Boolean network analysis of a neurotransmitter signaling pathway

BACKGROUND: A Boolean network is a simple computational model that may provide insight into the overall behavior of genetic networks and is represented by variables with two possible states (on/off), of the individual nodes/genes of the network. In this study, a Boolean network model has been used to simulate a molecular pathway between two neurotransmitter receptor, dopamine and glutamate receptor, systems in order to understand the consequence of using logic gate rules between nodes, which have two possible states (active and inactive). RESULTS: The dynamical properties of this Boolean network model of the biochemical pathway shows that, the pathway is stable and that, deletion/knockout of certain biologically important nodes cause significant perturbation to this network. The analysis clearly shows that in addition to the expected components dopamine and dopamine receptor 2 (DRD2), Ca(2+) ions play a critical role in maintaining stability of the pathway. CONCLUSION: So this method may be useful for the identification of potential genetic targets, whose loss of function in biochemical pathways may be responsible for disease onset. The molecular pathway considered in this study has been implicated with a complex disorder like schizophrenia, which has a complex multifactorial etiology.     

细胞信号网络功能鲁棒的简并性拓扑特征

细胞信号网络对于外界环境的干扰表现出优良的鲁棒性,但是其维持功能鲁棒的内在机制尚未明确,本文研究了细胞信号网络功能鲁棒性的拓扑特征。选择布尔网络模型模拟细胞网络的动态行为,利用网络节点状态的扰动模拟外界环境干扰。基于演化策略探寻不同网络拓扑的功能并分析其在干扰环境下的鲁棒性,采用埃德尔曼提出的基于信息论的计算方法评估网络拓扑的简并度、冗余度和复杂度等拓扑属性,对比分析它们与功能鲁棒度的相关性及作用机理。结果显示,在网络模型的演化过程中,其拓扑简并度与功能鲁棒度显著正相关,相关性水平高于拓扑冗余度与鲁棒度的相关性。并且,随着鲁棒度的提升,网络的节点数和复杂度也随之升高,同样简并度与网络的节点数和复杂度的相关性高于拓扑冗余度与网络的节点数和复杂度的相关性。这说明增加的网络节点以简并的方式同时提高了网络拓扑的鲁棒度和复杂度。因此,细胞网络功能鲁棒性的拓扑特征是简并而不是冗余,简并为解决生物系统的复杂问题提供了有效手段,为人工系统的可靠性设计提供有益的借鉴。     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.     

A Comprehensive,Multi-Scale Dynamical Model of ErbB Receptor Signal Transduction in Human Mammary Epithelial Cells

The non-receptor tyrosine kinase Src and receptor tyrosine kinase epidermal growth factor receptor (EGFR/ErbB1) have been established as collaborators in cellular signaling and their combined dysregulation plays key roles in human cancers, including breast cancer. In part due to the complexity of the biochemical network associated with the regulation of these proteins as well as their cellular functions, the role of Src in EGFR regulation remains unclear. Herein we present a new comprehensive, multi-scale dynamical model of ErbB receptor signal transduction in human mammary epithelial cells. This model, constructed manually from published biochemical literature, consists of 245 nodes representing proteins and their post-translational modifications sites, and over 1,000 biochemical interactions. Using computer simulations of the model, we find it is able to reproduce a number of cellular phenomena. Furthermore, the model predicts that overexpression of Src results in increased endocytosis of EGFR in the absence/low amount of the epidermal growth factor (EGF). Our subsequent laboratory experiments also suggest increased internalization of EGFR upon Src overexpression under EGF-deprived conditions, further supporting this model-generated hypothesis.     

Boolink: a graphical interface for open access Boolean network simulations and use in guard cell CO2 signaling

Signaling networks are at the heart of almost all biological processes. Most of these networks contain large number of components, and often either the connections between these components are not known or the rate equations that govern the dynamics of soluble signaling components are not quantified. This uncertainty in network topology and parameters can make it challenging to formulate detailed mathematical models. Boolean networks, in which all components are either on or off, have emerged as viable alternatives to detailed mathematical models that contain rate constants and other parameters. Therefore, open-source platforms of Boolean models for community use are desirable. Here, we present Boolink, a freely available graphical user interface that allows users to easily construct and analyze existing Boolean networks. Boolink can be applied to any Boolean network. We demonstrate its application using a previously published network for abscisic acid (ABA)-driven stomatal closure in Arabidopsis spp. (Arabidopsis thaliana). We also show how Boolink can be used to generate testable predictions by extending the network to include CO₂ regulation of stomatal movements. Predictions of the model were experimentally tested, and the model was iteratively modified based on experiments showing that ABA effectively closes Arabidopsis stomata at near-zero CO₂ concentrations (1.5-ppm CO₂). Thus, Boolink enables public generation and the use of existing Boolean models, including the prior developed ABA signaling model with added CO₂ signaling components.

An open-source, graphical interface for the simulation of Boolean networks is presented, applied to an abscisic acid signaling network in guard cells, and extended to include input from CO₂.     

TNFR1 Signaling Is Associated with Backbone Conformational Changes of Receptor Dimers Consistent with Overactivation in the R92Q TRAPS Mutant

The widely accepted model for tumor necrosis factor 1 (TNFR1) signaling is that ligand binding causes receptor trimerization, which triggers a reorganization of cytosolic domains and thus initiates intracellular signaling. This model of stoichiometrically driven receptor activation does not account for the occurrence of ligand independent signaling in overexpressed systems, nor does it explain the constitutive activity of the R92Q mutant associated with TRAPS. More recently, ligand binding has been shown to result in the formation of high molecular weight, oligomeric networks. Although the dimer, shown to be the preligand structure, is thought to remain present within ligand-receptor networks, it is unknown whether network formation or ligand-induced structural change to the dimer itself is the trigger for TNFR1 signaling. In the present study, we investigate the available crystal structures of TNFR1 to explore backbone dynamics and infer conformational transitions associated with ligand binding. Using normal-mode analysis, we characterize the dynamic coupling between the TNFR1 ligand binding and membrane proximal domains and suggest a mechanism for ligand-induced activation. Furthermore, our data are supported experimentally by FRET showing that the constitutively active R92Q mutant adopts an altered conformation compared to wild-type. Collectively, our results suggest that the signaling competent architecture is the receptor dimer and that ligand binding modifies domain mobilities intrinsic to the receptor structure, allowing it to sample a separate, active conformation mediated by network formation.     

Role of network branching in eliciting differential short-term signaling responses in the hypersensitive epidermal growth factor receptor mutants implicated in lung cancer

We study the effects of EGFR inhibition in wild-type and mutant cell lines upon tyrosine kinase inhibitor TKI treatment through a systems level deterministic and spatially homogeneous model to help characterize the hypersensitive response of the cancer cell lines harboring constitutively active mutant kinases to inhibitor treatment. By introducing a molecularly resolved branched network systems model (the molecular resolution is introduced for EGFR reactions and interactions in order to distinguish differences in activation between wild-type and mutants), we are able to quantify differences in (1) short-term signaling in downstream ERK and Akt activation, (2) the changes in the cellular inhibition EC50 associated with receptor phosphorylation (i.e., 50% inhibition of receptor phosphorylation in the cellular context), and (3) EC50 for the inhibition of activated downstream markers ERK-(p) and Akt-(p), where (p) denotes phosphorylated, upon treatment with the inhibitors in cell lines carrying both wild-type and mutant forms of the receptor. Using the branched signaling model, we illustrate a possible mechanism for preferential Akt activation in the cell lines harboring the oncogenic mutants of EGFR implicated in non-small-cell lung cancer and the enhanced efficacy of the inhibitor erlotinib especially in ablating the cellular Akt-(p) response. Using a simple phenomenological model to describe the effect of Akt activation on cellular decisions, we discuss how this preferential Akt activation is conducive to cellular oncogene addiction and how its disruption can lead to dramatic apoptotic response and hence remarkable inhibitor efficacies. We also identify key network nodes of our branched signaling model through sensitivity analysis as those rendering the network hypersensitive to enhanced ERK-(p) and Akt-(p); intriguingly, the identified nodes have a strong correlation with species implicated in oncogenic transformations in human cancers as well as in drug resistance mechanisms identified for the inhibitors in non-small-cell lung cancer therapy.     

Hub-centered gene network reconstruction using automatic relevance determination

Network inference deals with the reconstruction of biological networks from experimental data. A variety of different reverse engineering techniques are available; they differ in the underlying assumptions and mathematical models used. One common problem for all approaches stems from the complexity of the task, due to the combinatorial explosion of different network topologies for increasing network size. To handle this problem, constraints are frequently used, for example on the node degree, number of edges, or constraints on regulation functions between network components. We propose to exploit topological considerations in the inference of gene regulatory networks. Such systems are often controlled by a small number of hub genes, while most other genes have only limited influence on the network's dynamic. We model gene regulation using a Bayesian network with discrete, Boolean nodes. A hierarchical prior is employed to identify hub genes. The first layer of the prior is used to regularize weights on edges emanating from one specific node. A second prior on hyperparameters controls the magnitude of the former regularization for different nodes. The net effect is that central nodes tend to form in reconstructed networks. Network reconstruction is then performed by maximization of or sampling from the posterior distribution. We evaluate our approach on simulated and real experimental data, indicating that we can reconstruct main regulatory interactions from the data. We furthermore compare our approach to other state-of-the art methods, showing superior performance in identifying hubs. Using a large publicly available dataset of over 800 cell cycle regulated genes, we are able to identify several main hub genes. Our method may thus provide a valuable tool to identify interesting candidate genes for further study. Furthermore, the approach presented may stimulate further developments in regularization methods for network reconstruction from data.     

Intrinsic properties of Boolean dynamics in complex networks

We study intrinsic properties of attractor in Boolean dynamics of complex networks with scale-free topology, comparing with those of the so-called Kauffman's random Boolean networks. We numerically study both frozen and relevant nodes in each attractor in the dynamics of relatively small networks (20?N?200). We investigate numerically robustness of an attractor to a perturbation. An attractor with cycle length of ?_c in a network of size N consists of ?_c states in the state space of 2^N states; each attractor has the arrangement of N nodes, where the cycle of attractor sweeps ?_c states. We define a perturbation as a flip of the state on a single node in the attractor state at a given time step. We show that the rate between unfrozen and relevant nodes in the dynamics of a complex network with scale-free topology is larger than that in Kauffman's random Boolean network model. Furthermore, we find that in a complex scale-free network with fluctuation of the in-degree number, attractors are more sensitive to a state flip for a highly connected node (i.e. input-hub node) than to that for a less connected node. By some numerical examples, we show that the number of relevant nodes increases, when an input-hub node is coincident with and/or connected with an output-hub node (i.e. a node with large output-degree) one another.     

On the long-run sensitivity of probabilistic Boolean networks

Boolean networks and, more generally, probabilistic Boolean networks, as one class of gene regulatory networks, model biological processes with the network dynamics determined by the logic-rule regulatory functions in conjunction with probabilistic parameters involved in network transitions. While there has been significant research on applying different control policies to alter network dynamics as future gene therapeutic intervention, we have seen less work on understanding the sensitivity of network dynamics with respect to perturbations to networks, including regulatory rules and the involved parameters, which is particularly critical for the design of intervention strategies. This paper studies this less investigated issue of network sensitivity in the long run. As the underlying model of probabilistic Boolean networks is a finite Markov chain, we define the network sensitivity based on the steady-state distributions of probabilistic Boolean networks and call it long-run sensitivity. The steady-state distribution reflects the long-run behavior of the network and it can give insight into the dynamics or momentum existing in a system. The change of steady-state distribution caused by possible perturbations is the key measure for intervention. This newly defined long-run sensitivity can provide insight on both network inference and intervention. We show the results for probabilistic Boolean networks generated from random Boolean networks and the results from two real biological networks illustrate preliminary applications of sensitivity in intervention for practical problems.     

Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5-10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.     

Quantitative phosphoproteomic analysis of signaling network dynamics

Protein phosphorylation mediated cellular signaling is a highly regulated, dynamic process that controls many aspects of cellular biology. Over the past few years many methods have been developed to quantify temporal dynamics of protein phosphorylation, including mass spectrometry, which can be applied in both an unbiased, discovery mode and in a targeted mode to monitor specific phosphorylation sites. Other methods, such as kinase activity assays and antibody microarrays, have been applied to quantify central nodes in the signaling network, yielding intriguing biological insights. This review provides a concise overview of the latest advances in the quantitative analysis of signaling dynamics including a brief commentary on the future of the field.     

Deconstruction and Dynamical Robustness of Regulatory Networks: Application to the Yeast Cell Cycle Networks

Analyzing all the deterministic dynamics of a Boolean regulatory network is a difficult problem since it grows exponentially with the number of nodes. In this paper, we present mathematical and computational tools for analyzing the complete deterministic dynamics of Boolean regulatory networks. For this, the notion of alliance is introduced, which is a subconfiguration of states that remains fixed regardless of the values of the other nodes. Also, equivalent classes are considered, which are sets of updating schedules which have the same dynamics. Using these techniques, we analyze two yeast cell cycle models. Results show the effectiveness of the proposed tools for analyzing update robustness as well as the discovery of new information related to the attractors of the yeast cell cycle models considering all the possible deterministic dynamics, which previously have only been studied considering the parallel updating scheme.     

Information routing driven by background chatter in a signaling network

Living systems are capable of processing multiple sources of information simultaneously. This is true even at the cellular level, where not only coexisting signals stimulate the cell, but also the presence of fluctuating conditions is significant. When information is received by a cell signaling network via one specific input, the existence of other stimuli can provide a background activity -or chatter- that may affect signal transmission through the network and, therefore, the response of the cell. Here we study the modulation of information processing by chatter in the signaling network of a human cell, specifically, in a Boolean model of the signal transduction network of a fibroblast. We observe that the level of external chatter shapes the response of the system to information carrying signals in a nontrivial manner, modulates the activity levels of the network outputs, and effectively determines the paths of information flow. Our results show that the interactions and node dynamics, far from being random, confer versatility to the signaling network and allow transitions between different information-processing scenarios.     

Molecular network control through boolean canalization

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This work studies the role of canalization in the control of Boolean molecular networks. It provides a method for identifying the potential edges to control in the wiring diagram of a network for avoiding undesirable state transitions. The method is based on identifying appropriate input-output combinations on undesirable transitions that can be modified using the edges in the wiring diagram of the network. Moreover, a method for estimating the number of changed transitions in the state space of the system as a result of an edge deletion in the wiring diagram is presented. The control methods of this paper were applied to a mutated cell-cycle model and to a p53-mdm2 model to identify potential control targets.     

The effect of contact heterogeneity and multiple routes of transmission on final epidemic size

Heterogeneity in the number of potentially infectious contacts amongst members of a population increases the basic reproduction ratio (R(0)) and markedly alters disease dynamics compared to traditional mean-field models. Most models describing transmission on contact networks only account for one specific route of transmission. However, for many infectious diseases multiple routes of transmission exist. The model presented here captures transmission through a well defined network of contacts, complemented by mean-field type transmission amongst the nodes of the network that accounts for alternative routes of transmission. The impact of these combined transmission mechanisms on the final epidemic size is investigated analytically. The analytic predictions for the purely mean-field case and the transmission through the network-only case are confirmed by individual-based network simulations. There is a critical transmission potential above which an increased contribution of the mean-field type transmission increases the final epidemic size while an increased contribution of the transmission through the network decreases it. Below the critical transmission potential the opposite effect is observed.     

Perturbation Centrality and Turbine: A Novel Centrality Measure Obtained Using a Versatile Network Dynamics Tool

Analysis of network dynamics became a focal point to understand and predict changes of complex systems. Here we introduce Turbine, a generic framework enabling fast simulation of any algorithmically definable dynamics on very large networks. Using a perturbation transmission model inspired by communicating vessels, we define a novel centrality measure: perturbation centrality. Hubs and inter-modular nodes proved to be highly efficient in perturbation propagation. High perturbation centrality nodes of the Met-tRNA synthetase protein structure network were identified as amino acids involved in intra-protein communication by earlier studies. Changes in perturbation centralities of yeast interactome nodes upon various stresses well recapitulated the functional changes of stressed yeast cells. The novelty and usefulness of perturbation centrality was validated in several other model, biological and social networks. The Turbine software and the perturbation centrality measure may provide a large variety of novel options to assess signaling, drug action, environmental and social interventions.