title: L1 regularization facilitates detection of cell type-specific parameters in dynamical systems.
abstract: A major goal of drug development is to selectively target certain cell types. Cellular decisions influenced by drugs are often dependent on the dynamic processing of information. Selective responses can be achieved by differences between the involved cell types at levels of receptor, signaling, gene regulation or further downstream. Therefore, a systematic approach to detect and quantify cell type-specific parameters in dynamical systems becomes necessary.
  
  
  
  Here, we demonstrate that a combination of nonlinear modeling with L1 regularization is capable of detecting cell type-specific parameters. To adapt the least-squares numerical optimization routine to L1 regularization, sub-gradient strategies as well as truncation of proposed optimization steps were implemented. Likelihood-ratio tests were used to determine the optimal regularization strength resulting in a sparse solution in terms of a minimal number of cell type-specific parameters that is in agreement with the data. By applying our implementation to a realistic dynamical benchmark model of the DREAM6 challenge we were able to recover parameter differences with an accuracy of 78%. Within the subset of detected differences, 91% were in agreement with their true value. Furthermore, we found that the results could be improved using the profile likelihood. In conclusion, the approach constitutes a general method to infer an overarching model with a minimum number of individual parameters for the particular models.
  
  
  
  A MATLAB implementation is provided within the freely available, open-source modeling environment Data2Dynamics. Source code for all examples is provided online at http://www.data2dynamics.org/
  
  
  
  bernhard.steiert@fdm.uni-freiburg.de.
authors: Institute of Physics.
authors: Bernhard
authors: B
authors: Steiert
authors: Institute of Physics BIOSS Centre for Biological Signalling Studies Freiburg Center for Systems Biology (ZBSA), University of Freiburg, Germany.
authors: Jens
authors: J
authors: Timmer
authors: Institute of Physics Freiburg Center for Systems Biology (ZBSA), University of Freiburg, Germany.
authors: Clemens
authors: C
authors: Kreutz
mesh_terms: D000465:Algorithms; D002477:Cells / Q000145:classification*; D016503:Drug Delivery Systems; D016018:Least-Squares Analysis; D017711:Nonlinear Dynamics; D011336:Probability; D011381:Programming Languages; D015398:Signal Transduction