Reconstructing Boolean models of signaling

Bridging systems biology and tissue engineering: Unleashing the full potential of complex 3D in vitro tissue models of disease

Rapid advances in tissue engineering have resulted in more complex and physiologically relevant 3D in vitro tissue models with applications in fundamental biology and therapeutic development. However, the complexity provided by these models is often not leveraged fully due to the reductionist methods used to analyze them. Computational and mathematical models developed in the field of systems biology can address this issue. Yet, traditional systems biology has been mostly applied to simpler in vitro models with little physiological relevance and limited cellular complexity. Therefore, integrating these two inherently interdisciplinary fields can result in new insights and move both disciplines forward. In this review, we provide a systematic overview of how systems biology has been integrated with 3D in vitro tissue models and discuss key application areas where the synergies between both fields have led to important advances with potential translational impact. We then outline key directions for future research and discuss a framework for further integration between fields.

The Reasoning Engine: A Satisfiability Modulo Theories-Based Framework for Reasoning About Discrete Biological Models

We present a framework called the Reasoning Engine, which implements Satisfiability Modulo Theories (SMT)-based methods within a unified computational environment to address diverse biological analysis problems. The Reasoning Engine was used to reproduce results from key scientific studies, as well as supporting new research in stem cell biology. The framework utilizes an intermediate language for encoding partially specified discrete dynamical systems, which bridges the gap between high-level domain-specific languages and low-level SMT solvers. We provide this framework as open source together with various biological case studies, illustrating the synthesis, enumeration, optimization, and reasoning over models consistent with experimental observations to reveal novel biological insights.

Maximum Entropy Technique and Regularization Functional for Determining the Pharmacokinetic Parameters in DCE-MRI

This paper aims to solve the arterial input function (AIF) determination in dynamic contrast-enhanced MRI (DCE-MRI), an important linear ill-posed inverse problem, using the maximum entropy technique (MET) and regularization functionals. In addition, estimating the pharmacokinetic parameters from a DCE-MR image investigations is an urgent need to obtain the precise information about the AIF-the concentration of the contrast agent on the left ventricular blood pool measured over time. For this reason, the main idea is to show how to find a unique solution of linear system of equations generally in the form of [Formula: see text] named an ill-conditioned linear system of equations after discretization of the integral equations, which appear in different tomographic image restoration and reconstruction issues. Here, a new algorithm is described to estimate an appropriate probability distribution function for AIF according to the MET and regularization functionals for the contrast agent concentration when applying Bayesian estimation approach to estimate two different pharmacokinetic parameters. Moreover, by using the proposed approach when analyzing simulated and real datasets of the breast tumors according to pharmacokinetic factors, it indicates that using Bayesian inference-that infer the uncertainties of the computed solutions, and specific knowledge of the noise and errors-combined with the regularization functional of the maximum entropy problem, improved the convergence behavior and led to more consistent morphological and functional statistics and results. Finally, in comparison to the proposed exponential distribution based on MET and Newton's method, or Weibull distribution via the MET and teaching-learning-based optimization (MET/TLBO) in the previous studies, the family of Gamma and Erlang distributions estimated by the new algorithm are more appropriate and robust AIFs.

Modeling the C. elegans germline stem cell genetic network using automated reasoning

Computational methods and tools are a powerful complementary approach to experimental work for studying regulatory interactions in living cells and systems. We demonstrate the use of formal reasoning methods as applied to the Caenorhabditis elegans germ line, which is an accessible system for stem cell research. The dynamics of the underlying genetic networks and their potential regulatory interactions are key for understanding mechanisms that control cellular decision-making between stem cells and differentiation. We model the “stem cell fate” versus entry into the “meiotic development” pathway decision circuit in the young adult germ line based on an extensive study of published experimental data and known/hypothesized genetic interactions. We apply a formal reasoning framework to derive predictive networks for control of differentiation. Using this approach we simultaneously specify many possible scenarios and experiments together with potential genetic interactions, and synthesize genetic networks consistent with all encoded experimental observations. In silico analysis of knock-down and overexpression experiments within our model recapitulate published phenotypes of mutant animals and can be applied to make predictions on cellular decision-making. A methodological contribution of this work is demonstrating how to effectively model within a formal reasoning framework a complex genetic network with a wealth of known experimental data and constraints. We provide a summary of the steps we have found useful for the development and analysis of this model and can potentially be applicable to other genetic networks. This work also lays a foundation for developing realistic whole tissue models of the C. elegans germ line where each cell in the model will execute a synthesized genetic network.

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated—in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching (“method of moments”), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters.

A systematic approach to orient the human protein-protein interaction network

The protein-protein interaction (PPI) network of an organism serves as a skeleton for its signaling circuitry, which mediates cellular response to environmental and genetic cues. Understanding this circuitry could improve the prediction of gene function and cellular behavior in response to diverse signals. To realize this potential, one has to comprehensively map PPIs and their directions of signal flow. While the quality and the volume of identified human PPIs improved dramatically over the last decade, the directions of these interactions are still mostly unknown, thus precluding subsequent prediction and modeling efforts. Here we present a systematic approach to orient the human PPI network using drug response and cancer genomic data. We provide a diffusion-based method for the orientation task that significantly outperforms existing methods. The oriented network leads to improved prioritization of cancer driver genes and drug targets compared to the state-of-the-art unoriented network.

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.

Synthesizing Signaling Pathways from Temporal Phosphoproteomic Data

We present a method for automatically discovering signaling pathways from time-resolved phosphoproteomic data. The Temporal Pathway Synthesizer (TPS) algorithm uses constraint-solving techniques first developed in the context of formal verification to explore paths in an interaction network. It systematically eliminates all candidate structures for a signaling pathway where a protein is activated or inactivated before its upstream regulators. The algorithm can model more than one hundred thousand dynamic phosphosites and can discover pathway members that are not differentially phosphorylated. By analyzing temporal data, TPS defines signaling cascades without needing to experimentally perturb individual proteins. It recovers known pathways and proposes pathway connections when applied to the human epidermal growth factor and yeast osmotic stress responses. Independent kinase mutant studies validate predicted substrates in the TPS osmotic stress pathway.

Determining Relative Dynamic Stability of Cell States Using Boolean Network Model

Cell state transition is at the core of biological processes in metazoan, which includes cell differentiation, epithelial-to-mesenchymal transition (EMT) and cell reprogramming. In these cases, it is important to understand the molecular mechanism of cellular stability and how the transitions happen between different cell states, which is controlled by a gene regulatory network (GRN) hard-wired in the genome. Here we use Boolean modeling of GRN to study the cell state transition of EMT and systematically compare four available methods to calculate the cellular stability of three cell states in EMT in both normal and genetically mutated cases. The results produced from four methods generally agree but do not totally agree with each other. We show that distribution of one-degree neighborhood of cell states, which are the nearest states by Hamming distance, causes the difference among the methods. From that, we propose a new method based on one-degree neighborhood, which is the simplest one and agrees with other methods to estimate the cellular stability in all scenarios of our EMT model. This new method will help the researchers in the field of cell differentiation and cell reprogramming to calculate cellular stability using Boolean model, and then rationally design their experimental protocols to manipulate the cell state transition.

SCNS: a graphical tool for reconstructing executable regulatory networks from single-cell genomic data

Background

Reconstruction of executable mechanistic models from single-cell gene expression data represents a powerful approach to understanding developmental and disease processes. New ambitious efforts like the Human Cell Atlas will soon lead to an explosion of data with potential for uncovering and understanding the regulatory networks which underlie the behaviour of all human cells. In order to take advantage of this data, however, there is a need for general-purpose, user-friendly and efficient computational tools that can be readily used by biologists who do not have specialist computer science knowledge.

Results

The Single Cell Network Synthesis toolkit (SCNS) is a general-purpose computational tool for the reconstruction and analysis of executable models from single-cell gene expression data. Through a graphical user interface, SCNS takes single-cell qPCR or RNA-sequencing data taken across a time course, and searches for logical rules that drive transitions from early cell states towards late cell states. Because the resulting reconstructed models are executable, they can be used to make predictions about the effect of specific gene perturbations on the generation of specific lineages.

Conclusions

SCNS should be of broad interest to the growing number of researchers working in single-cell genomics and will help further facilitate the generation of valuable mechanistic insights into developmental, homeostatic and disease processes.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0581-y) contains supplementary material, which is available to authorized users.

An introduction to the maximum entropy approach and its application to inference problems in biology

A cornerstone of statistical inference, the maximum entropy framework is being increasingly applied to construct descriptive and predictive models of biological systems, especially complex biological networks, from large experimental data sets. Both its broad applicability and the success it obtained in different contexts hinge upon its conceptual simplicity and mathematical soundness. Here we try to concisely review the basic elements of the maximum entropy principle, starting from the notion of 'entropy', and describe its usefulness for the analysis of biological systems. As examples, we focus specifically on the problem of reconstructing gene interaction networks from expression data and on recent work attempting to expand our system-level understanding of bacterial metabolism. Finally, we highlight some extensions and potential limitations of the maximum entropy approach, and point to more recent developments that are likely to play a key role in the upcoming challenges of extracting structures and information from increasingly rich, high-throughput biological data.

A review of active learning approaches to experimental design for uncovering biological networks

Various types of biological knowledge describe networks of interactions among elementary entities. For example, transcriptional regulatory networks consist of interactions among proteins and genes. Current knowledge about the exact structure of such networks is highly incomplete, and laboratory experiments that manipulate the entities involved are conducted to test hypotheses about these networks. In recent years, various automated approaches to experiment selection have been proposed. Many of these approaches can be characterized as active machine learning algorithms. Active learning is an iterative process in which a model is learned from data, hypotheses are generated from the model to propose informative experiments, and the experiments yield new data that is used to update the model. This review describes the various models, experiment selection strategies, validation techniques, and successful applications described in the literature; highlights common themes and notable distinctions among methods; and identifies likely directions of future research and open problems in the area.

Sig2GRN: a software tool linking signaling pathway with gene regulatory network for dynamic simulation

Background

Linking computational models of signaling pathways to predicted cellular responses such as gene expression regulation is a major challenge in computational systems biology. In this work, we present Sig2GRN, a Cytoscape plugin that is able to simulate time-course gene expression data given the user-defined external stimuli to the signaling pathways.

Methods

A generalized logical model is used in modeling the upstream signaling pathways. Then a Boolean model and a thermodynamics-based model are employed to predict the downstream changes in gene expression based on the simulated dynamics of transcription factors in signaling pathways.

Results

Our empirical case studies show that the simulation of Sig2GRN can predict changes in gene expression patterns induced by DNA damage signals and drug treatments.

Conclusions

As a software tool for modeling cellular dynamics, Sig2GRN can facilitate studies in systems biology by hypotheses generation and wet-lab experimental design.

Availability: http://histone.scse.ntu.edu.sg/Sig2GRN/

EGFR Signal-Network Reconstruction Demonstrates Metabolic Crosstalk in EMT

Epithelial to mesenchymal transition (EMT) is an important event during development and cancer metastasis. There is limited understanding of the metabolic alterations that give rise to and take place during EMT. Dysregulation of signalling pathways that impact metabolism, including epidermal growth factor receptor (EGFR), are however a hallmark of EMT and metastasis. In this study, we report the investigation into EGFR signalling and metabolic crosstalk of EMT through constraint-based modelling and analysis of the breast epithelial EMT cell model D492 and its mesenchymal counterpart D492M. We built an EGFR signalling network for EMT based on stoichiometric coefficients and constrained the network with gene expression data to build epithelial (EGFR_E) and mesenchymal (EGFR_M) networks. Metabolic alterations arising from differential expression of EGFR genes was derived from a literature review of AKT regulated metabolic genes. Signaling flux differences between EGFR_E and EGFR_M models subsequently allowed metabolism in D492 and D492M cells to be assessed. Higher flux within AKT pathway in the D492 cells compared to D492M suggested higher glycolytic activity in D492 that we confirmed experimentally through measurements of glucose uptake and lactate secretion rates. The signaling genes from the AKT, RAS/MAPK and CaM pathways were predicted to revert D492M to D492 phenotype. Follow-up analysis of EGFR signaling metabolic crosstalk in three additional breast epithelial cell lines highlighted variability in in vitro cell models of EMT. This study shows that the metabolic phenotype may be predicted by in silico analyses of gene expression data of EGFR signaling genes, but this phenomenon is cell-specific and does not follow a simple trend.

Generalized logical model based on network topology to capture the dynamical trends of cellular signaling pathways

Background

Cellular responses to extracellular perturbations require signaling pathways to capture and transmit the signals. However, the underlying molecular mechanisms of signal transduction are not yet fully understood, thus detailed and comprehensive models may not be available for all the signaling pathways. In particular, insufficient knowledge of parameters, which is a long-standing hindrance for quantitative kinetic modeling necessitates the use of parameter-free methods for modeling and simulation to capture dynamic properties of signaling pathways.

Results

We present a computational model that is able to simulate the graded responses to degradations, the sigmoidal biological relationships between signaling molecules and the effects of scheduled perturbations to the cells. The simulation results are validated using experimental data of protein phosphorylation, demonstrating that the proposed model is capable of capturing the main trend of protein activities during the process of signal transduction. Compared with existing simulators, our model has better performance on predicting the state transitions of signaling networks.

Conclusion

The proposed simulation tool provides a valuable resource for modeling cellular signaling pathways using a knowledge-based method.

Designing Experiments to Discriminate Families of Logic Models

Logic models of signaling pathways are a promising way of building effective in silico functional models of a cell, in particular of signaling pathways. The automated learning of Boolean logic models describing signaling pathways can be achieved by training to phosphoproteomics data, which is particularly useful if it is measured upon different combinations of perturbations in a high-throughput fashion. However, in practice, the number and type of allowed perturbations are not exhaustive. Moreover, experimental data are unavoidably subjected to noise. As a result, the learning process results in a family of feasible logical networks rather than in a single model. This family is composed of logic models implementing different internal wirings for the system and therefore the predictions of experiments from this family may present a significant level of variability, and hence uncertainty. In this paper, we introduce a method based on Answer Set Programming to propose an optimal experimental design that aims to narrow down the variability (in terms of input-output behaviors) within families of logical models learned from experimental data. We study how the fitness with respect to the data can be improved after an optimal selection of signaling perturbations and how we learn optimal logic models with minimal number of experiments. The methods are applied on signaling pathways in human liver cells and phosphoproteomics experimental data. Using 25% of the experiments, we obtained logical models with fitness scores (mean square error) 15% close to the ones obtained using all experiments, illustrating the impact that our approach can have on the design of experiments for efficient model calibration.

Toward synthesizing executable models in biology

Over the last decade, executable models of biological behaviors have repeatedly provided new scientific discoveries, uncovered novel insights, and directed new experimental avenues. These models are computer programs whose execution mechanistically simulates aspects of the cell’s behaviors. If the observed behavior of the program agrees with the observed biological behavior, then the program explains the phenomena. This approach has proven beneficial for gaining new biological insights and directing new experimental avenues. One advantage of this approach is that techniques for analysis of computer programs can be applied to the analysis of executable models. For example, one can confirm that a model agrees with experiments for all possible executions of the model (corresponding to all environmental conditions), even if there are a huge number of executions. Various formal methods have been adapted for this context, for example, model checking or symbolic analysis of state spaces. To avoid manual construction of executable models, one can apply synthesis, a method to produce programs automatically from high-level specifications. In the context of biological modeling, synthesis would correspond to extracting executable models from experimental data. We survey recent results about the usage of the techniques underlying synthesis of computer programs for the inference of biological models from experimental data. We describe synthesis of biological models from curated mutation experiment data, inferring network connectivity models from phosphoproteomic data, and synthesis of Boolean networks from gene expression data. While much work has been done on automated analysis of similar datasets using machine learning and artificial intelligence, using synthesis techniques provides new opportunities such as efficient computation of disambiguating experiments, as well as the ability to produce different kinds of models automatically from biological data.