Julie Bachmann

Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood

MOTIVATION Mathematical description of biological reaction networks by differential equations leads to large models whose parameters are calibrated in order to optimally explain experimental data. Often only parts of the model can be observed directly. Given a model that sufficiently describes the measured data, it is important to infer how well model parameters are determined by the amount and quality of experimental data. This knowledge is essential for further investigation of model predictions. For this reason a major topic in modeling is identifiability analysis. RESULTS We suggest an approach that exploits the profile likelihood. It enables to detect structural non-identifiabilities, which manifest in functionally related model parameters. Furthermore, practical non-identifiabilities are detected, that might arise due to limited amount and quality of experimental data. Last but not least confidence intervals can be derived. The results are easy to interpret and can be used for experimental planning and for model reduction. AVAILABILITY An implementation is freely available for MATLAB and the PottersWheel modeling toolbox at http://web.me.com/andreas.raue/profile/software.html. SUPPLEMENTARY INFORMATION Supplementary data are available at Bioinformatics online.

Covering a Broad Dynamic Range: Information Processing at the Erythropoietin Receptor

Seeing EPO The supply of red blood cells in mammals is controlled by the cytokine erythropoietin (EPO). In physiological situations, the concentration of EPO can change by 1000-fold. Becker et al. (p. 1404, published online 20 May) used a combination of mathematical modeling and experimental analysis to discern how cells can maintain a linear response to such a broad range of EPO concentrations. Critical features included internalization of EPO-bound receptors and subsequent degradation of the EPO ligand. Replenishment of receptors at the cell surface required a large supply of EPO receptors maintained in reserve inside the cell. These mechanisms allow cells to experience large increases in EPO concentration without becoming refractory to further stimulation. Modeling and experiments help to explain responsiveness of red blood cell precursors to very large changes in a proliferative signal. Cell surface receptors convert extracellular cues into receptor activation, thereby triggering intracellular signaling networks and controlling cellular decisions. A major unresolved issue is the identification of receptor properties that critically determine processing of ligand-encoded information. We show by mathematical modeling of quantitative data and experimental validation that rapid ligand depletion and replenishment of the cell surface receptor are characteristic features of the erythropoietin (Epo) receptor (EpoR). The amount of Epo-EpoR complexes and EpoR activation integrated over time corresponds linearly to ligand input; this process is carried out over a broad range of ligand concentrations. This relation depends solely on EpoR turnover independent of ligand binding, which suggests an essential role of large intracellular receptor pools. These receptor properties enable the system to cope with basal and acute demand in the hematopoietic system.

Lessons learned from quantitative dynamical modeling in systems biology.

Due to the high complexity of biological data it is difficult to disentangle cellular processes relying only on intuitive interpretation of measurements. A Systems Biology approach that combines quantitative experimental data with dynamic mathematical modeling promises to yield deeper insights into these processes. Nevertheless, with growing complexity and increasing amount of quantitative experimental data, building realistic and reliable mathematical models can become a challenging task: the quality of experimental data has to be assessed objectively, unknown model parameters need to be estimated from the experimental data, and numerical calculations need to be precise and efficient. Here, we discuss, compare and characterize the performance of computational methods throughout the process of quantitative dynamic modeling using two previously established examples, for which quantitative, dose- and time-resolved experimental data are available. In particular, we present an approach that allows to determine the quality of experimental data in an efficient, objective and automated manner. Using this approach data generated by different measurement techniques and even in single replicates can be reliably used for mathematical modeling. For the estimation of unknown model parameters, the performance of different optimization algorithms was compared systematically. Our results show that deterministic derivative-based optimization employing the sensitivity equations in combination with a multi-start strategy based on latin hypercube sampling outperforms the other methods by orders of magnitude in accuracy and speed. Finally, we investigated transformations that yield a more efficient parameterization of the model and therefore lead to a further enhancement in optimization performance. We provide a freely available open source software package that implements the algorithms and examples compared here.

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

Cellular signal transduction is governed by multiple feedback mechanisms to elicit robust cellular decisions. The specific contributions of individual feedback regulators, however, remain unclear. Based on extensive time‐resolved data sets in primary erythroid progenitor cells, we established a dynamic pathway model to dissect the roles of the two transcriptional negative feedback regulators of the suppressor of cytokine signaling (SOCS) family, CIS and SOCS3, in JAK2/STAT5 signaling. Facilitated by the model, we calculated the STAT5 response for experimentally unobservable Epo concentrations and provide a quantitative link between cell survival and the integrated response of STAT5 in the nucleus. Model predictions show that the two feedbacks CIS and SOCS3 are most effective at different ligand concentration ranges due to their distinct inhibitory mechanisms. This divided function of dual feedback regulation enables control of STAT5 responses for Epo concentrations that can vary 1000‐fold in vivo. Our modeling approach reveals dose‐dependent feedback control as key property to regulate STAT5‐mediated survival decisions over a broad range of ligand concentrations.

A systems biology approach to analyse amplification in the JAK2-STAT5 signalling pathway

BackgroundThe amplification of signals, defined as an increase in the intensity of a signal through networks of intracellular reactions, is considered one of the essential properties in many cell signalling pathways. Despite of the apparent importance of signal amplification, there have been few attempts to formalise this concept.ResultsIn this work we investigate the amplification and responsiveness of the JAK2-STAT5 pathway using a kinetic model. The recruitment of EpoR to the plasma membrane, activation by Epo, and deactivation of the EpoR/JAK2 complex are considered as well as the activation and nucleocytoplasmic shuttling of STAT5. Using qualitative biological knowledge, we first establish the structure of a general power-law model. We then generate a family of models from which we select suitable candidates. The parameter values of the model are estimated from experimental quantitative time-course data. The final model, whether it is conventional model with fixed predefined integer kinetic orders or a model with variable non-integer kinetic orders, is selected on the basis of a good agreement between simulations and the experimental data. The model is used to analyse the responsiveness and amplification properties of the pathway with sustained, transient, and oscillatory stimulation.ConclusionThe selected kinetic model predicts that the system acts as an amplifier with maximum amplification and sensitivity for input signals whose intensity match physiological values for Epo concentration and with duration in the range of one to 100 minutes. The response of the system reaches saturation for more intense and longer stimulation with Epo. We hypothesise that these properties of the system directly relate to the saturation of Epo receptor activation, its low recruitment to the plasma membrane and intense deactivation as predicted by the model.

Predictive mathematical models of cancer signalling pathways.

Abstract.  Bachmann J, Raue A, Schilling M, Becker V, Timmer J, Klingmüller U (German Cancer Research Center, Heidelberg; BIOSS Centre for Biological Signalling Studies, Freiburg; and University of Freiburg, Freiburg; Germany). Predictive mathematical models of cancer signalling pathways (Key Symposium). J Intern Med 2012; 271:155–165.

High-dimensional Bayesian parameter estimation: case study for a model of JAK2/STAT5 signaling.

In this work we present results of a detailed Bayesian parameter estimation for an analysis of ordinary differential equation models. These depend on many unknown parameters that have to be inferred from experimental data. The statistical inference in a high-dimensional parameter space is however conceptually and computationally challenging. To ensure rigorous assessment of model and prediction uncertainties we take advantage of both a profile posterior approach and Markov chain Monte Carlo sampling. We analyzed a dynamical model of the JAK2/STAT5 signal transduction pathway that contains more than one hundred parameters. Using the profile posterior we found that the corresponding posterior distribution is bimodal. To guarantee efficient mixing in the presence of multimodal posterior distributions we applied a multi-chain sampling approach. The Bayesian parameter estimation enables the assessment of prediction uncertainties and the design of additional experiments that enhance the explanatory power of the model. This study represents a proof of principle that detailed statistical analysis for quantitative dynamical modeling used in systems biology is feasible also in high-dimensional parameter spaces.

Quenched Substrates for Live-Cell Labeling of SNAP-Tagged Fusion Proteins with Improved Fluorescent Background

Recent developments in fluorescence microscopy raise the demands for bright and photostable fluorescent tags for specific and background free labeling in living cells. Aside from fluorescent proteins and other tagging methods, labeling of SNAP-tagged proteins has become available thereby increasing the pool of potentially applicable fluorescent dyes for specific labeling of proteins. Here, we report on novel conjugates of benzylguanine (BG) which are quenched in their fluorescence and become highly fluorescent upon labeling of the SNAP-tag, the commercial variant of the human O(6)-alkylguanosyltransferase (hAGT). We identified four conjugates showing a strong increase, i.e., >10-fold, in fluorescence intensity upon labeling of SNAP-tag in vitro. Moreover, we screened a subset of nine BG-dye conjugates in living Escherichia coli and found them all suited for labeling of the SNAP-tag. Here, quenched BG-dye conjugates yield a higher specificity due to reduced contribution from excess conjugate to the fluorescence signal. We further extended the application of these conjugates by labeling a SNAP-tag fusion of the Tar chemoreceptor in live E. coli cells and the eukaryotic transcription factor STAT5b in NIH 3T3 mouse fibroblast cells. Aside from the labeling efficiency and specificity in living cells, we discuss possible mechanisms that might be responsible for the changes in fluorescence emission upon labeling of the SNAP-tag, as well as problems we encountered with nonspecific labeling with certain conjugates in eukaryotic cells.

Targeted Near-Infrared Imaging of the Erythropoietin Receptor in Human Lung Cancer Xenografts

The putative presence of the erythropoietin receptor (EpoR) on human cancer cells has given rise to controversial discussion about the use of recombinant human erythropoietin (rhuEpo) for treatment of patients with chemotherapy-induced anemia. In vivo analysis of the EpoR status in tumors could help in elucidating the role of erythropoietin in cancer. Thus, the aim of this study was to develop a targeted EpoR probe for the investigation of EpoR expression in human lung cancer xenografts by fluorescence-mediated tomography. Methods: Epo-Cy5.5 was generated by coupling Cy5.5 to rhuEpo. In vitro binding assays were performed using the EpoR-positive non–small cell lung cancer (NSCLC) cell lines A549 (lower EpoR expression) and H838 (higher EpoR expression), the EpoR-negative cell line H2030, and EpoR/EGFP-overexpressing HeLa cells. In vivo specificity of Epo-Cy5.5 was confirmed by competition analyses using micro-CT/fluorescence-mediated tomography fusion imaging. Biodistribution was analyzed over 50 h after injection. Binding of Epo-Cy5.5 was validated on tumor cryosections. Results: After intravenous injection, the probe was rapidly cleared from the circulation. An accumulation was observed in liver and kidneys, with a maximum at 7 h after injection followed by a decline, indicating renal excretion. Almost constant accumulation of Epo-Cy5.5 was found in bone marrow and tumors, indicating specific receptor binding. The probe allowed the discrimination between H838 with higher EpoR expression (89.54 ± 15.91 nM at 25 h) and A549 tumors with lower EpoR expression (60.45 ± 14.59 nM at 25 h, P < 0.05). Tumor accumulation of Epo-Cy5.5 could be significantly reduced by adding unlabeled rhuEpo (P < 0.05 at 4, 7, and 24 h). In vitro validation confirmed specific binding of Epo-Cy5.5 to the tumor cells, and this binding correlated with the EpoR expression level. Binding was also observed on endothelial cells. Vessel density and Epo-Cy5.5 binding on endothelial cells were comparable. Conclusion: Epo-Cy5.5 allows the longitudinal analysis of EpoR expression in tumors and thereby can investigate the influence of erythropoietin on EpoR expression, tumor growth, and angiogenesis.

Cellular ERK phospho-form profiles with conserved preference for a switch-like pattern.

ERK is a member of the MAPK pathway with essential functions in cell proliferation, differentiation, and survival. Complete ERK activation by the kinase MEK requires dual phosphorylation at T and Y within the activation motif TEY. We show that exposure of primary mouse hepatocytes to hepatocyte growth factor (HGF) results in phosphorylation at the activation motif, but not of other residues nearby. To determine the relative abundances of unphosphorylated ERK and the three ERK phospho-forms pT, pY, and pTpY, we employed an extended one-source peptide/phosphopeptide standard method in combination with nanoUPLC-MS. This method enabled us to determine the abundances of phospho-forms with a relative variability of ≤5% (SD). We observed a switch-like preference of ERK phospho-form abundances toward the active, doubly phosphorylated and the inactive, unphosphorylated form. Interestingly, ERK phospho-form profiles were similar upon growth factor and cytokine stimulation. A screening of several murine and human cell systems revealed that the balance between TY- and pTpY-ERK is conserved while the abundances of pT- and pY-ERK are more variable within cell types. We show that the phospho-form profiles do not change by blocking MEK activity suggesting that cellular phosphatases determine the ERK phospho-form distribution. This study provides novel quantitative insights into multisite phosphorylation.