Bayesian modelling of time series data (BayModTS)-a FAIR workflow to process sparse and highly variable data.

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.

A Provably Convergent Control Closure Scheme for the Method of Moments of the Chemical Master Equation.

In this article, we introduce a novel moment closure scheme based on concepts from model predictive control (MPC) to accurately describe the time evolution of the statistical moments of the solution of the chemical master equation (CME). The method of moments, a set of ordinary differential equations frequently used to calculate the first nm moments, is generally not closed since lower-order moments depend on higher-order moments. To overcome this limitation, we interpret the moment equations as a nonlinear dynamical system, where the first nm moments serve as states, and the closing moments serve as the control input. We demonstrate the efficacy of our approach using three example systems and show that it outperforms existing closure schemes. For polynomial systems, which encompass all mass-action systems, we provide probability bounds for the error between true and estimated moment trajectories. We achieve this by combining the convergence properties of a priori moment estimates from stochastic simulations with guarantees for nonlinear reference tracking MPC. Our proposed method offers an effective solution to accurately predict the time evolution of moments of the CME, which has wide-ranging implications for many fields, including biology, chemistry, and engineering.

The impossible challenge of estimating non-existent moments of the Chemical Master Equation.

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.

On the accuracy of the epigenetic copy machine: comprehensive specificity analysis of the DNMT1 DNA methyltransferase.

The specificity of DNMT1 for hemimethylated DNA is a central feature for the inheritance of DNA methylation. We investigated this property in competitive methylation kinetics using hemimethylated (HM), hemihydroxymethylated (OH) and unmethylated (UM) substrates with single CpG sites in a randomized sequence context. DNMT1 shows a strong flanking sequence dependent HM/UM specificity of 80-fold on average, which is slightly enhanced on long hemimethylated DNA substrates. To explain this strong effect of a single methyl group, we propose a novel model in which the presence of the 5mC methyl group changes the conformation of the DNMT1-DNA complex into an active conformation by steric repulsion. The HM/OH preference is flanking sequence dependent and on average only 13-fold, indicating that passive DNA demethylation by 5hmC generation is not efficient in many flanking contexts. The CXXC domain of DNMT1 has a moderate flanking sequence dependent contribution to HM/UM specificity during DNA association to DNMT1, but not if DNMT1 methylates long DNA molecules in processive methylation mode. Comparison of genomic methylation patterns from mouse ES cell lines with various deletions of DNMTs and TETs with our data revealed that the UM specificity profile is most related to cellular methylation patterns, indicating that de novo methylation activity of DNMT1 shapes the DNA methylome in these cells.

Bayesian estimation reveals that reproducible models in Systems Biology get more citations.

The Systems Biology community has taken numerous actions to develop data and modeling standards towards FAIR data and model handling. Nevertheless, the debate about incentives and rewards for individual researchers to make their results reproducible is ongoing. Here, we pose the specific question of whether reproducible models have a higher impact in terms of citations. Therefore, we statistically analyze 328 published models recently classified by Tiwari et al. based on their reproducibility. For hypothesis testing, we use a flexible Bayesian approach that provides complete distributional information for all quantities of interest and can handle outliers. The results show that in the period from 2013, i.e., 10 years after the introduction of SBML, to 2020, the group of reproducible models is significantly more cited than the non-reproducible group. We show that differences in journal impact factors do not explain this effect and that this effect increases with additional standardization of data and error model integration via PEtab. Overall, our statistical analysis demonstrates the long-term merits of reproducible modeling for the individual researcher in terms of citations. Moreover, it provides evidence for the increased use of reproducible models in the scientific community.

The effect of normalisation and error model choice on the distribution of the maximum likelihood estimator for a biochemical reaction.

Sparse and noisy measurements make parameter estimation for biochemical reaction networks difficult and might lead to ill-posed optimisation problems. This is potentiated if the data has to be normalised, and only fold changes rather than absolute amounts are available. Here, the authors consider the propagation of measurement noise to the distribution of the maximum likelihood (ML) estimator in an in silico study. Therefore, a model of a reversible reaction is considered, for which reaction rate constants using fold changes is estimated. Noise propagation is analysed for different normalisation strategies and different error models. In particular, accuracy, precision, and asymptotic properties of the ML estimator is investigated. Results show that normalisation by the mean of a time series outperforms normalisation by a single time point in the example provided by the authors. Moreover, the error model with a heavy-tail distribution is slightly more robust to large measurement noise, but, beyond this, the choice of the error model did not have a significant impact on the estimation results provided by the authors.

Reversible switching and stability of the epigenetic memory system in bacteria.

In previous work, we have developed a DNA methylation-based epigenetic memory system that operates in Escherichia coli to detect environmental signals, trigger a phenotypic switch of the cells and store the information in DNA methylation. The system is based on the CcrM DNA methyltransferase and a synthetic zinc finger (ZnF4), which binds DNA in a CcrM methylation-dependent manner and functions as a repressor for a ccrM gene expressed together with an egfp reporter gene. Here, we developed a reversible reset for this memory system by adding an increased concentration of ZnSO4 to the bacterial cultivation medium and demonstrate that one bacterial culture could be reversibly switched ON and OFF in several cycles. We show that a previously developed differential equation model of the memory system can also describe the new data. Then, we studied the long-term stability of the ON-state of the system over approximately 100 cell divisions showing a gradual loss of ON-state signal starting after 4 days of cultivation that is caused by individual cells switching from an ON- into the OFF-state. Over time, the methylation of the ZnF4-binding sites is not fully maintained leading to an increased OFF switching probability of cells, because stronger binding of ZnF4 to partially demethylated operator sites leads to further reductions in the cellular concentrations of CcrM. These data will support future design to further stabilize the ON-state and enforce the binary switching behaviour of the system. Together with the development of a reversible OFF switch, our new findings strongly increase the capabilities of bacterial epigenetic biosensors.

Periportal steatosis in mice affects distinct parameters of pericentral drug metabolism.

Little is known about the impact of morphological disorders in distinct zones on metabolic zonation. It was described recently that periportal fibrosis did affect the expression of CYP proteins, a set of pericentrally located drug-metabolizing enzymes. Here, we investigated whether periportal steatosis might have a similar effect. Periportal steatosis was induced in C57BL6/J mice by feeding a high-fat diet with low methionine/choline content for either two or four weeks. Steatosis severity was quantified using image analysis. Triglycerides and CYP activity were quantified in photometric or fluorometric assay. The distribution of CYP3A4, CYP1A2, CYP2D6, and CYP2E1 was visualized by immunohistochemistry. Pharmacokinetic parameters of test drugs were determined after injecting a drug cocktail (caffeine, codeine, and midazolam). The dietary model resulted in moderate to severe mixed steatosis confined to periportal and midzonal areas. Periportal steatosis did not affect the zonal distribution of CYP expression but the activity of selected CYPs was associated with steatosis severity. Caffeine elimination was accelerated by microvesicular steatosis, whereas midazolam elimination was delayed in macrovesicular steatosis. In summary, periportal steatosis affected parameters of pericentrally located drug metabolism. This observation calls for further investigations of the highly complex interrelationship between steatosis and drug metabolism and underlying signaling mechanisms.

Quasi-Entropy Closure: a fast and reliable approach to close the moment equations of the Chemical Master Equation.

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.

Model-Based Design of a Synthetic Oscillator Based on an Epigenetic Methylation Memory System.

Oscillations are an important component in biological systems; grasping their mechanisms and regulation, however, is difficult. Here, we use the theory of dynamical systems to support the design of oscillatory systems based on epigenetic control elements. Specifically, we use results that extend the Poincaré-Bendixson theorem for monotone control systems that are coupled to a negative feedback circuit. The methodology is applied to a synthetic epigenetic memory system based on DNA methylation that serves as a monotone control system, which is coupled to a negative feedback. This system is generally able to show sustained oscillations according to its structure; however, a first experimental implementation showed that fine-tuning of several parameters is required. We provide design support by exploring the experimental design space using systems-theoretic analysis of a computational model.

Flanking sequences influence the activity of TET1 and TET2 methylcytosine dioxygenases and affect genomic 5hmC patterns.

TET dioxygenases convert 5-methylcytosine (5mC) preferentially in a CpG context into 5-hydroxymethylcytosine (5hmC) and higher oxidized forms, thereby initiating DNA demethylation, but details regarding the effects of the DNA sequences flanking the target 5mC site on TET activity are unknown. We investigated oxidation of libraries of DNA substrates containing one 5mC or 5hmC residue in randomized sequence context using single molecule readout of oxidation activity and sequence and show pronounced 20 and 70-fold flanking sequence effects on the catalytic activities of TET1 and TET2, respectively. Flanking sequence preferences were similar for TET1 and TET2 and also for 5mC and 5hmC substrates. Enhanced flanking sequence preferences were observed at non-CpG sites together with profound effects of flanking sequences on the specificity of TET2. TET flanking sequence preferences are reflected in genome-wide and local patterns of 5hmC and DNA demethylation in human and mouse cells indicating that they influence genomic DNA modification patterns in combination with locus specific targeting of TET enzymes.

ROSIE: RObust Sparse ensemble for outlIEr detection and gene selection in cancer omics data.

The extraction of novel information from omics data is a challenging task, in particular, since the number of features (e.g. genes) often far exceeds the number of samples. In such a setting, conventional parameter estimation leads to ill-posed optimization problems, and regularization may be required. In addition, outliers can largely impact classification accuracy.Here we introduce ROSIE, an ensemble classification approach, which combines three sparse and robust classification methods for outlier detection and feature selection and further performs a bootstrap-based validity check. Outliers of ROSIE are determined by the rank product test using outlier rankings of all three methods, and important features are selected as features commonly selected by all methods.We apply ROSIE to RNA-Seq data from The Cancer Genome Atlas (TCGA) to classify observations into Triple-Negative Breast Cancer (TNBC) and non-TNBC tissue samples. The pre-processed dataset consists of 16,600 genes and more than 1,000 samples. We demonstrate that ROSIE selects important features and outliers in a robust way. Identified outliers are concordant with the distribution of the commonly selected genes by the three methods, and results are in line with other independent studies. Furthermore, we discuss the association of some of the selected genes with the TNBC subtype in other investigations. In summary, ROSIE constitutes a robust and sparse procedure to identify outliers and important genes through binary classification. Our approach is ad hoc applicable to other datasets, fulfilling the overall goal of simultaneously identifying outliers and candidate disease biomarkers to the targeted in therapy research and personalized medicine frameworks.

Hepatectomy-Induced Alterations in Hepatic Perfusion and Function - Toward Multi-Scale Computational Modeling for a Better Prediction of Post-hepatectomy Liver Function.

Liver resection causes marked perfusion alterations in the liver remnant both on the organ scale (vascular anatomy) and on the microscale (sinusoidal blood flow on tissue level). These changes in perfusion affect hepatic functions via direct alterations in blood supply and drainage, followed by indirect changes of biomechanical tissue properties and cellular function. Changes in blood flow impose compression, tension and shear forces on the liver tissue. These forces are perceived by mechanosensors on parenchymal and non-parenchymal cells of the liver and regulate cell-cell and cell-matrix interactions as well as cellular signaling and metabolism. These interactions are key players in tissue growth and remodeling, a prerequisite to restore tissue function after PHx. Their dysregulation is associated with metabolic impairment of the liver eventually leading to liver failure, a serious post-hepatectomy complication with high morbidity and mortality. Though certain links are known, the overall functional change after liver surgery is not understood due to complex feedback loops, non-linearities, spatial heterogeneities and different time-scales of events. Computational modeling is a unique approach to gain a better understanding of complex biomedical systems. This approach allows (i) integration of heterogeneous data and knowledge on multiple scales into a consistent view of how perfusion is related to hepatic function; (ii) testing and generating hypotheses based on predictive models, which must be validated experimentally and clinically. In the long term, computational modeling will (iii) support surgical planning by predicting surgery-induced perfusion perturbations and their functional (metabolic) consequences; and thereby (iv) allow minimizing surgical risks for the individual patient. Here, we review the alterations of hepatic perfusion, biomechanical properties and function associated with hepatectomy. Specifically, we provide an overview over the clinical problem, preoperative diagnostics, functional imaging approaches, experimental approaches in animal models, mechanoperception in the liver and impact on cellular metabolism, omics approaches with a focus on transcriptomics, data integration and uncertainty analysis, and computational modeling on multiple scales. Finally, we provide a perspective on how multi-scale computational models, which couple perfusion changes to hepatic function, could become part of clinical workflows to predict and optimize patient outcome after complex liver surgery.

Model-based robustness and bistability analysis for methylation-based, epigenetic memory systems.

In recent years, epigenetic memory systems have been developed based on DNA methylation and positive feedback systems. Achieving a robust design for these systems is generally a challenging and multifactorial task. We developed and validated a novel mathematical model to describe methylation-based epigenetic memory systems that capture switching dynamics of methylation levels and methyltransferase amounts induced by different inputs. A bifurcation analysis shows that the system operates in the bistable range, but in its current setup is not robust to changes in parameters. An expansion of the model captures heterogeneity of cell populations by accounting for distributed cell division rates. Simulations predict that the system is highly sensitive to variations in temperature, which affects cell division and the efficiency of the zinc finger repressor. A moderate decrease in temperature leads to a highly heterogeneous response to input signals and bistability on a single-cell level. The predictions of our model were confirmed by flow cytometry experiments conducted in this study. Overall, the results of our study give insights into the functional mechanisms of methylation-based memory systems and demonstrate that the switching dynamics can be highly sensitive to experimental conditions.

DNA sequence-dependent activity and base flipping mechanisms of DNMT1 regulate genome-wide DNA methylation.

DNA methylation maintenance by DNMT1 is an essential process in mammals but molecular mechanisms connecting DNA methylation patterns and enzyme activity remain elusive. Here, we systematically analyzed the specificity of DNMT1, revealing a pronounced influence of the DNA sequences flanking the target CpG site on DNMT1 activity. We determined DNMT1 structures in complex with preferred DNA substrates revealing that DNMT1 employs flanking sequence-dependent base flipping mechanisms, with large structural rearrangements of the DNA correlating with low catalytic activity. Moreover, flanking sequences influence the conformational dynamics of the active site and cofactor binding pocket. Importantly, we show that the flanking sequence preferences of DNMT1 highly correlate with genomic methylation in human and mouse cells, and 5-azacytidine triggered DNA demethylation is more pronounced at CpG sites with flanks disfavored by DNMT1. Overall, our findings uncover the intricate interplay between CpG-flanking sequence, DNMT1-mediated base flipping and the dynamic landscape of DNA methylation.

Inference of finite mixture models and the effect of binning.

Finite mixture models are widely used in the life sciences for data analysis. Yet, the calibration of these models to data is still challenging as the optimization problems are often ill-posed. This holds for censored and uncensored data, and is caused by symmetries and other types of non-identifiabilities. Here, we discuss the problem of parameter estimation and model selection for finite mixture models from a theoretical perspective. We provide a review of the existing literature and illustrate the ill-posedness of the calibration problem for mixtures of uniform distributions and mixtures of normal distributions. Furthermore, we assess the effect of interval censoring on this estimation problem. Interestingly, we find that a proper treatment of censoring can facilitate the estimation of the number of mixture components compared to inference from uncensored data, which is an at first glance surprising result. The aim of the manuscript is to raise awareness of challenges in the calibration of finite mixture models and to provide an overview about available techniques.

Impact of measurement noise, experimental design, and estimation methods on Modular Response Analysis based network reconstruction.

Modular Response Analysis (MRA) is a method to reconstruct signalling networks from steady-state perturbation data which has frequently been used in different settings. Since these data are usually noisy due to multi-step measurement procedures and biological variability, it is important to investigate the effect of this noise onto network reconstruction. Here we present a systematic study to investigate propagation of noise from concentration measurements to network structures. Therefore, we design an in silico study of the MAPK and the p53 signalling pathways with realistic noise settings. We make use of statistical concepts and measures to evaluate accuracy and precision of individual inferred interactions and resulting network structures. Our results allow to derive clear recommendations to optimize the performance of MRA based network reconstruction: First, large perturbations are favorable in terms of accuracy even for models with non-linear steady-state response curves. Second, a single control measurement for different perturbation experiments seems to be sufficient for network reconstruction, and third, we recommend to execute the MRA workflow with the mean of different replicates for concentration measurements rather than using computationally more involved regression strategies.

The tumor suppressor protein DLC1 maintains protein kinase D activity and Golgi secretory function.

Many newly synthesized cellular proteins pass through the Golgi complex from where secretory transport carriers sort them to the plasma membrane and the extracellular environment. The formation of these secretory carriers at the trans-Golgi network is promoted by the protein kinase D (PKD) family of serine/threonine kinases. Here, using mathematical modeling and experimental validation of the PKD activation and substrate phosphorylation kinetics, we reveal that the expression level of the PKD substrate deleted in liver cancer 1 (DLC1), a Rho GTPase-activating protein that is inhibited by PKD-mediated phosphorylation, determines PKD activity at the Golgi membranes. RNAi-mediated depletion of DLC1 reduced PKD activity in a Rho-Rho-associated protein kinase (ROCK)-dependent manner, impaired the exocytosis of the cargo protein horseradish peroxidase, and was associated with the accumulation of the small GTPase RAB6 on Golgi membranes, indicating a protein-trafficking defect. In summary, our findings reveal that DLC1 maintains basal activation of PKD at the Golgi and Golgi secretory activity, in part by down-regulating Rho-ROCK signaling. We propose that PKD senses cytoskeletal changes downstream of DLC1 to coordinate Rho signaling with Golgi secretory function.

The role of stochastic sequestration dynamics for intrinsic noise filtering in signaling network motifs.

The relation between design principles of signaling network motifs and their robustness against intrinsic noise still remains illusive. In this work we investigate the role of cascading for coping with intrinsic noise due to stochasticity in molecular reactions. We use stochastic approaches to quantify fluctuations in the terminal kinase of phosphorylation-dephosphorylation cascade motifs and demonstrate that cascading highly affects these fluctuations. We show that this purely stochastic effect can be explained by time-varying sequestration of upstream kinase molecules. In particular, we discuss conditions on time scales and parameter regimes which lead to a reduction of output fluctuations. Our results are put into biological context by adapting rate parameters of our modeling approach to biologically feasible ranges for general binding-unbinding and phosphorylation-dephosphorylation mechanisms. Overall, this study reveals a novel role of stochastic sequestration for dynamic noise filtering in signaling cascade motifs.