Modeling and identification of a gene regulatory network programming erythropoiesis (1)

The development of mature blood cells of distinct lineages from the hematopoietic stem cells (hematopoiesis) involves a progressive restriction of differentiation potential and the establishment of lineage-specific gene expression profiles. The establishment of these profiles relies on lineage-specific transcription factors to modulate the expression of their target genes. This work is embedded in a wider ErasmusMC/CWI collaboration that develops the informatics and mathematics to underpin studies on gene expression regulation by mapping and analyzing the regulatory pathways and networks of transcription factors that control cellular functions (so called 'Gene Regulatory Networks' or 'GRNs'). This project is concerned with the mathematical part and concentrates on a GRN central to erythropoiesis. Among the many housekeeping and tissue-specific genes involved in the differentiation and the commitment of hematopoietic stem cells to erythrocytes (erythropoiesis), we focus on a small pool of genes (Gata-1, Gata-2, Pu.1, EKLF, FOG-1, alpha/beta-globin) known to be critically involved in an intricate but well-less investigated regulatory circuit. Based on the regulatory interactions in the GRN we have developed models in the form of a system to account for the dynamics of gene expression and regulation involved in this process. Because of the lack of information about a significant number of model parameters, our focus is on system identification. In this first report some preliminary results are presented based on synthetic data. However, time series of the levels of all relevant mRNA’s are available from micro-array analysis of G1E cells, a murine cell line which recapitulates erythropoiesis. In the follow-up report a detailed account will be given of the parameter estimation and identifiability analysis with respect to these data. This will eventually allow for a thorough evaluation of the role of various characterized as well as hypothetical regulatory mechanisms. In depth characterization of the necessary expression patterns and gene regulatory interactions responsible for the the set of commitments all along the erythroid lineage is essential to gain fundamental insight into the behaviour of these complex networks and to design further experiments. Ultimately, this may lead to ways to rescue erythroid differentiation in several anemic diseases

Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods

Analysing the properties of a biological system through in silico experimentation requires a satisfactory mathematical representation of the system including accurate values of the model parameters. Fortunately, modern experimental techniques allow obtaining time-series data of appropriate quality which may then be used to estimate unknown parameters. However, in many cases, a subset of those parameters may not be uniquely estimated, independently of the experimental data available or the numerical techniques used for estimation. This lack of identifiability is related to the structure of the model, i.e. the system dynamics plus the observation function. Despite the interest in knowing a priori whether there is any chance of uniquely estimating all model unknown parameters, the structural identifiability analysis for general non-linear dynamic models is still an open question. There is no method amenable to every model, thus at some point we have to face the selection of one of the possibilities. This work presents a critical comparison of the currently available techniques. To this end, we perform the structural identifiability analysis of a collection of biological models. The results reveal that the generating series approach, in combination with identifiability tableaus, offers the most advantageous compromise among range of applicability, computational complexity and information provided

Systematic identifiability testing for unambiguous mechanistic modeling – application to JAK-STAT, MAP kinase, and NF-κB signaling pathway models

<p>Abstract</p> <p>Background</p> <p>When creating mechanistic mathematical models for biological signaling processes it is tempting to include as many known biochemical interactions into one large model as possible. For the JAK-STAT, MAP kinase, and NF-<it>κ</it>B pathways a lot of biological insight is available, and as a consequence, large mathematical models have emerged. For large models the question arises whether unknown model parameters can uniquely be determined by parameter estimation from measured data. Systematic approaches to answering this question are indispensable since the uniqueness of model parameter values is essential for predictive mechanistic modeling.</p> <p>Results</p> <p>We propose an eigenvalue based method for efficiently testing identifiability of large ordinary differential models and compare this approach to three existing ones. The methods are benchmarked by applying them to models of the signaling pathways mentioned above. In all cases the eigenvalue method proposed here and the orthogonal method find the largest set of identifiable parameters, thus clearly outperforming the other approaches. The identifiability analysis shows that the pathway models are not identifiable, even under the strong assumption that all system state variables are measurable. We demonstrate how the results of the identifiability analysis can be used for model simplification.</p> <p>Conclusion</p> <p>While it has undoubtedly contributed to recent advances in systems biology, mechanistic modeling by itself does not guarantee unambiguous descriptions of biological processes. We show that some recent signal transduction pathway models have reached a level of detail that is not warranted. Rigorous identifiability tests reveal that even if highly idealized experiments could be carried out to measure all state variables of these signaling pathways, some unknown parameters could still not be estimated. The identifiability tests therefore show that the level of detail of the investigated models is too high <it>in principle</it>, not just because too little experimental information is available. We demonstrate how the proposed method can be combined with biological insight, however, to simplify these models.</p