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

A systems biology analysis of feedback control in pheromone signalling of fission yeast

Cell signalling comprises the systems used by cells to detect changes in their environment and to transduce the information into appropriate adjustments enforced by regulatory proteins. Due to its central role in all life processes, the study of cell signalling is a major focus of current biomedical research. The fission yeast Schizosaccharomyces pombe (S. pombe) is a single-celled organism used as a model to simplify the study of eukaryotic cell signalling, as it shares many features of interest with human cells. In this thesis a systems biology approach was used to investigate the roles of feedback regulation to control the dynamics of pheromone signalling in S. pombe. To this end, a quantitative dynamical model was built describing the pheromone-induced activation of the master transcription factor Ste11, as well as the coupled positive and negative feedback loops that arise from Ste11 activity. To constrain the model, a collection of data sets were generated by performing absolute quantification measurements of pheromone-dependent changes in the concentration of the model species. Structural identifiability analyses were used to select the measured species, while confidence intervals of the estimated parameters were determined through profile likelihood estimation. Analysis of the resulting model revealed a role for the pheromone signalling feedback loops to aid in the discrimination of different pheromone input doses. Through their combined action, feedback control defines the concentration and time thresholds in Ste11 activity that must be satisfied for the cell to commit to a sexual development fate

Mathematical Models of Androgen Resistance in Prostate Cancer Patients under Intermittent Androgen Suppression Therapy

abstract: Predicting resistant prostate cancer is critical for lowering medical costs and improving the quality of life of advanced prostate cancer patients. I formulate, compare, and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). I accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). I demonstrate that the inverse problem of parameter estimation might be too complicated and simply relying on data fitting can give incorrect conclusions, since there is a large error in parameter values estimated and parameters might be unidentifiable. I provide confidence intervals to give estimate forecasts using data assimilation via an ensemble Kalman Filter. Using the ensemble Kalman Filter, I perform dual estimation of parameters and state variables to test the prediction accuracy of the models. Finally, I present a novel model with time delay and a delay-dependent parameter. I provide a geometric stability result to study the behavior of this model and show that the inclusion of time delay may improve the accuracy of predictions. Also, I demonstrate with clinical data that the inclusion of the delay-dependent parameter facilitates the identification and estimation of parameters.Dissertation/ThesisDoctoral Dissertation Applied Mathematics 201

Systematic inference of regulatory networks that drive cytokine-stimulus integration by T cells

Differenzierungsentscheidungen von Zellen werden durch die Integration mehrerer Stimuli bestimmt. Die Differenzierung von Helfer-T-Zellen (Th-Zellen) ist hierfür ein gut untersuchtes Beispiel: reife Th-Zellen entwickeln sich beim Kontakt mit einem für sie spezifischen Antigen zu einem spezialisierten Subtyp, der von den in ihrer Umgebung vorhandenen Zytokinen abhängt und exprimieren dann einen spezifischen Mastertranskriptionsfaktor. Die häufigsten Th-Zell-Subtypen sind T-bet-exprimierende Th1-Zellen und GATA-3-exprimierende Th2-Zellen. Neuere Entdeckungen bezüglich der Plastizität von Th-Zell-Subtypen sowie die Existenz von T-bet+GATA-3+ Hybrid-Phänotypen haben die detaillierte Untersuchung vom Differenzierungsprozessen von Th-Zellen mit komplexer Zytokinsignale motiviert. Dazu haben wir systematisch die Zytokine IFN-g, IL-12 und IL-4 während der primären Differenzierung Th-Zellen titriert und Signaltransduktion und Zielgenexpression quantifiziert. Der Umfang und die Komplexität der Daten machten eine systematische Analyse notwendig, um involvierte Mechanismen genau zu identifizieren. Lineare Regressionsanalyse wurde verwendet, um die Netzwerktopologie zu extrahieren, wobei schon bekannte und zahlreiche neue Interaktionen vorausgesagt wurden. Die prognostizierte Netzwerktopologie wurde dann verwendet, um ein mechanistisches, mathematisches Modell der Zytokinsignalintegration zu entwickeln. Diese Methode hat ein hochgradig vernetztes regulatorisches Netzwerk inferiert. Bisher nicht beschriebene Funktionen von STAT-Proteine, die die Neuverkabelung des Netzwerkes während der Differenzierung vermitteln, wurden vorhergesagt. Ausgewählte neue Interaktionen wurden in gezielten genetischen Experimenten bestätigt. Während gegenseitige Inhibitionsmotive oft als kanonische digitale Schalter interpretiert werden, funktioniert das Th-Zell-Netwerk als ein Rheostat, der Variationen der Zytokinsignale in graduelle Expressionsänderungen der Mastertranskriptionsfaktoren übersetzt. Unsere Arbeit erklärt mechanistisch das beobachtete Kontinuum von Th-Zelldifferenzierungszuständen entlang der Th1-Th2-Achse und beschreibt eine quantitative Methode für die datenbasierte Inferenz zellulärer Netzwerke der Signalintegration.Cell-fate decisions are governed by the integration of multiple stimuli. Th cell differentiation is a well-studied example thereof: mature Th cells differentiate into a specialised subtype upon encounter with their cognate antigen depending on the polarising cytokines present in their environment and start expressing specific master transcription factors. The most common Th cell subtypes are T-bet-expressing Th1 cells and GATA-3-expressing Th2 cells. Recent discoveries concerning the plasticity of Th cell subtypes as well as the existence of stable T-bet+GATA-3+ hybrid Th1/2 phenotypes have stimulated the detailed study of the differentiation process under different assumptions than the hitherto valid paradigm of single master transcription factor expression by using complex cytokine signals as inputs. Here, we developed a data-based approach for inferring the molecular network underlying the differentiation of T-bet- and/or GATA-3 expressing lymphocytes. We performed systematic titrations of the polarising cytokines IFN-g, IL-12 and IL-4 during primary differentiation of Th cells and quantified signal transduction as well as target-gene expression. The size and complexity of the dataset made a systematic analysis necessary to identify the mechanisms involved. To extract the network topology, we used linear regression analysis, retrieving known regulatory mechanisms and predicting numerous novel ones. This network topology was used to develop a mechanistic mathematical model of cytokine signal integration. This approach inferred a highly connected regulatory network. Previously undescribed functions of STAT proteins mediating network rewiring during differentiation were predicted. Selected new interactions were confirmed by experiments using gene-deficient cells. Importantly, while mutual-inhibition motifs are often considered canonical digital switches, the inferred Th-cell network acts as a rheostat, generating a continuum of differentiated states along the Th1-Th2 axis. This work explains the observed Th1-Th2 cell fate continuum mechanistically and provides a quantitative framework for the data-based inference of cellular signal integration networks

Model-based optimization of batch- and continuous crystallization processes

Crystallization is an important separation process, extensively used in most chemical industries and especially in pharmaceutical manufacturing, either as a method of production or as a method of purification or recovery of solids. Typically, crystallization can have a considerable impact on tuning the critical quality attributes (CQAs), such as crystal size and shape distribution (CSSD), purity and polymorphic form, that impact the final product quality performance indicators and inherent end-use properties, along with the downstream processability. Therefore, one of the critical targets in controlled crystallization processes, is to engineer specific properties of the final product. The purpose of this research is to develop systematic computer-aided methodologies for the design of batch and continuous mixed suspension mixed product removal (MSMPR) crystallization processes through the implementation of simulation models and optimization frameworks. By manipulating the critical process parameters (CPPs), the achievable range of CQAs and the feasible design space (FDS) can be identified. Paracetamol in water and potassium dihydrogen phosphate (KDP) in water are considered as the model chemical systems.The studied systems are modeled utilizing single and multi-dimensional population balance models (PBMs). For the batch crystallization systems, single and multi-objective optimization was carried out for the determination of optimal operating trajectories by considering mean crystal size, the distribution s standard deviation and the aspect ratio of the population of crystals, as the CQAs represented in the objective functions. For the continuous crystallization systems, the attainable region theory is employed to identify the performance of multi-stage MSMPRs for various operating conditions and configurations. Multi-objective optimization is also applied to determine a Pareto optimal attainable region with respect to multiple CQAs. By identifying the FDS of a crystallization system, the manufacturing capabilities of the process can be explored, in terms of mode of operation, CPPs, and equipment configurations, that would lead to the selection of optimum operation strategies for the manufacturing of products with desired CQAs under certain manufacturing and supply chain constraints. Nevertheless, developing reliable first principle mathematical models for crystallization processes can be very challenging due to the complexity of the underlying phenomena, inherent to population balance models (PBMs). Therefore, a novel framework for parameter estimability for guaranteed optimal model reliability is also proposed and implemented. Two estimability methods are combined and compared: the first is based on a sequential orthogonalization of the local sensitivity matrix and the second is Sobol, a variance-based global sensitivities technic. The framework provides a systematic way to assess the quality of two nominal sets of parameters: one obtained from prior knowledge and the second obtained by simultaneous identification using global optimization. A multi-dimensional population balance model that accounts for the combined effects of different crystal growth modifiers/ impurities on the crystal size and shape distribution of needle-like crystals was used to validate the methodology. A cut-off value is identified from an incremental least square optimization procedure for both estimability methods, providing the required optimal subset of model parameters. In addition, a model-based design of experiments (MBDoE) methodology approach is also reported to determine the optimal experimental conditions yielding the most informative process data. The implemented methodology showed that, although noisy aspect ratio data were used, the eight most influential and least correlated parameters could be reliably identified out of twenty-three, leading to a crystallization model with enhanced prediction capability. A systematic model-based optimization methodology for the design of crystallization processes under the presence of multiple impurities is also investigated. Supersaturation control and impurity inclusion is combined to evaluate the effect on the product's CQAs. To this end, a morphological PBM is developed for the modelling of the cooling crystallization of pure KDP in aqueous solution, as a model system, under the presence of two competitive crystal growth modifiers/ additives: aluminum sulfate and sodium hexametaphosphate. The effect of the optimal temperature control with and without the additives on the CQAs is presented via utilizing multi-objective optimization. The results indicate that the attainable size and shape attributes, can be considerably enhanced due to advanced operation flexibility. Especially it is shown that the shape of the KDP crystals can be affected even by the presence of small quantity of additives and their morphology can be modified from needle-like to spherical, which is more favourable for processing. In addition, the multi-impurity PBM model is extended by the utilization of a high-resolution finite volume (HR-FV) scheme, instead of the standard method of moments (SMOM), in order for the full reconstruction and dynamic modelling of the crystal size and shape distribution to be enabled. The implemented methodology illustrated the capabilities of utilizing high-fidelity computational models for the investigation of crystallization processes in impure media for process and product design and optimization purposes