MOTIVATION: Relating metabolite and enzyme abundances to metabolic fluxes requires reaction kinetics, core elements of dynamic and enzyme cost models. However, kinetic parameters have been measured only for a fraction of all known enzymes, and the reliability of the available values is unknown. RESULTS: The ENzyme KInetics Estimator (ENKIE) uses Bayesian Multilevel Models to predict value and uncertainty of KM and kcat parameters. Our models use five categorical predictors and achieve prediction performances comparable to deep learning approaches that use sequence and structure information. They provide calibrated uncertainty predictions and interpretable insights into the main sources of uncertainty. We expect our tool to simplify the construction of priors for Bayesian kinetic models of metabolism. AVAILABILITY AND IMPLEMENTATION: Code and Python package are available at https://gitlab.com/csb.ethz/enkie and https://pypi.org/project/enkie/.

BACKGROUND: Microbial community simulations using genome scale metabolic networks (GSMs) are relevant for many application areas, such as the analysis of the human microbiome. Such simulations rely on assumptions about the culturing environment, affecting if the culture may reach a metabolically stationary state with constant microbial concentrations. They also require assumptions on decision making by the microbes: metabolic strategies can be in the interest of individual community members or of the whole community. However, the impact of such common assumptions on community simulation results has not been investigated systematically. RESULTS: Here, we investigate four combinations of assumptions, elucidate how they are applied in literature, provide novel mathematical formulations for their simulation, and show how the resulting predictions differ qualitatively. Our results stress that different assumption combinations give qualitatively different predictions on microbial coexistence by differential substrate utilization. This fundamental mechanism is critically under explored in the steady state GSM literature with its strong focus on coexistence states due to crossfeeding (division of labor). Furthermore, investigating a realistic synthetic community, where the two involved strains exhibit no growth in isolation, but grow as a community, we predict multiple modes of cooperation, even without an explicit cooperation mechanism. CONCLUSIONS: Steady state GSM modelling of microbial communities relies both on assumed decision making principles and environmental assumptions. In principle, dynamic flux balance analysis addresses both. In practice, our methods that address the steady state directly may be preferable, especially if the community is expected to display multiple steady states.

BACKGROUND: Synthetic biologists use and combine diverse biological parts to build systems such as genetic circuits that perform desirable functions in, for example, biomedical or industrial applications. Computer-aided design methods have been developed to help choose appropriate network structures and biological parts for a given design objective. However, they almost always model the behavior of the network in an average cell, despite pervasive cell-to-cell variability. RESULTS: Here, we present a computational framework and an efficient algorithm to guide the design of synthetic biological circuits while accounting for cell-to-cell variability explicitly. Our design method integrates a Non-linear Mixed-Effects (NLME) framework into a Markov Chain Monte-Carlo (MCMC) algorithm for design based on ordinary differential equation (ODE) models. The analysis of a recently developed transcriptional controller demonstrates first insights into design guidelines when trying to achieve reliable performance under cell-to-cell variability. CONCLUSION: We anticipate that our method not only facilitates the rational design of synthetic networks under cell-to-cell variability, but also enables novel applications by supporting design objectives that specify the desired behavior of cell populations.

SUMMARY: Random flux sampling is a powerful tool for the constraint-based analysis of metabolic networks. The most efficient sampling method relies on a rounding transform of the constraint polytope, but no available rounding implementation can round all relevant models. By removing redundant polytope constraints on the go, PolyRound simplifies the numerical problem and rounds all the 108 models in the BiGG database without parameter tuning, compared to ∼50% for the state-of-the-art implementation. AVAILABILITY AND IMPLEMENTATION: The implementation is available on gitlab: https://gitlab.com/csb.ethz/PolyRound. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

This special issue brings together leading experts in the fields of systems and synthetic biology to provide a quantitative and analytical perspective of the state-of-the-art developments.

Metabolic network analysis is an accessible and versatile modeling approach for biology that has taken much inspiration from electric circuit analysis. After introducing its main concepts, we focus on numerical tools, such as optimization and sampling, to predict cellular features and behaviors at a large scale. Optimization approaches exploit that metabolic networks are shaped by evolution and are, thus, assumed to embed a fitness condition reflecting the environment that they evolved in. In the past ten years, there is a trend to generalize metabolic network analysis to consortia of interacting species. This raises technical questions on, for example, optimality in consortia but also more general ones on metabolic coevolution, information exchange, and adaptation. This suggests and allows us to explore interesting analogies to technological systems, specifically to smart grids.

MOTIVATION: Random sampling of metabolic fluxes can provide a comprehensive description of the capabilities of a metabolic network. However, current sampling approaches do not model thermodynamics explicitly, leading to inaccurate predictions of an organism's potential or actual metabolic operations. RESULTS: We present a probabilistic framework combining thermodynamic quantities with steady-state flux constraints to analyze the properties of a metabolic network. It includes methods for probabilistic metabolic optimization and for joint sampling of thermodynamic and flux spaces. Applied to a model of Escherichia coli, we use the methods to reveal known and novel mechanisms of substrate channeling, and to accurately predict reaction directions and metabolite concentrations. Interestingly, predicted flux distributions are multimodal, leading to discrete hypotheses on E.coli's metabolic capabilities. AVAILABILITY AND IMPLEMENTATION: Python and MATLAB packages available at https://gitlab.com/csb.ethz/pta. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Multi-steady state behaviour, and in particular multi-stability, provides biological systems with the capacity to take reliable decisions (such as cell fate determination). A problem arising frequently in systems biology is to elucidate whether a signal transduction mechanism or a gene regulatory network has the capacity for multi-steady state behaviour, and consequently for a switch-like response to stimuli. Bifurcation diagrams are a powerful instrument in non-linear analysis to study the qualitative and quantitative behaviour of equilibria including bifurcation into different equilibrium branches and bistability. However, in the context of signalling pathways, the inherent large parametric uncertainty hampers the (direct) use of standard bifurcation tools. RESULTS: We present BioSwitch, a toolbox to detect multi-steady state behaviour in signalling pathways and gene regulatory networks. The tool combines results from chemical reaction network theory with global optimization to efficiently detect whether a signalling pathway has the capacity to undergo a saddle node bifurcation, and in case of multi-stationarity, provides the exact coordinates of the bifurcation where to start a numerical continuation analysis with standard bifurcation tools, leading to two different branches of equilibria. Bistability detection in the G1/S transition pathway of Saccharomyces cerevisiae is included as an illustrative example. AVAILABILITY AND IMPLEMENTATION: BioSwitch runs under the popular MATLAB computational environment, and is available at https://sites.google.com/view/bioswitch.

BACKGROUND: To develop mechanistic dynamic models in systems biology, one often needs to identify all (or minimal) representations of the biological processes that are consistent with experimental data, out of a potentially large set of hypothetical mechanisms. However, a simple enumeration of all alternatives becomes quickly intractable when the number of model parameters grows. Selecting appropriate dynamic models out of a large ensemble of models, taking the uncertainty in our biological knowledge and in the experimental data into account, is therefore a key current problem in systems biology. RESULTS: The TopoFilter package addresses this problem in a heuristic and automated fashion by implementing the previously described topological filtering method for Bayesian model selection. It includes a core heuristic for searching the space of submodels of a parametrized model, coupled with a sampling-based exploration of the parameter space. Recent developments of the method allow to balance exhaustiveness and speed of the model space search, to efficiently re-sample parameters, to parallelize the search, and to use custom scoring functions. We use a theoretical example to motivate these features and then demonstrate TopoFilter's applicability for a yeast signaling network with more than 250'000 possible model structures. CONCLUSIONS: TopoFilter is a flexible software framework that makes Bayesian model selection and reduction efficient and scalable to network models of a complexity that represents contemporary problems in, for example, cell signaling. TopoFilter is open-source, available under the GPL-3.0 license at https://gitlab.com/csb.ethz/TopoFilter. It includes installation instructions, a quickstart guide, a description of all package options, and multiple examples.

Bistability has important implications in signaling pathways, since it indicates a potential cell decision between alternative outcomes. We present two approaches developed in the framework of the Chemical Reaction Network Theory for easy and efficient search of multiple steady state behavior in signaling networks (both with and without mass conservation), and apply them to search for sources of bistability at different levels of the interferon signaling pathway. Different type I interferon subtypes and/or doses are known to elicit differential bioactivities (ranging from antiviral, antiproliferative to immunomodulatory activities). How different signaling outcomes can be generated through the same receptor and activating the same JAK/STAT pathway is still an open question. Here, we detect bistability at the level of early STAT signaling, showing how two different cell outcomes are achieved under or above a threshold in ligand dose or ligand-receptor affinity. This finding could contribute to explain the differential signaling (antiviral vs apoptotic) depending on interferon dose and subtype (α vs β) observed in type I interferons.

Understanding cellular function requires accurate, comprehensive representations of metabolism. Genome-scale, constraint-based metabolic models (GSMs) provide such representations, but their usability is often hampered by inconsistencies at various levels, in particular for concurrent models. COMMGEN, our tool for COnsensus Metabolic Model GENeration, automatically identifies inconsistencies between concurrent models and semi-automatically resolves them, thereby contributing to consolidate knowledge of metabolic function. Tests of COMMGEN for four organisms showed that automatically generated consensus models were predictive and that they substantially increased coherence of knowledge representation. COMMGEN ought to be particularly useful for complex scenarios in which manual curation does not scale, such as for eukaryotic organisms, microbial communities, and host-pathogen interactions.

Parametric uncertainty is a particularly challenging and relevant aspect of systems analysis in domains such as systems biology where, both for inference and for assessing prediction uncertainties, it is essential to characterize the system behavior globally in the parameter space. However, current methods based on local approximations or on Monte-Carlo sampling cope only insufficiently with high-dimensional parameter spaces associated with complex network models. Here, we propose an alternative deterministic methodology that relies on sparse polynomial approximations. We propose a deterministic computational interpolation scheme which identifies most significant expansion coefficients adaptively. We present its performance in kinetic model equations from computational systems biology with several hundred parameters and state variables, leading to numerical approximations of the parametric solution on the entire parameter space. The scheme is based on adaptive Smolyak interpolation of the parametric solution at judiciously and adaptively chosen points in parameter space. As Monte-Carlo sampling, it is "non-intrusive" and well-suited for massively parallel implementation, but affords higher convergence rates. This opens up new avenues for large-scale dynamic network analysis by enabling scaling for many applications, including parameter estimation, uncertainty quantification, and systems design.

MOTIVATION: Identifying cells in an image (cell segmentation) is essential for quantitative single-cell biology via optical microscopy. Although a plethora of segmentation methods exists, accurate segmentation is challenging and usually requires problem-specific tailoring of algorithms. In addition, most current segmentation algorithms rely on a few basic approaches that use the gradient field of the image to detect cell boundaries. However, many microscopy protocols can generate images with characteristic intensity profiles at the cell membrane. This has not yet been algorithmically exploited to establish more general segmentation methods. RESULTS: We present an automatic cell segmentation method that decodes the information across the cell membrane and guarantees optimal detection of the cell boundaries on a per-cell basis. Graph cuts account for the information of the cell boundaries through directional cross-correlations, and they automatically incorporate spatial constraints. The method accurately segments images of various cell types grown in dense cultures that are acquired with different microscopy techniques. In quantitative benchmarks and comparisons with established methods on synthetic and real images, we demonstrate significantly improved segmentation performance despite cell-shape irregularity, cell-to-cell variability and image noise. As a proof of concept, we monitor the internalization of green fluorescent protein-tagged plasma membrane transporters in single yeast cells. AVAILABILITY AND IMPLEMENTATION: Matlab code and examples are available at http://www.csb.ethz.ch/tools/cellSegmPackage.zip.

MOTIVATION: A common problem in understanding a biochemical system is to infer its correct structure or topology. This topology consists of all relevant state variables-usually molecules and their interactions. Here we present a method called topological augmentation to infer this structure in a statistically rigorous and systematic way from prior knowledge and experimental data. RESULTS: Topological augmentation starts from a simple model that is unable to explain the experimental data and augments its topology by adding new terms that capture the experimental behavior. This process is guided by representing the uncertainty in the model topology through stochastic differential equations whose trajectories contain information about missing model parts. We first apply this semiautomatic procedure to a pharmacokinetic model. This example illustrates that a global sampling of the parameter space is critical for inferring a correct model structure. We also use our method to improve our understanding of glutamine transport in yeast. This analysis shows that transport dynamics is determined by glutamine permeases with two different kinds of kinetics. Topological augmentation can not only be applied to biochemical systems, but also to any system that can be described by ordinary differential equations. AVAILABILITY AND IMPLEMENTATION: Matlab code and examples are available at: http://www.csb.ethz.ch/tools/index

MOTIVATION: Biological systems are understood through iterations of modeling and experimentation. Not all experiments, however, are equally valuable for predictive modeling. This study introduces an efficient method for experimental design aimed at selecting dynamical models from data. Motivated by biological applications, the method enables the design of crucial experiments: it determines a highly informative selection of measurement readouts and time points. RESULTS: We demonstrate formal guarantees of design efficiency on the basis of previous results. By reducing our task to the setting of graphical models, we prove that the method finds a near-optimal design selection with a polynomial number of evaluations. Moreover, the method exhibits the best polynomial-complexity constant approximation factor, unless P = NP. We measure the performance of the method in comparison with established alternatives, such as ensemble non-centrality, on example models of different complexity. Efficient design accelerates the loop between modeling and experimentation: it enables the inference of complex mechanisms, such as those controlling central metabolic operation. AVAILABILITY: Toolbox 'NearOED' available with source code under GPL on the Machine Learning Open Source Software Web site (mloss.org).

MetaNetX.org is a website for accessing, analysing and manipulating genome-scale metabolic networks (GSMs) as well as biochemical pathways. It consistently integrates data from various public resources and makes the data accessible in a standardized format using a common namespace. Currently, it provides access to hundreds of GSMs and pathways that can be interactively compared (two or more), analysed (e.g. detection of dead-end metabolites and reactions, flux balance analysis or simulation of reaction and gene knockouts), manipulated and exported. Users can also upload their own metabolic models, choose to automatically map them into the common namespace and subsequently make use of the website's functionality.

One of the most obvious phenotypes of a cell is its metabolic activity, which is defined by the fluxes in the metabolic network. Although experimental methods to determine intracellular fluxes are well established, only a limited number of fluxes can be resolved. Especially in eukaryotes such as yeast, compartmentalization and the existence of many parallel routes render exact flux analysis impossible using current methods. To gain more insight into the metabolic operation of S. cerevisiae we developed a new computational approach where we characterize the flux solution space by determining elementary flux modes (EFMs) that are subsequently classified as thermodynamically feasible or infeasible on the basis of experimental metabolome data. This allows us to provably rule out the contribution of certain EFMs to the in vivo flux distribution. From the 71 million EFMs in a medium size metabolic network of S. cerevisiae, we classified 54% as thermodynamically feasible. By comparing the thermodynamically feasible and infeasible EFMs, we could identify reaction combinations that span the cytosol and mitochondrion and, as a system, cannot operate under the investigated glucose batch conditions. Besides conclusions on single reactions, we found that thermodynamic constraints prevent the import of redox cofactor equivalents into the mitochondrion due to limits on compartmental cofactor concentrations. Our novel approach of incorporating quantitative metabolite concentrations into the analysis of the space of all stoichiometrically feasible flux distributions allows generating new insights into the system-level operation of the intracellular fluxes without making assumptions on metabolic objectives of the cell.

De novo computational design of synthetic gene circuits that achieve well-defined target functions is a hard task. Existing, brute-force approaches run optimization algorithms on the structure and on the kinetic parameter values of the network. However, more direct rational methods for automatic circuit design are lacking. Focusing on digital synthetic gene circuits, we developed a methodology and a corresponding tool for in silico automatic design. For a given truth table that specifies a circuit's input-output relations, our algorithm generates and ranks several possible circuit schemes without the need for any optimization. Logic behavior is reproduced by the action of regulatory factors and chemicals on the promoters and on the ribosome binding sites of biological Boolean gates. Simulations of circuits with up to four inputs show a faithful and unequivocal truth table representation, even under parametric perturbations and stochastic noise. A comparison with already implemented circuits, in addition, reveals the potential for simpler designs with the same function. Therefore, we expect the method to help both in devising new circuits and in simplifying existing solutions.

Concepts and tools at the basis of electrical engineering can be borrowed to assemble genetic circuits in silico. As electrical components talk to each other by means of the electron current, standard biological parts exchange information through the fluxes of functional molecules, referred to as common signal carriers. Hence, synthetic circuits can be designed by connecting biological parts with wires where signal carriers flow. In this paper we present new features and applications of our model to computationally design synthetic gene circuits. In particular, we show a new design for polycistronic transcription units and a possible implementation of an enzyme-dependent pulse-generating network.

Promoters process signals through recruitment of transcription factors and RNA polymerase, and dynamic changes in promoter activity constitute a major noise source in gene expression. However, it is barely understood how complex promoter architectures determine key features of promoter dynamics. Here, we employ prototypical promoters of yeast ribosomal protein genes as well as simplified versions thereof to analyze the relations among promoter design, complexity, and function. These promoters combine the action of a general regulatory factor with that of specific transcription factors, a common motif of many eukaryotic promoters. By comprehensively analyzing stationary and dynamic promoter properties, this model-based approach enables us to pinpoint the structural characteristics underlying the observed behavior. Functional tradeoffs impose constraints on the promoter architecture of ribosomal protein genes. We find that a stable scaffold in the natural design results in low transcriptional noise and strong co-regulation of target genes in the presence of gene silencing. This configuration also exhibits superior shut-off properties, and it can serve as a tunable switch in living cells. Model validation with independent experimental data suggests that the models are sufficiently realistic. When combined, our results offer a mechanistic explanation for why specific factors are associated with low protein noise in vivo. Many of these findings hold for a broad range of model parameters and likely apply to other eukaryotic promoters of similar structure.

MOTIVATION: In principle, novel genetic circuits can be engineered using standard parts with well-understood functionalities. However, no model based on the simple composition of these parts has become a standard, mainly because it is difficult to define signal exchanges between biological units as unambiguously as in electrical engineering. Corresponding concepts and computational tools for easy circuit design in biology are missing. RESULTS: Taking inspiration from (and slightly modifying) ideas in the 'MIT Registry of Standard Biological Parts', we developed a method for the design of genetic circuits with composable parts. Gene expression requires four kinds of signal carriers: RNA polymerases, ribosomes, transcription factors and environmental 'messages' (inducers or corepressors). The flux of each of these types of molecules is a quantifiable biological signal exchanged between parts. Here, each part is modeled independently by the ordinary differential equations (ODE) formalism and integrated into the software ProMoT (Process Modeling Tool). In this way, we realized a 'drag and drop' tool, where genetic circuits are built just by placing biological parts on a canvas and by connecting them through 'wires' that enable flow of signal carriers, as it happens in electrical engineering. Our simulations of well-known synthetic circuits agree well with published computational and experimental results. AVAILABILITY: The code is available on request from the authors.

MOTIVATION: Elementary flux modes (EFMs)--non-decomposable minimal pathways--are commonly accepted tools for metabolic network analysis under steady state conditions. Valid states of the network are linear superpositions of elementary modes shaping a polyhedral cone (the flux cone), which is a well-studied convex set in computational geometry. Computing EFMs is thus basically equivalent to extreme ray enumeration of polyhedral cones. This is a combinatorial problem with poorly scaling algorithms, preventing the large-scale analysis of metabolic networks so far. RESULTS: Here, we introduce new algorithmic concepts that enable large-scale computation of EFMs. Distinguishing extreme rays from normal (composite) vectors is one critical aspect of the algorithm. We present a new recursive enumeration strategy with bit pattern trees for adjacent rays--the ancestors of extreme rays--that is roughly one order of magnitude faster than previous methods. Additionally, we introduce a rank updating method that is particularly well suited for parallel computation and a residue arithmetic method for matrix rank computations, which circumvents potential numerical instability problems. Multi-core architectures of modern CPUs can be exploited for further performance improvements. The methods are applied to a central metabolism network of Escherichia coli, resulting in approximately 26 Mio. EFMs. Within the top 2% modes considering biomass production, most of the gain in flux variability is achieved. In addition, we compute approximately 5 Mio. EFMs for the production of non-essential amino acids for a genome-scale metabolic network of Helicobacter pylori. Only large-scale EFM analysis reveals the >85% of modes that generate several amino acids simultaneously. AVAILABILITY: An implementation in Java, with integration into MATLAB and support of various input formats, including SBML, is available at http://www.csb.ethz.ch in the tools section; sources are available from the authors upon request.

Circadian entrainment is necessary for rhythmic physiological functions to be appropriately timed over the 24-hour day. Disruption of circadian rhythms has been associated with sleep and neuro-behavioral impairments as well as cancer. To date, light is widely accepted to be the most powerful circadian synchronizer, motivating its use as a key control input for phase resetting. Through sensitivity analysis, we identify additional control targets whose individual and simultaneous manipulation (via a model predictive control algorithm) out-perform the open-loop light-based phase recovery dynamics by nearly 3-fold. We further demonstrate the robustness of phase resetting by synchronizing short- and long-period mutant phenotypes to the 24-hour environment; the control algorithm is robust in the presence of model mismatch. These studies prove the efficacy and immediate application of model predictive control in experimental studies and medicine. In particular, maintaining proper circadian regulation may significantly decrease the chance of acquiring chronic illness.

MOTIVATION: Sensitivity analysis provides key measures that aid in unraveling the design principles responsible for the robust performance of biological networks. Such metrics allow researchers to investigate comprehensively model performance, to develop more realistic models, and to design informative experiments. However, sensitivity analysis of oscillatory systems focuses on period and amplitude characteristics, while biologically relevant effects on phase are neglected. RESULTS: Here, we introduce a novel set of phase-based sensitivity metrics for performance: period, phase, corrected phase and relative phase. Both state- and phase-based tools are applied to free-running Drosophila melanogaster and Mus musculus circadian models. Each metric produces unique sensitivity values used to rank parameters from least to most sensitive. Similarities among the resulting rank distributions strongly suggest a conservation of sensitivity with respect to parameter function and type. A consistent result, for instance, is that model performance of biological oscillators is more sensitive to global parameters than local (i.e. circadian specific) parameters. Discrepancies among these distributions highlight the individual metrics' definition of performance as specific parametric sensitivity values depend on the defined metric, or output. AVAILABILITY: An implementation of the algorithm in MATLAB (Mathworks, Inc.) is available from the authors. SUPPLEMENTARY INFORMATION: Supplementary Data are available at Bioinformatics online.

MOTIVATION: Molecular biotechnology now makes it possible to build elaborate systems models, but the systems biology community needs information standards if models are to be shared, evaluated and developed cooperatively. RESULTS: We summarize the Systems Biology Markup Language (SBML) Level 1, a free, open, XML-based format for representing biochemical reaction networks. SBML is a software-independent language for describing models common to research in many areas of computational biology, including cell signaling pathways, metabolic pathways, gene regulation, and others. AVAILABILITY: The specification of SBML Level 1 is freely available from http://www.sbml.org/

MOTIVATION: The analysis of structure, pathways and flux distributions in metabolic networks has become an important approach for understanding the functionality of metabolic systems. The need of a user-friendly platform for stoichiometric modeling of metabolic networks in silico is evident. RESULTS: The FluxAnalyzer is a package for MATLAB and facilitates integrated pathway and flux analysis for metabolic networks within a graphical user interface. Arbitrary metabolic network models can be composed by instances of four types of network elements. The abstract network model is linked with network graphics leading to interactive flux maps which allow for user input and display of calculation results within a network visualization. Therein, a large and powerful collection of tools and algorithms can be applied interactively including metabolic flux analysis, flux optimization, detection of topological features and pathway analysis by elementary flux modes or extreme pathways. The FluxAnalyzer has been applied and tested for complex networks with more than 500,000 elementary modes. Some aspects of the combinatorial complexity of pathway analysis in metabolic networks are discussed. AVAILABILITY: Upon request from the corresponding author. Free for academic users (license agreement). Special contracts are available for industrial corporations. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer.