Likelihood based observability analysis and confidence intervals for predictions of dynamic models

Mechanistic dynamic models of biochemical networks such as Ordinary Differential Equations (ODEs) contain unknown parameters like the reaction rate constants and the initial concentrations of the compounds. The large number of parameters as well as their nonlinear impact on the model responses hamper the determination of confidence regions for parameter estimates. At the same time, classical approaches translating the uncertainty of the parameters into confidence intervals for model predictions are hardly feasible. In this article it is shown that a so-called prediction profile likelihood yields reliable confidence intervals for model predictions, despite arbitrarily complex and high-dimensional shapes of the confidence regions for the estimated parameters. Prediction confidence intervals of the dynamic states allow a data-based observability analysis. The approach renders the issue of sampling a high-dimensional parameter space into evaluating one-dimensional prediction spaces. The method is also applicable if there are non-identifiable parameters yielding to some insufficiently specified model predictions that can be interpreted as non-observability. Moreover, a validation profile likelihood is introduced that should be applied when noisy validation experiments are to be interpreted. The properties and applicability of the prediction and validation profile likelihood approaches are demonstrated by two examples, a small and instructive ODE model describing two consecutive reactions, and a realistic ODE model for the MAP kinase signal transduction pathway. The presented general approach constitutes a concept for observability analysis and for generating reliable confidence intervals of model predictions, not only, but especially suitable for mathematical models of biological systems

In silico labeling reveals the time-dependent label half-life and transit-time in dynamical systems

Background: Mathematical models of dynamical systems facilitate the computation of characteristic properties that are not accessible experimentally. In cell biology, two main properties of interest are (1) the time-period a protein is accessible to other molecules in a certain state - its half-life - and (2) the time it spends when passing through a subsystem - its transit-time. We discuss two approaches to quantify the half-life, present the novel method of in silico labeling, and introduce the label half-life and label transit-time. The developed method has been motivated by laboratory tracer experiments. To investigate the kinetic properties and behavior of a substance of interest, we computationally label this species in order to track it throughout its life cycle. The corresponding mathematical model is extended by an additional set of reactions for the labeled species, avoiding any double-counting within closed circuits, correcting for the influences of upstream fluxes, and taking into account combinatorial multiplicity for complexes or reactions with several reactants or products. A profile likelihood approach is used to estimate confidence intervals on the label half-life and transit-time. Results: Application to the JAK-STAT signaling pathway in Epo-stimulated BaF3-EpoR cells enabled the calculation of the time-dependent label half-life and transit-time of STAT species. The results were robust against parameter uncertainties. Conclusions: Our approach renders possible the estimation of species and label half-lives and transit-times. It is applicable to large non-linear systems and an implementation is provided within the PottersWheel modeling framework (http://www.potterswheel.de)

IL-1β-induced and p38MAPK-dependent activation of the mitogen-activated protein kinase-activated protein kinase 2 (MK2) in hepatocytes: signal transduction with robust and concentration-independent signal amplification

The IL-1β induced activation of the p38MAPK/MAPK-activated protein kinase 2 (MK2) pathway in hepatocytes is important for control of the acute phase response and regulation of liver regeneration. Many aspects of the regulatory relevance of this pathway have been investigated in immune cells in the context of inflammation. However, very little is known about concentration-dependent activation kinetics and signal propagation in hepatocytes and the role of MK2. We established a mathematical model for IL-1β-induced activation of the p38MAPK/MK2 pathway in hepatocytes that was calibrated to quantitative data on time- and IL-1β concentration-dependent phosphorylation of p38MAPK and MK2 in primary mouse hepatocytes. This analysis showed that, in hepatocytes, signal transduction from IL-1β via p38MAPK to MK2 is characterized by strong signal amplification. Quantification of p38MAPK and MK2 revealed that, in hepatocytes, at maximum, 11.3% of p38MAPK molecules and 36.5% of MK2 molecules are activated in response to IL-1β. The mathematical model was experimentally validated by employing phosphatase inhibitors and the p38MAPK inhibitor SB203580. Model simulations predicted an IC50 of 1–1.2 μm for SB203580 in hepatocytes. In silico analyses and experimental validation demonstrated that the kinase activity of p38MAPK determines signal amplitude, whereas phosphatase activity affects both signal amplitude and duration. p38MAPK and MK2 concentrations and responsiveness toward IL-1β were quantitatively compared between hepatocytes and macrophages. In macrophages, the absolute p38MAPK and MK2 concentration was significantly higher. Finally, in line with experimental observations, the mathematical model predicted a significantly higher half-maximal effective concentration for IL-1β-induced pathway activation in macrophages compared with hepatocytes, underscoring the importance of cell type-specific differences in pathway regulation

Division of labor by dual feedback regulators controls JAK2/STAT5 signaling over broad ligand range

Quantitative analysis of time-resolved data in primary erythroid progenitor cells reveals that a dual negative transcriptional feedback mechanism underlies the ability of STAT5 to respond to the broad spectrum of physiologically relevant Epo concentrations

Effect of a multinutrient intervention after ischemic stroke in female C57Bl/6 mice.

Stroke can affect females very differently from males, and therefore preclinical research on underlying mechanisms and the effects of interventions should not be restricted to male subjects, and treatment strategies for stroke should be tailored to benefit both sexes. Previously, we demonstrated that a multinutrient intervention (Fortasyn) improved impairments after ischemic stroke induction in male C57Bl/6 mice, but the therapeutic potential of this dietary treatment remained to be investigated in females. We now induced a transient middle cerebral artery occlusion (tMCAo) in C57Bl/6 female mice and immediately after surgery switched to either Fortasyn or an isocaloric Control diet. The stroke females performed several behavioral and motor tasks before and after tMCAo and were scanned in an 11.7 Tesla MRI scanner to assess brain perfusion, integrity and functional connectivity. To assess brain plasticity, inflammation and vascular integrity, immunohistochemistry was performed after sacrifice of the mice. We found that the multinutrient intervention had diverse effects on the stroke-induced impairments in females. Similar to previous observations in male stroke mice, brain integrity, sensorimotor integration and neurogenesis benefitted from Fortasyn, but impairments in activity and motor skills were not improved in female stroke mice. Overall, Fortasyn effects in the stroked females seem more modest in comparison to previously investigated stroked male mice. We suggest that with further optimization of treatment protocols more information on the efficacy of specific interventions in stroked females can be gathered. This in turn will help with the development of (gender-specific) treatment regimens for cerebrovascular diseases such as stroke

Dissecting the action of an evolutionary conserved non-coding region on renin promoter activity

Elucidating the mechanisms of the human transcriptional regulatory network is a major challenge of the post-genomic era. One important aspect is the identification and functional analysis of regulatory elements in non-coding DNA. Genomic sequence comparisons between related species can guide the discovery of cis-regulatory sequences. Using this technique, we identify a conserved region CNSmd of ∼775 bp in size, ∼14 kb upstream of the renin gene. Renin plays a pivotal role for mammalian blood pressure regulation and electrolyte balance. To analyse the cis-regulatory role of this region in detail, we perform 132 combinatorial reporter gene assays in an in vitro Calu-6 cell line model. To dissect the role of individual subregions, we fit several mathematical models to the experimental data. We show that a multiplicative switch model fits best the experimental data and that one subregion has a dominant effect on promoter activity. Mapping of the sub-sequences on phylogenetic conservation data reveals that the dominant regulatory region is the one with the highest multi-species conservation score

Comprehensive characterization of the prostate tumor microenvironment identifies CXCR4/CXCL12 crosstalk as a novel antiangiogenic therapeutic target in prostate cancer

Background: Crosstalk between neoplastic and stromal cells fosters prostate cancer (PCa) progression and dissemination. Insight in cell-to-cell communication networks provides new therapeutic avenues to mold processes that contribute to PCa tumor microenvironment (TME) alterations. Here we performed a detailed characterization of PCa tumor endothelial cells (TEC) to delineate intercellular crosstalk between TEC and the PCa TME. Methods: TEC isolated from 67 fresh radical prostatectomy (RP) specimens underwent multi-omic ex vivo characterization as well as orthogonal validation of both TEC functions and key markers by immunohistochemistry (IHC) and immunofluorescence (IF). To identify cell-cell interaction targets in TEC, we performed single-cell RNA sequencing (scRNA-seq) in four PCa patients who underwent a RP to catalogue cellular TME composition. Targets were cross-validated using IHC, publicly available datasets, cell culture expriments as well as a PCa xenograft mouse model. Results: Compared to adjacent normal endothelial cells (NEC) bulk RNA-seq analysis revealed upregulation of genes associated with tumor vasculature, collagen modification and extracellular matrix remodeling in TEC. PTGIR, PLAC9, CXCL12 and VDR were identified as TEC markers and confirmed by IF and IHC in an independent patient cohort. By scRNA-seq we identified 27 cell (sub)types, including endothelial cells (EC) with arterial, venous and immature signatures, as well as angiogenic tip EC. A focused molecular analysis revealed that arterial TEC displayed highest CXCL12 mRNA expression levels when compared to all other TME cell (sub)populations and showed a negative prognostic role. Receptor-ligand interaction analysis predicted interactions between arterial TEC derived CXCL12 and its cognate receptor CXCR4 on angiogenic tip EC. CXCL12 was in vitro and in vivo validated as actionable TEC target by highlighting the vessel number- and density- reducing activity of the CXCR4-inhibitor AMD3100 in murine PCa as well as by inhibition of TEC proliferation and migration in vitro. Conclusions: Overall, our comprehensive analysis identified novel PCa TEC targets and highlights CXCR4/CXCL12 interaction as a potential novel target to interfere with tumor angiogenesis in PCa

FGF-2 Deficiency Does Not Influence FGF Ligand and Receptor Expression during Development of the Nigrostriatal System

Secreted proteins of the fibroblast growth factor (FGF) family play important roles during development of various organ systems. A detailed knowledge of their temporal and spatial expression profiles, especially of closely related FGF family members, are essential to further identification of specific functions in distinct tissues. In the central nervous system dopaminergic neurons of the substantia nigra and their axonal projections into the striatum progressively degenerate in Parkinson's disease. In contrast, FGF-2 deficient mice display increased numbers of dopaminergic neurons. In this study, we determined the expression profiles of all 22 FGF-ligands and 10 FGF-receptor isoforms, in order to clarify, if FGF-2 deficiency leads to compensatory up-regulation of other FGFs in the nigrostriatal system. Three tissues, ventral mesencephalon (VM), striatum (STR) and as reference tissue spinal cord (SC) of wild-type and FGF-2 deficient mice at four developmental stages E14.5, P0, P28, and adult were comparatively analyzed by quantitative RT-PCR. As no differences between the genotypes were observed, a compensatory up-regulation can be excluded. Moreover, this analysis revealed that the majority of FGF-ligands (18/22) and FGF-receptors (9/10) are expressed during normal development of the nigrostriatal system and identified dynamic changes for some family members. By comparing relative expression level changes to SC reference tissue, general alterations in all 3 tissues, such as increased expression of FGF-1, -2, -22, FgfR-2c, -3c and decreased expression of FGF-13 during postnatal development were identified. Further, specific changes affecting only one tissue, such as increased FGF-16 (STR) or decreased FGF-17 (VM) expression, or two tissues, such as decreased expression of FGF-8 (VM, STR) and FGF-15 (SC, VM) were found. Moreover, 3 developmentally down-regulated FGFs (FGF-8b, FGF-15, FGF-17a) were functionally characterized by plasmid-based over-expression in dissociated E11.5 VM cell cultures, however, such a continuous exposure had no influence on the yield of dopaminergic neurons in vitro