations describing the multiple repression mechanisms, we find that their combination can reduce noise in the transcription while generating an ultrasensitive transcription response and thus, strong oscillation. This rationalizes why multiple repression mechanisms are used in various biological oscillators.
[04800] Reduction of Chemical Reaction Networks with Approximate Conservation Laws
Format : Talk at Waseda University
Author(s) :
Ovidiu Radulescu (University of Montpellier)
Aurelien Desoeuvres (University of Montpelleir)
Alexandre Iosif (Rey Juan Carlos University of Madrid)
Christopher Lueders (University of Bonn)
Hamid Rahkooy (University of Oxford)
Matthias Seiss (University of Kassel)
Thomas Sturm (CNRS )
Abstract : Singular perturbation methods are used to reduce multiple timescale chemical reaction networks, but their practical applicability is limited by the manual identification of the small parameters required by the theory. Recently, we have shown that tropical geometry provides ways to rescale CRNs and to identify the small parameters used by singular perturbation theories. Here we consider the case when the fast subsystem has first integrals, not covered by our previous results.
[04454] A deep dive into the quasi-steady-state approximation to the Michaelis-Menten system
Abstract : Although the quasi-steady state approximation (QSSA) is justifiable from singular perturbation theory, the results addressing its accuracy rely on heuristic timescale estimates. We take a different approach. By combining phase plane analysis with differential inequalities, we obtain rigorous bounds on the accuracy of the QSSA. Moreover, under the assumption the QSSA is valid at the onset of the reaction, we obtain an error estimate that is order one in the Segel--Slemrod parameter.
[04203] Multiple timescales in reaction networks and the parametrisation method
Format : Talk at Waseda University
Author(s) :
Martin Wechselberger (University of Sydney)
Ian Lizarraga (University of Sydney)
Bob Rink (Vrije Universiteit Amsterdam)
Abstract : Many biochemical reaction network problems display distinct temporal features, which can be attributed to processes taking place on multiple timescales. In mathematical terms, such multiple timescale models are in fact singular perturbation problems. We present a parametrisation method for computing slow manifolds and their fast fibre bundles in such singular perturbation problems. In particular, we highlight the emergence of hidden timescales and show how our method can uncover these surprising multiple timescale structures.
