Distilling identifiable and interpretable dynamic models from biological data

Mechanistic dynamical models allow us to study the behavior of complex biological systems. They can provide an objective and quantitative understanding that would be difficult to achieve through other means. However, the systematic development of these models is a non-trivial exercise and an open problem in computational biology. Currently, many research efforts are focused on model discovery, i.e. automating the development of interpretable models from data. One of the main frameworks is sparse regression, where the sparse identification of nonlinear dynamics (SINDy) algorithm and its variants have enjoyed great success. SINDy-PI is an extension which allows the discovery of rational nonlinear terms, thus enabling the identification of kinetic functions common in biochemical networks, such as Michaelis-Menten. SINDy-PI also pays special attention to the recovery of parsimonious models (Occam's razor). Here we focus on biological models composed of sets of deterministic nonlinear ordinary differential equations. We present a methodology that, combined with SINDy-PI, allows the automatic discovery of structurally identifiable and observable models which are also mechanistically interpretable. The lack of structural identifiability and observability makes it impossible to uniquely infer parameter and state variables, which can compromise the usefulness of a model by distorting its mechanistic significance and hampering its ability to produce biological insights. We illustrate the performance of our method with six case studies. We find that, despite enforcing sparsity, SINDy-PI sometimes yields models that are unidentifiable. In these cases we show how our method transforms their equations in order to obtain a structurally identifiable and observable model which is also interpretable.

A rationally engineered decoder of transient intracellular signals

Cells can encode information about their environment by modulating signaling dynamics and responding accordingly. Yet, the mechanisms cells use to decode these dynamics remain unknown when cells respond exclusively to transient signals. Here, we approach design principles underlying such decoding by rationally engineering a synthetic short-pulse decoder in budding yeast. A computational method for rapid prototyping, TopoDesign, allowed us to explore 4122 possible circuit architectures, design targeted experiments, and then rationally select a single circuit for implementation. This circuit demonstrates short-pulse decoding through incoherent feedforward and positive feedback. We predict incoherent feedforward to be essential for decoding transient signals, thereby complementing proposed design principles of temporal filtering, the ability to respond to sustained signals, but not to transient signals. More generally, we anticipate TopoDesign to help designing other synthetic circuits with non-intuitive dynamics, simply by assembling available biological components.

TopoFilter: a MATLAB package for mechanistic model identification in systems biology

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.

Distilling Robust Design Principles of Biocircuits Using Mixed Integer Dynamic Optimization

A major challenge in model-based design of synthetic biochemical circuits is how to address uncertainty in the parameters. A circuit whose behavior is robust to variations in the parameters will have more chances to behave as predicted when implemented in practice, and also to function reliably in presence of fluctuations and noise. Here, we extend our recent work on automated-design based on mixed-integer multi-criteria dynamic optimization to take into account parametric uncertainty. We exploit the intensive sampling of the design space performed by a global optimization algorithm to obtain the robustness of the topologies without significant additional computational effort. Our procedure provides automatically topologies that best trade-off performance and robustness against parameter fluctuations. We illustrate our approach considering the automated design of gene circuits achieving adaptation.

Parametric and non-parametric gradient matching for network inference: a comparison

Background

Reverse engineering of gene regulatory networks from time series gene-expression data is a challenging problem, not only because of the vast sets of candidate interactions but also due to the stochastic nature of gene expression. We limit our analysis to nonlinear differential equation based inference methods. In order to avoid the computational cost of large-scale simulations, a two-step Gaussian process interpolation based gradient matching approach has been proposed to solve differential equations approximately.

Results

We apply a gradient matching inference approach to a large number of candidate models, including parametric differential equations or their corresponding non-parametric representations, we evaluate the network inference performance under various settings for different inference objectives. We use model averaging, based on the Bayesian Information Criterion (BIC), to combine the different inferences. The performance of different inference approaches is evaluated using area under the precision-recall curves.

Conclusions

We found that parametric methods can provide comparable, and often improved inference compared to non-parametric methods; the latter, however, require no kinetic information and are computationally more efficient.

Electronic supplementary material

The online version of this article (10.1186/s12859-018-2590-7) contains supplementary material, which is available to authorized users.

Regulation of Yeast-to-Hyphae Transition in Yarrowia lipolytica

Many yeasts undergo a morphological transition from yeast-to-hyphal growth in response to environmental conditions. We used forward and reverse genetic techniques to identify genes regulating this transition in Yarrowia lipolytica. We confirmed that the transcription factor Ylmsn2 is required for the transition to hyphal growth and found that signaling by the histidine kinases Ylchk1 and Ylnik1 as well as the MAP kinases of the HOG pathway (Ylssk2, Ylpbs2, and Ylhog1) regulates the transition to hyphal growth. These results suggest that Y. lipolytica transitions to hyphal growth in response to stress through multiple kinase pathways. Intriguingly, we found that a repetitive portion of the genome containing telomere-like and rDNA repeats may be involved in the transition to hyphal growth, suggesting a link between this region and the general stress response.

The yeast Yarrowia lipolytica undergoes a morphological transition from yeast-to-hyphal growth in response to environmental conditions. A forward genetic screen was used to identify mutants that reliably remain in the yeast phase, which were then assessed by whole-genome sequencing. All the smooth mutants identified, so named because of their colony morphology, exhibit independent loss of DNA at a repetitive locus made up of interspersed ribosomal DNA and short 10- to 40-mer telomere-like repeats. The loss of repetitive DNA is associated with downregulation of genes with stress response elements (5′-CCCCT-3′) and upregulation of genes with cell cycle box (5′-ACGCG-3′) motifs in their promoter region. The stress response element is bound by the transcription factor Msn2p in Saccharomyces cerevisiae. We confirmed that the Y. lipolyticamsn2 (Ylmsn2) ortholog is required for hyphal growth and found that overexpression of Ylmsn2 enables hyphal growth in smooth strains. The cell cycle box is bound by the Mbp1p/Swi6p complex in S. cerevisiae to regulate G₁-to-S phase progression. We found that overexpression of either the Ylmbp1 or Ylswi6 homologs decreased hyphal growth and that deletion of either Ylmbp1 or Ylswi6 promotes hyphal growth in smooth strains. A second forward genetic screen for reversion to hyphal growth was performed with the smooth-33 mutant to identify additional genetic factors regulating hyphal growth in Y. lipolytica. Thirteen of the mutants sequenced from this screen had coding mutations in five kinases, including the histidine kinases Ylchk1 and Ylnik1 and kinases of the high-osmolarity glycerol response (HOG) mitogen-activated protein (MAP) kinase cascade Ylssk2, Ylpbs2, and Ylhog1. Together, these results demonstrate that Y. lipolytica transitions to hyphal growth in response to stress through multiple signaling pathways.

IMPORTANCE Many yeasts undergo a morphological transition from yeast-to-hyphal growth in response to environmental conditions. We used forward and reverse genetic techniques to identify genes regulating this transition in Yarrowia lipolytica. We confirmed that the transcription factor Ylmsn2 is required for the transition to hyphal growth and found that signaling by the histidine kinases Ylchk1 and Ylnik1 as well as the MAP kinases of the HOG pathway (Ylssk2, Ylpbs2, and Ylhog1) regulates the transition to hyphal growth. These results suggest that Y. lipolytica transitions to hyphal growth in response to stress through multiple kinase pathways. Intriguingly, we found that a repetitive portion of the genome containing telomere-like and rDNA repeats may be involved in the transition to hyphal growth, suggesting a link between this region and the general stress response.

Integrating -omics data into genome-scale metabolic network models: principles and challenges

At genome scale, it is not yet possible to devise detailed kinetic models for metabolism because data on the in vivo biochemistry are too sparse. Predictive large-scale models for metabolism most commonly use the constraint-based framework, in which network structures constrain possible metabolic phenotypes at steady state. However, these models commonly leave many possibilities open, making them less predictive than desired. With increasingly available -omics data, it is appealing to increase the predictive power of constraint-based models (CBMs) through data integration. Many corresponding methods have been developed, but data integration is still a challenge and existing methods perform less well than expected. Here, we review main approaches for the integration of different types of -omics data into CBMs focussing on the methods' assumptions and limitations. We argue that key assumptions - often derived from single-enzyme kinetics - do not generally apply in the context of networks, thereby explaining current limitations. Emerging methods bridging CBMs and biochemical kinetics may allow for -omics data integration in a common framework to provide more accurate predictions.

Self-Amplifying Pulsatile Protein Dynamics without Positive Feedback

Many proteins exhibit dynamic activation patterns in the form of irregular pulses. Such behavior is typically attributed to a combination of positive and negative feedback loops in the underlying regulatory network. However, the presence of positive feedbacks is difficult to demonstrate unequivocally, raising the question of whether stochastic pulses can arise from negative feedback only. Here, we use the protein kinase A (PKA) system, a key regulator of the yeast pulsatile transcription factor Msn2, as a case example to show that irregular pulses of protein activity can arise from a negative feedback loop alone. Simplification to two variables reveals that a combination of zero-order ultrasensitivity, timescale separation between the activator and the repressor, and an effective delay in the feedback are sufficient to amplify a perturbation into a pulse. The same circuit topology can account for both activation and inactivation pulses, pointing toward a general mechanism of stochastic pulse generation.

Reserve Flux Capacity in the Pentose Phosphate Pathway Enables Escherichia coli's Rapid Response to Oxidative Stress

To counteract oxidative stress and reactive oxygen species (ROS), bacteria evolved various mechanisms, primarily reducing ROS through antioxidant systems that utilize cofactor NADPH. Cells must stabilize NADPH levels by increasing flux through replenishing metabolic pathways like pentose phosphate (PP) pathway. Here, we investigate the mechanism enabling the rapid increase in NADPH supply by exposing Escherichia coli to hydrogen peroxide and quantifying the immediate metabolite dynamics. To systematically infer active regulatory interactions governing this response, we evaluated ensembles of kinetic models of glycolysis and PP pathway, each with different regulation mechanisms. Besides the known inactivation of glyceraldehyde 3-phosphate dehydrogenase by ROS, we reveal the important allosteric inhibition of the first PP pathway enzyme by NADPH. This NADPH feedback inhibition maintains a below maximum-capacity PP pathway flux under non-stress conditions. Relieving this inhibition instantly increases PP pathway flux upon oxidative stress. We demonstrate that reducing cells' capacity to rapidly reroute their flux through the PP pathway increases their oxidative stress sensitivity.

Formulation, construction and analysis of kinetic models of metabolism: A review of modelling frameworks

Kinetic models are critical to predict the dynamic behaviour of metabolic networks. Mechanistic kinetic models for large networks remain uncommon due to the difficulty of fitting their parameters. Recent modelling frameworks promise new ways to overcome this obstacle while retaining predictive capabilities. In this review, we present an overview of the relevant mathematical frameworks for kinetic formulation, construction and analysis. Starting with kinetic formalisms, we next review statistical methods for parameter inference, as well as recent computational frameworks applied to the construction and analysis of kinetic models. Finally, we discuss opportunities and limitations hindering the development of larger kinetic reconstructions.

How to deal with parameters for whole-cell modelling

Dynamical systems describing whole cells are on the verge of becoming a reality. But as models of reality, they are only useful if we have realistic parameters for the molecular reaction rates and cell physiological processes. There is currently no suitable framework to reliably estimate hundreds, let alone thousands, of reaction rate parameters. Here, we map out the relative weaknesses and promises of different approaches aimed at redressing this issue. While suitable procedures for estimation or inference of the whole (vast) set of parameters will, in all likelihood, remain elusive, some hope can be drawn from the fact that much of the cellular behaviour may be explained in terms of smaller sets of parameters. Identifying such parameter sets and assessing their behaviour is now becoming possible even for very large systems of equations, and we expect such methods to become central tools in the development and analysis of whole-cell models.

Quantifying time-varying cellular secretions with local linear models

Extracellular protein concentrations and gradients initiate a wide range of cellular responses, such as cell motility, growth, proliferation and death. Understanding inter-cellular communication requires spatio-temporal knowledge of these secreted factors and their causal relationship with cell phenotype. Techniques which can detect cellular secretions in real time are becoming more common but generalizable data analysis methodologies which can quantify concentration from these measurements are still lacking. Here we introduce a probabilistic approach in which local-linear models and the law of mass action are applied to obtain time-varying secreted concentrations from affinity-based biosensor data. We first highlight the general features of this approach using simulated data which contains both static and time-varying concentration profiles. Next we apply the technique to determine concentration of secreted antibodies from 9E10 hybridoma cells as detected using nanoplasmonic biosensors. A broad range of time-dependent concentrations was observed: from steady-state secretions of 230 pM near the cell surface to large transients which reached as high as 56 nM over several minutes and then dissipated.

Data-driven reverse engineering of signaling pathways using ensembles of dynamic models

Despite significant efforts and remarkable progress, the inference of signaling networks from experimental data remains very challenging. The problem is particularly difficult when the objective is to obtain a dynamic model capable of predicting the effect of novel perturbations not considered during model training. The problem is ill-posed due to the nonlinear nature of these systems, the fact that only a fraction of the involved proteins and their post-translational modifications can be measured, and limitations on the technologies used for growing cells in vitro, perturbing them, and measuring their variations. As a consequence, there is a pervasive lack of identifiability. To overcome these issues, we present a methodology called SELDOM (enSEmbLe of Dynamic lOgic-based Models), which builds an ensemble of logic-based dynamic models, trains them to experimental data, and combines their individual simulations into an ensemble prediction. It also includes a model reduction step to prune spurious interactions and mitigate overfitting. SELDOM is a data-driven method, in the sense that it does not require any prior knowledge of the system: the interaction networks that act as scaffolds for the dynamic models are inferred from data using mutual information. We have tested SELDOM on a number of experimental and in silico signal transduction case-studies, including the recent HPN-DREAM breast cancer challenge. We found that its performance is highly competitive compared to state-of-the-art methods for the purpose of recovering network topology. More importantly, the utility of SELDOM goes beyond basic network inference (i.e. uncovering static interaction networks): it builds dynamic (based on ordinary differential equation) models, which can be used for mechanistic interpretations and reliable dynamic predictions in new experimental conditions (i.e. not used in the training). For this task, SELDOM's ensemble prediction is not only consistently better than predictions from individual models, but also often outperforms the state of the art represented by the methods used in the HPN-DREAM challenge.

Respectful Modeling: Addressing Uncertainty in Dynamic System Models for Molecular Biology

Although there is still some skepticism in the biological community regarding the value and significance of quantitative computational modeling, important steps are continually being taken to enhance its accessibility and predictive power. We view these developments as essential components of an emerging 'respectful modeling' framework which has two key aims: (i) respecting the models themselves and facilitating the reproduction and update of modeling results by other scientists, and (ii) respecting the predictions of the models and rigorously quantifying the confidence associated with the modeling results. This respectful attitude will guide the design of higher-quality models and facilitate the use of models in modern applications such as engineering and manipulating microbial metabolism by synthetic biology.

Sparse Regression Based Structure Learning of Stochastic Reaction Networks from Single Cell Snapshot Time Series

Stochastic chemical reaction networks constitute a model class to quantitatively describe dynamics and cell-to-cell variability in biological systems. The topology of these networks typically is only partially characterized due to experimental limitations. Current approaches for refining network topology are based on the explicit enumeration of alternative topologies and are therefore restricted to small problem instances with almost complete knowledge. We propose the reactionet lasso, a computational procedure that derives a stepwise sparse regression approach on the basis of the Chemical Master Equation, enabling large-scale structure learning for reaction networks by implicitly accounting for billions of topology variants. We have assessed the structure learning capabilities of the reactionet lasso on synthetic data for the complete TRAIL induced apoptosis signaling cascade comprising 70 reactions. We find that the reactionet lasso is able to efficiently recover the structure of these reaction systems, ab initio, with high sensitivity and specificity. With only < 1% false discoveries, the reactionet lasso is able to recover 45% of all true reactions ab initio among > 6000 possible reactions and over 10²⁰⁰⁰ network topologies. In conjunction with information rich single cell technologies such as single cell RNA sequencing or mass cytometry, the reactionet lasso will enable large-scale structure learning, particularly in areas with partial network structure knowledge, such as cancer biology, and thereby enable the detection of pathological alterations of reaction networks. We provide software to allow for wide applicability of the reactionet lasso.

Virtually all biological processes are driven by biochemical reactions. However, their quantitative description in terms of stochastic chemical reaction networks is often precluded by the computational difficulty of structure learning, i.e. the identification of biologically active reaction networks among the combinatorially many possible topologies. This work describes the reactionet lasso, a structure learning approach that takes advantage of novel, information-rich single cell data and a tractable problem formulation to achieve structure learning for problem instances hundreds of orders of magnitude larger than previously reported. This approach opens the prospect of obtaining quantitative and predictive reaction models in many areas of biology and medicine, and in particular areas such as cancer biology, which are characterized by significant system alterations and many unknown reactions.

Construction of feasible and accurate kinetic models of metabolism: A Bayesian approach

Kinetic models are essential to quantitatively understand and predict the behaviour of metabolic networks. Detailed and thermodynamically feasible kinetic models of metabolism are inherently difficult to formulate and fit. They have a large number of heterogeneous parameters, are non-linear and have complex interactions. Many powerful fitting strategies are ruled out by the intractability of the likelihood function. Here, we have developed a computational framework capable of fitting feasible and accurate kinetic models using Approximate Bayesian Computation. This framework readily supports advanced modelling features such as model selection and model-based experimental design. We illustrate this approach on the tightly-regulated mammalian methionine cycle. Sampling from the posterior distribution, the proposed framework generated thermodynamically feasible parameter samples that converged on the true values, and displayed remarkable prediction accuracy in several validation tests. Furthermore, a posteriori analysis of the parameter distributions enabled appraisal of the systems properties of the network (e.g., control structure) and key metabolic regulations. Finally, the framework was used to predict missing allosteric interactions.

Elucidation of Genetic Interactions in the Yeast GATA-Factor Network Using Bayesian Model Selection

Understanding the structure and function of complex gene regulatory networks using classical genetic assays is an error-prone procedure that frequently generates ambiguous outcomes. Even some of the best-characterized gene networks contain interactions whose validity is not conclusively proven. Founded on dynamic experimental data, mechanistic mathematical models are able to offer detailed insights that would otherwise require prohibitively large numbers of genetic experiments. Here we attempt mechanistic modeling of the transcriptional network formed by the four GATA-factor proteins, a well-studied system of central importance for nitrogen-source regulation of transcription in the yeast Saccharomyces cerevisiae. To resolve ambiguities in the network organization, we encoded a set of five interactions hypothesized in the literature into a set of 32 mathematical models, and employed Bayesian model selection to identify the most plausible set of interactions based on dynamic gene expression data. The top-ranking model was validated on newly generated GFP reporter dynamic data and was subsequently used to gain a better understanding of how yeast cells organize their transcriptional response to dynamic changes of nitrogen sources. Our work constitutes a necessary and important step towards obtaining a holistic view of the yeast nitrogen regulation mechanisms; on the computational side, it provides a demonstration of how powerful Monte Carlo techniques can be creatively combined and used to address the great challenges of large-scale dynamical system inference.

Gene regulatory networks underlie all key processes that enable a cell to maintain long-term homeostasis in a changing environment. Understanding the structure and function of complex gene networks is an experimentally difficult and error-prone procedure. Mechanistic mathematical modeling promises to alleviate these problems, as we demonstrate here for the yeast GATA-factor network, the central controller of the cellular response to nitrogen source quality. Despite years of targeted studies, the interaction pattern of this network is still not known precisely. To resolve several still-remaining ambiguities, we generated a set of alternative mathematical models, and compared them against each other using Bayesian model selection based on dynamic gene expression data. The top-ranking model was then validated on a separate, newly generated dataset. Our work thus provides new insights to the mechanism of nitrogen regulation in yeast, while at the same time overcoming some key computational inference problems for large models in systems biology.

Learning (from) the errors of a systems biology model

Mathematical modelling is a labour intensive process involving several iterations of testing on real data and manual model modifications. In biology, the domain knowledge guiding model development is in many cases itself incomplete and uncertain. A major problem in this context is that biological systems are open. Missed or unknown external influences as well as erroneous interactions in the model could thus lead to severely misleading results. Here we introduce the dynamic elastic-net, a data driven mathematical method which automatically detects such model errors in ordinary differential equation (ODE) models. We demonstrate for real and simulated data, how the dynamic elastic-net approach can be used to automatically (i) reconstruct the error signal, (ii) identify the target variables of model error, and (iii) reconstruct the true system state even for incomplete or preliminary models. Our work provides a systematic computational method facilitating modelling of open biological systems under uncertain knowledge.

Kinetic modeling of cell metabolism for microbial production

Kinetic models of cellular metabolism are important tools for the rational design of metabolic engineering strategies and to explain properties of complex biological systems. The recent developments in high-throughput experimental data are leading to new computational approaches for building kinetic models of metabolism. Herein, we briefly survey the available databases, standards and software tools that can be applied for kinetic models of metabolism. In addition, we give an overview about recently developed ordinary differential equations (ODE)-based kinetic models of metabolism and some of the main applications of such models are illustrated in guiding metabolic engineering design. Finally, we review the kinetic modeling approaches of large-scale networks that are emerging, discussing their main advantages, challenges and limitations.

Robust and efficient parameter estimation in dynamic models of biological systems

Background

Dynamic modelling provides a systematic framework to understand function in biological systems. Parameter estimation in nonlinear dynamic models remains a very challenging inverse problem due to its nonconvexity and ill-conditioning. Associated issues like overfitting and local solutions are usually not properly addressed in the systems biology literature despite their importance.

Here we present a method for robust and efficient parameter estimation which uses two main strategies to surmount the aforementioned difficulties: (i) efficient global optimization to deal with nonconvexity, and (ii) proper regularization methods to handle ill-conditioning. In the case of regularization, we present a detailed critical comparison of methods and guidelines for properly tuning them. Further, we show how regularized estimations ensure the best trade-offs between bias and variance, reducing overfitting, and allowing the incorporation of prior knowledge in a systematic way.

Results

We illustrate the performance of the presented method with seven case studies of different nature and increasing complexity, considering several scenarios of data availability, measurement noise and prior knowledge. We show how our method ensures improved estimations with faster and more stable convergence. We also show how the calibrated models are more generalizable. Finally, we give a set of simple guidelines to apply this strategy to a wide variety of calibration problems.

Conclusions

Here we provide a parameter estimation strategy which combines efficient global optimization with a regularization scheme. This method is able to calibrate dynamic models in an efficient and robust way, effectively fighting overfitting and allowing the incorporation of prior information.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0219-2) contains supplementary material, which is available to authorized users.

Quantitative time-resolved analysis reveals intricate, differential regulation of standard- and immuno-proteasomes

Proteasomal protein degradation is a key determinant of protein half-life and hence of cellular processes ranging from basic metabolism to a host of immunological processes. Despite its importance the mechanisms regulating proteasome activity are only incompletely understood. Here we use an iterative and tightly integrated experimental and modelling approach to develop, explore and validate mechanistic models of proteasomal peptide-hydrolysis dynamics. The 20S proteasome is a dynamic enzyme and its activity varies over time because of interactions between substrates and products and the proteolytic and regulatory sites; the locations of these sites and the interactions between them are predicted by the model, and experimentally supported. The analysis suggests that the rate-limiting step of hydrolysis is the transport of the substrates into the proteasome. The transport efficiency varies between human standard- and immuno-proteasomes thereby impinging upon total degradation rate and substrate cleavage-site usage.

DOI:http://dx.doi.org/10.7554/eLife.07545.001

Cells have to be able to reliably destroy or remove molecules from their interior that they no longer need. Structures called proteasomes play a central part in this complex process by cutting up and digesting proteins. Mammals have several different types of proteasomes, each made up of several protein ‘subunits’. For example, when a cell experiences inflammation some proteasomes change some of their subunits and form an immuno-proteasome. These immuno-proteasomes tend to break down proteins more quickly than ‘standard’ proteasomes, but it was not clear how they are able to do so.

Liepe et al. have now combined experiments and mathematical modelling to construct a detailed model of proteasome activity. The model shows that protein transport into and out of the proteasome chamber are the steps that limit how quickly the proteasomes can break down proteins. Furthermore, these transport processes are also to a large extent responsible for the different rates at which standard and immuno-proteasomes process proteins. Liepe et al. were also able to confirm the existence of regulatory sites within the proteasome, and describe how these are arranged.

Problems that alter the rate at which proteasomes break down proteins have been linked to tumors and neurological and autoimmune diseases. Liepe et al.'s model opens up the ability to study how the proteasome's activity is affected by drugs and therefore makes it easier to investigate ways of interfering with this activity for therapeutic purposes.

DOI:http://dx.doi.org/10.7554/eLife.07545.002

Transcriptomic analysis of the GCN5 gene reveals mechanisms of the epigenetic regulation of virulence and morphogenesis in Ustilago maydis

Chromatin in the eukaryotic nucleus is highly organized in the form of nucleosomes where histones wrap DNA. This structure may be altered by some chemical modifications of histones, one of them, acetylation by histone acetyltransferases (HATs) that originates relaxation of the nucleosome structure, providing access to different transcription factors and other effectors. In this way, HATs regulate cellular processes including DNA replication, and gene transcription. Previously, we isolated Ustilago maydis mutants deficient in the GCN5 HAT that are avirulent, and grow constitutively as mycelium. In this work, we proceeded to identify the genes differentially regulated by GCN5, comparing the transcriptomes of the mutant and the wild type using microarrays, to analyse the epigenetic control of virulence and morphogenesis. We identified 1203 genes, 574 positively and 629 negatively regulated in the wild type. We found that genes belonging to different categories involved in pathogenesis were downregulated in the mutant, and that genes involved in mycelial growth were negatively regulated in the wild type, offering a working hypothesis on the epigenetic control of virulence and morphogenesis of U. maydis. Interestingly, several differentially regulated genes appeared in clusters, suggesting a common regulation. Some of these belonged to pathogenesis or secondary metabolism.

Topological sensitivity analysis for systems biology

Mathematical models of natural systems are abstractions of much more complicated processes. Developing informative and realistic models of such systems typically involves suitable statistical inference methods, domain expertise, and a modicum of luck. Except for cases where physical principles provide sufficient guidance, it will also be generally possible to come up with a large number of potential models that are compatible with a given natural system and any finite amount of data generated from experiments on that system. Here we develop a computational framework to systematically evaluate potentially vast sets of candidate differential equation models in light of experimental and prior knowledge about biological systems. This topological sensitivity analysis enables us to evaluate quantitatively the dependence of model inferences and predictions on the assumed model structures. Failure to consider the impact of structural uncertainty introduces biases into the analysis and potentially gives rise to misleading conclusions.

Cutting the wires: modularization of cellular networks for experimental design

Understanding naturally evolved cellular networks requires the consecutive identification and revision of the interactions between relevant molecular species. In this process, initially often simplified and incomplete networks are extended by integrating new reactions or whole subnetworks to increase consistency between model predictions and new measurement data. However, increased consistency with experimental data alone is not sufficient to show the existence of biomolecular interactions, because the interplay of different potential extensions might lead to overall similar dynamics. Here, we present a graph-based modularization approach to facilitate the design of experiments targeted at independently validating the existence of several potential network extensions. Our method is based on selecting the outputs to measure during an experiment, such that each potential network extension becomes virtually insulated from all others during data analysis. Each output defines a module that only depends on one hypothetical network extension, and all other outputs act as virtual inputs to achieve insulation. Given appropriate experimental time-series measurements of the outputs, our modules can be analyzed, simulated, and compared to the experimental data separately. Our approach exemplifies the close relationship between structural systems identification and modularization, an interplay that promises development of related approaches in the future.

Visualizing and manipulating temporal signaling dynamics with fluorescence-based tools

The use of genome-wide proteomic and RNA interference approaches has moved our understanding of signal transduction from linear pathways to highly integrated networks centered on core nodes. However, probing the dynamics of flow of information through such networks remains technically challenging. In particular, how the temporal dynamics of an individual pathway can elicit distinct outcomes in a single cell type and how multiple pathways may interact sequentially or synchronously to influence cell fate remain open questions in many contexts. The development of fluorescence-based reporters and optogenetic regulators of pathway activity enables the analysis of signaling in living cells and organisms with unprecedented spatiotemporal resolution and holds the promise of addressing these key questions. We present a brief overview of the evidence for the importance of temporal dynamics in cellular regulation, introduce these fluorescence-based tools, and highlight specific studies that leveraged these tools to probe the dynamics of information flow through signaling networks. In particular, we highlight two studies in Caenorhabditis elegans sensory neurons and cultured mammalian cells that demonstrate the importance of signal dynamics in determining cellular responses.

Yeast AMP-activated protein kinase monitors glucose concentration changes and absolute glucose levels

Analysis of the time-dependent behavior of a signaling system can provide insight into its dynamic properties. We employed the nucleocytoplasmic shuttling of the transcriptional repressor Mig1 as readout to characterize Snf1-Mig1 dynamics in single yeast cells. Mig1 binds to promoters of target genes and mediates glucose repression. Mig1 is predominantly located in the nucleus when glucose is abundant. Upon glucose depletion, Mig1 is phosphorylated by the yeast AMP-activated kinase Snf1 and exported into the cytoplasm. We used a three-channel microfluidic device to establish a high degree of control over the glucose concentration exposed to cells. Following regimes of glucose up- and downshifts, we observed a very rapid response reaching a new steady state within less than 1 min, different glucose threshold concentrations depending on glucose up- or downshifts, a graded profile with increased cell-to-cell variation at threshold glucose concentrations, and biphasic behavior with a transient translocation of Mig1 upon the shift from high to intermediate glucose concentrations. Fluorescence loss in photobleaching and fluorescence recovery after photobleaching data demonstrate that Mig1 shuttles constantly between the nucleus and cytoplasm, although with different rates, depending on the presence of glucose. Taken together, our data suggest that the Snf1-Mig1 system has the ability to monitor glucose concentration changes as well as absolute glucose levels. The sensitivity over a wide range of glucose levels and different glucose concentration-dependent response profiles are likely determined by the close integration of signaling with the metabolism and may provide for a highly flexible and fast adaptation to an altered nutritional status.

Advancing metabolic models with kinetic information

Kinetic models are crucial to quantitatively understand and predict how functional behavior emerges from dynamic concentration changes of cellular components. The current challenge is on resolving uncertainties about parameter values of reaction kinetics. Additionally, there are also major structural uncertainties due to unknown molecular interactions and only putatively assigned regulatory functions. What if one or few key regulators of biochemical reactions are missing in a metabolic model? By reviewing current advances in building kinetic models of metabolism, we found that such models experience a paradigm shift away from fitting parameters towards identifying key regulatory interactions.

Topological augmentation to infer hidden processes in biological systems

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

Near-optimal experimental design for model selection in systems biology

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).