Simulating quantitative cellular responses using asynchronous threshold Boolean network ensembles

Modelling brain dynamics by Boolean networks

Understanding the relationship between brain architecture and brain function is a central issue in neuroscience. We modeled realistic spatio-temporal patterns of brain activity on a human connectome with a Boolean networks model with the aim of computationally replicating certain cognitive functions as they emerge from the standardization of many fMRI studies, identified as patterns of human brain activity. Results from the analysis of simulation data, carried out for different parameters and initial conditions identified many possible paths in the space of parameters of these network models, with normal (ordered asymptotically constant patterns), chaotic (oscillating or disordered) but also highly organized configurations, with countless spatial–temporal patterns. We interpreted these results as routes to chaos, permanence of the systems in regimes of complexity, and ordered stationary behavior, associating these dynamics to cognitive processes. The most important result of this work is the study of emergent neural circuits, i.e., configurations of areas that synchronize over time, both locally and globally, determining the emergence of computational analogues of cognitive processes, which may or may not be similar to the functioning of biological brain. Furthermore, results put in evidence the creation of how the brain creates structures of remote communication. These structures have hierarchical organization, where each level allows for the emergence of brain organizations which behave at the next superior level. Taken together these results allow the interplay of dynamical and topological roots of the multifaceted brain dynamics to be understood.

Lac Operon Boolean Models: Dynamical Robustness and Alternative Improvements

In Veliz-Cuba and Stigler 2011, Boolean models were proposed for the lac operon in Escherichia coli capable of reproducing the operon being OFF, ON and bistable for three (low, medium and high) and two (low and high) parameters, representing the concentration ranges of lactose and glucose, respectively. Of these 6 possible combinations of parameters, 5 produce results that match with the biological experiments of Ozbudak et al., 2004. In the remaining one, the models predict the operon being OFF while biological experiments show a bistable behavior. In this paper, we first explore the robustness of two such models in the sense of how much its attractors change against any deterministic update schedule. We prove mathematically that, in cases where there is no bistability, all the dynamics in both models lack limit cycles while, when bistability appears, one model presents 30% of its dynamics with limit cycles while the other only 23%. Secondly, we propose two alternative improvements consisting of biologically supported modifications; one in which both models match with Ozbudak et al., 2004 in all 6 combinations of parameters and, the other one, where we increase the number of parameters to 9, matching in all these cases with the biological experiments of Ozbudak et al., 2004.

High-throughput toxicogenomic screening of chemicals in the environment using metabolically competent hepatic cell cultures

The ToxCast in vitro screening program has provided concentration-response bioactivity data across more than a thousand assay endpoints for thousands of chemicals found in our environment and commerce. However, most ToxCast screening assays have evaluated individual biological targets in cancer cell lines lacking integrated physiological functionality (such as receptor signaling, metabolism). We evaluated differentiated HepaRGTM cells, a human liver-derived cell model understood to effectively model physiologically relevant hepatic signaling. Expression of 93 gene transcripts was measured by quantitative polymerase chain reaction using Fluidigm 96.96 dynamic arrays in response to 1060 chemicals tested in eight-point concentration-response. A Bayesian framework quantitatively modeled chemical-induced changes in gene expression via six transcription factors including: aryl hydrocarbon receptor, constitutive androstane receptor, pregnane X receptor, farnesoid X receptor, androgen receptor, and peroxisome proliferator-activated receptor alpha. For these chemicals the network model translates transcriptomic data into Bayesian inferences about molecular targets known to activate toxicological adverse outcome pathways. These data also provide new insights into the molecular signaling network of HepaRGTM cell cultures.

Characterizing cleft palate toxicants using ToxCast data, chemical structure, and the biomedical literature

Cleft palate has been linked to both genetic and environmental factors that perturb key events during palatal morphogenesis. As a developmental outcome, it presents a challenging, mechanistically complex endpoint for predictive modeling. A data set of 500 chemicals evaluated for their ability to induce cleft palate in animal prenatal developmental studies was compiled from Toxicity Reference Database and the biomedical literature, which included 63 cleft palate active and 437 inactive chemicals. To characterize the potential molecular targets for chemical-induced cleft palate, we mined the ToxCast high-throughput screening database for patterns and linkages in bioactivity profiles and chemical structural descriptors. ToxCast assay results were filtered for cytotoxicity and grouped by target gene activity to produce a "gene score." Following unsuccessful attempts to derive a global prediction model using structural and gene score descriptors, hierarchical clustering was applied to the set of 63 cleft palate positives to extract local structure-bioactivity clusters for follow-up study. Patterns of enrichment were confirmed on the complete data set, that is, including cleft palate inactives, and putative molecular initiating events identified. The clusters corresponded to ToxCast assays for cytochrome P450s, G-protein coupled receptors, retinoic acid receptors, the glucocorticoid receptor, and tyrosine kinases/phosphatases. These patterns and linkages were organized into preliminary decision trees and the resulting inferences were mapped to a putative adverse outcome pathway framework for cleft palate supported by literature evidence of current mechanistic understanding. This general data-driven approach offers a promising avenue for mining chemical-bioassay drivers of complex developmental endpoints where data are often limited.

Multiplicity of Mathematical Modeling Strategies to Search for Molecular and Cellular Insights into Bacteria Lung Infection

Even today two bacterial lung infections, namely pneumonia and tuberculosis, are among the 10 most frequent causes of death worldwide. These infections still lack effective treatments in many developing countries and in immunocompromised populations like infants, elderly people and transplanted patients. The interaction between bacteria and the host is a complex system of interlinked intercellular and the intracellular processes, enriched in regulatory structures like positive and negative feedback loops. Severe pathological condition can emerge when the immune system of the host fails to neutralize the infection. This failure can result in systemic spreading of pathogens or overwhelming immune response followed by a systemic inflammatory response. Mathematical modeling is a promising tool to dissect the complexity underlying pathogenesis of bacterial lung infection at the molecular, cellular and tissue levels, and also at the interfaces among levels. In this article, we introduce mathematical and computational modeling frameworks that can be used for investigating molecular and cellular mechanisms underlying bacterial lung infection. Then, we compile and discuss published results on the modeling of regulatory pathways and cell populations relevant for lung infection and inflammation. Finally, we discuss how to make use of this multiplicity of modeling approaches to open new avenues in the search of the molecular and cellular mechanisms underlying bacterial infection in the lung.

The Bioavailability of Soluble Cigarette Smoke Extract Is Reduced through Interactions with Cells and Affects the Cellular Response to CSE Exposure

Cellular exposure to cigarette smoke leads to an array of complex responses including apoptosis, cellular senescence, telomere dysfunction, cellular aging, and neoplastic transformation. To study the cellular response to cigarette smoke, a common in vitro model exposes cultured cells to a nominal concentration (i.e. initial concentration) of soluble cigarette smoke extract (CSE). However, we report that use of the nominal concentration of CSE as the only measure of cellular exposure is inadequate. Instead, we demonstrate that cellular response to CSE exposure is dependent not only on the nominal concentration of CSE, but also on specific experimental variables, including the total cell number, and the volume of CSE solution used. As found in other similar xenobiotic assays, our work suggests that the effective dose of CSE is more accurately related to the amount of bioavailable chemicals per cell. In particular, interactions of CSE components both with cells and other physical factors limit CSE bioavailability, as demonstrated by a quantifiably reduced cellular response to CSE that is first modified by such interactions. This has broad implications for the nature of cellular response to CSE exposure, and for the design of in vitro assays using CSE.

Angiogenic activity of breast cancer patients' monocytes reverted by combined use of systems modeling and experimental approaches

Angiogenesis plays a key role in tumor growth and cancer progression. TIE-2-expressing monocytes (TEM) have been reported to critically account for tumor vascularization and growth in mouse tumor experimental models, but the molecular basis of their pro-angiogenic activity are largely unknown. Moreover, differences in the pro-angiogenic activity between blood circulating and tumor infiltrated TEM in human patients has not been established to date, hindering the identification of specific targets for therapeutic intervention. In this work, we investigated these differences and the phenotypic reversal of breast tumor pro-angiogenic TEM to a weak pro-angiogenic phenotype by combining Boolean modelling and experimental approaches. Firstly, we show that in breast cancer patients the pro-angiogenic activity of TEM increased drastically from blood to tumor, suggesting that the tumor microenvironment shapes the highly pro-angiogenic phenotype of TEM. Secondly, we predicted in silico all minimal perturbations transitioning the highly pro-angiogenic phenotype of tumor TEM to the weak pro-angiogenic phenotype of blood TEM and vice versa. In silico predicted perturbations were validated experimentally using patient TEM. In addition, gene expression profiling of TEM transitioned to a weak pro-angiogenic phenotype confirmed that TEM are plastic cells and can be reverted to immunological potent monocytes. Finally, the relapse-free survival analysis showed a statistically significant difference between patients with tumors with high and low expression values for genes encoding transitioning proteins detected in silico and validated on patient TEM. In conclusion, the inferred TEM regulatory network accurately captured experimental TEM behavior and highlighted crosstalk between specific angiogenic and inflammatory signaling pathways of outstanding importance to control their pro-angiogenic activity. Results showed the successful in vitro reversion of such an activity by perturbation of in silico predicted target genes in tumor derived TEM, and indicated that targeting tumor TEM plasticity may constitute a novel valid therapeutic strategy in breast cancer.

Systems Biology and Synthetic Biology: A New Epoch for Toxicology Research

Systems biology and synthetic biology are emerging disciplines which are becoming increasingly utilised in several areas of bioscience. Toxicology is beginning to benefit from systems biology and we suggest in the future that is will also benefit from synthetic biology. Thus, a new era is on the horizon. This review illustrates how a suite of innovative techniques and tools can be applied to understanding complex health and toxicology issues. We review limitations confronted by the traditional computational approaches to toxicology and epidemiology research, using polycyclic aromatic hydrocarbons (PAHs) and their effects on adverse birth outcomes as an illustrative example. We introduce how systems toxicology (and their subdisciplines, genomic, proteomic, and metabolomic toxicology) will help to overcome such limitations. In particular, we discuss the advantages and disadvantages of mathematical frameworks that computationally represent biological systems. Finally, we discuss the nascent discipline of synthetic biology and highlight relevant toxicological centred applications of this technique, including improvements in personalised medicine. We conclude this review by presenting a number of opportunities and challenges that could shape the future of these rapidly evolving disciplines.

Controllability of time-delayed Boolean multiplex control networks under asynchronous stochastic update

In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) with time delay is studied. Firstly, dynamical model of Boolean multiplex control networks is constructed, which is assumed to be under Harvey' asynchronous update and time delay is introduced both in states and controls. By using of semi-tensor product (STP) approach, the logical dynamics is converted into an equivalent algebraic form by obtaining the control-depending network transition matrices of delayed system. Secondly, a necessary and sufficient condition is proved that only control-depending fixed points of the studied dynamics can be controlled with probability one. Thirdly, respectively for two types of controls, the controllability of dynamical control system is investigated. When initial states and time delay are given, formulae are obtained to show a) the reachable set at time s under specified controls; b) the reachable set at time s under arbitrary controls; c) the reachable probabilities to different destination states. Furthermore, an approach is discussed to find a precise control sequence which can steer dynamical system into a specified target with the maximum reachable probability. Examples are shown to illustrate the feasibility of the proposed scheme.

Controllability of asynchronous Boolean multiplex control networks

In this article, the controllability of asynchronous Boolean multiplex control networks (ABMCNs) is studied. First, the model of Boolean multiplex control networks under Harvey' asynchronous update is presented. By means of semi-tensor product approach, the logical dynamics is converted into linear representation, and a generalized formula of control-depending network transition matrices is achieved. Second, a necessary and sufficient condition is proposed to verify that only control-depending fixed points of ABMCNs can be controlled with probability one. Third, using two types of controls, the controllability of system is studied and formulae are given to show: (a) when an initial state is given, the reachable set at time s under a group of specified controls; (b) the reachable set at time s under arbitrary controls; (c) the specific probability values from a given initial state to destination states. Based on the above formulae, an algorithm to calculate overall reachable states from a specified initial state is presented. Moreover, we also discuss an approach to find the particular control sequence which steers the system between two states with maximum probability. Examples are shown to illustrate the feasibility of the proposed scheme.

Data mining reveals a network of early-response genes as a consensus signature of drug-induced in vitro and in vivo toxicity

Gene signatures of drug-induced toxicity are of broad interest, but they are often identified from small-scale, single-time point experiments, and are therefore of limited applicability. To address this issue, we performed multivariate analysis of gene expression, cell-based assays, and histopathological data in the TG-GATEs (Toxicogenomics Project-Genomics Assisted Toxicity Evaluation system) database. Data mining highlights four genes-EGR1, ATF3, GDF15 and FGF21-that are induced 2 h after drug administration in human and rat primary hepatocytes poised to eventually undergo cytotoxicity-induced cell death. Modelling and simulation reveals that these early stress-response genes form a functional network with evolutionarily conserved structure and intrinsic dynamics. This is underlined by the fact that early induction of this network in vivo predicts drug-induced liver and kidney pathology with high accuracy. Our findings demonstrate the value of early gene-expression signatures in predicting and understanding compound-induced toxicity. The identified network can empower first-line tests that reduce animal use and costs of safety evaluation.

Recent development and biomedical applications of probabilistic Boolean networks

Probabilistic Boolean network (PBN) modelling is a semi-quantitative approach widely used for the study of the topology and dynamic aspects of biological systems. The combined use of rule-based representation and probability makes PBN appealing for large-scale modelling of biological networks where degrees of uncertainty need to be considered.A considerable expansion of our knowledge in the field of theoretical research on PBN can be observed over the past few years, with a focus on network inference, network intervention and control. With respect to areas of applications, PBN is mainly used for the study of gene regulatory networks though with an increasing emergence in signal transduction, metabolic, and also physiological networks. At the same time, a number of computational tools, facilitating the modelling and analysis of PBNs, are continuously developed.A concise yet comprehensive review of the state-of-the-art on PBN modelling is offered in this article, including a comparative discussion on PBN versus similar models with respect to concepts and biomedical applications. Due to their many advantages, we consider PBN to stand as a suitable modelling framework for the description and analysis of complex biological systems, ranging from molecular to physiological levels.

Rule-based multi-scale simulation for drug effect pathway analysis

Background

Biological systems are robust and complex to maintain stable phenotypes under various conditions. In these systems, drugs reported the limited efficacy and unexpected side-effects. To remedy this situation, many pharmaceutical laboratories have begun to research combination drugs and some of them have shown successful clinical results. Complementary action of multiple compounds could increase efficacy as well as reduce side-effects through pharmacological interactions. However, experimental approach requires vast cost of preclinical experiments and tests as the number of possible combinations of compound dosages increases exponentially. Computer model-based experiments have been emerging as one of the most promising solutions to cope with such complexity. Though there have been many efforts to model specific molecular pathways using qualitative and quantitative formalisms, they suffer from unexpected results caused by distant interactions beyond their localized models.

Results

In this work, we propose a rule-based multi-scale modelling platform. We have tested this platform with Type 2 diabetes (T2D) model, which involves the malfunction of numerous organs such as pancreas, circulation system, liver, and adipocyte. We have extracted T2D-related 190 rules by manual curation from literature, pathway databases and converting from different types of existing models. We have simulated twenty-two T2D drugs. The results of our simulation show drug effect pathways of T2D drugs and whether combination drugs have efficacy or not and how combination drugs work on the multi-scale model.

Conclusions

We believe that our simulation would help to understand drug mechanism for the drug development and provide a new way to effectively apply existing drugs for new target. It also would give insight for identifying effective combination drugs.

Systems toxicology from genes to organs

This unique overview of systems toxicology methods and techniques begins with a brief account of systems thinking in biology over the last century. We discuss how systems biology and toxicology continue to leverage advances in computational modeling, informatics, large-scale computing, and biotechnology. Next, we chart the genesis of systems toxicology from previous work in physiologically based models, models of early development, and more recently, molecular systems biology. For readers interested in further details this background provides useful linkages to the relevant literature. It also lays the foundations for new ideas in systems toxicology that could translate laboratory measurements of molecular responses from xenobiotic perturbations to adverse organ level effects in humans. By providing innovative solutions across disciplinary boundaries and highlighting key scientific gaps, we believe this chapter provides useful information about the current state, and valuable insight about future directions in systems toxicity.

Modeling drug- and chemical-induced hepatotoxicity with systems biology approaches

We provide an overview of computational systems biology approaches as applied to the study of chemical- and drug-induced toxicity. The concept of “toxicity pathways” is described in the context of the 2007 US National Academies of Science report, “Toxicity testing in the 21st Century: A Vision and A Strategy.” Pathway mapping and modeling based on network biology concepts are a key component of the vision laid out in this report for a more biologically based analysis of dose-response behavior and the safety of chemicals and drugs. We focus on toxicity of the liver (hepatotoxicity) – a complex phenotypic response with contributions from a number of different cell types and biological processes. We describe three case studies of complementary multi-scale computational modeling approaches to understand perturbation of toxicity pathways in the human liver as a result of exposure to environmental contaminants and specific drugs. One approach involves development of a spatial, multicellular “virtual tissue” model of the liver lobule that combines molecular circuits in individual hepatocytes with cell–cell interactions and blood-mediated transport of toxicants through hepatic sinusoids, to enable quantitative, mechanistic prediction of hepatic dose-response for activation of the aryl hydrocarbon receptor toxicity pathway. Simultaneously, methods are being developing to extract quantitative maps of intracellular signaling and transcriptional regulatory networks perturbed by environmental contaminants, using a combination of gene expression and genome-wide protein-DNA interaction data. A predictive physiological model (DILIsym™) to understand drug-induced liver injury (DILI), the most common adverse event leading to termination of clinical development programs and regulatory actions on drugs, is also described. The model initially focuses on reactive metabolite-induced DILI in response to administration of acetaminophen, and spans multiple biological scales.

Understanding cancer mechanisms through network dynamics

Cancer is a complex, multifaceted disease. Cellular systems are perturbed both during the onset and development of cancer, and the behavioural change of tumour cells usually involves a broad range of dynamic variations. To an extent, the difficulty of monitoring the systemic change has been alleviated by recent developments in the high-throughput technologies. At both the genomic as well as proteomic levels, the technological advances in microarray and mass spectrometry, in conjunction with computational simulations and the construction of human interactome maps have facilitated the progress of identifying disease-associated genes. On a systems level, computational approaches developed for network analysis are becoming especially useful for providing insights into the mechanism behind tumour development and metastasis. This review emphasizes network approaches that have been developed to study cancer and provides an overview of our current knowledge of protein-protein interaction networks, and how their systemic perturbation can be analysed by two popular network simulation methods: Boolean network and ordinary differential equations.

Nonparametric simulation of signal transduction networks with semi-synchronized update

Simulating signal transduction in cellular signaling networks provides predictions of network dynamics by quantifying the changes in concentration and activity-level of the individual proteins. Since numerical values of kinetic parameters might be difficult to obtain, it is imperative to develop non-parametric approaches that combine the connectivity of a network with the response of individual proteins to signals which travel through the network. The activity levels of signaling proteins computed through existing non-parametric modeling tools do not show significant correlations with the observed values in experimental results. In this work we developed a non-parametric computational framework to describe the profile of the evolving process and the time course of the proportion of active form of molecules in the signal transduction networks. The model is also capable of incorporating perturbations. The model was validated on four signaling networks showing that it can effectively uncover the activity levels and trends of response during signal transduction process.

Integration of Boolean models exemplified on hepatocyte signal transduction

The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.