Section: New Results
Transient Behavior in Parametrized Dynamic Models
Participants : Macha Nikolski [ correspondant ] , Hayssam Soueidan, Grégoire Sutre.
Dynamic models in System Biology rely on kinetic parameters to represent the range of possible behaviors of when enzymatic information is incomplete. Analysis of these parametrized models aims at identifying either parameter ranges yielding similar qualitative behaviors, or parameter values yielding a given behavior of interest. Qualitative transient behavior can be successfully analyzed by model checking algorithms applied on models admitting a computable path semantics. However, in Systems Biology, state explosion and negative decidability results limit the scope of model checking to a certain subset of models. Moreover, some published and curated Systems Biology models lack explicit semantics, and for these “black box” models, not much can be assumed, except the possibility of generating simulation results. Mining these simulation results to identify parameter regions yielding similar behaviors is hindered by the size of the parameter space to explore, numerical artifacts and the lack of formal definition of what it means for simulation results to be similar.
We introduce Qualitative Transition Systems (QTS) and define their probabilistic semantics[22] . A novel abstraction operation is defined in with the goal of building QTSs from simulation results. We show that when constructing a QTS from an ODE, the QTS construction can be made independent of the numerical integration scheme. Trajectory comparison using QTS can be made more resistant to noise by detecting points of interest (extremums and inflection) through the construction of a piecewise linear approximation (PLA). We have validated our approach on a large set of SBML models from the BioModels database, including:

The cell cycle model of Tyson et al. (1991) based on interactions between Cdc2 and cyclin, where we investigate “similar” oscillatory behaviors with different transient behaviors.

The MAPK cascade model with negative feedback of Kholodenko (2000), in which we can compute the probability of oscillatory behavior in a large parameter subspace.

The model of crosstalk between an extracellular signal regulated kinase ERK and the Wnt pathway of Kim, Rath et al. (2007), successfully detecting the irreversible pathological response in the oncogenic positive feedback loop.