A methodology for the structural and functional analysis of signaling and regulatory networks

Logic-based modeling and drug repurposing for the prediction of novel therapeutic targets and combination regimens against E2F1-driven melanoma progression

Melanoma presents increasing prevalence and poor outcomes. Progression to aggressive stages is characterized by overexpression of the transcription factor E2F1 and activation of downstream prometastatic gene regulatory networks (GRNs). Appropriate therapeutic manipulation of the E2F1-governed GRNs holds the potential to prevent metastasis however, these networks entail complex feedback and feedforward regulatory motifs among various regulatory layers, which make it difficult to identify druggable components. To this end, computational approaches such as mathematical modeling and virtual screening are important tools to unveil the dynamics of these signaling networks and identify critical components that could be further explored as therapeutic targets. Herein, we integrated a well-established E2F1-mediated epithelial-mesenchymal transition (EMT) map with transcriptomics data from E2F1-expressing melanoma cells to reconstruct a core regulatory network underlying aggressive melanoma. Using logic-based in silico perturbation experiments of a core regulatory network, we identified that simultaneous perturbation of Protein kinase B (AKT1) and oncoprotein murine double minute 2 (MDM2) drastically reduces EMT in melanoma. Using the structures of the two protein signatures, virtual screening strategies were performed with the FDA-approved drug library. Furthermore, by combining drug repurposing and computer-aided drug design techniques, followed by molecular dynamics simulation analysis, we identified two potent drugs (Tadalafil and Finasteride) that can efficiently inhibit AKT1 and MDM2 proteins. We propose that these two drugs could be considered for the development of therapeutic strategies for the management of aggressive melanoma.

Dynamical methods for target control of biological networks

Estimating the influence that individual nodes have on one another in a Boolean network is essential to predict and control the system's dynamical behaviour, for example, detecting key therapeutic targets to control pathways in models of biological signalling and regulation. Exact estimation is generally not possible due to the fact that the number of configurations that must be considered grows exponentially with the system size. However, approximate, scalable methods exist in the literature. These methods can be divided into two main classes: (i) graph-theoretic methods that rely on representations of Boolean dynamics into static graphs and (ii) mean-field approaches that describe average trajectories of the system but neglect dynamical correlations. Here, we compare systematically the performance of these state-of-the-art methods on a large collection of real-world gene regulatory networks. We find comparable performance across methods. All methods underestimate the ground truth, with mean-field approaches having a better recall but a worse precision than graph-theoretic methods. Computationally speaking, graph-theoretic methods are faster than mean-field ones in sparse networks, but are slower in dense networks. The preference of which method to use, therefore, depends on a network's connectivity and the relative importance of recall versus precision for the specific application at hand.

From time-series transcriptomics to gene regulatory networks: A review on inference methods

Inference of gene regulatory networks has been an active area of research for around 20 years, leading to the development of sophisticated inference algorithms based on a variety of assumptions and approaches. With the ever increasing demand for more accurate and powerful models, the inference problem remains of broad scientific interest. The abstract representation of biological systems through gene regulatory networks represents a powerful method to study such systems, encoding different amounts and types of information. In this review, we summarize the different types of inference algorithms specifically based on time-series transcriptomics, giving an overview of the main applications of gene regulatory networks in computational biology. This review is intended to give an updated reference of regulatory networks inference tools to biologists and researchers new to the topic and guide them in selecting the appropriate inference method that best fits their questions, aims, and experimental data.

Reducing Boolean networks with backward equivalence

BACKGROUND

Boolean Networks (BNs) are a popular dynamical model in biology where the state of each component is represented by a variable taking binary values that express, for instance, activation/deactivation or high/low concentrations. Unfortunately, these models suffer from the state space explosion, i.e., there are exponentially many states in the number of BN variables, which hampers their analysis.

RESULTS

We present Boolean Backward Equivalence (BBE), a novel reduction technique for BNs which collapses system variables that, if initialized with same value, maintain matching values in all states. A large-scale validation on 86 models from two online model repositories reveals that BBE is effective, since it is able to reduce more than 90% of the models. Furthermore, on such models we also show that BBE brings notable analysis speed-ups, both in terms of state space generation and steady-state analysis. In several cases, BBE allowed the analysis of models that were originally intractable due to the complexity. On two selected case studies, we show how one can tune the reduction power of BBE using model-specific information to preserve all dynamics of interest, and selectively exclude behavior that does not have biological relevance.

CONCLUSIONS

BBE complements existing reduction methods, preserving properties that other reduction methods fail to reproduce, and vice versa. BBE drops all and only the dynamics, including attractors, originating from states where BBE-equivalent variables have been initialized with different activation values The remaining part of the dynamics is preserved exactly, including the length of the preserved attractors, and their reachability from given initial conditions, without adding any spurious behaviours. Given that BBE is a model-to-model reduction technique, it can be combined with further reduction methods for BNs.

Multi-scale model suggests the trade-off between protein and ATP demand as a driver of metabolic changes during yeast replicative ageing

The accumulation of protein damage is one of the major drivers of replicative ageing, describing a cell’s reduced ability to reproduce over time even under optimal conditions. Reactive oxygen and nitrogen species are precursors of protein damage and therefore tightly linked to ageing. At the same time, they are an inevitable by-product of the cell’s metabolism. Cells are able to sense high levels of reactive oxygen and nitrogen species and can subsequently adapt their metabolism through gene regulation to slow down damage accumulation. However, the older or damaged a cell is the less flexibility it has to allocate enzymes across the metabolic network, forcing further adaptions in the metabolism. To investigate changes in the metabolism during replicative ageing, we developed an multi-scale mathematical model using budding yeast as a model organism. The model consists of three interconnected modules: a Boolean model of the signalling network, an enzyme-constrained flux balance model of the central carbon metabolism and a dynamic model of growth and protein damage accumulation with discrete cell divisions. The model can explain known features of replicative ageing, like average lifespan and increase in generation time during successive division, in yeast wildtype cells by a decreasing pool of functional enzymes and an increasing energy demand for maintenance. We further used the model to identify three consecutive metabolic phases, that a cell can undergo during its life, and their influence on the replicative potential, and proposed an intervention span for lifespan control.

Identification of dynamic driver sets controlling phenotypical landscapes

Controlling phenotypical landscapes is of vital interest to modern biology. This task becomes highly demanding because cellular decisions involve complex networks engaging in crosstalk interactions. Previous work on control theory indicates that small sets of compounds can control single phenotypes. However, a dynamic approach is missing to determine the drivers of the whole network dynamics. By analyzing 35 biologically motivated Boolean networks, we developed a method to identify small sets of compounds sufficient to decide on the entire phenotypical landscape. These compounds do not strictly prefer highly related compounds and show a smaller impact on the stability of the attractor landscape. The dynamic driver sets include many intervention targets and cellular reprogramming drivers in human networks. Finally, by using a new comprehensive model of colorectal cancer, we provide a complete workflow on how to implement our approach to shift from in silico to in vitro guided experiments.

Optimising Boolean Synthetic Regulatory Networks to Control Cell States

Controlling the dynamics of gene regulatory networks is a challenging problem. In recent years, a number of control methods have been proposed, but most of these approaches do not address the problem of how they could be implemented in practice. In this paper, we consider the idea of using a synthetic regulatory network as a closed-loop controller that can control and respond to the dynamics of a cell's native regulatory network in situ. We explore this idea using a computational model in which both native and synthetic regulatory networks are represented by Boolean networks. We then use an evolutionary algorithm to optimise both the structure and parameters of the synthetic Boolean network. To test this approach, we look at whether controllers can be optimised to target specific steady states in five different Boolean regulatory circuit models. Our results show that in most cases the controllers are able to drive the dynamics of the target system to a specified steady state, often using few interventions, and further experiments using random Boolean networks show that the approach scales well to larger controlled networks.

Capturing dynamic relevance in Boolean networks using graph theoretical measures

Motivation

Interaction graphs are able to describe regulatory dependencies between compounds without capturing dynamics. In contrast, mathematical models that are based on interaction graphs allow to investigate the dynamics of biological systems. However, since dynamic complexity of these models grows exponentially with their size, exhaustive analyses of the dynamics and consequently screening all possible interventions eventually becomes infeasible. Thus, we designed an approach to identify dynamically relevant compounds based on the static network topology.

Results

Here, we present a method only based on static properties to identify dynamically influencing nodes. Coupling vertex betweenness and determinative power, we could capture relevant nodes for changing dynamics with an accuracy of 75% in a set of 35 published logical models. Further analyses of the selected compounds’ connectivity unravelled a new class of not highly connected nodes with high impact on the networks’ dynamics, which we call gatekeepers. We validated our method’s working concept on logical models, which can be readily scaled up to complex interaction networks, where dynamic analyses are not even feasible.

Availability and implementation

Code is freely available at https://github.com/sysbio-bioinf/BNStatic.

Supplementary information

Supplementary data are available at Bioinformatics online.

Modeling Cell Communication with Time-Dependent Signaling Hypergraphs

Signaling pathways describe a group of molecules in a cell that collaborate to control one or more cell functions, such as cell division or cell death. The pathways communicate by sending signals between molecules, and this process is repeated until the terminal molecule is activated and the cell function is executed. Signaling pathways are often represented as directed graphs, which does not provide enough information when modeling cell functions and reactions. Recently, directed hypergraphs have been proposed to more accurately represent reactions such as protein activation and interaction. To further improve the representation of signaling pathways, time dependency must be considered to improve the representation of cell signaling at any given time. In this paper, the importance of time dependency in modeling signaling pathways is presented. An algorithm that finds the shortest a priori path using time-dependent hypergraphs to more robustly model signaling pathways is adopted. The shortest time-dependent hyperpaths representing signaling pathways are an improvement to the recent adoption of hypergraphs representing these pathways. The results display the improved representation of signaling pathways and motivate the adoption of time-dependent signaling hypergraphs.

The effective graph reveals redundancy, canalization, and control pathways in biochemical regulation and signaling

The ability to map causal interactions underlying genetic control and cellular signaling has led to increasingly accurate models of the complex biochemical networks that regulate cellular function. These network models provide deep insights into the organization, dynamics, and function of biochemical systems: for example, by revealing genetic control pathways involved in disease. However, the traditional representation of biochemical networks as binary interaction graphs fails to accurately represent an important dynamical feature of these multivariate systems: some pathways propagate control signals much more effectively than do others. Such heterogeneity of interactions reflects canalization-the system is robust to dynamical interventions in redundant pathways but responsive to interventions in effective pathways. Here, we introduce the effective graph, a weighted graph that captures the nonlinear logical redundancy present in biochemical network regulation, signaling, and control. Using 78 experimentally validated models derived from systems biology, we demonstrate that 1) redundant pathways are prevalent in biological models of biochemical regulation, 2) the effective graph provides a probabilistic but precise characterization of multivariate dynamics in a causal graph form, and 3) the effective graph provides an accurate explanation of how dynamical perturbation and control signals, such as those induced by cancer drug therapies, propagate in biochemical pathways. Overall, our results indicate that the effective graph provides an enriched description of the structure and dynamics of networked multivariate causal interactions. We demonstrate that it improves explainability, prediction, and control of complex dynamical systems in general and biochemical regulation in particular.

Multiscale Regulation of the Intervertebral Disc: Achievements in Experimental, In Silico, and Regenerative Research

Intervertebral disc (IVD) degeneration is a major risk factor of low back pain. It is defined by a progressive loss of the IVD structure and functionality, leading to severe impairments with restricted treatment options due to the highly demanding mechanical exposure of the IVD. Degenerative changes in the IVD usually increase with age but at an accelerated rate in some individuals. To understand the initiation and progression of this disease, it is crucial to identify key top-down and bottom-up regulations' processes, across the cell, tissue, and organ levels, in health and disease. Owing to unremitting investigation of experimental research, the comprehension of detailed cell signaling pathways and their effect on matrix turnover significantly rose. Likewise, in silico research substantially contributed to a holistic understanding of spatiotemporal effects and complex, multifactorial interactions within the IVD. Together with important achievements in the research of biomaterials, manifold promising approaches for regenerative treatment options were presented over the last years. This review provides an integrative analysis of the current knowledge about (1) the multiscale function and regulation of the IVD in health and disease, (2) the possible regenerative strategies, and (3) the in silico models that shall eventually support the development of advanced therapies.

Symbolic Coloured SCC Decomposition

Problems arising in many scientific disciplines are often modelled using edge-coloured directed graphs. These can be enormous in the number of both vertices and colours. Given such a graph, the original problem frequently translates to the detection of the graph’s strongly connected components, which is challenging at this scale.

We propose a new, symbolic algorithm that computes all the monochromatic strongly connected components of an edge-coloured graph. In the worst case, the algorithm performs \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O(p\cdot n\cdot \log n)$$\end{document}O(p·n·logn) symbolic steps, where p is the number of colours and n the number of vertices. We evaluate the algorithm using an experimental implementation based on Binary Decision Diagrams (BDDs) and large (up to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2^{48}$$\end{document}248) coloured graphs produced by models appearing in systems biology.

Robust network inference using response logic

Motivation

A major challenge in molecular and cellular biology is to map out the regulatory networks of cells. As regulatory interactions can typically not be directly observed experimentally, various computational methods have been proposed to disentangling direct and indirect effects. Most of these rely on assumptions that are rarely met or cannot be adapted to a given context.

Results

We present a network inference method that is based on a simple response logic with minimal presumptions. It requires that we can experimentally observe whether or not some of the system’s components respond to perturbations of some other components, and then identifies the directed networks that most accurately account for the observed propagation of the signal. To cope with the intractable number of possible networks, we developed a logic programming approach that can infer networks of hundreds of nodes, while being robust to noisy, heterogeneous or missing data. This allows to directly integrate prior network knowledge and additional constraints such as sparsity. We systematically benchmark our method on KEGG pathways, and show that it outperforms existing approaches in DREAM3 and DREAM4 challenges. Applied to a novel perturbation dataset on PI3K and MAPK pathways in isogenic models of a colon cancer cell line, it generates plausible network hypotheses that explain distinct sensitivities toward various targeted inhibitors due to different PI3K mutants.

Availability and implementation

A Python/Answer Set Programming implementation can be accessed at github.com/GrossTor/response-logic. Data and analysis scripts are available at github.com/GrossTor/response-logic-projects.

Supplementary information

Supplementary data are available at Bioinformatics online.

An Integrative Network Modeling Approach to T CD4 Cell Activation

The adaptive immune response is initiated by the interaction of the T cell antigen receptor/CD3 complex (TCR) with a cognate peptide bound to a MHC molecule. This interaction, along with the activity of co-stimulatory molecules and cytokines in the microenvironment, enables cells to proliferate and produce soluble factors that stimulate other branches of the immune response for inactivation of infectious agents. The intracellular activation signals are reinforced, amplified and diversified by a complex network of biochemical interactions, and includes the activity of molecules that modulate the activation process and stimulate the metabolic changes necessary for fulfilling the cell energy demands. We present an approach to the analysis of the main early signaling events of T cell activation by proposing a concise 46-node hybrid Boolean model of the main steps of TCR and CD28 downstream signaling, encompassing the activity of the anergy factor Ndrg1, modulation of activation by CTLA-4, and the activity of the nutrient sensor AMPK as intrinsic players of the activation process. The model generates stable states that reflect the overcoming of activation signals and induction of anergy by the expression of Ndrg1 in the absence of co-stimulation. The model also includes the induction of CTLA-4 upon activation and its competition with CD28 for binding to the co-stimulatory CD80/86 molecules, leading to stable states that reflect the activation arrest. Furthermore, the model integrates the activity of AMPK to the general pathways driving differentiation to functional cell subsets (Th1, Th2, Th17, and Treg). Thus, the network topology incorporates basic mechanism associated to activation, regulation and induction of effector cell phenotypes. The model puts forth a conceptual framework for the integration of functionally relevant processes in the analysis of the T CD4 cell function.

Automated inference of gene regulatory networks using explicit regulatory modules

Gene regulatory networks are a popular tool for modelling important biological phenomena, such as cell differentiation or oncogenesis. Efficient identification of the causal connections between genes, their products and regulating transcription factors, is key to understanding how defects in their function may trigger diseases. Modelling approaches should keep up with the ever more detailed descriptions of the biological phenomena at play, as provided by new experimental findings and technical improvements. In recent years, we have seen great improvements in mapping of specific binding sites of many transcription factors to distinct regulatory regions. Recent gene regulatory network models use binding measurements; but usually only to define gene-to-gene interactions, ignoring regulatory module structure. Moreover, current huge amount of transcriptomic data, and exploration of all possible cis-regulatory arrangements which can lead to the same transcriptomic response, makes manual model building both tedious and time-consuming. In our paper, we propose a method to specify possible regulatory connections in a given Boolean network, based on transcription factor binding evidence. This is implemented by an algorithm which expands a regular Boolean network model into a "cis-regulatory" Boolean network model. This expanded model explicitly defines regulatory regions as additional nodes in the network, and adds new, valuable biological insights to the system dynamics. The expanded model can automatically be compared with expression data. And, for each node, a regulatory function, consistent with the experimental data, can be found. The resulting models are usually more constrained (by biologically-motivated metadata), and can then be inspected in in silico simulations. The fully automated method for model identification has been implemented in Python, and the expansion algorithm in R. The method resorts to the Z3 Satisfiability Modulo Theories (SMT) solver, and is similar to the RE:IN application (Yordanov et al., 2016). It is available on https://github.com/regulomics/expansion-network.

Revision of Boolean Models of Regulatory Networks Using Stable State Observations

Models of biological regulatory networks are essential to understand cellular processes. However, the definition of such models is still mostly manually performed, and consequently prone to error. Moreover, as new experimental data are acquired, models need to be revised and updated. Here, we propose a model revision procedure and associated tool, capable of providing the set of minimal repairs to render a model consistent with a set of experimental observations. We consider four possible repair operations, using a lexicographic optimization criterion, giving preference to function repairs over topological ones. Also, we consider observations at stable state discarding the model dynamics. In this article, we extend our previous work to tackle the problem of repairing nodes with multiple reasons of inconsistency. We evaluate our tool on five publicly available logical models. We perform random changes considering several parameter configurations to assess the tool repairing capabilities. Whenever a model is repaired under the time limit, the tool successfully produces the optimal solutions to repair the model. Instances were generated without the previous limitation to validate this extended approach.

Reverse engineering directed gene regulatory networks from transcriptomics and proteomics data of biomining bacterial communities with approximate Bayesian computation and steady-state signalling simulations

BACKGROUND

Network inference is an important aim of systems biology. It enables the transformation of OMICs datasets into biological knowledge. It consists of reverse engineering gene regulatory networks from OMICs data, such as RNAseq or mass spectrometry-based proteomics data, through computational methods. This approach allows to identify signalling pathways involved in specific biological functions. The ability to infer causality in gene regulatory networks, in addition to correlation, is crucial for several modelling approaches and allows targeted control in biotechnology applications.

METHODS

We performed simulations according to the approximate Bayesian computation method, where the core model consisted of a steady-state simulation algorithm used to study gene regulatory networks in systems for which a limited level of details is available. The simulations outcome was compared to experimentally measured transcriptomics and proteomics data through approximate Bayesian computation.

RESULTS

The structure of small gene regulatory networks responsible for the regulation of biological functions involved in biomining were inferred from multi OMICs data of mixed bacterial cultures. Several causal inter- and intraspecies interactions were inferred between genes coding for proteins involved in the biomining process, such as heavy metal transport, DNA damage, replication and repair, and membrane biogenesis. The method also provided indications for the role of several uncharacterized proteins by the inferred connection in their network context.

CONCLUSIONS

The combination of fast algorithms with high-performance computing allowed the simulation of a multitude of gene regulatory networks and their comparison to experimentally measured OMICs data through approximate Bayesian computation, enabling the probabilistic inference of causality in gene regulatory networks of a multispecies bacterial system involved in biomining without need of single-cell or multiple perturbation experiments. This information can be used to influence biological functions and control specific processes in biotechnology applications.

AEON: Attractor Bifurcation Analysis of Parametrised Boolean Networks

Boolean networks (BNs) provide an effective modelling tool for various phenomena from science and engineering. Any long-term behaviour of a BN eventually converges to a so-called attractor. Depending on various logical parameters, the structure and quality of attractors can undergo a significant change, known as a bifurcation. We present a tool for analysing bifurcations in asynchronous parametrised Boolean networks. To fight the state-space and parameter-space explosion problem the tool uses a parallel semi-symbolic algorithm.

Control of Intracellular Molecular Networks Using Algebraic Methods

Many problems in biology and medicine have a control component. Often, the goal might be to modify intracellular networks, such as gene regulatory networks or signaling networks, in order for cells to achieve a certain phenotype, what happens in cancer. If the network is represented by a mathematical model for which mathematical control approaches are available, such as systems of ordinary differential equations, then this problem might be solved systematically. Such approaches are available for some other model types, such as Boolean networks, where structure-based approaches have been developed, as well as stable motif techniques. However, increasingly many published discrete models are mixed-state or multistate, that is, some or all variables have more than two states, and thus the development of control strategies for multistate networks is needed. This paper presents a control approach broadly applicable to general multistate models based on encoding them as polynomial dynamical systems over a finite algebraic state set, and using computational algebra for finding appropriate intervention strategies. To demonstrate the feasibility and applicability of this method, we apply it to a recently developed multistate intracellular model of E2F-mediated bladder cancerous growth and to a model linking intracellular iron metabolism and oncogenic pathways. The control strategies identified for these published models are novel in some cases and represent new hypotheses, or are supported by the literature in others as potential drug targets. Our Macaulay2 scripts to find control strategies are publicly available through GitHub at https://github.com/luissv7/multistatepdscontrol.

A feedback loop of conditionally stable circuits drives the cell cycle from checkpoint to checkpoint

We perform logic-based network analysis on a model of the mammalian cell cycle. This model is composed of a Restriction Switch driving cell cycle commitment and a Phase Switch driving mitotic entry and exit. By generalizing the concept of stable motif, i.e., a self-sustaining positive feedback loop that maintains an associated state, we introduce the concept of a conditionally stable motif, the stability of which is contingent on external conditions. We show that the stable motifs of the Phase Switch are contingent on the state of three nodes through which it receives input from the rest of the network. Biologically, these conditions correspond to cell cycle checkpoints. Holding these nodes locked (akin to a checkpoint-free cell) transforms the Phase Switch into an autonomous oscillator that robustly toggles through the cell cycle phases G1, G2 and mitosis. The conditionally stable motifs of the Phase Switch Oscillator are organized into an ordered sequence, such that they serially stabilize each other but also cause their own destabilization. Along the way they channel the dynamics of the module onto a narrow path in state space, lending robustness to the oscillation. Self-destabilizing conditionally stable motifs suggest a general negative feedback mechanism leading to sustained oscillations.

From Discrete to Continuous Modeling of Lymphocyte Development and Plasticity in Chronic Diseases

The molecular events leading to differentiation, development, and plasticity of lymphoid cells have been subject of intense research due to their key roles in multiple pathologies, such as lymphoproliferative disorders, tumor growth maintenance and chronic diseases. The emergent roles of lymphoid cells and the use of high-throughput technologies have led to an extensive accumulation of experimental data allowing the reconstruction of gene regulatory networks (GRN) by integrating biochemical signals provided by the microenvironment with transcriptional modules of lineage-specific genes. Computational modeling of GRN has been useful for the identification of molecular switches involved in lymphoid specification, prediction of microenvironment-dependent cell plasticity, and analyses of signaling events occurring downstream the activation of antigen recognition receptors. Among most common modeling strategies to analyze the dynamical behavior of GRN, discrete dynamic models are widely used for their capacity to capture molecular interactions when a limited knowledge of kinetic parameters is present. However, they are less powerful when modeling complex systems sensitive to biochemical gradients. To compensate it, discrete models may be transformed into regulatory networks that includes state variables and parameters varying within a continuous range. This approach is based on a system of differential equations dynamics with regulatory interactions described by fuzzy logic propositions. Here, we discuss the applicability of this method on modeling of development and plasticity processes of adaptive lymphocytes, and its potential implications in the study of pathological landscapes associated to chronic diseases.

Dynamics of gene regulatory networks and their dependence on network topology and quantitative parameters - the case of phage λ

BACKGROUND

Gene regulatory networks can be modelled in various ways depending on the level of detail required and biological questions addressed. One of the earliest formalisms used for modeling is a Boolean network, although these models cannot describe most temporal aspects of a biological system. Differential equation models have also been used to model gene regulatory networks, but these frameworks tend to be too detailed for large models and many quantitative parameters might not be deducible in practice. Hybrid models bridge the gap between these two model classes - these are useful when concentration changes are important while the information about precise concentrations and binding site affinities is partial.

RESULTS

In this paper we study the stable behaviours of phage λ via a hybrid system based model. We identify wild type and mutant behaviours that arise for various orderings of binding site affinities. We propose experiments for detecting these behaviours: we suggest several ways of altering binding affinities with either mutations or genome rearrangements to achieve modified behaviours. The feasibility of these experiments is assessed. The interplay between the qualitative aspects of a network, e.g. network topology, and quantitative parameters, e.g. growth and degradation rates of proteins, is demonstrated. We also provide a software for exploring all feasible states of a hybrid system model and identifying all attractors.

CONCLUSIONS

The behaviours of phage λ are determined mainly by the topology of this network and by the mutual order of binding affinities. Exact affinities and growth and degradation rates of proteins fine tune the system. We show that only two stable behaviours are possible for phage λ if the main constraints of λ switch are preserved - these behaviours correspond to lysis and lysogeny. We identify several variants of both lysis and lysogeny - one wild type and one modified behaviour for each. We elucidate the necessary constraints for binding site affinities to achieve both wild type lysis and lysogeny. Our software is applicable to a wide range of biological models described as a hybrid system.

A Boolean network control algorithm guided by forward dynamic programming

Control problem in a biological system is the problem of finding an interventional policy for changing the state of the biological system from an undesirable state, e.g. disease, into a desirable healthy state. Boolean networks are utilized as a mathematical model for gene regulatory networks. This paper provides an algorithm to solve the control problem in Boolean networks. The proposed algorithm is implemented and applied on two biological systems: T-cell receptor network and Drosophila melanogaster network. Results show that the proposed algorithm works faster in solving the control problem over these networks, while having similar accuracy, in comparison to previous exact methods. Source code and a simple web service of the proposed algorithm is available at http://goliaei.ir/net-control/www/.

Identifying (un)controllable dynamical behavior in complex networks

We present a technique applicable in any dynamical framework to identify control-robust subsets of an interacting system. These robust subsystems, which we call stable modules, are characterized by constraints on the variables that make up the subsystem. They are robust in the sense that if the defining constraints are satisfied at a given time, they remain satisfied for all later times, regardless of what happens in the rest of the system, and can only be broken if the constrained variables are externally manipulated. We identify stable modules as graph structures in an expanded network, which represents causal links between variable constraints. A stable module represents a system "decision point", or trap subspace. Using the expanded network, small stable modules can be composed sequentially to form larger stable modules that describe dynamics on the system level. Collections of large, mutually exclusive stable modules describe the system's repertoire of long-term behaviors. We implement this technique in a broad class of dynamical systems and illustrate its practical utility via examples and algorithmic analysis of two published biological network models. In the segment polarity gene network of Drosophila melanogaster, we obtain a state-space visualization that reproduces by novel means the four possible cell fates and predicts the outcome of cell transplant experiments. In the T-cell signaling network, we identify six signaling elements that determine the high-signal response and show that control of an element connected to them cannot disrupt this response.

Integrative workflows for network analysis

Due to genetic heterogeneity across patients, the identification of effective disease signatures and therapeutic targets is challenging. Addressing this challenge, we have previously developed a network-based approach, which integrates heterogeneous sources of biological information to identify disease specific core-regulatory networks. In particular, our workflow uses a multi-objective optimization function to calculate a ranking score for network components (e.g. feedback/feedforward loops) based on network properties, biomedical and high-throughput expression data. High ranked network components are merged to identify the core-regulatory network(s) that is then subjected to dynamical analysis using stimulus–response and in silico perturbation experiments for the identification of disease gene signatures and therapeutic targets. In a case study, we implemented our workflow to identify bladder and breast cancer specific core-regulatory networks underlying epithelial–mesenchymal transition from the E2F1 molecular interaction map.

In this study, we review our workflow and described how it has developed over time to understand the mechanisms underlying disease progression and prediction of signatures for clinical decision making.

Reduction of Qualitative Models of Biological Networks for Transient Dynamics Analysis

Qualitative models of dynamics of signalling pathways and gene regulatory networks allow for the capturing of temporal properties of biological networks while requiring few parameters. However, these discrete models typically suffer from the so-called state space explosion problem which makes the formal assessment of their potential behaviors very challenging. In this paper, we describe a method to reduce a qualitative model for enhancing the tractability of analysis of transient reachability properties. The reduction does not change the dimension of the model, but instead limits its degree of freedom, therefore reducing the set of states and transitions to consider. We rely on a transition-centered specification of qualitative models by the mean of automata networks. Our framework encompasses the usual asynchronous Boolean and multi-valued network, as well as 1-bounded Petri nets. Applied to different large-scale biological networks from the litterature, we show that the reduction can lead to a drastic improvement for the scalability of verification methods.

P_UNSAT approach of attractor calculation for Boolean gene regulatory networks

Boolean network models provide an efficient way for studying gene regulatory networks. The main dynamics of a Boolean network is determined by its attractors. Attractor calculation plays a key role for analyzing Boolean gene regulatory networks. An approach of attractor calculation was proposed in this study, which combined the predecessor approach and the logic unsatisfiability approach to accelerate attractor calculation. The proposed algorithm is effective to calculate all attractors for large-scale Boolean gene regulatory networks even the networks with a relatively large average degree.

Simulating heterogeneous populations using Boolean models

Background

Certain biological processes, such as the development of cancer and immune activation, can be controlled by rare cellular events that are difficult to capture computationally through simulations of individual cells. Information about such rare events can be gleaned from an attractor analysis, for which a variety of methods exist (in particular for Boolean models). However, explicitly simulating a defined mixed population of cells in a way that tracks even the rarest subpopulations remains an open challenge.

Results

Here we show that when cellular states are described using a Boolean network model, one can exactly simulate the dynamics of non-interacting, highly heterogeneous populations directly, without having to model the various subpopulations. This strategy captures even the rarest outcomes of the model with no sampling error. Our method can incorporate heterogeneity in both cell state and, by augmenting the model, the underlying rules of the network as well (e.g., introducing loss-of-function genetic alterations). We demonstrate our method by using it to simulate a heterogeneous population of Boolean networks modeling the T-cell receptor, spanning ∼ 10²⁰ distinct cellular states and mutational profiles.

Conclusions

We have developed a method for using Boolean models to perform a population-level simulation, in which the population consists of non-interacting individuals existing in different states. This approach can be used even when there are far too many distinct subpopulations to model individually.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0591-9) contains supplementary material, which is available to authorized users.

Target Control in Logical Models Using the Domain of Influence of Nodes

Dynamical models of biomolecular networks are successfully used to understand the mechanisms underlying complex diseases and to design therapeutic strategies. Network control and its special case of target control, is a promising avenue toward developing disease therapies. In target control it is assumed that a small subset of nodes is most relevant to the system's state and the goal is to drive the target nodes into their desired states. An example of target control would be driving a cell to commit to apoptosis (programmed cell death). From the experimental perspective, gene knockout, pharmacological inhibition of proteins, and providing sustained external signals are among practical intervention techniques. We identify methodologies to use the stabilizing effect of sustained interventions for target control in Boolean network models of biomolecular networks. Specifically, we define the domain of influence (DOI) of a node (in a certain state) to be the nodes (and their corresponding states) that will be ultimately stabilized by the sustained state of this node regardless of the initial state of the system. We also define the related concept of the logical domain of influence (LDOI) of a node, and develop an algorithm for its identification using an auxiliary network that incorporates the regulatory logic. This way a solution to the target control problem is a set of nodes whose DOI can cover the desired target node states. We perform greedy randomized adaptive search in node state space to find such solutions. We apply our strategy to in silico biological network models of real systems to demonstrate its effectiveness.

Identifying a Probabilistic Boolean Threshold Network From Samples

This paper studies the problem of exactly identifying the structure of a probabilistic Boolean network (PBN) from a given set of samples, where PBNs are probabilistic extensions of Boolean networks. Cheng et al. studied the problem while focusing on PBNs consisting of pairs of AND/OR functions. This paper considers PBNs consisting of Boolean threshold functions while focusing on those threshold functions that have unit coefficients. The treatment of Boolean threshold functions, and triplets and -tuplets of such functions, necessitates a deepening of the theoretical analyses. It is shown that wide classes of PBNs with such threshold functions can be exactly identified from samples under reasonable constraints, which include: 1) PBNs in which any number of threshold functions can be assigned provided that all have the same number of input variables and 2) PBNs consisting of pairs of threshold functions with different numbers of input variables. It is also shown that the problem of deciding the equivalence of two Boolean threshold functions is solvable in pseudopolynomial time but remains co-NP complete.

Designing optimal experiments to discriminate interaction graph models

Modern methods for the inference of cellular networks from experimental data often express nondeterminism through an ensemble of candidate models. To discriminate among these candidates new experiments need to be carried out. Theoretically, the number of possible experiments is exponential in the number of possible perturbations. In praxis, experiments are expensive and there exist several limiting constraints. Limiting factors exist on the combinations of perturbations that are technically possible, which components can be measured, and on the number of affordable experiments. Further, not all experiments are equally well suited to discriminate model candidates. The goal of optimal experiment design is to determine those experiments that discriminate most of the candidates while minimizing the costs. We present an approach for experiment planning with interaction graph models and sign consistency methods. This new approach can be used in combination with methods for network inference and consistency checking. We applied our method to study the Erythropoietin signal transduction in human kidney cells HEK293. We first used simulated experiment data from an ODE model to demonstrate in silico that our experimental design results in the inference of the gold standard model. Finally, we used the approach to plan in vivo experiments that discriminate model candidates for the Erythropoietin signal transduction in this cell line.

Boolean network modeling in systems pharmacology

Quantitative systems pharmacology (QSP) is an emerging discipline that aims to discover how drugs modulate the dynamics of biological components in molecular and cellular networks and the impact of those perturbations on human pathophysiology. The integration of systems-based experimental and computational approaches is required to facilitate the advancement of this field. QSP models typically consist of a series of ordinary differential equations (ODE). However, this mathematical framework requires extensive knowledge of parameters pertaining to biological processes, which is often unavailable. An alternative framework that does not require knowledge of system-specific parameters, such as Boolean network modeling, could serve as an initial foundation prior to the development of an ODE-based model. Boolean network models have been shown to efficiently describe, in a qualitative manner, the complex behavior of signal transduction and gene/protein regulatory processes. In addition to providing a starting point prior to quantitative modeling, Boolean network models can also be utilized to discover novel therapeutic targets and combinatorial treatment strategies. Identifying drug targets using a network-based approach could supplement current drug discovery methodologies and help to fill the innovation gap across the pharmaceutical industry. In this review, we discuss the process of developing Boolean network models and the various analyses that can be performed to identify novel drug targets and combinatorial approaches. An example for each of these analyses is provided using a previously developed Boolean network of signaling pathways in multiple myeloma. Selected examples of Boolean network models of human (patho-)physiological systems are also reviewed in brief.

A network modeling approach to elucidate drug resistance mechanisms and predict combinatorial drug treatments in breast cancer

Background

Mechanistic models of within-cell signal transduction networks can explain how these networks integrate internal and external inputs to give rise to the appropriate cellular response. These models can be fruitfully used in cancer cells, whose aberrant decision-making regarding their survival or death, proliferation or quiescence can be connected to errors in the state of nodes or edges of the signal transduction network.

Results

Here we present a comprehensive network, and discrete dynamic model, of signal transduction in ER+ breast cancer based on the literature of ER+, HER2+, and PIK3CA-mutant breast cancers. The network model recapitulates known resistance mechanisms to PI3K inhibitors and suggests other possibilities for resistance. The model also reveals known and novel combinatorial interventions that are more effective than PI3K inhibition alone.

Conclusions

The use of a logic-based, discrete dynamic model enables the identification of results that are mainly due to the organization of the signaling network, and those that also depend on the kinetics of individual events. Network-based models such as this will play an increasing role in the rational design of high-order therapeutic combinations.

Electronic supplementary material

The online version of this article (10.1186/s41236-017-0007-6) contains supplementary material, which is available to authorized users.

Insight into glucocorticoid receptor signalling through interactome model analysis

Glucocorticoid hormones (GCs) are used to treat a variety of diseases because of their potent anti-inflammatory effect and their ability to induce apoptosis in lymphoid malignancies through the glucocorticoid receptor (GR). Despite ongoing research, high glucocorticoid efficacy and widespread usage in medicine, resistance, disease relapse and toxicity remain factors that need addressing. Understanding the mechanisms of glucocorticoid signalling and how resistance may arise is highly important towards improving therapy. To gain insight into this we undertook a systems biology approach, aiming to generate a Boolean model of the glucocorticoid receptor protein interaction network that encapsulates functional relationships between the GR, its target genes or genes that target GR, and the interactions between the genes that interact with the GR. This model named GEB052 consists of 52 nodes representing genes or proteins, the model input (GC) and model outputs (cell death and inflammation), connected by 241 logical interactions of activation or inhibition. 323 changes in the relationships between model constituents following in silico knockouts were uncovered, and steady-state analysis followed by cell-based microarray genome-wide model validation led to an average of 57% correct predictions, which was taken further by assessment of model predictions against patient microarray data. Lastly, semi-quantitative model analysis via microarray data superimposed onto the model with a score flow algorithm has also been performed, which demonstrated significantly higher correct prediction ratios (average of 80%), and the model has been assessed as a predictive clinical tool using published patient microarray data. In summary we present an in silico simulation of the glucocorticoid receptor interaction network, linked to downstream biological processes that can be analysed to uncover relationships between GR and its interactants. Ultimately the model provides a platform for future development both by directing laboratory research and allowing for incorporation of further components, encapsulating more interactions/genes involved in glucocorticoid receptor signalling.

Here we present modelling of the glucocorticoid receptor (GR) signalling network. The GR is the effector for a class of drugs known as corticosteroids, which are widely used in medicine for their anti-inflammatory effects and ability to induce apoptosis in leukaemic cells. However, side effects, treatment-related toxicity and glucocorticoid resistance remain and therefore increased understanding of the glucocorticoid receptor mechanism of action may improve therapeutic outcomes. The GEB052 model presented herein has been used to generate predictions for how the network is altered between glucocorticoid-sensitive and glucocorticoid-resistant scenarios, and these predictions have been verified using published gene expression data from established cell lines (for both qualitative and semi-quantitative analysis). The model has also been preliminarily assessed as a predictive clinical tool by correlating model predictions with clinical outcomes of thirteen leukaemia patients. Thus, the GEB052 model demonstrates successful modelling to understand GR function. GEB052 provides accurate predictions and has indicated potential routes through which glucocorticoid resistance may arise. The work presented herein thus demonstrates a proof-of-principle of this modelling approach to furthering GR research, and provides insight into potential mechanisms of corticosteroids resistance.

Maximal aggregation of polynomial dynamical systems

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory.

ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks

BACKGROUND

This paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors.

RESULTS

We present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature.

CONCLUSION

The originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.

Unraveling a tumor type-specific regulatory core underlying E2F1-mediated epithelial-mesenchymal transition to predict receptor protein signatures

Cancer is a disease of subverted regulatory pathways. In this paper, we reconstruct the regulatory network around E2F, a family of transcription factors whose deregulation has been associated to cancer progression, chemoresistance, invasiveness, and metastasis. We integrate gene expression profiles of cancer cell lines from two E2F1-driven highly aggressive bladder and breast tumors, and use network analysis methods to identify the tumor type-specific core of the network. By combining logic-based network modeling, in vitro experimentation, and gene expression profiles from patient cohorts displaying tumor aggressiveness, we identify and experimentally validate distinctive, tumor type-specific signatures of receptor proteins associated to epithelial-mesenchymal transition in bladder and breast cancer. Our integrative network-based methodology, exemplified in the case of E2F1-induced aggressive tumors, has the potential to support the design of cohort- as well as tumor type-specific treatments and ultimately, to fight metastasis and therapy resistance.Deregulation of E2F family transcription factors is associated with cancer progression and metastasis. Here, the authors construct a map of the regulatory network around the E2F family, and using gene expression profiles, identify tumour type-specific regulatory cores and receptor expression signatures associated with epithelial-mesenchymal transition in bladder and breast cancer.

Logic Modeling in Quantitative Systems Pharmacology

Here we present logic modeling as an approach to understand deregulation of signal transduction in disease and to characterize a drug's mode of action. We discuss how to build a logic model from the literature and experimental data and how to analyze the resulting model to obtain insights of relevance for systems pharmacology. Our workflow uses the free tools OmniPath (network reconstruction from the literature), CellNOpt (model fit to experimental data), MaBoSS (model analysis), and Cytoscape (visualization).

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.

Simulation of the dynamics of primary immunodeficiencies in CD4+ T-cells

Primary immunodeficiencies (PIDs) form a large and heterogeneous group of mainly rare disorders that affect the immune system. T-cell deficiencies account for about one-tenth of PIDs, most of them being monogenic. Apart from genetic and clinical information, lots of other data are available for PID proteins and genes, including functions and interactions. Thus, it is possible to perform systems biology studies on the effects of PIDs on T-cell physiology and response. To achieve this, we reconstructed a T-cell network model based on literature mining and TPPIN, a previously published core T-cell network, and performed semi-quantitative dynamic network simulations on both normal and T-cell PID failure modes. The results for several loss-of-function PID simulations correspond to results of previously reported molecular studies. The simulations for TCR PTPRC, LCK, ZAP70 and ITK indicate profound changes to numerous proteins in the network. Significant effects were observed also in the BCL10, CARD11, MALT1, NEMO, IKKB and MAP3K14 simulations. No major effects were observed for PIDs that are caused by constitutively active proteins. The T-cell model facilitates the understanding of the underlying dynamics of PID disease processes. The approach confirms previous knowledge about T-cell signaling network and indicates several new important proteins that may be of interest when developing novel diagnosis and therapies to treat immunological defects.

Protein abundance of AKT and ERK pathway components governs cell type-specific regulation of proliferation

Signaling through the AKT and ERK pathways controls cell proliferation. However, the integrated regulation of this multistep process, involving signal processing, cell growth and cell cycle progression, is poorly understood. Here, we study different hematopoietic cell types, in which AKT and ERK signaling is triggered by erythropoietin (Epo). Although these cell types share the molecular network topology for pro‐proliferative Epo signaling, they exhibit distinct proliferative responses. Iterating quantitative experiments and mathematical modeling, we identify two molecular sources for cell type‐specific proliferation. First, cell type‐specific protein abundance patterns cause differential signal flow along the AKT and ERK pathways. Second, downstream regulators of both pathways have differential effects on proliferation, suggesting that protein synthesis is rate‐limiting for faster cycling cells while slower cell cycles are controlled at the G1‐S progression. The integrated mathematical model of Epo‐driven proliferation explains cell type‐specific effects of targeted AKT and ERK inhibitors and faithfully predicts, based on the protein abundance, anti‐proliferative effects of inhibitors in primary human erythroid progenitor cells. Our findings suggest that the effectiveness of targeted cancer therapy might become predictable from protein abundance.

COMPUTATIONAL METHODS FOR ASYNCHRONOUS BASINS

For a Boolean network we consider asynchronous updates and define the exclusive asynchronous basin of attraction for any steady state or cyclic attractor. An algorithm based on commutative algebra is presented to compute the exclusive basin. Finally its use for targeting desirable attractors by selective intervention on network nodes is illustrated with two examples, one cell signalling network and one sensor network measuring human mobility.

An Algorithm for Finding the Singleton Attractors and Pre-Images in Strong-Inhibition Boolean Networks

The detection of the singleton attractors is of great significance for the systematic study of genetic regulatory network. In this paper, we design an algorithm to compute the singleton attractors and pre-images of the strong-inhibition Boolean networks which is a biophysically plausible gene model. Our algorithm can not only identify accurately the singleton attractors, but also find easily the pre-images of the network. Based on extensive computational experiments, we show that the computational time of the algorithm is proportional to the number of the singleton attractors, which indicates the algorithm has much advantage in finding the singleton attractors for the networks with high average degree and less inhibitory interactions. Our algorithm may shed light on understanding the function and structure of the strong-inhibition Boolean networks.

MUFINS: multi-formalism interaction network simulator

Systems Biology has established numerous approaches for mechanistic modeling of molecular networks in the cell and a legacy of models. The current frontier is the integration of models expressed in different formalisms to address the multi-scale biological system organization challenge. We present MUFINS (MUlti-Formalism Interaction Network Simulator) software, implementing a unique set of approaches for multi-formalism simulation of interaction networks. We extend the constraint-based modeling (CBM) framework by incorporation of linear inhibition constraints, enabling for the first time linear modeling of networks simultaneously describing gene regulation, signaling and whole-cell metabolism at steady state. We present a use case where a logical hypergraph model of a regulatory network is expressed by linear constraints and integrated with a Genome-Scale Metabolic Network (GSMN) of mouse macrophage. We experimentally validate predictions, demonstrating application of our software in an iterative cycle of hypothesis generation, validation and model refinement. MUFINS incorporates an extended version of our Quasi-Steady State Petri Net approach to integrate dynamic models with CBM, which we demonstrate through a dynamic model of cortisol signaling integrated with the human Recon2 GSMN and a model of nutrient dynamics in physiological compartments. Finally, we implement a number of methods for deriving metabolic states from ~omics data, including our new variant of the iMAT congruency approach. We compare our approach with iMAT through the analysis of 262 individual tumor transcriptomes, recovering features of metabolic reprogramming in cancer. The software provides graphics user interface with network visualization, which facilitates use by researchers who are not experienced in coding and mathematical modeling environments.

Model-Based Characterization of Inflammatory Gene Expression Patterns of Activated Macrophages

Macrophages are cells with remarkable plasticity. They integrate signals from their microenvironment leading to context-dependent polarization into classically (M1) or alternatively (M2) activated macrophages, representing two extremes of a broad spectrum of divergent phenotypes. Thereby, macrophages deliver protective and pro-regenerative signals towards injured tissue but, depending on the eliciting damage, may also be responsible for the generation and aggravation of tissue injury. Although incompletely understood, there is emerging evidence that macrophage polarization is critical for these antagonistic roles. To identify activation-specific expression patterns of chemokines and cytokines that may confer these distinct effects a systems biology approach was applied. A comprehensive literature-based Boolean model was developed to describe the M1 (LPS-activated) and M2 (IL-4/13-activated) polarization types. The model was validated using high-throughput transcript expression data from murine bone marrow derived macrophages. By dynamic modeling of gene expression, the chronology of pathway activation and autocrine signaling was estimated. Our results provide a deepened understanding of the physiological balance leading to M1/M2 activation, indicating the relevance of co-regulatory signals at the level of Akt1 or Akt2 that may be important for directing macrophage polarization.

Macrophages are essential cells of the immune system and indispensable for a defense against bacterial infection. They reside as resting, immune modulatory cells in several tissues of the human body where they continuously sense inputs from their local environment. They react to stimuli such as toxins, injury or bacterial products in a process termed macrophage activation or polarization. For example, the bacterial component lipopolysaccharide induces so-called classical activation of macrophages into the M1 phenotype that secretes a number of inflammatory cytokines and chemokines leading to killing of bacteria and resolution of inflammation. Another prominent phenotype of macrophages is the M2 polarization state that is associated with wound healing and tissue regeneration. Unbalanced activation of macrophages is implicated in a number of diseases. An improved knowledge and extensive characterization of these macrophages as well as the factors determining their phenotypes will improve the understanding of the role of macrophages in disease progression.

Node-independent elementary signaling modes: A measure of redundancy in Boolean signaling transduction networks

The redundancy of a system denotes the amount of duplicate components or mechanisms in it. For a network, especially one in which mass or information is being transferred from an origin to a destination, redundancy is related to the robustness of the system. Existing network measures of redundancy rely on local connectivity (e.g. clustering coefficients) or the existence of multiple paths. As in many systems there are functional dependencies between components and paths, a measure that not only characterizes the topology of a network, but also takes into account these functional dependencies, becomes most desirable.

We propose a network redundancy measure in a prototypical model that contains functionally dependent directed paths: a Boolean model of a signal transduction network. The functional dependencies are made explicit by using an expanded network and the concept of elementary signaling modes (ESMs). We define the redundancy of a Boolean signal transduction network as the maximum number of node-independent ESMs and develop a methodology for identifying all maximal node-independent ESM combinations. We apply our measure to a number of signal transduction network models and show that it successfully distills known properties of the systems and offers new functional insights. The concept can be easily extended to similar related forms, e.g. edge-independent ESMs.

Temporal-logic analysis of microglial phenotypic conversion with exposure to amyloid-β

Alzheimer Disease (AD) remains a leading killer with no adequate treatment. Ongoing research increasingly implicates the brain's immune system as a critical contributor to AD pathogenesis, but the complexity of the immune contribution poses a barrier to understanding. Here I use temporal logic to analyze a computational specification of the immune component of AD. Temporal logic is an extension of logic to propositions expressed in terms of time. It has traditionally been used to analyze computational specifications of complex engineered systems but applications to complex biological systems are now appearing. The inflammatory component of AD involves the responses of microglia to the peptide amyloid-β (Aβ), which is an inflammatory stimulus and a likely causative AD agent. Temporal-logic analysis of the model provides explanations for the puzzling findings that Aβ induces an anti-inflammatory and well as a pro-inflammatory response, and that Aβ is phagocytized by microglia in young but not in old animals. To potentially explain the first puzzle, the model suggests that interferon-γ acts as an "autocrine bridge" over which an Aβ-induced increase in pro-inflammatory cytokines leads to an increase in anti-inflammatory mediators also. To potentially explain the second puzzle, the model identifies a potential instability in signaling via insulin-like growth factor 1 that could explain the failure of old microglia to phagocytize Aβ. The model predicts that augmentation of insulin-like growth factor 1 signaling, and activation of protein kinase C in particular, could move old microglia from a neurotoxic back toward a more neuroprotective and phagocytic phenotype.

CABeRNET: a Cytoscape app for augmented Boolean models of gene regulatory NETworks

BACKGROUND

Dynamical models of gene regulatory networks (GRNs) are highly effective in describing complex biological phenomena and processes, such as cell differentiation and cancer development. Yet, the topological and functional characterization of real GRNs is often still partial and an exhaustive picture of their functioning is missing.

RESULTS

We here introduce CABERNET, a Cytoscape app for the generation, simulation and analysis of Boolean models of GRNs, specifically focused on their augmentation when a only partial topological and functional characterization of the network is available. By generating large ensembles of networks in which user-defined entities and relations are added to the original core, CABERNET allows to formulate hypotheses on the missing portions of real networks, as well to investigate their generic properties, in the spirit of complexity science.

CONCLUSIONS

CABERNET offers a series of innovative simulation and modeling functions and tools, including (but not being limited to) the dynamical characterization of the gene activation patterns ruling cell types and differentiation fates, and sophisticated robustness assessments, as in the case of gene knockouts. The integration within the widely used Cytoscape framework for the visualization and analysis of biological networks, makes CABERNET a new essential instrument for both the bioinformatician and the computational biologist, as well as a computational support for the experimentalist. An example application concerning the analysis of an augmented T-helper cell GRN is provided.