Epithelial-mesenchymal transition (EMT) plays an essential role in embryonic development, wound healing, and tumor progression. Partial EMT states have been linked to metastatic dissemination and drug resistance. Several interconnected feedback loops at the RNA and protein levels control the transition between different cellular states. Using a combination of mathematical modeling and experimental analyses in the TGFβ-responsive breast epithelial MCF10A cell model, we identify a central role for the tumor suppressor protein Deleted in Liver Cancer 1 (DLC1) during EMT. By extending a previous model of EMT comprising key transcription factors and microRNAs, our work shows that DLC1 acts as a positive regulator of TGFβ-driven EMT, mainly by promoting SNAIL1 expression. Our model predictions indicate that DLC1 loss impairs EMT progression. Experimental analyses confirm this prediction and reveal the acquisition of a partial EMT phenotype in DLC1-depleted cells. Furthermore, our model results indicate a possible EMT reversion to partial or epithelial states upon DLC1 loss in MCF10A cells induced toward mesenchymal phenotypes. The increased EMT plasticity of cells lacking DLC1 may explain its importance as a tumor suppressor.

MOTIVATION: Systems biology aims to better understand living systems through mathematical modelling of experimental and clinical data. A pervasive challenge in quantitative dynamical modelling is the integration of time series measurements, which often have high variability and low sampling resolution. Approaches are required to utilize such information while consistently handling uncertainties. RESULTS: We present BayModTS (Bayesian modelling of time series data), a new FAIR (findable, accessible, interoperable, and reusable) workflow for processing and analysing sparse and highly variable time series data. BayModTS consistently transfers uncertainties from data to model predictions, including process knowledge via parameterized models. Further, credible differences in the dynamics of different conditions can be identified by filtering noise. To demonstrate the power and versatility of BayModTS, we applied it to three hepatic datasets gathered from three different species and with different measurement techniques: (i) blood perfusion measurements by magnetic resonance imaging in rat livers after portal vein ligation, (ii) pharmacokinetic time series of different drugs in normal and steatotic mice, and (iii) CT-based volumetric assessment of human liver remnants after clinical liver resection. AVAILABILITY AND IMPLEMENTATION: The BayModTS codebase is available on GitHub at https://github.com/Systems-Theory-in-Systems-Biology/BayModTS. The repository contains a Python script for the executable BayModTS workflow and a widely applicable SBML (systems biology markup language) model for retarded transient functions. In addition, all examples from the paper are included in the repository. Data and code of the application examples are stored on DaRUS: https://doi.org/10.18419/darus-3876. The raw MRI ROI voxel data were uploaded to DaRUS: https://doi.org/10.18419/darus-3878. The steatosis metabolite data are published on FairdomHub: 10.15490/fairdomhub.1.study.1070.1.

MOTIVATION: The Chemical Master Equation (CME) is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge is moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter fat-tailedness and do not possess statistical moments. RESULTS: We show that estimation via stochastic simulation algorithm (SSA) trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the method of moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution's fat-tailedness on SSA run times and explain inherent difficulties. While moment-estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment-estimation techniques themselves reliably indicate the potential fat-tailedness of the CME's solution.

MOTIVATION: The Chemical Master Equation is a stochastic approach to describe the evolution of a (bio)chemical reaction system. Its solution is a time-dependent probability distribution on all possible configurations of the system. As this number is typically large, the Master Equation is often practically unsolvable. The Method of Moments reduces the system to the evolution of a few moments, which are described by ordinary differential equations. Those equations are not closed, since lower order moments generally depend on higher order moments. Various closure schemes have been suggested to solve this problem. Two major problems with these approaches are first that they are open loop systems, which can diverge from the true solution, and second, some of them are computationally expensive. RESULTS: Here we introduce Quasi-Entropy Closure, a moment-closure scheme for the Method of Moments. It estimates higher order moments by reconstructing the distribution that minimizes the distance to a uniform distribution subject to lower order moment constraints. Quasi-Entropy Closure can be regarded as an advancement of Zero-Information Closure, which similarly maximizes the information entropy. Results show that both approaches outperform truncation schemes. Quasi-Entropy Closure is computationally much faster than Zero-Information Closure, although both methods consider solutions on the space of configurations and hence do not completely overcome the curse of dimensionality. In addition, our scheme includes a plausibility check for the existence of a distribution satisfying a given set of moments on the feasible set of configurations. All results are evaluated on different benchmark problems. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: The statistical analysis of single-cell data is a challenge in cell biological studies. Tailored statistical models and computational methods are required to resolve the subpopulation structure, i.e. to correctly identify and characterize subpopulations. These approaches also support the unraveling of sources of cell-to-cell variability. Finite mixture models have shown promise, but the available approaches are ill suited to the simultaneous consideration of data from multiple experimental conditions and to censored data. The prevalence and relevance of single-cell data and the lack of suitable computational analytics make automated methods, that are able to deal with the requirements posed by these data, necessary. RESULTS: We present MEMO, a flexible mixture modeling framework that enables the simultaneous, automated analysis of censored and uncensored data acquired under multiple experimental conditions. MEMO is based on maximum-likelihood inference and allows for testing competing hypotheses. MEMO can be applied to a variety of different single-cell data types. We demonstrate the advantages of MEMO by analyzing right and interval censored single-cell microscopy data. Our results show that an examination of censoring and the simultaneous consideration of different experimental conditions are necessary to reveal biologically meaningful subpopulation structures. MEMO allows for a stringent analysis of single-cell data and enables researchers to avoid misinterpretation of censored data. Therefore, MEMO is a valuable asset for all fields that infer the characteristics of populations by looking at single individuals such as cell biology and medicine. AVAILABILITY AND IMPLEMENTATION: MEMO is implemented in MATLAB and freely available via github (https://github.com/MEMO-toolbox/MEMO). CONTACTS: [email protected] or [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

SUMMARY: We present a new C implementation of an advanced Markov chain Monte Carlo (MCMC) method for the sampling of ordinary differential equation (ode) model parameters. The software mcmc_clib uses the simplified manifold Metropolis-adjusted Langevin algorithm (SMMALA), which is locally adaptive; it uses the parameter manifold's geometry (the Fisher information) to make efficient moves. This adaptation does not diminish with MC length, which is highly advantageous compared with adaptive Metropolis techniques when the parameters have large correlations and/or posteriors substantially differ from multivariate Gaussians. The software is standalone (not a toolbox), though dependencies include the GNU scientific library and sundials libraries for ode integration and sensitivity analysis. AVAILABILITY AND IMPLEMENTATION: The source code and binary files are freely available for download at http://a-kramer.github.io/mcmc_clib/. This also includes example files and data. A detailed documentation, an example model and user manual are provided with the software. CONTACT: [email protected].

BACKGROUND: Parameter estimation for differential equation models of intracellular processes is a highly relevant bu challenging task. The available experimental data do not usually contain enough information to identify all parameters uniquely, resulting in ill-posed estimation problems with often highly correlated parameters. Sampling-based Bayesian statistical approaches are appropriate for tackling this problem. The samples are typically generated via Markov chain Monte Carlo, however such methods are computationally expensive and their convergence may be slow, especially if there are strong correlations between parameters. Monte Carlo methods based on Euclidean or Riemannian Hamiltonian dynamics have been shown to outperform other samplers by making proposal moves that take the local sensitivities of the system's states into account and accepting these moves with high probability. However, the high computational cost involved with calculating the Hamiltonian trajectories prevents their widespread use for all but the smallest differential equation models. The further development of efficient sampling algorithms is therefore an important step towards improving the statistical analysis of predictive models of intracellular processes. RESULTS: We show how state of the art Hamiltonian Monte Carlo methods may be significantly improved for steady state dynamical models. We present a novel approach for efficiently calculating the required geometric quantities by tracking steady states across the Hamiltonian trajectories using a Newton-Raphson method and employing local sensitivity information. Using our approach, we compare both Euclidean and Riemannian versions of Hamiltonian Monte Carlo on three models for intracellular processes with real data and demonstrate at least an order of magnitude improvement in the effective sampling speed. We further demonstrate the wider applicability of our approach to other gradient based MCMC methods, such as those based on Langevin diffusions. CONCLUSION: Our approach is strictly benefitial in all test cases. The Matlab sources implementing our MCMC methodology is available from https://github.com/a-kramer/ode_rmhmc.

BACKGROUND: Mathematical models are nowadays widely used to describe biochemical reaction networks. One of the main reasons for this is that models facilitate the integration of a multitude of different data and data types using parameter estimation. Thereby, models allow for a holistic understanding of biological processes. However, due to measurement noise and the limited amount of data, uncertainties in the model parameters should be considered when conclusions are drawn from estimated model attributes, such as reaction fluxes or transient dynamics of biological species. METHODS AND RESULTS: We developed the visual analytics system iVUN that supports uncertainty-aware analysis of static and dynamic attributes of biochemical reaction networks modeled by ordinary differential equations. The multivariate graph of the network is visualized as a node-link diagram, and statistics of the attributes are mapped to the color of nodes and links of the graph. In addition, the graph view is linked with several views, such as line plots, scatter plots, and correlation matrices, to support locating uncertainties and the analysis of their time dependencies. As demonstration, we use iVUN to quantitatively analyze the dynamics of a model for Epo-induced JAK2/STAT5 signaling. CONCLUSION: Our case study showed that iVUN can be used to perform an in-depth study of biochemical reaction networks, including attribute uncertainties, correlations between these attributes and their uncertainties as well as the attribute dynamics. In particular, the linking of different visualization options turned out to be highly beneficial for the complex analysis tasks that come with the biological systems as presented here.

MOTIVATION: Experiment design strategies for biomedical models with the purpose of parameter estimation or model discrimination are in the focus of intense research. Experimental limitations such as sparse and noisy data result in unidentifiable parameters and render-related design tasks challenging problems. Often, the temporal resolution of data is a limiting factor and the amount of possible experimental interventions is finite. To address this issue, we propose a Bayesian experiment design algorithm to minimize the prediction uncertainty for a given set of experiments and compare it to traditional A-optimal design. RESULTS: In an in depth numerical study involving an ordinary differential equation model of the trans-Golgi network with 12 partly non-identifiable parameters, we minimized the prediction uncertainty efficiently for predefined scenarios. The introduced method results in twice the prediction precision as the same amount of A-optimal designed experiments while introducing a useful stopping criterion. The simulation intensity of the algorithm's major design step is thereby reasonably affordable. Besides smaller variances in the predicted trajectories compared with Fisher design, we could also achieve smaller parameter posterior distribution entropies, rendering this method superior to A-optimal Fisher design also in the parameter space. AVAILABILITY: Necessary software/toolbox information are available in the supplementary material. The project script including example data can be downloaded from http://www.ist.uni-stuttgart.de/%7eweber/BayesFisher2012. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Most of the modeling performed in the area of systems biology aims at achieving a quantitative description of the intracellular pathways within a "typical cell". However, in many biologically important situations even clonal cell populations can show a heterogeneous response. These situations require study of cell-to-cell variability and the development of models for heterogeneous cell populations. RESULTS: In this paper we consider cell populations in which the dynamics of every single cell is captured by a parameter dependent differential equation. Differences among cells are modeled by differences in parameters which are subject to a probability density. A novel Bayesian approach is presented to infer this probability density from population snapshot data, such as flow cytometric analysis, which do not provide single cell time series data. The presented approach can deal with sparse and noisy measurement data. Furthermore, it is appealing from an application point of view as in contrast to other methods the uncertainty of the resulting parameter distribution can directly be assessed. CONCLUSIONS: The proposed method is evaluated using artificial experimental data from a model of the tumor necrosis factor signaling network. We demonstrate that the methods are computationally efficient and yield good estimation result even for sparse data sets.

MOTIVATION: Feedback circuits are important motifs in biological networks and part of virtually all regulation processes that are needed for a reliable functioning of the cell. Mathematically, feedback is connected to complex behavior of the systems, which is often related to bifurcations of fixed points. Therefore, several approaches for the investigation of fixed points in biological networks have been developed in recent years. Many of them assume the fixed point coordinates to be known, and an efficient way to calculate the entire set of fixed points for interrelated feedback structures is highly desirable. RESULTS: In this article, we consider regulatory network models, which are differential equations with an underlying directed graph that illustrates independencies among variables. We introduce the circuit-breaking algorithm (CBA), a method that constructs one-dimensional characteristics for these network models, which inherit important information about the system. In particular, fixed points are related to the zeros of these characteristics. The CBA operates on the graph topology, and results from graph theory are used in order to make calculations efficient. Our framework provides a general scheme for analyzing network models in terms of interrelated feedback circuits. The efficiency of the approach is demonstrated on a model for calcium oscillations based on experiments in hepatocytes, which consists of several interrelated feedback circuits.

MOTIVATION: A quantitative description of interactions between cell components is a major challenge in Computational Biology. As a method of choice, differential equations are used for this purpose, because they provide a detailed insight into the dynamic behavior of the system. In most cases, the number of time points of experimental time series is usually too small to estimate the parameters of a model of a whole gene regulatory network based on differential equations, such that one needs to focus on subnetworks consisting of only a few components. For most approaches, the set of components of the subsystem is given in advance and only the structure has to be estimated. However, the set of components that influence the system significantly are not always known in advance, making a method desirable that determines both, the components that are included into the model and the parameters. RESULTS: We have developed a method that uses gene expression data as well as interaction data between cell components to define a set of genes that we use for our modeling. In a subsequent step, we estimate the parameters of our model of piecewise linear differential equations and evaluate the results simulating the behavior of the system with our model. We have applied our method to the DNA repair system of Mycobacterium tuberculosis. Our analysis predicts that the gene Rv2719c plays an important role in this system.