A dynamic model of growth phase of bio-conversion of methane to polyhydroxybutyrate using dynamic flux balance analysis.

Biological conversion of waste methane to biodegradable plastics is a way of reducing their production cost. This study addresses the computational modeling of the growth phase reactor of the process of polyhydroxybutyrate production. The model was used for investigating the effect of gas recycling and inlet gas retention time on the reactor performance. The model was run by the use of a genome-scale metabolic network of Methylocystis hirsuta in a dynamic flux balance analysis framework. The reactor has been modeled for two separate feeding scenarios: a pure methane feed and a biogas feed. The mass transfer coefficient parameter was predicted as a function of superficial gas velocities by the regression of data from published experiments. The results show an increase of removal efficiency by 38% and biomass concentration by 2.8 g/L with the increase of gas recycle ratio from 0 to 30 at the empty bed residence time of 60  min .

The Growth Yield of Aminobacter niigataensis MSH1 on the Micropollutant 2,6-Dichlorobenzamide Decreases Substantially at Trace Substrate Concentrations.

2,6-Dichlorobenzamide (BAM) is an omnipresent micropollutant in European groundwaters. Aminobacter niigataensis MSH1 is a prime candidate for biologically treating BAM-contaminated groundwater since this organism is capable of utilizing BAM as a carbon and energy source. However, detailed information on the BAM degradation kinetics by MSH1 at trace concentrations is lacking, while this knowledge is required for predicting and optimizing the degradation process. Contaminating assimilable organic carbon (AOC) in media makes the biodegradation experiment a mixed-substrate assay and hampers exploration of pollutant degradation at trace concentrations. In this study, we examined how the BAM concentration affects MSH1 growth and BAM substrate utilization kinetics in a AOC-restricted background to avoid mixed-substrate conditions. Conventional Monod kinetic models were unable to predict kinetic parameters at low concentrations from kinetics determined at high concentrations. Growth yields on BAM were concentration-dependent and decreased substantially at trace concentrations; i.e., growth of MSH1 diminished until undetectable levels at BAM concentrations below 217 µg-C/L. Nevertheless, BAM degradation continued. Decreasing growth yields at lower BAM concentrations might relate to physiological adaptations to low substrate availability or decreased expression of downstream steps of the BAM catabolic pathway beyond 2,6-dichlorobenzoic acid (2,6-DCBA) that ultimately leads to Krebs cycle intermediates for growth and energy conservation.

COVRECON: automated integration of genome- and metabolome-scale network reconstruction and data-driven inverse modeling of metabolic interaction networks.

MOTIVATION: One central goal of systems biology is to infer biochemical regulations from large-scale OMICS data. Many aspects of cellular physiology and organismal phenotypes can be understood as results of metabolic interaction network dynamics. Previously, we have proposed a convenient mathematical method, which addresses this problem using metabolomics data for the inverse calculation of biochemical Jacobian matrices revealing regulatory checkpoints of biochemical regulations. The proposed algorithms for this inference are limited by two issues: they rely on structural network information that needs to be assembled manually, and they are numerically unstable due to ill-conditioned regression problems for large-scale metabolic networks. RESULTS: To address these problems, we developed a novel regression loss-based inverse Jacobian algorithm, combining metabolomics COVariance and genome-scale metabolic RECONstruction, which allows for a fully automated, algorithmic implementation of the COVRECON workflow. It consists of two parts: (i) Sim-Network and (ii) inverse differential Jacobian evaluation. Sim-Network automatically generates an organism-specific enzyme and reaction dataset from Bigg and KEGG databases, which is then used to reconstruct the Jacobian's structure for a specific metabolomics dataset. Instead of directly solving a regression problem as in the previous workflow, the new inverse differential Jacobian is based on a substantially more robust approach and rates the biochemical interactions according to their relevance from large-scale metabolomics data. The approach is illustrated by in silico stochastic analysis with differently sized metabolic networks from the BioModels database and applied to a real-world example. The characteristics of the COVRECON implementation are that (i) it automatically reconstructs a data-driven superpathway model; (ii) more general network structures can be investigated, and (iii) the new inverse algorithm improves stability, decreases computation time, and extends to large-scale models. AVAILABILITY AND IMPLEMENTATION: The code is available in the website https://bitbucket.org/mosys-univie/covrecon.

PANOMICS at the interface of root-soil microbiome and BNI.

Nitrification and denitrification are soil biological processes responsible for large nitrogen losses from agricultural soils and generation of the greenhouse gas (GHG) N2O. Increased use of nitrogen fertilizer and the resulting decline in nitrogen use efficiency (NUE) are a major concern in agroecosystems. This nitrogen cycle in the rhizosphere is influenced by an intimate soil microbiome-root exudate interaction and biological nitrification inhibition (BNI). A PANOMICS approach can dissect these processes. We review breakthroughs in this area, including identification and characterization of root exudates by metabolomics and proteomics, which facilitate better understanding of belowground chemical communications and help identify new biological nitrification inhibitors (BNIs). We also address challenges for advancing the understanding of the role root exudates play in biotic and abiotic stresses.

Interpretable machine learning methods for predictions in systems biology from omics data.

Machine learning has become a powerful tool for systems biologists, from diagnosing cancer to optimizing kinetic models and predicting the state, growth dynamics, or type of a cell. Potential predictions from complex biological data sets obtained by "omics" experiments seem endless, but are often not the main objective of biological research. Often we want to understand the molecular mechanisms of a disease to develop new therapies, or we need to justify a crucial decision that is derived from a prediction. In order to gain such knowledge from data, machine learning models need to be extended. A recent trend to achieve this is to design "interpretable" models. However, the notions around interpretability are sometimes ambiguous, and a universal recipe for building well-interpretable models is missing. With this work, we want to familiarize systems biologists with the concept of model interpretability in machine learning. We consider data sets, data preparation, machine learning methods, and software tools relevant to omics research in systems biology. Finally, we try to answer the question: "What is interpretability?" We introduce views from the interpretable machine learning community and propose a scheme for categorizing studies on omics data. We then apply these tools to review and categorize recent studies where predictive machine learning models have been constructed from non-sequential omics data.

The tyrosine phosphatase SHP2 increases robustness and information transfer within IL-6-induced JAK/STAT signalling.

BACKGROUND: Cell-to-cell heterogeneity is an inherent feature of multicellular organisms and is central in all physiological and pathophysiological processes including cellular signal transduction. The cytokine IL-6 is an essential mediator of pro- and anti-inflammatory processes. Dysregulated IL-6-induced intracellular JAK/STAT signalling is associated with severe inflammatory and proliferative diseases. Under physiological conditions JAK/STAT signalling is rigorously controlled and timely orchestrated by regulatory mechanisms such as expression of the feedback-inhibitor SOCS3 and activation of the protein-tyrosine phosphatase SHP2 (PTPN11). Interestingly, the function of negative regulators seems not to be restricted to controlling the strength and timely orchestration of IL-6-induced STAT3 activation. Exemplarily, SOCS3 increases robustness of late IL-6-induced STAT3 activation against heterogenous STAT3 expression and reduces the amount of information transferred through JAK/STAT signalling. METHODS: Here we use multiplexed single-cell analyses and information theoretic approaches to clarify whether also SHP2 contributes to robustness of STAT3 activation and whether SHP2 affects the amount of information transferred through IL-6-induced JAK/STAT signalling. RESULTS: SHP2 increases robustness of both basal, cytokine-independent STAT3 activation and early IL-6-induced STAT3 activation against differential STAT3 expression. However, SHP2 does not affect robustness of late IL-6-induced STAT3 activation. In contrast to SOCS3, SHP2 increases the amount of information transferred through IL-6-induced JAK/STAT signalling, probably by reducing cytokine-independent STAT3 activation and thereby increasing sensitivity of the cells. These effects are independent of SHP2-dependent MAPK activation. CONCLUSION: In summary, the results of this study extend our knowledge of the functions of SHP2 in IL-6-induced JAK/STAT signalling. SHP2 is not only a repressor of basal and cytokine-induced STAT3 activity, but also ensures robustness and transmission of information. Plain English summary Cells within a multicellular organism communicate with each other to exchange information about the environment. Communication between cells is facilitated by soluble molecules that transmit information from one cell to the other. Cytokines such as interleukin-6 are important soluble mediators that are secreted when an organism is faced with infections or inflammation. Secreted cytokines bind to receptors within the membrane of their target cells. This binding induces activation of an intracellular cascade of reactions called signal transduction, which leads to cellular responses. An important example of intracellular signal transduction is JAK/STAT signalling. In healthy organisms signalling is controlled and timed by regulatory mechanisms, whose activation results in a controlled shutdown of signalling pathways. Interestingly, not all cells within an organism are identical. They differ in the amount of proteins involved in signal transduction, such as STAT3. These differences shape cellular communication and responses to intracellular signalling. Here, we show that an important negative regulatory protein called SHP2 (or PTPN11) is not only responsible for shutting down signalling, but also for steering signalling in heterogeneous cell populations. SHP2 increases robustness of STAT3 activation against variable STAT3 amounts in individual cells. Additionally, it increases the amount of information transferred through JAK/STAT signalling by increasing the dynamic range of pathway activation in heterogeneous cell populations. This is an amazing new function of negative regulatory proteins that contributes to communication in heterogeneous multicellular organisms in health and disease. Video Abstract.

Robustness and Information Transfer within IL-6-induced JAK/STAT Signalling.

Cellular communication via intracellular signalling pathways is crucial. Expression and activation of signalling proteins is heterogenous between isogenic cells of the same cell-type. However, mechanisms evolved to enable sufficient communication and to ensure cellular functions. We use information theory to clarify mechanisms facilitating IL-6-induced JAK/STAT signalling despite cell-to-cell variability. We show that different mechanisms enabling robustness against variability complement each other. Early STAT3 activation is robust as long as cytokine concentrations are low. Robustness at high cytokine concentrations is ensured by high STAT3 expression or serine phosphorylation. Later the feedback-inhibitor SOCS3 increases robustness. Channel Capacity of JAK/STAT signalling is limited by cell-to-cell variability in STAT3 expression and is affected by the same mechanisms governing robustness. Increasing STAT3 amount increases Channel Capacity and robustness, whereas increasing STAT3 tyrosine phosphorylation reduces robustness but increases Channel Capacity. In summary, we elucidate mechanisms preventing dysregulated signalling by enabling reliable JAK/STAT signalling despite cell-to-cell heterogeneity.

Estimation methods for heterogeneous cell population models in systems biology.

Heterogeneity among individual cells is a characteristic and relevant feature of living systems. A range of experimental techniques to investigate this heterogeneity is available, and multiple modelling frameworks have been developed to describe and simulate the dynamics of heterogeneous populations. Measurement data are used to adjust computational models, which results in parameter and state estimation problems. Methods to solve these estimation problems need to take the specific properties of data and models into account. The aim of this review is to give an overview on the state of the art in estimation methods for heterogeneous cell population data and models. The focus is on models based on the population balance equation, but stochastic and individual-based models are also discussed. It starts with a brief discussion of common experimental approaches and types of measurement data that can be obtained in this context. The second part describes computational modelling frameworks for heterogeneous populations and the types of estimation problems occurring for these models. The third part starts with a discussion of observability and identifiability properties, after which the computational methods to solve the various estimation problems are described.

Optimization of bioprocess productivity based on metabolic-genetic network models with bilevel dynamic programming.

One of the main goals of metabolic engineering is to obtain high levels of a microbial product through genetic modifications. To improve the productivity of such a process, the dynamic implementation of metabolic engineering strategies has been proven to be more beneficial compared to static genetic manipulations in which the gene expression is not controlled over time, by resolving the trade-off between growth and production. In this work, a bilevel optimization framework based on constraint-based models is applied to identify an optimal strategy for dynamic genetic and process level manipulations to increase productivity. The dynamic enzyme-cost flux balance analysis (deFBA) as underlying metabolic network model captures the network dynamics and enables the analysis of temporal regulation in the metabolic-genetic network. We apply our computational framework to maximize ethanol productivity in a batch process with Escherichia coli. The results highlight the importance of integrating the genetic level and enzyme production and degradation processes for obtaining optimal dynamic gene and process manipulations.

A Protocol for Generating and Exchanging (Genome-Scale) Metabolic Resource Allocation Models.

In this article, we present a protocol for generating a complete (genome-scale) metabolic resource allocation model, as well as a proposal for how to represent such models in the systems biology markup language (SBML). Such models are used to investigate enzyme levels and achievable growth rates in large-scale metabolic networks. Although the idea of metabolic resource allocation studies has been present in the field of systems biology for some years, no guidelines for generating such a model have been published up to now. This paper presents step-by-step instructions for building a (dynamic) resource allocation model, starting with prerequisites such as a genome-scale metabolic reconstruction, through building protein and noncatalytic biomass synthesis reactions and assigning turnover rates for each reaction. In addition, we explain how one can use SBML level 3 in combination with the flux balance constraints and our resource allocation modeling annotation to represent such models.

Dynamic optimization of metabolic networks coupled with gene expression.

The regulation of metabolic activity by tuning enzyme expression levels is crucial to sustain cellular growth in changing environments. Metabolic networks are often studied at steady state using constraint-based models and optimization techniques. However, metabolic adaptations driven by changes in gene expression cannot be analyzed by steady state models, as these do not account for temporal changes in biomass composition. Here we present a dynamic optimization framework that integrates the metabolic network with the dynamics of biomass production and composition. An approximation by a timescale separation leads to a coupled model of quasi-steady state constraints on the metabolic reactions, and differential equations for the substrate concentrations and biomass composition. We propose a dynamic optimization approach to determine reaction fluxes for this model, explicitly taking into account enzyme production costs and enzymatic capacity. In contrast to the established dynamic flux balance analysis, our approach allows predicting dynamic changes in both the metabolic fluxes and the biomass composition during metabolic adaptations. Discretization of the optimization problems leads to a linear program that can be efficiently solved. We applied our algorithm in two case studies: a minimal nutrient uptake network, and an abstraction of core metabolic processes in bacteria. In the minimal model, we show that the optimized uptake rates reproduce the empirical Monod growth for bacterial cultures. For the network of core metabolic processes, the dynamic optimization algorithm predicted commonly observed metabolic adaptations, such as a diauxic switch with a preference ranking for different nutrients, re-utilization of waste products after depletion of the original substrate, and metabolic adaptation to an impending nutrient depletion. These examples illustrate how dynamic adaptations of enzyme expression can be predicted solely from an optimization principle.

Pain modulators regulate the dynamics of PKA-RII phosphorylation in subgroups of sensory neurons.

Knowledge about the molecular structure of protein kinase A (PKA) isoforms is substantial. In contrast, the dynamics of PKA isoform activity in living primary cells has not been investigated in detail. Using a high content screening microscopy approach, we identified the RIIß subunit of PKA-II to be predominantly expressed in a subgroup of sensory neurons. The RIIß-positive subgroup included most neurons expressing nociceptive markers (TRPV1, NaV1.8, CGRP, IB4) and responded to pain-eliciting capsaicin with calcium influx. Isoform-specific PKA reporters showed in sensory-neuron-derived F11 cells that the inflammatory mediator PGE2 specifically activated PKA-II but not PKA-I. Accordingly, pain-sensitizing inflammatory mediators and activators of PKA increased the phosphorylation of RII subunits (pRII) in subgroups of primary sensory neurons. Detailed analyses revealed basal pRII to be regulated by the phosphatase PP2A. Increase of pRII was followed by phosphorylation of CREB in a PKA-dependent manner. Thus, we propose RII phosphorylation to represent an isoform-specific readout for endogenous PKA-II activity in vivo, suggest RIIß as a novel nociceptive subgroup marker, and extend the current model of PKA-II activation by introducing a PP2A-dependent basal state.

Efficient parametric analysis of the chemical master equation through model order reduction.

BACKGROUND: Stochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation. RESULTS: In this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations. CONCLUSIONS: The results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.

Identification of models of heterogeneous cell populations from population snapshot data.

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.

Autonomous synchronization of chemically coupled synthetic oscillators.

Synthetic biology has recently provided functional single-cell oscillators. With a few exceptions, however, synchronization across a population has not been achieved yet. In particular, designing a cell coupling mechanism to achieve autonomous synchronization is not straightforward since there are usually several different design alternatives. Here, we propose a method to mathematically predict autonomous synchronization properties, and to identify the network structure with the best performance, thus increasing the feasibility for a successful implementation in vivo.Our method relies on the reduction of ODE-based models for synthetic oscillators to a phase description, and the subsequent analysis of the phase model either in the spatially homogeneous or heterogeneous case. This analysis identifies three major factors determining if and when autonomous synchronization can be achieved, namely cell density, cell to cell variability, and structural design decisions. Moreover, when considering a spatially heterogeneous medium, we observe phase waves. These waves may hinder synchronization substantially, and their suppression should be considered in the design process.In contrast to previous work, we analyze the synchronization process of models of experimentally validated synthetic oscillators in mammalian cells. Alternative designs for cell-to-cell communication via a quorum sensing mechanism differ in few mechanistic details, but these differences have important implications for autonomous synchronization. Our analysis suggests that not only the periodical transcription of the protein producing the signaling molecule, but also of the receptor protein is necessary to achieve good performance.

Robust signal processing in living cells.

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations.

Bridging time scales in cellular decision making with a stochastic bistable switch.

BACKGROUND: Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. Some of these transformations act over a very long time scale on the cell population level, up to the entire lifespan of the organism. RESULTS: In this work, we aim at linking cellular decisions taking place on a time scale of years to decades with the biochemical dynamics in signal transduction and gene regulation, occurring on a time scale of minutes to hours. We show that a stochastic bistable switch forms a viable biochemical mechanism to implement decision processes on long time scales. As a case study, the mechanism is applied to model the initiation of follicle growth in mammalian ovaries, where the physiological time scale of follicle pool depletion is on the order of the organism's lifespan. We construct a simple mathematical model for this process based on experimental evidence for the involved genetic mechanisms. CONCLUSIONS: Despite the underlying stochasticity, the proposed mechanism turns out to yield reliable behavior in large populations of cells subject to the considered decision process. Our model explains how the physiological time constant may emerge from the intrinsic stochasticity of the underlying gene regulatory network. Apart from ovarian follicles, the proposed mechanism may also be of relevance for other physiological systems where cells take binary decisions over a long time scale.

Amplitude distribution of stochastic oscillations in biochemical networks due to intrinsic noise.

Intrinsic noise is a common phenomenon in biochemical reaction networks and may affect the occurence and amplitude of sustained oscillations in the states of the network. To evaluate properties of such oscillations in the time domain, it is usually required to conduct long-term stochastic simulations, using for example the Gillespie algorithm. In this paper, we present a new method to compute the amplitude distribution of the oscillations without the need for long-term stochastic simulations. By the derivation of the method, we also gain insight into the structural features underlying the stochastic oscillations. The method is applicable to a wide class of non-linear stochastic differential equations that exhibit stochastic oscillations. The application is exemplified for the MAPK cascade, a fundamental element of several biochemical signalling pathways. This example shows that the proposed method can accurately predict the amplitude distribution for the stochastic oscillations even when using further computational approximations.PACS Codes: 87.10.Mn, 87.18.Tt, 87.18.VfMSC Codes: 92B05, 60G10, 65C30.

Steady state and (bi-) stability evaluation of simple protease signalling networks.

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis. The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is. Experimentally, some so-called "inactive" components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation.