Modeling Signal Transduction in Enzyme Cascades with the Concept of Elementary Flux Modes

isiKnock: in silico knockouts in signaling pathways

SUMMARY

isiKnock is a new software that automatically conducts in silico knockouts for mathematical models of signaling pathways. The software allows for the prediction of the behavior of biological systems after single or multiple knockout. The implemented algorithm applies transition invariants and the novel concept of Manatee invariants. A knockout matrix visualizes the results. The tool enables the analysis of dependencies, for example, in signal flows from the receptor activation to the cell response at steady state.

AVAILABILITY AND IMPLEMENTATION

isiKnock is an open-source tool, freely available at http://www.bioinformatik.uni-frankfurt.de/tools/isiKnock/. It requires at least Java 8 and runs under Microsoft Windows, Linux, and Mac OS.

Modelling and mathematical analysis of the M$_{2}$ receptor-dependent joint signalling and secondary messenger network in CHO cells

The muscarinic M$_{2}$ receptor is a prominent member of the GPCR family and strongly involved in heart diseases. Recently published experimental work explored the cellular response to iperoxo-induced M$_{2}$ receptor stimulation in Chinese hamster ovary (CHO) cells. To better understand these responses, we modelled and analysed the muscarinic M$_{2}$ receptor-dependent signalling pathway combined with relevant secondary messenger molecules using mass action. In our literature-based joint signalling and secondary messenger model, all binding and phosphorylation events are explicitly taken into account in order to enable subsequent stoichiometric matrix analysis. We propose constraint flux sampling (CFS) as a method to characterize the expected shift of the steady state reaction flux distribution due to the known amount of cAMP production and PDE4 activation. CFS correctly predicts an experimentally observable influence on the cytoskeleton structure (marked by actin and tubulin) and in consequence a change of the optical density of cells. In a second step, we use CFS to simulate the effect of knock-out experiments within our biological system, and thus to rank the influence of individual molecules on the observed change of the optical cell density. In particular, we confirm the relevance of the protein RGS14, which is supported by current literature. A combination of CFS with Elementary Flux Mode analysis enabled us to determine the possible underlying mechanism. Our analysis suggests that mathematical tools developed for metabolic network analysis can also be applied to mixed secondary messenger and signalling models. This could be very helpful to perform model checking with little effort and to generate hypotheses for further research if parameters are not known.

Manatee invariants reveal functional pathways in signaling networks

Background

Signal transduction pathways are important cellular processes to maintain the cell’s integrity. Their imbalance can cause severe pathologies. As signal transduction pathways feature complex regulations, they form intertwined networks. Mathematical models aim to capture their regulatory logic and allow an unbiased analysis of robustness and vulnerability of the signaling network. Pathway detection is yet a challenge for the analysis of signaling networks in the field of systems biology. A rigorous mathematical formalism is lacking to identify all possible signal flows in a network model.

Results

In this paper, we introduce the concept of Manatee invariants for the analysis of signal transduction networks. We present an algorithm for the characterization of the combinatorial diversity of signal flows, e.g., from signal reception to cellular response. We demonstrate the concept for a small model of the TNFR1-mediated NF- κB signaling pathway. Manatee invariants reveal all possible signal flows in the network. Further, we show the application of Manatee invariants for in silico knockout experiments. Here, we illustrate the biological relevance of the concept.

Conclusions

The proposed mathematical framework reveals the entire variety of signal flows in models of signaling systems, including cyclic regulations. Thereby, Manatee invariants allow for the analysis of robustness and vulnerability of signaling networks. The application to further analyses such as for in silico knockout was shown. The new framework of Manatee invariants contributes to an advanced examination of signaling systems.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-017-0448-7) contains supplementary material, which is available to authorized users.

The steady-state assumption in oscillating and growing systems

The steady-state assumption, which states that the production and consumption of metabolites inside the cell are balanced, is one of the key aspects that makes an efficient analysis of genome-scale metabolic networks possible. It can be motivated from two different perspectives. In the time-scales perspective, we use the fact that metabolism is much faster than other cellular processes such as gene expression. Hence, the steady-state assumption is derived as a quasi-steady-state approximation of the metabolism that adapts to the changing cellular conditions. In this article we focus on the second perspective, stating that on the long run no metabolite can accumulate or deplete. In contrast to the first perspective it is not immediately clear how this perspective can be captured mathematically and what assumptions are required to obtain the steady-state condition. By presenting a mathematical framework based on the second perspective we demonstrate that the assumption of steady-state also applies to oscillating and growing systems without requiring quasi-steady-state at any time point. However, we also show that the average concentrations may not be compatible with the average fluxes. In summary, we establish a mathematical foundation for the steady-state assumption for long time periods that justifies its successful use in many applications. Furthermore, this mathematical foundation also pinpoints unintuitive effects in the integration of metabolite concentrations using nonlinear constraints into steady-state models for long time periods.

Detecting structural invariants in biological reaction networks

The detection and analysis of structural invariants in cellular reaction networks is of central importance to achieve a more comprehensive understanding of metabolism. In this work, we review different kinds of structural invariants in reaction networks and their Petri net-based representation. In particular, we discuss invariants that can be obtained from the left and right null spaces of the stoichiometric matrix which correspond to conserved moieties (P-invariants) and elementary flux modes (EFMs, minimal T-invariants). While conserved moieties can be used to detect stoichiometric inconsistencies in reaction networks, EFMs correspond to a mathematically rigorous definition of the concept of a biochemical pathway. As outlined here, EFMs allow to devise strategies for strain improvement, to assess the robustness of metabolic networks subject to perturbations, and to analyze the information flow in regulatory and signaling networks. Another important aspect addressed by this review is the limitation of metabolic pathway analysis using EFMs to small or medium-scale reaction networks. We discuss two recently introduced approaches to circumvent these limitations. The first is an algorithm to enumerate a subset of EFMs in genome-scale metabolic networks starting from the EFM with the least number of reactions. The second approach, elementary flux pattern analysis, allows to analyze pathways through specific subsystems of genome-scale metabolic networks. In contrast to EFMs, elementary flux patterns much more accurately reflect the metabolic capabilities of a subsystem of metabolism as well as its integration into the entire system.

Elementary signaling modes predict the essentiality of signal transduction network components

Background

Understanding how signals propagate through signaling pathways and networks is a central goal in systems biology. Quantitative dynamic models help to achieve this understanding, but are difficult to construct and validate because of the scarcity of known mechanistic details and kinetic parameters. Structural and qualitative analysis is emerging as a feasible and useful alternative for interpreting signal transduction.

Results

In this work, we present an integrative computational method for evaluating the essentiality of components in signaling networks. This approach expands an existing signaling network to a richer representation that incorporates the positive or negative nature of interactions and the synergistic behaviors among multiple components. Our method simulates both knockout and constitutive activation of components as node disruptions, and takes into account the possible cascading effects of a node's disruption. We introduce the concept of elementary signaling mode (ESM), as the minimal set of nodes that can perform signal transduction independently. Our method ranks the importance of signaling components by the effects of their perturbation on the ESMs of the network. Validation on several signaling networks describing the immune response of mammals to bacteria, guard cell abscisic acid signaling in plants, and T cell receptor signaling shows that this method can effectively uncover the essentiality of components mediating a signal transduction process and results in strong agreement with the results of Boolean (logical) dynamic models and experimental observations.

Conclusions

This integrative method is an efficient procedure for exploratory analysis of large signaling and regulatory networks where dynamic modeling or experimental tests are impractical. Its results serve as testable predictions, provide insights into signal transduction and regulatory mechanisms and can guide targeted computational or experimental follow-up studies. The source codes for the algorithms developed in this study can be found at http://www.phys.psu.edu/~ralbert/ESM.