MOTIVATION: Apparent time delays in partly observed, biochemical reaction networks can be modelled by lumping a more complex reaction into a series of linear reactions often referred to as the linear chain trick. Since most delays in biochemical reactions are no true, hard delays but a consequence of complex unobserved processes, this approach often more closely represents the true system compared with delay differential equations. In this paper, we address the question of how to select the optimal number of additional equations, i.e. the chain length (CL). RESULTS: We derive a criterion based on parameter identifiability to infer CLs and compare this method to choosing the model with a CL that leads to the best fit in a maximum likelihood sense, which corresponds to optimizing the Bayesian information criterion. We evaluate performance with simulated data as well as with measured biological data for a model of JAK2/STAT5 signalling and access the influence of different model structures and data characteristics. Our analysis revealed that the proposed method features a superior performance when applied to biological models and data compared with choosing the model that maximizes the likelihood. AVAILABILITY AND IMPLEMENTATION: Models and data used for simulations are available at https://github.com/Data2Dynamics/d2d and http://jeti.uni-freiburg.de/PNAS_Swameye_Data. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

UNLABELLED: Modeling of dynamical systems using ordinary differential equations is a popular approach in the field of systems biology. Two of the most critical steps in this approach are to construct dynamical models of biochemical reaction networks for large datasets and complex experimental conditions and to perform efficient and reliable parameter estimation for model fitting. We present a modeling environment for MATLAB that pioneers these challenges. The numerically expensive parts of the calculations such as the solving of the differential equations and of the associated sensitivity system are parallelized and automatically compiled into efficient C code. A variety of parameter estimation algorithms as well as frequentist and Bayesian methods for uncertainty analysis have been implemented and used on a range of applications that lead to publications. AVAILABILITY AND IMPLEMENTATION: The Data2Dynamics modeling environment is MATLAB based, open source and freely available at http://www.data2dynamics.org. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.