Extensions of ℓ₁ regularization increase detection specificity for cell-type specific parameters in dynamic models

Ordinary differential equation systems are frequently utilized to model biological systems and to infer knowledge about underlying properties. For instance, the development of drugs requires the knowledge to which extent malign cells differ from healthy ones to provide a specific treatment with least side effects. As these cell-type specific properties may stem from any part of biochemical cell processes, systematic quantitative approaches are necessary to identify the relevant potential drug targets. An ℓ₁ regularization for the maximum likelihood parameter estimation proved to be successful, but falsely predicted cell-type dependent behaviour had to be corrected manually by using a Profile Likelihood approach.

The choice of extended ℓ₁ penalty functions significantly decreased the number of falsely detected cell-type specific parameters. Thus, the total accuracy of the prediction could be increased. This was tested on a realistic dynamical benchmark model used for the DREAM6 challenge. Among Elastic Net, Adaptive Lasso and a non-convex ℓ_q penalty, the latter one showed the best predictions whilst also requiring least computation time. All extended methods include a hyper-parameter in the regularization function. For an Erythropoietin (EPO) induced signalling pathway, the extended methods ℓ_q and Adaptive Lasso revealed an unpublished alternative parsimonious model when varying the respective hyper-parameters.

Using ℓ_q or Adaptive Lasso with an a-priori choice for the hyper-parameter can lead to a more specific and accurate result than ℓ₁. Scanning different hyper-parameters can yield additional pieces of information about the system.