Paradoxical results in perturbation-based signaling network reconstruction

Network regulation meets substrate modification chemistry

Biochemical networks are at the heart of cellular information processing. These networks contain distinct facets: (i) processing of information from the environment via cascades/pathways along with network regulation and (ii) modification of substrates in different ways, to confer protein functionality, stability and processing. While many studies focus on these factors individually, how they interact and the consequences for cellular systems behaviour are poorly understood. We develop a systems framework for this purpose by examining the interplay of network regulation (canonical feedback and feed-forward circuits) and multisite modification, as an exemplar of substrate modification. Using computational, analytical and semi-analytical approaches, we reveal distinct and unexpected ways in which the substrate modification and network levels combine and the emergent behaviour arising therefrom. This has important consequences for dissecting the behaviour of specific signalling networks, tracing the origins of systems behaviour, inference of networks from data, robustness/evolvability and multi-level engineering of biomolecular networks. Overall, we repeatedly demonstrate how focusing on only one level (say network regulation) can lead to profoundly misleading conclusions about all these aspects, and reveal a number of important consequences for experimental/theoretical/data-driven interrogations of cellular signalling systems.

A framework for reconstructing transmission networks in infectious diseases

In this paper, we propose a general framework for the reconstruction of the underlying cross-regional transmission network contributing to the spread of an infectious disease. We employ an autoregressive model that allows to decompose the mean number of infections into three components that describe: intra-locality infections, inter-locality infections, and infections from other sources such as travelers arriving to a country from abroad. This model is commonly used in the identification of spatiotemporal patterns in seasonal infectious diseases and thus in forecasting infection counts. However, our contribution lies in identifying the inter-locality term as a time-evolving network, and rather than using the model for forecasting, we focus on the network properties without any assumption on seasonality or recurrence of the disease. The topology of the network is then studied to get insight into the disease dynamics. Building on this, and particularly on the centrality of the nodes of the identified network, a strategy for intervention and disease control is devised.

Data-driven network models for genetic circuits from time-series data with incomplete measurements

Synthetic gene networks are frequently conceptualized and visualized as static graphs. This view of biological programming stands in stark contrast to the transient nature of biomolecular interaction, which is frequently enacted by labile molecules that are often unmeasured. Thus, the network topology and dynamics of synthetic gene networks can be difficult to verify in vivo or in vitro, due to the presence of unmeasured biological states. Here we introduce the dynamical structure function as a new mesoscopic, data-driven class of models to describe gene networks with incomplete measurements of state dynamics. We develop a network reconstruction algorithm and a code base for reconstructing the dynamical structure function from data, to enable discovery and visualization of graphical relationships in a genetic circuit diagram as time-dependent functions rather than static, unknown weights. We prove a theorem, showing that dynamical structure functions can provide a data-driven estimate of the size of crosstalk fluctuations from an idealized model. We illustrate this idea with numerical examples. Finally, we show how data-driven estimation of dynamical structure functions can explain failure modes in two experimentally implemented genetic circuits, a previously reported in vitro genetic circuit and a new E. coli-based transcriptional event detector.

Identifiability and experimental design in perturbation studies

MOTIVATION

A common strategy to infer and quantify interactions between components of a biological system is to deduce them from the network's response to targeted perturbations. Such perturbation experiments are often challenging and costly. Therefore, optimizing the experimental design is essential to achieve a meaningful characterization of biological networks. However, it remains difficult to predict which combination of perturbations allows to infer specific interaction strengths in a given network topology. Yet, such a description of identifiability is necessary to select perturbations that maximize the number of inferable parameters.

RESULTS

We show analytically that the identifiability of network parameters can be determined by an intuitive maximum-flow problem. Furthermore, we used the theory of matroids to describe identifiability relationships between sets of parameters in order to build identifiable effective network models. Collectively, these results allowed to device strategies for an optimal design of the perturbation experiments. We benchmarked these strategies on a database of human pathways. Remarkably, full network identifiability was achieved, on average, with less than a third of the perturbations that are needed in a random experimental design. Moreover, we determined perturbation combinations that additionally decreased experimental effort compared to single-target perturbations. In summary, we provide a framework that allows to infer a maximal number of interaction strengths with a minimal number of perturbation experiments.

AVAILABILITY AND IMPLEMENTATION

IdentiFlow is available at github.com/GrossTor/IdentiFlow.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Exploring the intrinsic behaviour of multisite phosphorylation systems as part of signalling pathways

Multisite phosphorylation is a basic way of chemically encoding substrate function and a recurring feature of cell signalling pathways. A number of studies have explored information processing characteristics of multisite phosphorylation, through studies of the intrinsic kinetics. Many of these studies focus on the module in isolation. In this paper, we build a bridge to connect the behaviour of multisite modification in isolation to that as part of pathways. We study the effect of activation of the enzymes (which are basic ways in which the module may be regulated), as well the effects of the modified substrates being involved in further modifications or exiting reaction compartments. We find that these effects can induce multiple kinds of transitions, including to behaviour not seen intrinsically in the multisite modification module. We then build on these insights to investigate how these multisite modification systems can be tuned by enzyme activation to realize a range of information processing outcomes for the design of synthetic phosphorylation circuits. Connecting the complexity of multisite modification kinetics, with the pathways in which they are embedded, serves as a basis for teasing out many aspects of their interaction, providing insights of relevance in systems biology, synthetic biology/chemistry and chemical information processing.

Mapping connections in signaling networks with ambiguous modularity

Modular Response Analysis (MRA) is a suite of methods that under certain assumptions permits the precise reconstruction of both the directions and strengths of connections between network modules from network responses to perturbations. Standard MRA assumes that modules are insulated, thereby neglecting the existence of inter-modular protein complexes. Such complexes sequester proteins from different modules and propagate perturbations to the protein abundance of a downstream module retroactively to an upstream module. MRA-based network reconstruction detects retroactive, sequestration-induced connections when an enzyme from one module is substantially sequestered by its substrate that belongs to a different module. Moreover, inferred networks may surprisingly depend on the choice of protein abundances that are experimentally perturbed, and also some inferred connections might be false. Here, we extend MRA by introducing a combined computational and experimental approach, which allows for a computational restoration of modular insulation, unmistakable network reconstruction and discrimination between solely regulatory and sequestration-induced connections for a range of signaling pathways. Although not universal, our approach extends MRA methods to signaling networks with retroactive interactions between modules arising from enzyme sequestration effects.

Application of targeted mass spectrometry in bottom-up proteomics for systems biology research

The enormous diversity of proteoforms produces tremendous complexity within cellular proteomes, facilitates intricate networks of molecular interactions, and constitutes a formidable analytical challenge for biomedical researchers. Currently, quantitative whole-proteome profiling often relies on non-targeted liquid chromatography-mass spectrometry (LC-MS), which samples proteoforms broadly, but can suffer from lower accuracy, sensitivity, and reproducibility compared with targeted LC-MS. Recent advances in bottom-up proteomics using targeted LC-MS have enabled previously unachievable identification and quantification of target proteins and posttranslational modifications within complex samples. Consequently, targeted LC-MS is rapidly advancing biomedical research, especially systems biology research in diverse areas that include proteogenomics, interactomics, kinomics, and biological pathway modeling. With the recent development of targeted LC-MS assays for nearly the entire human proteome, targeted LC-MS is positioned to enable quantitative proteomic profiling of unprecedented quality and accessibility to support fundamental and clinical research. Here we review recent applications of bottom-up proteomics using targeted LC-MS for systems biology research. SIGNIFICANCE: Advances in targeted proteomics are rapidly advancing systems biology research. Recent applications include systems-level investigations focused on posttranslational modifications (such as phosphoproteomics), protein conformation, protein-protein interaction, kinomics, proteogenomics, and metabolic and signaling pathways. Notably, absolute quantification of metabolic and signaling pathway proteins has enabled accurate pathway modeling and engineering. Integration of targeted proteomics with other technologies, such as RNA-seq, has facilitated diverse research such as the identification of hundreds of "missing" human proteins (genes and transcripts that appear to encode proteins but direct experimental evidence was lacking).

Sensitivity and network topology in chemical reaction systems

In living cells, biochemical reactions are catalyzed by specific enzymes and connect to one another by sharing substrates and products, forming complex networks. In our previous studies, we established a framework determining the responses to enzyme perturbations only from network topology, and then proved a theorem, called the law of localization, explaining response patterns in terms of network topology. In this paper, we generalize these results to reaction networks with conserved concentrations, which allows us to study any reaction system. We also propose network characteristics quantifying robustness. We compare E. coli metabolic network with randomly rewired networks, and find that the robustness of the E. coli network is significantly higher than that of the random networks.

A Discrete Dynamical System Approach to Pathway Activation Profiles of Signaling Cascades

In living organisms, cascades of covalent modification cycles are one of the major intracellular signaling mechanisms, allowing to transduce physical or chemical stimuli of the external world into variations of activated biochemical species within the cell. In this paper, we develop a novel method to study the stimulus-response of signaling cascades and overall the concept of pathway activation profile which is, for a given stimulus, the sequence of activated proteins at each tier of the cascade. Our approach is based on a correspondence that we establish between the stationary states of a cascade and pieces of orbits of a 2D discrete dynamical system. The study of its possible phase portraits in function of the biochemical parameters, and in particular of the contraction/expansion properties around the fixed points of this discrete map, as well as their bifurcations, yields a classification of the cascade tiers into three main types, whose biological impact within a signaling network is examined. In particular, our approach enables to discuss quantitatively the notion of cascade amplification/attenuation from this new perspective. The method allows also to study the interplay between forward and "retroactive" signaling, i.e., the upstream influence of an inhibiting drug bound to the last tier of the cascade.

Sustained oscillations in the MAP kinase cascade

The MAP kinase cascade is a network of enzymatic reactions arranged in layers. In each layer occurs a multiple futile cycle of phosphorylations. The fully phosphorylated substrate then serves as an enzyme for the layer below. This paper focusses on the existence of parameters for which Hopf bifurcations occur and generate periodic orbits. Furthermore it is explained how geometric singular perturbation theory allows to generalize results from simple models to more complex ones.

Long-term dynamics of multisite phosphorylation

A systematic framework for exploring the long-term dynamics of a reaction network is applied to a minimal model of ERK regulation that distinguishes both monophosphorylated forms and allows for nonzero enzyme processivity. Bistability and oscillations can be observed at high levels of processivity.

Multisite phosphorylation cycles are ubiquitous in cell regulation systems and are studied at multiple levels of complexity, from molecules to organisms, with the ultimate goal of establishing predictive understanding of the effects of genetic and pharmacological perturbations of protein phosphorylation in vivo. Achieving this goal is essentially impossible without mathematical models, which provide a systematic framework for exploring dynamic interactions of multiple network components. Most of the models studied to date do not discriminate between the distinct partially phosphorylated forms and focus on two limiting reaction regimes, distributive and processive, which differ in the number of enzyme–substrate binding events needed for complete phosphorylation or dephosphorylation. Here we use a minimal model of extracellular signal-related kinase regulation to explore the dynamics of a reaction network that includes all essential phosphorylation forms and arbitrary levels of reaction processivity. In addition to bistability, which has been studied extensively in distributive mechanisms, this network can generate periodic oscillations. Both bistability and oscillations can be realized at high levels of reaction processivity. Our work provides a general framework for systematic analysis of dynamics in multisite phosphorylation systems.

A technique for determining the signs of sensitivities of steady states in chemical reaction networks

This paper studies the direction of change of steady states to parameter perturbations in chemical reaction networks, and, in particular, to changes in conserved quantities. Theoretical considerations lead to the formulation of a computational procedure that provides a set of possible signs of such sensitivities. The procedure is purely algebraic and combinatorial, only using information on stoichiometry, and is independent of the values of kinetic constants. Three examples of important intracellular signal transduction models are worked out as an illustration. In these examples, the set of signs found is minimal, but there is no general guarantee that the set found will always be minimal in other examples. The paper also briefly discusses the relationship of the sign problem to the question of uniqueness of steady states in stoichiometry classes.