Data2Dynamics: a modeling environment tailored to parameter estimation in dynamical systems.

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: andreas.raue@fdm.uni-freiburg.de SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Spatial aspects in the SMAD signaling pathway.

Among other approaches, differential equations are used for a deterministic quantitative description of time-dependent biological processes. For intracellular systems, such as signaling pathways, most existing models are based on ordinary differential equations. These models describe temporal processes, while they neglect spatial aspects. We present a model for the SMAD signaling pathway, which gives a temporal and spatial description on the basis of reaction diffusion equations to answer the question whether cell geometry plays a role in signaling. In this article we simulate the ordinary differential equations as well as partial differential equations of parabolic type with suile numerical methods, the latter on different cell geometries. In addition to manual construction of idealized cells, we also construct meshes from microscopy images of real cells. The main focus of the paper is to compare the results of the model without and with spatial aspects to answer the addressed question. The results show that diffusion in the model can lead to significant intracellular gradients of signaling molecules and changes the level of response to the signal transduced by the signaling pathway. In particular, the extent of these observations depends on the geometry of the cell.

Predictive mathematical models of cancer signalling pathways.

Complex intracellular signalling networks integrate extracellular signals and convert them into cellular responses. In cancer cells, the tightly regulated and fine-tuned dynamics of information processing in signalling networks is altered, leading to uncontrolled cell proliferation, survival and migration. Systems biology combines mathematical modelling with comprehensive, quantitative, time-resolved data and is most advanced in addressing dynamic properties of intracellular signalling networks. Here, we introduce different modelling approaches and their application to medical systems biology, focusing on the identifiability of parameters in ordinary differential equation models and their importance in network modelling to predict cellular decisions. Two related examples are given, which include processing of ligand-encoded information and dual feedback regulation in erythropoietin (Epo) receptor signalling. Finally, we review the current understanding of how systems biology could foster the development of new treatment strategies in the context of lung cancer and anaemia.

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.

Identifiability and observability analysis for experimental design in nonlinear dynamical models.

Dynamical models of cellular processes promise to yield new insights into the underlying systems and their biological interpretation. The processes are usually nonlinear, high dimensional, and time-resolved experimental data of the processes are sparse. Therefore, parameter estimation faces the challenges of structural and practical nonidentifiability. Nonidentifiability of parameters induces nonobservability of trajectories, reducing the predictive power of the model. We will discuss a generic approach for nonlinear models that allows for identifiability and observability analysis by means of a realistic example from systems biology. The results will be utilized to design new experiments that enhance model predictiveness, illustrating the iterative cycle between modeling and experimentation in systems biology.

Expression ratio of the TGFß-inducible gene MYO10 is prognostic for overall survival of squamous cell lung cancer patients and predicts chemotherapy response.

In lung cancer a deregulation of Transforming Growth Factor-ß (TGFß) signaling has been observed. Yet, the impact of TGFß in squamous cell carcinoma of the lung (LUSC) remained to be determined. We combined phenotypic and transcriptome-wide studies and showed that the stimulation of the LUSC cell line SK-MES1 with TGFß results in an increase of migratory invasive properties. The analysis of the dynamics of gene expression by next-generation sequencing revealed that TGFß stimulation orchestrates the upregulation of numerous motility- and actin cytoskeleton-related genes. Among these the non-muscle myosin 10 (MYO10) showed the highest upregulation in a LUSC patient cohort of the Cancer Genome Atlas (TCGA). Knockdown of MYO10 abrogated TGFß-induced collagen gel invasion of SK-MES1 cells. The analysis of MYO10 mRNA expression in paired tissues of 151 LUSC patients with corresponding 80-month clinical follow-up data showed that the mRNA expression ratio of MYO10 in tumor and tumor-free tissue is prognostic for overall survival of LUSC patients and predictive for the response of these patients to adjuvant chemotherapy. Thus, MYO10 represents a new clinical biomarker for this aggressive disease and due to its role in cellular motility and invasion could serve as a potential molecular target for therapeutic interventions in patients with LUSC.

Self assembly of the transmembrane domain promotes signal transduction through the erythropoietin receptor.

Hematopoietic cytokine receptors, such as the erythropoietin receptor (EpoR), are single membrane-spanning proteins. Signal transduction through EpoR is crucial for the formation of mature erythrocytes. Structural evidence shows that in the unliganded form EpoR exists as a preformed homodimer in an open scissor-like conformation precluding the activation of signaling. In contrast to the extracellular domain of the growth hormone receptor (GHR), the structure of the agonist-bound EpoR extracellular region shows only minimal contacts between the membrane-proximal regions. This evidence suggests that the domains facilitating receptor dimerization may differ between cytokine receptors. We show that the EpoR transmembrane domain (TM) has a strong potential to self interact in a bacterial reporter system. Abolishing self assembly of the EpoR TM by a double point mutation (Leu 240-Leu 241 mutated to Gly-Pro) impairs signal transduction by EpoR in hematopoietic cells and the formation of erythroid colonies upon reconstitution in erythroid progenitor cells from EpoR(-/-) mice. Interestingly, inhibiting TM self assembly in the constitutively active mutant EpoR R129C abrogates formation of disulfide-linked receptor homodimers and consequently results in the loss of ligand-independent signal transduction. Thus, efficient signal transduction through EpoR and possibly other preformed receptor oligomers may be determined by the dynamics of TM self assembly.

Interleukin-6 and oncostatin M-induced growth inhibition of human A375 melanoma cells is STAT-dependent and involves upregulation of the cyclin-dependent kinase inhibitor p27/Kip1.

Interleukin-6 (IL-6)-type cytokines lead to growth arrest of human A375 melanoma cells. The present study demonstrates that this effect depends on the activation of STAT transcription factors. We observed a correlation between the extent of growth inhibition exerted by IL-6, IL-6 plus soluble IL-6 receptor or oncostatin M (OSM) and the intensities of STAT3 and STAT1 signals. A truncated chimeric receptor retaining only the membrane-proximal region of gp130, the common signal transducer of IL-6-type cytokines, did neither activate STATs nor mediate growth arrest of stable transfectants. These functions were restored by the addition of short STAT recruitment modules comprising critical tyrosine residues from gp130 (Y767, Y814). A receptor carrying tyrosine module Y759 of gp130 effectively mediated activation of the phosphatase SHP-2 but did not alter cell growth. Overexpression of dominant negative forms of STAT3 but not STAT1 abrogated the inhibitory effect of OSM and IL-6 in A375 cells. In addition, we have identified the cyclin-dependent kinase inhibitor p27/Kipl as a novel target to be regulated by IL-6-type cytokines. Stimulation-dependent upregulation of p27 mRNA occurred STAT3-dependently. Also p27 protein accumulated which coincided with the disappearance of hyperphosphorylated retinoblastoma protein in three human melanoma cell lines sensitive to IL-6-type cytokines.

Unraveling liver complexity from molecular to organ level: challenges and perspectives.

Biological responses are determined by information processing at multiple and highly interconnected scales. Within a tissue the individual cells respond to extracellular stimuli by regulating intracellular signaling pathways that in turn determine cell fate decisions and influence the behavior of neighboring cells. As a consequence the cellular responses critically impact tissue composition and architecture. Understanding the regulation of these mechanisms at different scales is key to unravel the emergent properties of biological systems. In this perspective, a multidisciplinary approach combining experimental data with mathematical modeling is introduced. We report the approach applied within the Virtual Liver Network to analyze processes that regulate liver functions from single cell responses to the organ level using a number of examples. By facilitating interdisciplinary collaborations, the Virtual Liver Network studies liver regeneration and inflammatory processes as well as liver metabolic functions at multiple scales, and thus provides a suitable example to identify challenges and point out potential future application of multi-scale systems biology.

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.

Centrosomal targeting of tyrosine kinase activity does not enhance oncogenicity in chronic myeloproliferative disorders.

Constitutive tyrosine kinase activation by reciprocal chromosomal translocation is a common pathogenetic mechanism in chronic myeloproliferative disorders. Since centrosomal proteins have been recurrently identified as translocation partners of tyrosine kinases FGFR1, JAK2, PDGFRα and PDGFRß in these diseases, a role for the centrosome in oncogenic transformation has been hypothesized. In this study, we addressed the functional role of centrosomally targeted tyrosine kinase activity. First, centrosomal localization was not routinely found for all chimeric fusion proteins tested. Second, targeting of tyrosine kinases to the centrosome by creating artificial chimeric fusion kinases with the centrosomal targeting domain of AKAP450 failed to enhance the oncogenic transforming potential in both Ba/F3 and U2OS cells, although phospho-tyrosine-mediated signal transduction pathways were initiated at the centrosome. We conclude that the centrosomal localization of constitutively activated tyrosine kinases does not contribute to disease pathogenesis in chronic myeloproliferative disorders.

Addressing parameter identifiability by model-based experimentation.

Mathematical description of biological processes such as gene regulatory networks or signalling pathways by dynamic models utilising ordinary differential equations faces challenges if the model parameters like rate constants are estimated from incomplete and noisy experimental data. Typically, biological networks are only partially observed. Only a fraction of the modelled molecular species is measurable directly. This can result in structurally non-identifiable model parameters. Furthermore, practical non-identifiability can arise from limited amount and quality of experimental data. In the challenge of growing model complexity on one side, and experimental limitations on the other side, both types of non-identifiability arise frequently in systems biological applications often prohibiting reliable prediction of system dynamics. On theoretical grounds this article summarises how and why both types of non-identifiability arise. It exemplifies pitfalls where models do not yield reliable predictions of system dynamics because of non-identifiabilities. Subsequently, several approaches for identifiability analysis proposed in the literature are discussed. The aim is to provide an overview of applicable methods for detecting parameter identifiability issues. Once non-identifiability is detected, it can be resolved either by experimental design, measuring additional data under suitable conditions; or by model reduction, tailoring the size of the model to the information content provided by the experimental data. Both strategies enhance model predictability and will be elucidated by an example application. [Includes supplementary material].

Primary mouse hepatocytes for systems biology approaches: a standardized in vitro system for modelling of signal transduction pathways.

Complex cellular networks regulate regeneration, detoxification and differentiation of hepatocytes. By combining experimental data with mathematical modelling, systems biology holds great promises to elucidate the key regulatory mechanisms involved and predict targets for efficient intervention. For the generation of high-quality quantitative data suitable for mathematical modelling a standardised in vitro system is essential. Therefore the authors developed standard operating procedures for the preparation and cultivation of primary mouse hepatocytes. To reliably monitor the dynamic induction of signalling pathways, the authors established starvation conditions and evaluated the extent of starvation-associated stress by quantifying several metabolic functions of cultured primary hepatocytes, namely activities of glutathione-S-transferase, glutamine synthetase, CYP3A as well as secretion of lactate and urea into the culture medium. Establishment of constant metabolic activities after an initial decrease compared with freshly isolated hepatocytes showed that the cultured hepatocytes achieve a new equilibrium state that was not affected by our starving conditions. To verify the highly reproducible dynamic activation of signalling pathways in the in vitro system, the authors examined the JAK-STAT, SMAD, PI3 kinase, MAP kinase, NF-kappaB and Wnt/beta-catenin signalling pathways. For the induction of gp130, JAK1 and STAT3 phosphorylation IL6 was used, whereas TGFbeta was applied to activate the phosphorylation of SMAD1, SMAD2 and SMAD3. Both Akt/PKB and ERK1/2 phosphorylation were stimulated by the addition of hepatocyte growth factor. The time-dependent induction of a pool of signalling competent beta-catenin was monitored in response to the inhibition of GSK3beta. To analyse whether phosphorylation is actually leading to transcriptional responses, luciferase reporter gene constructs driven by multiple copies of TGFbeta-responsive motives were applied, demonstrating a dose-dependent increase in luciferase activity. Moreover, the induction of apoptosis by the TNF-like cytokine Fas ligand was studied in the in vitro system. Thus, the mouse hepatocyte in vitro system provides an important basis for the generation of high-quality quantitative data under standardised cell culture conditions that is essential to elucidate critical hepatocellular functions by the systems biology approach.

Quantitative data generation for systems biology: the impact of randomisation, calibrators and normalisers.

Systems biology is an approach to the analysis and prediction of the dynamic behaviour of biological networks through mathematical modelling based on experimental data. The current lack of reliable quantitative data, especially in the field of signal transduction, means that new methodologies in data acquisition and processing are needed. Here, we present methods to advance the established techniques of immunoprecipitation and immunoblotting to more accurate and quantitative procedures. We propose randomisation of sample loading to disrupt lane correlations and the use of normalisers and calibrators for data correction. To predict the impact of each method on improving the data quality we used simulations. These studies showed that randomisation reduces the standard deviation of a smoothed signal by 55% +/- 10%, independently from most experimental settings. Normalisation with appropriate endogenous or external proteins further reduces the deviation from the true values. As the improvement strongly depends on the quality of the normaliser measurement, a criteria-based normalisation procedure was developed. Our approach was experimentally verified by application of the proposed methods to time course data obtained by the immunoblotting technique. This analysis showed that the procedure is robust and can significantly improve the quality of experimental data.

The role of tyrosine phosphorylation in proliferation and maturation of erythroid progenitor cells--signals emanating from the erythropoietin receptor.

Red blood cells arise continuously from pluripotent stem cells which mature and become functionally specialized upon commitment to the erythroid lineage. In mammals, the key regulator of this process is the hormone erythropoietin (EPO). Hormone binding to the cognate receptor, the erythropoietin receptor (EPO-R), causes receptor homodimerization and transiently triggers tyrosine phosphorylation within target cells. Although the EPO-R lacks intrinsic enzymatic activity it couples, presumably sequentially, to the protein tyrosine kinase receptor c-KIT and the cytosolic protein tyrosine kinase JAK2. Signaling through the EPO-R is promoted by tyrosine phosphorylation of the cytosolic domain and the recruitment of secondary signaling molecules such as the lipid kinase inositolphospholipid 3-kinase (phosphatidylinositol 3-kinase) and protein tyrosine phosphatase SHP-2 to the activated receptor. Complex formation of the activated EPO-R with the protein tyrosine phosphatase SHP-1 terminates signaling. In primary fetal liver cells redundant signals emanating from phosphotyrosine residues in the EPO-R support formation of erythroid colonies in vitro. However, since the last tyrosine residue in the cytosolic domain of the EPO-R, Y479, uniquely supports in the absence of other tyrosine residues an almost normal level of colony-forming unit-erythroid (CFU-E) colony formation, Y479 represents one of the key residues required in vivo for erythroid proliferation and differentiation. The signal emanating from Y479 involves sequential EPO-induced recruitment of phosphoinositol lipid 3-kinase to the EPO-R and activation of mitogen-activated-protein(MAP)kinase activity. The MAP-kinase signaling cascade could serve as an intracellular switch integrating signals mediated by several phosphotyrosine residues in the cytosolic domain of the EPO-R and provide a possible explanation for partial redundancy in signaling.

Hepadnavirus infection requires interaction between the viral pre-S domain and a specific hepatocellular receptor.

To better define the molecules involved in the initial interaction between hepadnaviruses and hepatocytes, we performed binding and infectivity studies with the duck hepatitis B virus (DHBV) and cultured primary duck hepatocytes. In competition experiments with naturally occurring subviral particles containing DHBV surface proteins, these DNA-free particles were found to interfere with viral infectivity if used at sufficiently high concentrations. In direct binding saturation experiments with radiolabelled subviral particles, a biphasic titration curve containing a saturable component was obtained. Quantitative evaluation of both the binding and the infectivity data indicates that the duck hepatocyte presents about 10(4) high-affinity binding sites for viral and subviral particles. Binding to these productive sites may be preceded by reversible virus attachment to a large number of less specific, nonsaturable primary binding sites. To identify which of the viral envelope proteins is responsible for hepatocyte-specific attachment, subviral particles containing only one of the two DHBV surface proteins were produced in Saccharomyces cerevisiae. In infectivity competition experiments, only particles containing the large pre-S/S protein were found to markedly reduce the efficiency of DHBV infection, while particles containing the small S protein had only a minor effect. Similarly, physical binding of radiolabelled serum-derived subviral particles to primary duck hepatocytes was inhibited well only by the yeast-derived pre-S/S particles. Together, these results strongly support the notion that hepadnaviral infection is initiated by specific attachment of the pre-S domain of the large DHBV envelope protein to a limited number of hepatocellular binding sites.

Interaction of the erythropoietin and stem-cell-factor receptors.

Mutations in the KIT transmembrane protein-tyrosine kinase receptor affect erythropoiesis, resulting in fewer committed late progenitors (colony-forming unit erythroid, CFU-E) in the fetal liver. As the survival and proliferation of CFU-Es depend absolutely on erythropoietin (EPO), these results suggest that CFU-Es cannot proliferate or mature further unless both the KIT and EPO receptor signalling pathways are functional. How KIT affects proliferation or differentiation of CFU-Es is not clear. Here we show that the KIT ligand SCF (for stem-cell factor) can replace EPO in supporting the growth and survival of HCD57 cells, an EPO-dependent erythroid-progenitor cell line expressing high levels of KIT. SCF supports the proliferation of 32D cells that express KIT only if they also express the EPO receptor. In HCD57 cells, SCF rapidly induces tyrosine phosphorylation of the EPO receptor, and KIT physically associates with the extended box 2 region in the cytoplasmic domain of the EPO receptor. Our results indicate that KIT may activate the EPO receptor by tyrosine phosphorylation to induce further proliferation and maturation of CFU-Es.

Specific recruitment of SH-PTP1 to the erythropoietin receptor causes inactivation of JAK2 and termination of proliferative signals.

The binding of erythropoietin (EPO) to its receptor (EPO-R) activates the protein tyrosine kinase JAK2. The mechanism of JAK2 inactivation has been unclear. We show that the hematopoietic protein tyrosine phosphatase SH-PTP1 (also called HCP and PTP1C) associates via its SH2 domains with the tyrosine-phosphorylated EPO-R. In vitro binding studies suggest that Y429 in the cytoplasmic domain of the EPO-R is the binding site for SH-PTP1. Mutant EPO-Rs lacking Y429 are unable to bind SH-PTP1; cells expressing such mutants are hypersensitive to EPO and display prolonged EPO-induced autophosphorylation of JAK2. Our results suggest that activation of SH-PTP1 by binding to the EPO-R plays a major role in terminating proliferative signals.

Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling.

Considerable progress has been made in identifying the molecular composition of complex signaling networks controlling cell proliferation, differentiation, and survival. However, to discover general building principles and predict the dynamic behavior of signaling networks, it is necessary to develop quantitative models based on experimental observations. Here we report a mathematical model of the core module of the Janus family of kinases (JAK)-signal transducer and activator of transcription (STAT) signaling pathway based on time-resolved measurements of receptor and STAT5 phosphorylation. Applying the fitted model, we can determine the quantitative behavior of STAT5 populations not accessible to experimental measurement. By in silico investigations, we identify the parameters of nuclear shuttling as the most sensitive to perturbations and verify experimentally the model prediction that inhibition of nuclear export results in a reduced transcriptional yield. The model reveals that STAT5 undergoes rapid nucleocytoplasmic cycles, continuously coupling receptor activation and target gene transcription, thereby forming a remote sensor between nucleus and receptor. Thus, dynamic modeling of signaling pathways can promote functional understanding at the systems level.

Functional interaction of erythropoietin and stem cell factor receptors is essential for erythroid colony formation.

Production of mature erythrocytes requires multiple growth factors, but we do not know how their actions are coordinated. Here we show that erythroid progenitors from erythropoietin receptor (Epo-R)-/- fetal livers, infected in vitro with a retrovirus expressing the wild-type Epo-R, require addition of both Epo and stem cell factor (SCF) to form colony-forming unit erythroid (CFU-E) colonies. Thus, a functional interaction between KIT and the Epo-R, similar to what we reported in cultured cells, is essential for the function of CFU-E progenitors. In contrast, CFU-E colony formation in vitro by normal fetal liver progenitors requires only Epo; the essential interaction between activated KIT and the Epo-R must have occurred in vivo before or at the CFU-E progenitor stage. Using truncated dominant-negative mutant Epo-Rs, we show that KIT does not activate the Epo-R by inducing its dimerization, but presumably does so by phosphorylating tyrosine residue(s) in its cytosolic domain. By expressing mutant Epo-Rs containing only one of eight cytosolic tyrosines, we show that either tyrosine residue Y464 or Y479 suffices for Epo-dependent cell proliferation. However, only Epo-R F7Y479 is capable of supporting erythroid colony formation when expressed in (Epo-R)-/- fetal liver cells, indicating that Y464 either cannot send a differentiation signal or fails to respond to SCF/KIT activation. This work employs a novel experimental system to study the function of growth factors and their receptors in normal hematopoiesis.