Logic-based models in systems biology: a predictive and parameter-free network analysis method

From Data to Cure: A Comprehensive Exploration of Multi-omics Data Analysis for Targeted Therapies

In the dynamic landscape of targeted therapeutics, drug discovery has pivoted towards understanding underlying disease mechanisms, placing a strong emphasis on molecular perturbations and target identification. This paradigm shift, crucial for drug discovery, is underpinned by big data, a transformative force in the current era. Omics data, characterized by its heterogeneity and enormity, has ushered biological and biomedical research into the big data domain. Acknowledging the significance of integrating diverse omics data strata, known as multi-omics studies, researchers delve into the intricate interrelationships among various omics layers. This review navigates the expansive omics landscape, showcasing tailored assays for each molecular layer through genomes to metabolomes. The sheer volume of data generated necessitates sophisticated informatics techniques, with machine-learning (ML) algorithms emerging as robust tools. These datasets not only refine disease classification but also enhance diagnostics and foster the development of targeted therapeutic strategies. Through the integration of high-throughput data, the review focuses on targeting and modeling multiple disease-regulated networks, validating interactions with multiple targets, and enhancing therapeutic potential using network pharmacology approaches. Ultimately, this exploration aims to illuminate the transformative impact of multi-omics in the big data era, shaping the future of biological research.

COSMIC-dFBA: A novel multi-scale hybrid framework for bioprocess modeling

Metabolism governs cell performance in biomanufacturing, as it fuels growth and productivity. However, even in well-controlled culture systems, metabolism is dynamic, with shifting objectives and resources, thus limiting the predictive capability of mechanistic models for process design and optimization. Here, we present Cellular Objectives and State Modulation In bioreaCtors (COSMIC)-dFBA, a hybrid multi-scale modeling paradigm that accurately predicts cell density, antibody titer, and bioreactor metabolite concentration profiles. Using machine-learning, COSMIC-dFBA decomposes the instantaneous metabolite uptake and secretion rates in a bioreactor into weighted contributions from each cell state (growth or antibody-producing state) and integrates these with a genome-scale metabolic model. A major strength of COSMIC-dFBA is that it can be parameterized with only metabolite concentrations from spent media, although constraining the metabolic model with other omics data can further improve its capabilities. Using COSMIC-dFBA, we can predict the final cell density and antibody titer to within 10% of the measured data, and compared to a standard dFBA model, we found the framework showed a 90% and 72% improvement in cell density and antibody titer prediction, respectively. Thus, we demonstrate our hybrid modeling framework effectively captures cellular metabolism and expands the applicability of dFBA to model the dynamic conditions in a bioreactor.

Large-scale computational modelling of the M1 and M2 synovial macrophages in rheumatoid arthritis

Macrophages play an essential role in rheumatoid arthritis. Depending on their phenotype (M1 or M2), they can play a role in the initiation or resolution of inflammation. The M1/M2 ratio in rheumatoid arthritis is higher than in healthy controls. Despite this, no treatment targeting specifically macrophages is currently used in clinics. Thus, devising strategies to selectively deplete proinflammatory macrophages and promote anti-inflammatory macrophages could be a promising therapeutic approach. State-of-the-art molecular interaction maps of M1 and M2 macrophages in rheumatoid arthritis are available and represent a dense source of knowledge; however, these maps remain limited by their static nature. Discrete dynamic modelling can be employed to study the emergent behaviours of these systems. Nevertheless, handling such large-scale models is challenging. Due to their massive size, it is computationally demanding to identify biologically relevant states in a cell- and disease-specific context. In this work, we developed an efficient computational framework that converts molecular interaction maps into Boolean models using the CaSQ tool. Next, we used a newly developed version of the BMA tool deployed to a high-performance computing cluster to identify the models' steady states. The identified attractors are then validated using gene expression data sets and prior knowledge. We successfully applied our framework to generate and calibrate the M1 and M2 macrophage Boolean models for rheumatoid arthritis. Using KO simulations, we identified NFkB, JAK1/JAK2, and ERK1/Notch1 as potential targets that could selectively suppress proinflammatory macrophages and GSK3B as a promising target that could promote anti-inflammatory macrophages in rheumatoid arthritis.

Combined mechanistic modeling and machine-learning approaches in systems biology - A systematic literature review

BACKGROUND AND OBJECTIVE

Mechanistic-based Model simulations (MM) are an effective approach commonly employed, for research and learning purposes, to better investigate and understand the inherent behavior of biological systems. Recent advancements in modern technologies and the large availability of omics data allowed the application of Machine Learning (ML) techniques to different research fields, including systems biology. However, the availability of information regarding the analyzed biological context, sufficient experimental data, as well as the degree of computational complexity, represent some of the issues that both MMs and ML techniques could present individually. For this reason, recently, several studies suggest overcoming or significantly reducing these drawbacks by combining the above-mentioned two methods. In the wake of the growing interest in this hybrid analysis approach, with the present review, we want to systematically investigate the studies available in the scientific literature in which both MMs and ML have been combined to explain biological processes at genomics, proteomics, and metabolomics levels, or the behavior of entire cellular populations.

METHODS

Elsevier Scopus®, Clarivate Web of Science™ and National Library of Medicine PubMed® databases were enquired using the queries reported in Table 1, resulting in 350 scientific articles.

RESULTS

Only 14 of the 350 documents returned by the comprehensive search conducted on the three major online databases met our search criteria, i.e. present a hybrid approach consisting of the synergistic combination of MMs and ML to treat a particular aspect of systems biology.

CONCLUSIONS

Despite the recent interest in this methodology, from a careful analysis of the selected papers, it emerged how examples of integration between MMs and ML are already present in systems biology, highlighting the great potential of this hybrid approach to both at micro and macro biological scales.

Statistical control of structural networks with limited interventions to minimize cellular phenotypic diversity represented by point attractors

The underlying genetic networks of cells give rise to diverse behaviors known as phenotypes. Control of this cellular phenotypic diversity (CPD) may reveal key targets that govern differentiation during development or drug resistance in cancer. This work establishes an approach to control CPD that encompasses practical constraints, including model limitations, the number of simultaneous control targets, which targets are viable for control, and the granularity of control. Cellular networks are often limited to the structure of interactions, due to the practical difficulty of modeling interaction dynamics. However, these dynamics are essential to CPD. In response, our statistical control approach infers the CPD directly from the structure of a network, by considering an ensemble average function over all possible Boolean dynamics for each node in the network. These ensemble average functions are combined with an acyclic form of the network to infer the number of point attractors. Our approach is applied to several known biological models and shown to outperform existing approaches. Statistical control of CPD offers a new avenue to contend with systemic processes such as differentiation and cancer, despite practical limitations in the field.

A multiscale mechanistic model of human dendritic cells for in-silico investigation of immune responses and novel therapeutics discovery

Dendritic cells (DCs) are professional antigen-presenting cells (APCs) with the unique ability to mediate inflammatory responses of the immune system. Given the critical role of DCs in shaping immunity, they present an attractive avenue as a therapeutic target to program the immune system and reverse immune disease disorders. To ensure appropriate immune response, DCs utilize intricate and complex molecular and cellular interactions that converge into a seamless phenotype. Computational models open novel frontiers in research by integrating large-scale interaction to interrogate the influence of complex biological behavior across scales. The ability to model large biological networks will likely pave the way to understanding any complex system in more approachable ways. We developed a logical and predictive model of DC function that integrates the heterogeneity of DCs population, APC function, and cell-cell interaction, spanning molecular to population levels. Our logical model consists of 281 components that connect environmental stimuli with various layers of the cell compartments, including the plasma membrane, cytoplasm, and nucleus to represent the dynamic processes within and outside the DC, such as signaling pathways and cell-cell interactions. We also provided three sample use cases to apply the model in the context of studying cell dynamics and disease environments. First, we characterized the DC response to Sars-CoV-2 and influenza co-infection by in-silico experiments and analyzed the activity level of 107 molecules that play a role in this co-infection. The second example presents simulations to predict the crosstalk between DCs and T cells in a cancer microenvironment. Finally, for the third example, we used the Kyoto Encyclopedia of Genes and Genomes enrichment analysis against the model's components to identify 45 diseases and 24 molecular pathways that the DC model can address. This study presents a resource to decode the complex dynamics underlying DC-derived APC communication and provides a platform for researchers to perform in-silico experiments on human DC for vaccine design, drug discovery, and immunotherapies.

BDEtools: A MATLAB Package for Boolean Delay Equation Modeling

Boolean Delay Equations (BDEs) can simulate surprisingly complex behavior, despite their relative simplicity. In addition to steady-state dynamics, BDEs can also generate periodic and quasiperiodic oscillations, m:n frequency locking, and even chaos. Further, the enumerability of Boolean update functions and their compact parametrization means that BDEs can be leveraged to generate low-level descriptions of biological networks, from which more detailed formulations (e.g., differential equation models) can be constructed. However, although several studies have demonstrated the utility of BDE modeling in computational biology, a current barrier to the wider adoption of the BDE approach is the absence of freely available simulation software. In this work, we present BDEtools-an open-source MATLAB package for numerically solving BDE models. After giving a brief introduction to BDE modeling, we describe the package's solver algorithms, together with several utility functions that can be used to provide solver inputs and to process solver outputs. We also demonstrate the functionality of BDEtools by illustrating its application to an established model of a gene regulatory network that controls circadian rhythms. BDEtools makes it straightforward for researchers to quickly build reliable BDE models of biological networks. We hope that its ease of use and free availability will encourage more researchers to explore BDE formulations of their systems of interest. Through the continued use of BDEs by the computational biology community, we will, no doubt, discover their potential applicability to a broader class of biological networks.

Vitamin D and Systems Biology

The biological actions of the vitamin D receptor (VDR) have been investigated intensively for over 100 years and has led to the identification of significant insights into the repertoire of its biological actions. These were initially established to be centered on the regulation of calcium transport in the colon and deposition in bone. Beyond these well-known calcemic roles, other roles have emerged in the regulation of cell differentiation processes and have an impact on metabolism. The purpose of the current review is to consider where applying systems biology (SB) approaches may begin to generate a more precise understanding of where the VDR is, and is not, biologically impactful. Two SB approaches have been developed and begun to reveal insight into VDR biological functions. In a top-down SB approach genome-wide scale data are statistically analyzed, and from which a role for the VDR emerges in terms of being a hub in a biological network. Such approaches have confirmed significant roles, for example, in myeloid differentiation and the control of inflammation and innate immunity. In a bottom-up SB approach, current biological understanding is built into a kinetic model which is then applied to existing biological data to explain the function and identify unknown behavior. To date, this has not been applied to the VDR, but has to the related ERα and identified previously unknown mechanisms of control. One arena where applying top-down and bottom-up SB approaches may be informative is in the setting of prostate cancer health disparities.

Predictive Modelling in Clinical Bioinformatics: Key Concepts for Startups

Clinical bioinformatics is a newly emerging field that applies bioinformatics techniques for facilitating the identification of diseases, discovery of biomarkers, and therapy decision. Mathematical modelling is part of bioinformatics analysis pipelines and a fundamental step to extract clinical insights from genomes, transcriptomes and proteomes of patients. Often, the chosen modelling techniques relies on either statistical, machine learning or deterministic approaches. Research that combines bioinformatics with modelling techniques have been generating innovative biomedical technology, algorithms and models with biotech applications, attracting private investment to develop new business; however, startups that emerge from these technologies have been facing difficulties to implement clinical bioinformatics pipelines, protect their technology and generate profit. In this commentary, we discuss the main concepts that startups should know for enabling a successful application of predictive modelling in clinical bioinformatics. Here we will focus on key modelling concepts, provide some successful examples and briefly discuss the modelling framework choice. We also highlight some aspects to be taken into account for a successful implementation of cost-effective bioinformatics from a business perspective.

Inference of a Boolean Network From Causal Logic Implications

Biological systems contain a large number of molecules that have diverse interactions. A fruitful path to understanding these systems is to represent them with interaction networks, and then describe flow processes in the network with a dynamic model. Boolean modeling, the simplest discrete dynamic modeling framework for biological networks, has proven its value in recapitulating experimental results and making predictions. A first step and major roadblock to the widespread use of Boolean networks in biology is the laborious network inference and construction process. Here we present a streamlined network inference method that combines the discovery of a parsimonious network structure and the identification of Boolean functions that determine the dynamics of the system. This inference method is based on a causal logic analysis method that associates a logic type (sufficient or necessary) to node-pair relationships (whether promoting or inhibitory). We use the causal logic framework to assimilate indirect information obtained from perturbation experiments and infer relationships that have not yet been documented experimentally. We apply this inference method to a well-studied process of hormone signaling in plants, the signaling underlying abscisic acid (ABA)—induced stomatal closure. Applying the causal logic inference method significantly reduces the manual work typically required for network and Boolean model construction. The inferred model agrees with the manually curated model. We also test this method by re-inferring a network representing epithelial to mesenchymal transition based on a subset of the information that was initially used to construct the model. We find that the inference method performs well for various likely scenarios of inference input information. We conclude that our method is an effective approach toward inference of biological networks and can become an efficient step in the iterative process between experiments and computations.

Structure-based approach to identifying small sets of driver nodes in biological networks

In network control theory, driving all the nodes in the Feedback Vertex Set (FVS) by node-state override forces the network into one of its attractors (long-term dynamic behaviors). The FVS is often composed of more nodes than can be realistically manipulated in a system; for example, only up to three nodes can be controlled in intracellular networks, while their FVS may contain more than 10 nodes. Thus, we developed an approach to rank subsets of the FVS on Boolean models of intracellular networks using topological, dynamics-independent measures. We investigated the use of seven topological prediction measures sorted into three categories-centrality measures, propagation measures, and cycle-based measures. Using each measure, every subset was ranked and then evaluated against two dynamics-based metrics that measure the ability of interventions to drive the system toward or away from its attractors: To Control and Away Control. After examining an array of biological networks, we found that the FVS subsets that ranked in the top according to the propagation metrics can most effectively control the network. This result was independently corroborated on a second array of different Boolean models of biological networks. Consequently, overriding the entire FVS is not required to drive a biological network to one of its attractors, and this method provides a way to reliably identify effective FVS subsets without the knowledge of the network dynamics.

Epigenetic forest and flower morphogenesis

This paper studies the epigenetic process that leads to Angiosperms' flower architecture (flowering plants). As a case study, we analyze the flower Arabidopsis thaliana's GRN obtained during cell fate determination in the early stages of the flower's development, which was constructed in a previous work using experimental data. We start by constructing and analyzing the Epigenetic Forest, a discrete representation of Waddington's Epigenetic Landscape, obtained as the transition graph of the discrete dynamical system associated with the GRN. Next, we propose an optimization problem to model morphogenesis by defining a biologically meaningful function that accounts for the work involved in cell specialization. Finally, the problem is solved using a genetic algorithm. The optimal solution found by the algorithm correctly recovers the flower's architecture, as observed in wild type flowers and recovered in other theoretical works. Even though the case study addresses this specific problem, the method is directly applicable to other GRN's with attractors consisting of equilibrium points only and could be extended to the situation where there are periodic attractors.

Inference of regulatory networks through temporally sparse data

A major goal in genomics is to properly capture the complex dynamical behaviors of gene regulatory networks (GRNs). This includes inferring the complex interactions between genes, which can be used for a wide range of genomics analyses, including diagnosis or prognosis of diseases and finding effective treatments for chronic diseases such as cancer. Boolean networks have emerged as a successful class of models for capturing the behavior of GRNs. In most practical settings, inference of GRNs should be achieved through limited and temporally sparse genomics data. A large number of genes in GRNs leads to a large possible topology candidate space, which often cannot be exhaustively searched due to the limitation in computational resources. This paper develops a scalable and efficient topology inference for GRNs using Bayesian optimization and kernel-based methods. Rather than an exhaustive search over possible topologies, the proposed method constructs a Gaussian Process (GP) with a topology-inspired kernel function to account for correlation in the likelihood function. Then, using the posterior distribution of the GP model, the Bayesian optimization efficiently searches for the topology with the highest likelihood value by optimally balancing between exploration and exploitation. The performance of the proposed method is demonstrated through comprehensive numerical experiments using a well-known mammalian cell-cycle network.

Can Systems Biology Advance Clinical Precision Oncology?

Precision oncology is perceived as a way forward to treat individual cancer patients. However, knowing particular cancer mutations is not enough for optimal therapeutic treatment, because cancer genotype-phenotype relationships are nonlinear and dynamic. Systems biology studies the biological processes at the systems' level, using an array of techniques, ranging from statistical methods to network reconstruction and analysis, to mathematical modeling. Its goal is to reconstruct the complex and often counterintuitive dynamic behavior of biological systems and quantitatively predict their responses to environmental perturbations. In this paper, we review the impact of systems biology on precision oncology. We show examples of how the analysis of signal transduction networks allows to dissect resistance to targeted therapies and inform the choice of combinations of targeted drugs based on tumor molecular alterations. Patient-specific biomarkers based on dynamical models of signaling networks can have a greater prognostic value than conventional biomarkers. These examples support systems biology models as valuable tools to advance clinical and translational oncological research.

Unsupervised logic-based mechanism inference for network-driven biological processes

Modern analytical techniques enable researchers to collect data about cellular states, before and after perturbations. These states can be characterized using analytical techniques, but the inference of regulatory interactions that explain and predict changes in these states remains a challenge. Here we present a generalizable, unsupervised approach to generate parameter-free, logic-based models of cellular processes, described by multiple discrete states. Our algorithm employs a Hamming-distance based approach to formulate, test, and identify optimized logic rules that link two states. Our approach comprises two steps. First, a model with no prior knowledge except for the mapping between initial and attractor states is built. We then employ biological constraints to improve model fidelity. Our algorithm automatically recovers the relevant dynamics for the explored models and recapitulates key aspects of the biochemical species concentration dynamics in the original model. We present the advantages and limitations of our work and discuss how our approach could be used to infer logic-based mechanisms of signaling, gene-regulatory, or other input-output processes describable by the Boolean formalism.

Integration of temporal single cell cellular stress response activity with logic-ODE modeling reveals activation of ATF4-CHOP axis as a critical predictor of drug-induced liver injury

Drug-induced liver injury (DILI) is the most prevalent adversity encountered in drug development and clinical settings leading to urgent needs to understand the underlying mechanisms. In this study, we have systematically investigated the dynamics of the activation of cellular stress response pathways and cell death outcomes upon exposure of a panel of liver toxicants using live cell imaging of fluorescent reporter cell lines. We established a comprehensive temporal dynamic response profile of a large set of BAC-GFP HepG2 cell lines representing the following components of stress signaling: i) unfolded protein response (UPR) [ATF4, XBP1, BIP and CHOP]; ii) oxidative stress [NRF2, SRXN1, HMOX1]; iii) DNA damage [P53, P21, BTG2, MDM2]; and iv) NF-κB pathway [A20, ICAM1]. We quantified the single cell GFP expression as a surrogate for endogenous protein expression using live cell imaging over > 60 h upon exposure to 14 DILI compounds at multiple concentrations. Using logic-based ordinary differential equation (Logic-ODE), we modelled the dynamic profiles of the different stress responses and extracted specific descriptors potentially predicting the progressive outcomes. We identified the activation of ATF4-CHOP axis of the UPR as the key pathway showing the highest correlation with cell death upon DILI compound perturbation. Knocking down main components of the UPR provided partial protection from compound-induced cytotoxicity, indicating a complex interplay among UPR components as well as other stress pathways. Our results suggest that a systematic analysis of the temporal dynamics of ATF4-CHOP axis activation can support the identification of DILI risk for new candidate drugs.

Personizing the prediction of future susceptibility to a specific disease

A traceable biomarker is a member of a disease's molecular pathway. A disease may be associated with several molecular pathways. Each different combination of these molecular pathways, to which detected traceable biomarkers belong, may serve as an indicative of the elicitation of the disease at a different time frame in the future. Based on this notion, we introduce a novel methodology for personalizing an individual's degree of future susceptibility to a specific disease. We implemented the methodology in a working system called Susceptibility Degree to a Disease Predictor (SDDP). For a specific disease d, let S be the set of molecular pathways, to which traceable biomarkers detected from most patients of d belong. For the same disease d, let S' be the set of molecular pathways, to which traceable biomarkers detected from a certain individual belong. SDDP is able to infer the subset S'' ⊆{S-S'} of undetected molecular pathways for the individual. Thus, SDDP can infer undetected molecular pathways of a disease for an individual based on few molecular pathways detected from the individual. SDDP can also help in inferring the combination of molecular pathways in the set {S'+S''}, whose traceable biomarkers collectively is an indicative of the disease. SDDP is composed of the following four components: information extractor, interrelationship between molecular pathways modeler, logic inferencer, and risk indicator. The information extractor takes advantage of the exponential increase of biomedical literature to automatically extract the common traceable biomarkers for a specific disease. The interrelationship between molecular pathways modeler models the hierarchical interrelationships between the molecular pathways of the traceable biomarkers. The logic inferencer transforms the hierarchical interrelationships between the molecular pathways into rule-based specifications. It employs the specification rules and the inference rules for predicate logic to infer as many as possible undetected molecular pathways of a disease for an individual. The risk indicator outputs a risk indicator value that reflects the individual's degree of future susceptibility to the disease. We evaluated SDDP by comparing it experimentally with other methods. Results revealed marked improvement.

A practical guide to mechanistic systems modeling in biology using a logic-based approach

Mechanistic computational models enable the study of regulatory mechanisms implicated in various biological processes. These models provide a means to analyze the dynamics of the systems they describe, and to study and interrogate their properties, and provide insights about the emerging behavior of the system in the presence of single or combined perturbations. Aimed at those who are new to computational modeling, we present here a practical hands-on protocol breaking down the process of mechanistic modeling of biological systems in a succession of precise steps. The protocol provides a framework that includes defining the model scope, choosing validation criteria, selecting the appropriate modeling approach, constructing a model and simulating the model. To ensure broad accessibility of the protocol, we use a logical modeling framework, which presents a lower mathematical barrier of entry, and two easy-to-use and popular modeling software tools: Cell Collective and GINsim. The complete modeling workflow is applied to a well-studied and familiar biological process-the lac operon regulatory system. The protocol can be completed by users with little to no prior computational modeling experience approximately within 3 h.

Fuzzy modeling and global optimization to predict novel therapeutic targets in cancer cells

Motivation

The elucidation of dysfunctional cellular processes that can induce the onset of a disease is a challenging issue from both the experimental and computational perspectives. Here we introduce a novel computational method based on the coupling between fuzzy logic modeling and a global optimization algorithm, whose aims are to (1) predict the emergent dynamical behaviors of highly heterogeneous systems in unperturbed and perturbed conditions, regardless of the availability of quantitative parameters, and (2) determine a minimal set of system components whose perturbation can lead to a desired system response, therefore facilitating the design of a more appropriate experimental strategy.

Results

We applied this method to investigate what drives K-ras-induced cancer cells, displaying the typical Warburg effect, to death or survival upon progressive glucose depletion. The optimization analysis allowed to identify new combinations of stimuli that maximize pro-apoptotic processes. Namely, our results provide different evidences of an important protective role for protein kinase A in cancer cells under several cellular stress conditions mimicking tumor behavior. The predictive power of this method could facilitate the assessment of the response of other complex heterogeneous systems to drugs or mutations in fields as medicine and pharmacology, therefore paving the way for the development of novel therapeutic treatments.

Availability and implementation

The source code of FUMOSO is available under the GPL 2.0 license on GitHub at the following URL: https://github.com/aresio/FUMOSO

Supplementary information

Supplementary data are available at Bioinformatics online.

Integration of single-cell multi-omics for gene regulatory network inference

The advancement of single-cell sequencing technology in recent years has provided an opportunity to reconstruct gene regulatory networks (GRNs) with the data from thousands of single cells in one sample. This uncovers regulatory interactions in cells and speeds up the discoveries of regulatory mechanisms in diseases and biological processes. Therefore, more methods have been proposed to reconstruct GRNs using single-cell sequencing data. In this review, we introduce technologies for sequencing single-cell genome, transcriptome, and epigenome. At the same time, we present an overview of current GRN reconstruction strategies utilizing different single-cell sequencing data. Bioinformatics tools were grouped by their input data type and mathematical principles for reader's convenience, and the fundamental mathematics inherent in each group will be discussed. Furthermore, the adaptabilities and limitations of these different methods will also be summarized and compared, with the hope to facilitate researchers recognizing the most suitable tools for them.

Exact solving and sensitivity analysis of stochastic continuous time Boolean models

Background

Solutions to stochastic Boolean models are usually estimated by Monte Carlo simulations, but as the state space of these models can be enormous, there is an inherent uncertainty about the accuracy of Monte Carlo estimates and whether simulations have reached all attractors. Moreover, these models have timescale parameters (transition rates) that the probability values of stationary solutions depend on in complex ways, raising the necessity of parameter sensitivity analysis. We address these two issues by an exact calculation method for this class of models.

Results

We show that the stationary probability values of the attractors of stochastic (asynchronous) continuous time Boolean models can be exactly calculated. The calculation does not require Monte Carlo simulations, instead it uses graph theoretical and matrix calculation methods previously applied in the context of chemical kinetics. In this version of the asynchronous updating framework the states of a logical model define a continuous time Markov chain and for a given initial condition the stationary solution is fully defined by the right and left nullspace of the master equation’s kinetic matrix. We use topological sorting of the state transition graph and the dependencies between the nullspaces and the kinetic matrix to derive the stationary solution without simulations. We apply this calculation to several published Boolean models to analyze the under-explored question of the effect of transition rates on the stationary solutions and show they can be sensitive to parameter changes. The analysis distinguishes processes robust or, alternatively, sensitive to parameter values, providing both methodological and biological insights.

Conclusion

Up to an intermediate size (the biggest model analyzed is 23 nodes) stochastic Boolean models can be efficiently solved by an exact matrix method, without using Monte Carlo simulations. Sensitivity analysis with respect to the model’s timescale parameters often reveals a small subset of all parameters that primarily determine the stationary probability of attractor states.

Logic-based analysis of gene expression data predicts association between TNF, TGFB1 and EGF pathways in basal-like breast cancer

For breast cancer, clinically important subtypes are well characterized at the molecular level in terms of gene expression profiles. In addition, signaling pathways in breast cancer have been extensively studied as therapeutic targets due to their roles in tumor growth and metastasis. However, it is challenging to put signaling pathways and gene expression profiles together to characterize biological mechanisms of breast cancer subtypes since many signaling events result from post-translational modifications, rather than gene expression differences. We designed a logic-based computational framework to explain the differences in gene expression profiles among breast cancer subtypes using Pathway Logic and transcriptional network information. Pathway Logic is a rewriting-logic-based formal system for modeling biological pathways including post-translational modifications. Our method demonstrated its utility by constructing subtype-specific path from key receptors (TNFR, TGFBR1 and EGFR) to key transcription factor (TF) regulators (RELA, ATF2, SMAD3 and ELK1) and identifying potential association between pathways via TFs in basal-specific paths, which could provide a novel insight on aggressive breast cancer subtypes. Codes and results are available at http://epigenomics.snu.ac.kr/PL/.

Identifying inhibitors of epithelial-mesenchymal plasticity using a network topology-based approach

Metastasis is the cause of over 90% of cancer-related deaths. Cancer cells undergoing metastasis can switch dynamically between different phenotypes, enabling them to adapt to harsh challenges, such as overcoming anoikis and evading immune response. This ability, known as phenotypic plasticity, is crucial for the survival of cancer cells during metastasis, as well as acquiring therapy resistance. Various biochemical networks have been identified to contribute to phenotypic plasticity, but how plasticity emerges from the dynamics of these networks remains elusive. Here, we investigated the dynamics of various regulatory networks implicated in Epithelial–mesenchymal plasticity (EMP)—an important arm of phenotypic plasticity—through two different mathematical modelling frameworks: a discrete, parameter-independent framework (Boolean) and a continuous, parameter-agnostic modelling framework (RACIPE). Results from either framework in terms of phenotypic distributions obtained from a given EMP network are qualitatively similar and suggest that these networks are multi-stable and can give rise to phenotypic plasticity. Neither method requires specific kinetic parameters, thus our results emphasize that EMP can emerge through these networks over a wide range of parameter sets, elucidating the importance of network topology in enabling phenotypic plasticity. Furthermore, we show that the ability to exhibit phenotypic plasticity correlates positively with the number of positive feedback loops in a given network. These results pave a way toward an unorthodox network topology-based approach to identify crucial links in a given EMP network that can reduce phenotypic plasticity and possibly inhibit metastasis—by reducing the number of positive feedback loops.

Phenotype stability under dynamic brain-tumor environment stimuli maps glioblastoma progression in patients

Although tumor invasiveness is known to drive glioblastoma (GBM) recurrence, current approaches to treatment assume a fairly simple GBM phenotype transition map. We provide new analyses to estimate the likelihood of reaching or remaining in a phenotype under dynamic, physiologically likely perturbations of stimuli ("phenotype stability"). We show that higher stability values of the motile phenotype (Go) are associated with reduced patient survival. Moreover, induced motile states are capable of driving GBM recurrence. We found that the Dormancy and Go phenotypes are equally represented in advanced GBM samples, with natural transitioning between the two. Furthermore, Go and Grow phenotype transitions are mostly driven by tumor-brain stimuli. These are difficult to regulate directly, but could be modulated by reprogramming tumor-associated cell types. Our framework provides a foundation for designing targeted perturbations of the tumor-brain environment, by assessing their impact on GBM phenotypic plasticity, and is corroborated by analyses of patient data.

Computational models to explore the complexity of the epithelial to mesenchymal transition in cancer

Epithelial to mesenchymal transition (EMT) is a complex biological process that plays a key role in cancer progression and metastasis formation. Its activation results in epithelial cells losing adhesion and polarity and becoming capable of migrating from their site of origin. At this step the disease is generally considered incurable. As EMT execution involves several individual molecular components, connected by nontrivial relations, in vitro techniques are often inadequate to capture its complexity. Computational models can be used to complement experiments and provide additional knowledge difficult to build up in a wetlab. Indeed in silico analysis gives the user total control on the system, allowing to identify the contribution of each independent element. In the following, two kinds of approaches to the computational study of EMT will be presented. The first relies on signal transduction networks description and details how changes in gene expression could influence this process, both focusing on specific aspects of the EMT and providing a general frame for this phenomenon easily comparable with experimental data. The second integrates single cell and population level descriptions in a multiscale model that can be considered a more accurate representation of the EMT. The advantages and disadvantages of each approach will be highlighted, together with the importance of coupling computational and experimental results. Finally, the main challenges that need to be addressed to improve our knowledge of the role of EMT in the neoplastic disease and the scientific and translational value of computational models in this respect will be presented. This article is categorized under: Analytical and Computational Methods > Computational Methods.

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.

The logic behind neural control of breathing pattern

The respiratory rhythm generator is spectacular in its ability to support a wide range of activities and adapt to changing environmental conditions, yet its operating mechanisms remain elusive. We show how selective control of inspiration and expiration times can be achieved in a new representation of the neural system (called a Boolean network). The new framework enables us to predict the behavior of neural networks based on properties of neurons, not their values. Hence, it reveals the logic behind the neural mechanisms that control the breathing pattern. Our network mimics many features seen in the respiratory network such as the transition from a 3-phase to 2-phase to 1-phase rhythm, providing novel insights and new testable predictions.

Predicting protein functions by applying predicate logic to biomedical literature

BACKGROUND

A large number of computational methods have been proposed for predicting protein functions. The underlying techniques adopted by most of these methods revolve around predicting the functions of an unannotated protein p from already annotated proteins that have similar characteristics as p. Recent Information Extraction methods take advantage of the huge growth of biomedical literature to predict protein functions. They extract biological molecule terms that directly describe protein functions from biomedical texts. However, they consider only explicitly mentioned terms that co-occur with proteins in texts. We observe that some important biological molecule terms pertaining functional categories may implicitly co-occur with proteins in texts. Therefore, the methods that rely solely on explicitly mentioned terms in texts may miss vital functional information implicitly mentioned in the texts.

RESULTS

To overcome the limitations of methods that rely solely on explicitly mentioned terms in texts to predict protein functions, we propose in this paper an Information Extraction system called PL-PPF. The proposed system employs techniques for predicting the functions of proteins based on their co-occurrences with explicitly and implicitly mentioned biological molecule terms that pertain functional categories in biomedical literature. That is, PL-PPF employs a combination of statistical-based explicit term extraction techniques and logic-based implicit term extraction techniques. The statistical component of PL-PPF predicts some of the functions of a protein by extracting the explicitly mentioned functional terms that directly describe the functions of the protein from the biomedical texts associated with the protein. The logic-based component of PL-PPF predicts additional functions of the protein by inferring the functional terms that co-occur implicitly with the protein in the biomedical texts associated with it. First, the system employs its statistical-based component to extract the explicitly mentioned functional terms. Then, it employs its logic-based component to infer additional functions of the protein. Our hypothesis is that important biological molecule terms pertaining functional categories of proteins are likely to co-occur implicitly with the proteins in biomedical texts. We evaluated PL-PPF experimentally and compared it with five systems. Results revealed better prediction performance.

CONCLUSIONS

The experimental results showed that PL-PPF outperformed the other five systems. This is an indication of the effectiveness and practical viability of PL-PPF's combination of explicit and implicit techniques. We also evaluated two versions of PL-PPF: one adopting the complete techniques (i.e., adopting both the implicit and explicit techniques) and the other adopting only the explicit terms co-occurrence extraction techniques (i.e., without the inference rules for predicate logic). The experimental results showed that the complete version outperformed significantly the other version. This is attributed to the effectiveness of the rules of predicate logic to infer functional terms that co-occur implicitly with proteins in biomedical texts. A demo application of PL-PPF can be accessed through the following link: http://ecesrvr.kustar.ac.ae:8080/plppf/.

Edgetic perturbations to eliminate fixed-point attractors in Boolean regulatory networks

The dynamics of complex biological networks may be modeled in a Boolean framework, where the state of each system component is either abundant (ON) or scarce/absent (OFF), and each component's dynamic trajectory is determined by a logical update rule involving the state(s) of its regulator(s). It is possible to encode the update rules in the topology of the so-called expanded graph, analysis of which reveals the long-term behavior, or attractors, of the network. Here, we develop an algorithm to perturb the expanded graph (or, equivalently, the logical update rules) to eliminate stable motifs: subgraphs that cause a subset of components to stabilize to one state. Depending on the topology of the expanded graph, these perturbations lead to the modification or loss of the corresponding attractor. While most perturbations of biological regulatory networks in the literature involve the knockout (fixing to OFF) or constitutive activation (fixing to ON) of one or more nodes, we here consider edgetic perturbations, where a node's update rule is modified such that one or more of its regulators is viewed as ON or OFF regardless of its actual state. We apply the methodology to two biological networks. In a network representing T-LGL leukemia, we identify edgetic perturbations that eliminate the cancerous attractor, leaving only the healthy attractor representing cell death. In a network representing drought-induced closure of plant stomata, we identify edgetic perturbations that modify the single attractor such that stomata, instead of being fixed in the closed state, oscillates between the open and closed states.

On the number of driver nodes for controlling a Boolean network when the targets are restricted to attractors

It is known that many driver nodes are required to control complex biological networks. Previous studies imply that O(N) driver nodes are required in both linear complex network and Boolean network models with N nodes if an arbitrary state is specified as the target. In order to cope with this intrinsic difficulty, we consider a special case of the control problem in which the targets are restricted to attractors. For this special case, we mathematically prove under the uniform distribution of states in basins that the expected number of driver nodes is only O(log₂N+log₂M) for controlling Boolean networks, where M is the number of attractors. Since it is expected that M is not very large in many practical networks, the new model requires a much smaller number of driver nodes. This result is based on discovery of novel relationships between control problems on Boolean networks and the coupon collector's problem, a well-known concept in combinatorics. We also provide lower bounds of the number of driver nodes as well as simulation results using artificial and realistic network data, which support our theoretical findings.

Ambiguity in logic-based models of gene regulatory networks: An integrative multi-perturbation analysis

Most studies of gene regulatory network (GRN) inference have focused extensively on identifying the interaction map of the GRNs. However, in order to predict the cellular behavior, modeling the GRN in terms of logic circuits, i.e., Boolean networks, is necessary. The perturbation techniques, e.g., knock-down and over-expression, should be utilized for identifying the underlying logic behind the interactions. However, we will show that by using only transcriptomic data obtained by single-perturbation experiments, we cannot observe all regulatory interactions, and this invisibility causes ambiguity in our model. Consequently, we need to employ the data of multiple omics layers (genome, transcriptome, and proteome) as well as multiple perturbation experiments to reduce or eliminate ambiguity in our modeling. In this paper, we introduce a multi-step perturbation experiment to deal with ambiguity. Moreover, we perform a thorough analysis to investigate which types of perturbations and omics layers play the most important role in the unambiguous modeling of the GRNs and how much ambiguity will be eliminated by considering more perturbations and more omics layers. Our analysis shows that performing both knock-down and over-expression is necessary in order to achieve the least ambiguous model. Moreover, the more steps of the perturbation are taken, the more ambiguity is eliminated. In addition, we can even achieve an unambiguous model of the GRN by using multi-step perturbation and integrating transcriptomic, protein-protein interaction, and cis-element data. Finally, we demonstrate the effect of utilizing different types of perturbation experiment and integrating multi-omics data on identifying the logic behind the regulatory interactions in a synthetic GRN. In conclusion, relying on the results of only knock-down experiments and not including as many omics layers as possible in the GRN inference, makes the results ambiguous, unreliable, and less accurate.

Computational discovery of dynamic cell line specific Boolean networks from multiplex time-course data

Protein signaling networks are static views of dynamic processes where proteins go through many biochemical modifications such as ubiquitination and phosphorylation to propagate signals that regulate cells and can act as feed-back systems. Understanding the precise mechanisms underlying protein interactions can elucidate how signaling and cell cycle progression occur within cells in different diseases such as cancer. Large-scale protein signaling networks contain an important number of experimentally verified protein relations but lack the capability to predict the outcomes of the system, and therefore to be trained with respect to experimental measurements. Boolean Networks (BNs) are a simple yet powerful framework to study and model the dynamics of the protein signaling networks. While many BN approaches exist to model biological systems, they focus mainly on system properties, and few exist to integrate experimental data in them. In this work, we show an application of a method conceived to integrate time series phosphoproteomic data into protein signaling networks. We use a large-scale real case study from the HPN-DREAM Breast Cancer challenge. Our efficient and parameter-free method combines logic programming and model-checking to infer a family of BNs from multiple perturbation time series data of four breast cancer cell lines given a prior protein signaling network. Because each predicted BN family is cell line specific, our method highlights commonalities and discrepancies between the four cell lines. Our models have a Root Mean Square Error (RMSE) of 0.31 with respect to the testing data, while the best performant method of this HPN-DREAM challenge had a RMSE of 0.47. To further validate our results, BNs are compared with the canonical mTOR pathway showing a comparable AUROC score (0.77) to the top performing HPN-DREAM teams. In addition, our approach can also be used as a complementary method to identify erroneous experiments. These results prove our methodology as an efficient dynamic model discovery method in multiple perturbation time course experimental data of large-scale signaling networks. The software and data are publicly available at https://github.com/misbahch6/caspo-ts.

Traditional canonical signaling pathways help to understand overall signaling processes inside the cell. Large scale phosphoproteomic data provide insight into alterations among different proteins under different experimental settings. Our goal is to combine the traditional signaling networks with complex phosphoproteomic time-series data in order to unravel cell specific signaling networks. In this study, we have applied the caspo time series (caspo-ts) approach which is a combination of logic programming and model checking, over the time series phosphoproteomic dataset of the HPN-DREAM challenge to learn cell specific BNs. The learned BNs can be used to identify the cell specific topology. Our analysis suggests that caspo-ts scales to real datasets, outputting networks that are not random with a lower fitness error than the models used by the 178 methods which participated in the HPN-DREAM challenge. On the biological side, we identified the cell specific and common mechanisms (logical gates) of the cell lines.

p53 modeling as a route to mesothelioma patients stratification and novel therapeutic identification

Background

Malignant pleural mesothelioma (MPM) is an orphan disease that is difficult to treat using traditional chemotherapy, an approach which has been effective in other types of cancer. Most chemotherapeutics cause DNA damage leading to cell death. Recent discoveries have highlighted a potential role for the p53 tumor suppressor in this disease. Given the pivotal role of p53 in the DNA damage response, here we investigated the predictive power of the p53 interactome model for MPM patients’ stratification.

Methods

We used bioinformatics approaches including omics type analysis of data from MPM cells and from MPM patients in order to predict which pathways are crucial for patients’ survival. Analysis of the PKT206 model of the p53 network was validated by microarrays from the Mero-14 MPM cell line and RNA-seq data from 71 MPM patients, whilst statistical analysis was used to identify the deregulated pathways and predict therapeutic schemes by linking the affected pathway with the patients’ clinical state.

Results

In silico simulations demonstrated successful predictions ranging from 52 to 85% depending on the drug, algorithm or sample used for validation. Clinical outcomes of individual patients stratified in three groups and simulation comparisons identified 30 genes that correlated with survival. In patients carrying wild-type p53 either treated or not treated with chemotherapy, FEN1 and MMP2 exhibited the highest inverse correlation, whereas in untreated patients bearing mutated p53, SIAH1 negatively correlated with survival. Numerous repositioned and experimental drugs targeting FEN1 and MMP2 were identified and selected drugs tested. Epinephrine and myricetin, which target FEN1, have shown cytotoxic effect on Mero-14 cells whereas marimastat and batimastat, which target MMP2 demonstrated a modest but significant inhibitory effect on MPM cell migration. Finally, 8 genes displayed correlation with disease stage, which may have diagnostic implications.

Conclusions

Clinical decisions related to MPM personalized therapy based on individual patients’ genetic profile and previous chemotherapeutic treatment could be reached using computational tools and the predictions reported in this study upon further testing in animal models.

Electronic supplementary material

The online version of this article (10.1186/s12967-018-1650-0) contains supplementary material, which is available to authorized users.

Expert curation for building network-based dynamical models: a case study on atherosclerotic plaque formation

Knowledgebases play an increasingly important role in scientific research, where the expert curation of biological knowledge in forms that are amenable to computational analysis (using ontologies for example)–provides a significant added value and enables new types of computational analyses for high throughput datasets. In this work, we demonstrate how expert curation can also play a more direct role in research, by supporting the use of network-based dynamical models to study a specific biological process. This curation effort is focused on the regulatory interactions between biological entities, such as genes or proteins and compounds, which may interact with each other in a complex manner, including regulatory complexes and conditional dependencies between co-regulators. This critical information has to be captured and encoded in a computable manner, which is currently far beyond the current capabilities of automatically constructed network. As a case study, we report here the prior knowledge network constructed by the sysVASC consortium to model the biological events leading to the formation of atherosclerotic plaques, during the onset of cardiovascular disease and discuss some specific examples to illustrate the main pitfalls and added value provided by the expert curation during this endeavor.

Database URL: http://biomodels.caltech.edu

High-fidelity discrete modeling of the HPA axis: a study of regulatory plasticity in biology

BACKGROUND

The hypothalamic-pituitary-adrenal (HPA) axis is a central regulator of stress response and its dysfunction has been associated with a broad range of complex illnesses including Gulf War Illness (GWI) and Chronic Fatigue Syndrome (CFS). Though classical mathematical approaches have been used to model HPA function in isolation, its broad regulatory interactions with immune and central nervous function are such that the biological fidelity of simulations is undermined by the limited availability of reliable parameter estimates.

METHOD

Here we introduce and apply a generalized discrete formalism to recover multiple stable regulatory programs of the HPA axis using little more than connectivity between physiological components. This simple discrete model captures cyclic attractors such as the circadian rhythm by applying generic constraints to a minimal parameter set; this is distinct from Ordinary Differential Equation (ODE) models, which require broad and precise parameter sets. Parameter tuning is accomplished by decomposition of the overall regulatory network into isolated sub-networks that support cyclic attractors. Network behavior is simulated using a novel asynchronous updating scheme that enforces priority with memory within and between physiological compartments.

RESULTS

Consistent with much more complex conventional models of the HPA axis, this parsimonious framework supports two cyclic attractors, governed by higher and lower levels of cortisol respectively. Importantly, results suggest that stress may remodel the stability landscape of this system, favoring migration from one stable circadian cycle to the other. Access to each regime is dependent on HPA axis tone, captured here by the tunable parameters of the multi-valued logic. Likewise, an idealized glucocorticoid receptor blocker alters the regulatory topology such that maintenance of persistently low cortisol levels is rendered unstable, favoring a return to normal circadian oscillation in both cortisol and glucocorticoid receptor expression.

CONCLUSION

These results emphasize the significance of regulatory connectivity alone and how regulatory plasticity may be explored using simple discrete logic and minimal data compared to conventional methods.

Predicting neuroblastoma using developmental signals and a logic-based model

Genomic information from human patient samples of pediatric neuroblastoma cancers and known outcomes have led to specific gene lists put forward as high risk for disease progression. However, the reliance on gene expression correlations rather than mechanistic insight has shown limited potential and suggests a critical need for molecular network models that better predict neuroblastoma progression. In this study, we construct and simulate a molecular network of developmental genes and downstream signals in a 6-gene input logic model that predicts a favorable/unfavorable outcome based on the outcome of the four cell states including cell differentiation, proliferation, apoptosis, and angiogenesis. We simulate the mis-expression of the tyrosine receptor kinases, trkA and trkB, two prognostic indicators of neuroblastoma, and find differences in the number and probability distribution of steady state outcomes. We validate the mechanistic model assumptions using RNAseq of the SHSY5Y human neuroblastoma cell line to define the input states and confirm the predicted outcome with antibody staining. Lastly, we apply input gene signatures from 77 published human patient samples and show that our model makes more accurate disease outcome predictions for early stage disease than any current neuroblastoma gene list. These findings highlight the predictive strength of a logic-based model based on developmental genes and offer a better understanding of the molecular network interactions during neuroblastoma disease progression.

Mapping gene regulatory networks from single-cell omics data

Single-cell techniques are advancing rapidly and are yielding unprecedented insight into cellular heterogeneity. Mapping the gene regulatory networks (GRNs) underlying cell states provides attractive opportunities to mechanistically understand this heterogeneity. In this review, we discuss recently emerging methods to map GRNs from single-cell transcriptomics data, tackling the challenge of increased noise levels and data sparsity compared with bulk data, alongside increasing data volumes. Next, we discuss how new techniques for single-cell epigenomics, such as single-cell ATAC-seq and single-cell DNA methylation profiling, can be used to decipher gene regulatory programmes. We finally look forward to the application of single-cell multi-omics and perturbation techniques that will likely play important roles for GRN inference in the future.

Discrete dynamic network modeling of oncogenic signaling: Mechanistic insights for personalized treatment of cancer

Targeted drugs disrupting proteins that are dysregulated in cancer have emerged as promising treatments because of their specificity to cancer cell aberrations and thus their improved side effect profile. However, their success remains limited, largely due to existing or emergent therapy resistance. We suggest that this is due to limited understanding of the entire relevant cellular landscape. A class of mathematical models called discrete dynamic network models can be used to understand the integrated effect of an individual tumor's aberrations. We review the recent literature on discrete dynamic models of cancer and highlight their predicted therapeutic strategies. We believe dynamic network modeling can be used to drive treatment decision-making in a personalized manner to direct improved treatments in cancer.

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Cancer is rooted in incorrect cellular decisions caused by genetic alterations.

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Dynamic models of signaling networks can map the relevant repertoire of alterations.

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Discrete dynamic network models can predict therapeutic interventions.

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Progress in personalized medicine needs integration of multiple data and model types.

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.

Network-Based Analysis of Bortezomib Pharmacodynamic Heterogeneity in Multiple Myeloma Cells

The objective of this study is to evaluate the heterogeneity in pharmacodynamic response in four in vitro multiple myeloma cell lines to treatment with bortezomib, and to assess whether such differences are associated with drug-induced intracellular signaling protein dynamics identified via a logic-based network modeling approach. The in vitro pharmacodynamic-efficacy of bortezomib was evaluated through concentration-effect and cell proliferation dynamical studies in U266, RPMI8226, MM.1S, and NCI-H929 myeloma cell lines. A Boolean logic-based network model incorporating intracellular protein signaling pathways relevant to myeloma cell growth, proliferation, and apoptosis was developed based on information available in the literature and used to identify key proteins regulating bortezomib pharmacodynamics. The time-course of network-identified proteins was measured using the MAGPIX protein assay system. Traditional pharmacodynamic modeling endpoints revealed variable responses of the cell lines to bortezomib treatment, classifying cell lines as more sensitive (MM.1S and NCI-H929) and less sensitive (U266 and RPMI8226). Network centrality and model reduction identified key proteins (e.g., phosphorylated nuclear factor-κB, phosphorylated protein kinase B, phosphorylated mechanistic target of rapamycin, Bcl-2, phosphorylated c-Jun N-terminal kinase, phosphorylated p53, p21, phosphorylated Bcl-2-associated death promoter, caspase 8, and caspase 9) that govern bortezomib pharmacodynamics. The corresponding relative expression (normalized to 0-hour untreated-control cells) of proteins demonstrated a greater magnitude and earlier onset of stimulation/inhibition in cells more sensitive (MM.1S and NCI-H929) to bortezomib-induced cell death at 20 nM, relative to the less sensitive cells (U266 and RPMI8226). Overall, differences in intracellular signaling appear to be associated with bortezomib pharmacodynamic heterogeneity, and key proteins may be potential biomarkers to evaluate bortezomib responses.

Cell signaling heterogeneity is modulated by both cell-intrinsic and -extrinsic mechanisms: An integrated approach to understanding targeted therapy

During the last decade, our understanding of cancer cell signaling networks has significantly improved, leading to the development of various targeted therapies that have elicited profound but, unfortunately, short-lived responses. This is, in part, due to the fact that these targeted therapies ignore context and average out heterogeneity. Here, we present a mathematical framework that addresses the impact of signaling heterogeneity on targeted therapy outcomes. We employ a simplified oncogenic rat sarcoma (RAS)-driven mitogen-activated protein kinase (MAPK) and phosphoinositide 3-kinase-protein kinase B (PI3K-AKT) signaling pathway in lung cancer as an experimental model system and develop a network model of the pathway. We measure how inhibition of the pathway modulates protein phosphorylation as well as cell viability under different microenvironmental conditions. Training the model on this data using Monte Carlo simulation results in a suite of in silico cells whose relative protein activities and cell viability match experimental observation. The calibrated model predicts distributional responses to kinase inhibitors and suggests drug resistance mechanisms that can be exploited in drug combination strategies. The suggested combination strategies are validated using in vitro experimental data. The validated in silico cells are further interrogated through an unsupervised clustering analysis and then integrated into a mathematical model of tumor growth in a homogeneous and resource-limited microenvironment. We assess posttreatment heterogeneity and predict vast differences across treatments with similar efficacy, further emphasizing that heterogeneity should modulate treatment strategies. The signaling model is also integrated into a hybrid cellular automata (HCA) model of tumor growth in a spatially heterogeneous microenvironment. As a proof of concept, we simulate tumor responses to targeted therapies in a spatially segregated tissue structure containing tumor and stroma (derived from patient tissue) and predict complex cell signaling responses that suggest a novel combination treatment strategy.

A signaling pathway is a network of molecules in a cell that is typically initiated by stimuli (e.g., microenvironmental cues) acting on receptors and internal signaling molecules to determine cell fate. Signaling pathways in cancer cells are different from those in normal cells, and this difference helps cancer cells to grow and thrive indefinitely. Drugs that target the aberrant signaling pathways in cancer cells (often referred to as targeted therapy) are promising for improving treatment outcomes of many different cancers in patients. However, most patients eventually develop resistance to these drugs. Resistance may already be present in the tumor or may emerge via mutation or via microenvironmental mediation. Tumor heterogeneity, which is characterized by subtle or dramatic differences among tumor cells, plays a key role in the development of drug resistance. Some tumor cells respond well to therapy, while others may adapt to the stress induced by the drug within the microenvironment. Moreover, removal of drug-sensitive cells may result in the competitive release of drug-resistant cells. Here, we present mathematical models to assess the impact of heterogeneity in signaling pathways within tumor cells on the outcomes of targeted therapy. We consider a simplified version of two well-known signaling pathways that modulate the growth of lung cancer cells. By using different targeted therapies, we quantify the effect of pathway inhibition on protein activity and cell viability and developed a mathematical model of the network, which is trained to reproduce these data and to develop a panel of heterogeneous in silico cells. The model predicts potential mechanisms of drug resistance and proposes combination therapies that are effective across the panel. We validate these combination therapies experimentally using the lung cancer cells and integrated the in silico cells into a computational lung tissue model that explicitly captures the microenvironment of lung cancer. Our results suggest that heterogeneity in both the tumor and microenvironment impacts treatment response in different ways and suggest a novel combination therapy for a better response.

A systems pharmacology model for inflammatory bowel disease

Motivation

The literature on complex diseases is abundant but not always quantitative. This is particularly so for Inflammatory Bowel Disease (IBD), where many molecular pathways are qualitatively well described but this information cannot be used in traditional quantitative mathematical models employed in drug development. We propose the elaboration and validation of a logic network for IBD able to capture the information available in the literature that will facilitate the identification/validation of therapeutic targets.

Results

In this article, we propose a logic model for Inflammatory Bowel Disease (IBD) which consists of 43 nodes and 298 qualitative interactions. The model presented is able to describe the pathogenic mechanisms of the disorder and qualitatively describes the characteristic chronic inflammation. A perturbation analysis performed on the IBD network indicates that the model is robust. Also, as described in clinical trials, a simulation of anti-TNFα, anti-IL2 and Granulocyte and Monocyte Apheresis showed a decrease in the Metalloproteinases node (MMPs), which means a decrease in tissue damage. In contrast, as clinical trials have demonstrated, a simulation of anti-IL17 and anti-IFNγ or IL10 overexpression therapy did not show any major change in MMPs expression, as corresponds to a failed therapy. The model proved to be a promising in silico tool for the evaluation of potential therapeutic targets, the identification of new IBD biomarkers, the integration of IBD polymorphisms to anticipate responders and non-responders and can be reduced and transformed in quantitative model/s.

Therapeutic target discovery using Boolean network attractors: improvements of kali

In a previous article, an algorithm for identifying therapeutic targets in Boolean networks modelling pathological mechanisms was introduced. In the present article, the improvements made on this algorithm, named kali, are described. These improvements are (i) the possibility to work on asynchronous Boolean networks, (ii) a finer assessment of therapeutic targets and (iii) the possibility to use multivalued logic. kali assumes that the attractors of a dynamical system, such as a Boolean network, are associated with the phenotypes of the modelled biological system. Given a logic-based model of pathological mechanisms, kali searches for therapeutic targets able to reduce the reachability of the attractors associated with pathological phenotypes, thus reducing their likeliness. kali is illustrated on an example network and used on a biological case study. The case study is a published logic-based model of bladder tumorigenesis from which kali returns consistent results. However, like any computational tool, kali can predict but cannot replace human expertise: it is a supporting tool for coping with the complexity of biological systems in the field of drug discovery.

Computational Systems Biology Approach for the Study of Rheumatoid Arthritis: From a Molecular Map to a Dynamical Model

In this work we present a systematic effort to summarize current biological pathway knowledge concerning Rheumatoid Arthritis (RA). We are constructing a detailed molecular map based on exhaustive literature scanning, strict curation criteria, re-evaluation of previously published attempts and most importantly experts' advice. The RA map will be web-published in the coming months in the form of an interactive map, using the MINERVA platform, allowing for easy access, navigation and search of all molecular pathways implicated in RA, serving thus, as an on line knowledgebase for the disease. Moreover the map could be used as a template for Omics data visualization offering a first insight about the pathways affected in different experimental datasets. The second goal of the project is a dynamical study focused on synovial fibroblasts' behavior under different initial conditions specific to RA, as recent studies have shown that synovial fibroblasts play a crucial role in driving the persistent, destructive characteristics of the disease. Leaning on the RA knowledgebase and using the web platform Cell Collective, we are currently building a Boolean large scale dynamical model for the study of RA fibroblasts' activation.

Inferring Intracellular Signal Transduction Circuitry from Molecular Perturbation Experiments

The development of network inference methodologies that accurately predict connectivity in dysregulated pathways may enable the rational selection of patient therapies. Accurately inferring an intracellular network from data remains a very challenging problem in molecular systems biology. Living cells integrate extremely robust circuits that exhibit significant heterogeneity, but still respond to external stimuli in predictable ways. This phenomenon allows us to introduce a network inference methodology that integrates measurements of protein activation from perturbation experiments. The methodology relies on logic-based networks to provide a predictive approximation of the transfer of signals in a network. The approach presented was validated in silico with a set of test networks and applied to investigate the epidermal growth factor receptor signaling of a breast epithelial cell line, MFC10A. In our analysis, we predict the potential signaling circuitry most likely responsible for the experimental readouts of several proteins in the mitogen-activated protein kinase and phosphatidylinositol-3 kinase pathways. The approach can also be used to identify additional necessary perturbation experiments to distinguish between a set of possible candidate networks.

Novel Hybrid Phenotype Revealed in Small Cell Lung Cancer by a Transcription Factor Network Model That Can Explain Tumor Heterogeneity

Small cell lung cancer (SCLC) is a devastating disease due to its propensity for early invasion and refractory relapse after initial treatment response. Although these aggressive traits have been associated with phenotypic heterogeneity, our understanding of this association remains incomplete. To fill this knowledge gap, we inferred a set of 33 transcription factors (TF) associated with gene signatures of the known neuroendocrine/epithelial (NE) and non-neuroendocrine/mesenchymal-like (ML) SCLC phenotypes. The topology of this SCLC TF network was derived from prior knowledge and was simulated using Boolean modeling. These simulations predicted that the network settles into attractors, or TF expression patterns, that correlate with NE or ML phenotypes, suggesting that TF network dynamics underlie the emergence of heterogeneous SCLC phenotypes. However, several cell lines and patient tumor specimens failed to correlate with either the NE or ML attractors. By flow cytometry, single cells within these cell lines simultaneously expressed surface markers of both NE and ML differentiation, confirming the existence of a "hybrid" phenotype. Upon exposure to standard-of-care cytotoxic drugs or epigenetic modifiers, NE and ML cell populations converged toward the hybrid state, suggesting possible escape from treatment. Our findings indicate that SCLC phenotypic heterogeneity can be specified dynamically by attractor states of a master regulatory TF network. Thus, SCLC heterogeneity may be best understood as states within an epigenetic landscape. Understanding phenotypic transitions within this landscape may provide insights to clinical applications. Cancer Res; 77(5); 1063-74. ©2016 AACR.