title: Parameter estimation for dynamical systems with discrete events and logical operations.
abstract: Ordinary differential equation (ODE) models are frequently used to describe the dynamic behaviour of biochemical processes. Such ODE models are often extended by events to describe the effect of fast latent processes on the process dynamics. To exploit the predictive power of ODE models, their parameters have to be inferred from experimental data. For models without events, gradient based optimization schemes perform well for parameter estimation, when sensitivity equations are used for gradient computation. Yet, sensitivity equations for models with parameter- and state-dependent events and event-triggered observations are not supported by existing toolboxes.
  
  
  
  In this manuscript, we describe the sensitivity equations for differential equation models with events and demonstrate how to estimate parameters from event-resolved data using event-triggered observations in parameter estimation. We consider a model for GFP expression after transfection and a model for spiking neurons and demonstrate that we can improve computational efficiency and robustness of parameter estimation by using sensitivity equations for systems with events. Moreover, we demonstrate that, by using event-outputs, it is possible to consider event-resolved data, such as time-to-event data, for parameter estimation with ODE models. By providing a user-friendly, modular implementation in the toolbox AMICI, the developed methods are made publicly available and can be integrated in other systems biology toolboxes.
  
  
  
  We implement the methods in the open-source toolbox Advanced MATLAB Interface for CVODES and IDAS (AMICI, https://github.com/ICB-DCM/AMICI ).
  
  
  
  jan.hasenauer@helmholtz-muenchen.de.
  
  
  
  Supplementary data are available at Bioinformatics online.
authors.affiliation: Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg 85764, Germany.|Center for Mathematics, Technische Universität München, Garching 85748, Germany.
authors.forename: Fabian
authors.initials: F
authors.lastname: Fröhlich
authors.affiliation: Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg 85764, Germany.|Center for Mathematics, Technische Universität München, Garching 85748, Germany.
authors.forename: Fabian J
authors.initials: FJ
authors.lastname: Theis
authors.affiliation: Faculty of Physics, Ludwig-Maximilians-Universität, München 80539, Germany.
authors.forename: Joachim O
authors.initials: JO
authors.lastname: Rädler
authors.affiliation: Institute of Computational Biology, Helmholtz Zentrum München, Neuherberg 85764, Germany.|Center for Mathematics, Technische Universität München, Garching 85748, Germany.
authors.forename: Jan
authors.initials: J
authors.lastname: Hasenauer
mesh_terms: D019295:Computational Biology / Q000379:methods; D049452:Green Fluorescent Proteins / Q000235:genetics / Q000378:metabolism; D008564:Membrane Potentials; D008954:Models, Biological; D009474:Neurons / Q000502:physiology; D012984:Software; D049490:Systems Biology; D014162:Transfection
chemical_list: D049452:Green Fluorescent Proteins