SEEDS: data driven inference of structural model errors and unknown inputs for dynamic systems biology.

SUMMARY: Dynamic models formulated as ordinary differential equations can provide information about the mechanistic and causal interactions in biological systems to guide targeted interventions and to design further experiments. Inaccurate knowledge about the structure, functional form and parameters of interactions is a major obstacle to mechanistic modeling. A further challenge is the open nature of biological systems which receive unknown inputs from their environment. The R-package SEEDS implements two recently developed algorithms to infer structural model errors and unknown inputs from output measurements. This information can facilitate efficient model recalibration as well as experimental design in the case of misfits between the initial model and data. AVAILABILITY AND IMPLEMENTATION: For the R-package seeds, see the CRAN server https://cran.r-project.org/package=seeds.

Searching for Errors in Models of Complex Dynamic Systems.

Mathematical modeling is seen as a key step to understand, predict, and control the temporal dynamics of interacting systems in such diverse areas like physics, biology, medicine, and economics. However, for large and complex systems we usually have only partial knowledge about the network, the coupling functions, and the interactions with the environment governing the dynamic behavior. This incomplete knowledge induces structural model errors which can in turn be the cause of erroneous model predictions or misguided interpretations. Uncovering the location of such structural model errors in large networks can be a daunting task for a modeler. Here, we present a data driven method to search for structural model errors and to confine their position in large and complex dynamic networks. We introduce a coherence measure for pairs of network nodes, which indicates, how difficult it is to distinguish these nodes as sources of an error. By clustering network nodes into coherence groups and inferring the cluster inputs we can decide, which cluster is affected by an error. We demonstrate the utility of our method for the C. elegans neural network, for a signal transduction model for UV-B light induced morphogenesis and for synthetic examples.