Paradoxical Results in Perturbation-Based Signaling Network Reconstruction

Mathematical models are extensively employed to understand physicochemical processes in biological systems. In the absence of detailed mechanistic knowledge, models are often based on network inference methods, which in turn rely upon perturbations to nodes by biochemical means. We have discovered a potential pitfall of the approach underpinning such methods when applied to signaling networks. We first show experimentally, and then explain mathematically, how even in the simplest signaling systems, perturbation methods may lead to paradoxical conclusions: for any given pair of two components X and Y, and depending upon the specific intervention on Y, either an activation or a repression of X could be inferred. This effect is of a different nature from incomplete network identification due to underdetermined data and is a phenomenon intrinsic to perturbations. Our experiments are performed in an in vitro minimal system, thus isolating the effect and showing that it cannot be explained by feedbacks due to unknown intermediates. Moreover, our in vitro system utilizes proteins from a pathway in mammalian (and other eukaryotic) cells that play a central role in proliferation, gene expression, differentiation, mitosis, cell survival, and apoptosis. This pathway is the perturbation target of contemporary therapies for various types of cancers. The results presented here show that the simplistic view of intracellular signaling networks being made up of activation and repression links is seriously misleading, and call for a fundamental rethinking of signaling network analysis and inference methods.     

Dynamic probabilistic threshold networks to infer signaling pathways from time-course perturbation data

Background

Network inference deals with the reconstruction of molecular networks from experimental data. Given N molecular species, the challenge is to find the underlying network. Due to data limitations, this typically is an ill-posed problem, and requires the integration of prior biological knowledge or strong regularization. We here focus on the situation when time-resolved measurements of a system’s response after systematic perturbations are available.

Results

We present a novel method to infer signaling networks from time-course perturbation data. We utilize dynamic Bayesian networks with probabilistic Boolean threshold functions to describe protein activation. The model posterior distribution is analyzed using evolutionary MCMC sampling and subsequent clustering, resulting in probability distributions over alternative networks. We evaluate our method on simulated data, and study its performance with respect to data set size and levels of noise. We then use our method to study EGF-mediated signaling in the ERBB pathway.

Conclusions

Dynamic Probabilistic Threshold Networks is a new method to infer signaling networks from time-series perturbation data. It exploits the dynamic response of a system after external perturbation for network reconstruction. On simulated data, we show that the approach outperforms current state of the art methods. On the ERBB data, our approach recovers a significant fraction of the known interactions, and predicts novel mechanisms in the ERBB pathway.

Electronic supplementary material

The online version of this article (doi:10.1186/1471-2105-15-250) contains supplementary material, which is available to authorized users.     

X-Y Exchange and the Coevolution of the X and Y Rdna Arrays in Drosophila melanogaster

The nucleolus organizers on the X and Y chromosomes of Drosophila melanogaster are the sites of 200-250 tandemly repeated genes for ribosomal RNA. As there is no meiotic crossing over in male Drosophila, the X and Y chromosomal rDNA arrays should be evolutionarily independent, and therefore divergent. The rRNAs produced by X and Y are, however, very similar, if not identical. Molecular, genetic and cytological analyses of a series of X chromosome rDNA deletions (bb alleles) showed that they arose by unequal exchange through the nucleolus organizers of the X and Y chromosomes. Three separate exchange events generated compound X·Y ^L chromosomes carrying mainly Y-specific rDNA. This led to the hypothesis that X-Y exchange is responsible for the coevolution of X and Y chromosomal rDNA. We have tested and confirmed several of the predictions of this hypothesis: First, X· Y^L chromosomes must be found in wild populations. We have found such a chromosome. Second, the X·Y^L chromosome must lose the Y^L arm, and/or be at a selective disadvantage to normal X⁺ chromosomes, to retain the normal morphology of the X chromosome. Six of seventeen sublines founded from homozygous X·Y^Lbb stocks have become fixed for chromosomes with spontaneous loss of part or all of the appended Y^L. Third, rDNA variants on the X chromosome are expected to be clustered within the X⁺ nucleolus organizer, recently donated (" Y") forms being proximal, and X-specific forms distal. We present evidence for clustering of rRNA genes containing Type 1 insertions. Consequently, X-Y exchange is probably responsible for the coevolution of X and Y rDNA arrays.     

Quarnet Inference Rules for Level-1 Networks

An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set X of species from a collection of trees, each having leaf-set some subset of X. In the 1980s, Colonius and Schulze gave certain inference rules for deciding when a collection of 4-leaved trees, one for each 4-element subset of X, can be simultaneously displayed by a single supertree with leaf-set X. Recently, it has become of interest to extend this and related results to phylogenetic networks. These are a generalization of phylogenetic trees which can be used to represent reticulate evolution (where species can come together to form a new species). It has recently been shown that a certain type of phylogenetic network, called a (unrooted) level-1 network, can essentially be constructed from 4-leaved trees. However, the problem of providing appropriate inference rules for such networks remains unresolved. Here, we show that by considering 4-leaved networks, called quarnets, as opposed to 4-leaved trees, it is possible to provide such rules. In particular, we show that these rules can be used to characterize when a collection of quarnets, one for each 4-element subset of X, can all be simultaneously displayed by a level-1 network with leaf-set X. The rules are an intriguing mixture of tree inference rules, and an inference rule for building up a cyclic ordering of X from orderings on subsets of X of size 4. This opens up several new directions of research for inferring phylogenetic networks from smaller ones, which could yield new algorithms for solving the supernetwork problem in phylogenetics.     

Harmonic analysis of Boolean networks: determinative power and perturbations

Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer this question, a notion that quantifies the determinative power of an input over the states of the nodes in the network is needed. We argue that the mutual information (MI) between a given subset of the inputs X={X₁,...,X_n} of some node i and its associated function f_i(X) quantifies the determinative power of this set of inputs over node i. We compare the determinative power of a set of inputs to the sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large sensitivity to perturbations does not necessarily have large determinative power. However, for unate functions, which play an important role in genetic regulatory networks, we find a direct relation between MI and sensitivity to perturbations. As an application of our results, we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs.     

Formulation of Dacarbazine-Loaded Cubosomes—Part I: Influence of Formulation Variables

The purpose of this study was to investigate the combined influence of three-level, three-factor variables on the formulation of dacarbazine (a water-soluble drug) loaded cubosomes. Box–Behnken design was used to obtain a second-order polynomial equation with interaction terms to predict response values. In this study, the selected and coded variables X₁, X₂, and X₃ representing the amount of monoolein, polymer, and drug as the independent variables, respectively. Fifteen runs of experiments were conducted, and the particle size (Y₁) and encapsulation efficiency (Y₂) were evaluated as dependent variables. We performed multiple regression to establish a full-model second-order polynomial equation relating independent and dependent variables. A second-order polynomial regression model was constructed for Y₁ and confirmed by performing checkpoint analysis. The optimization process and Pareto charts were obtained automatically, and they predicted the levels of independent coded variables X₁, X₂, and X₃ (−1, 0.53485, and −1, respectively) and minimized Y₁ while maximizing Y₂. These corresponded to a cubosome formulation made from 100 mg of monoolein, 107 mg of polymer, and 2 mg with average diameter of 104.7 nm and an encapsulation efficiency of 6.9%. The Box–Behnken design proved to be a useful tool to optimize the particle size of these drug-loaded cubosomes. For encapsulation efficiency (Y₂), further studies are needed to identify appropriate regression model.Key words: Box–Behnken design, cubosomes, dacarbazine, formulation variables     

Regulation of the activity of the bacterial histidine kinase PleC by the scaffolding protein PodJ

Scaffolding proteins can customize the response of signaling networks to support cell development and behaviors. PleC is a bifunctional histidine kinase whose signaling activity coordinates asymmetric cell division to yield a motile swarmer cell and a stalked cell in the gram-negative bacterium Caulobacter crescentus. Past studies have shown that PleC’s switch in activity from kinase to phosphatase correlates with a change in its subcellular localization pattern from diffuse to localized at the new cell pole. Here we investigated how the bacterial scaffolding protein PodJ regulates the subcellular positioning and activity of PleC. We reconstituted the PleC-PodJ signaling complex through both heterologous expressions in Escherichia coli and in vitro studies. In vitro, PodJ phase separates as a biomolecular condensate that recruits PleC and inhibits its kinase activity. We also constructed an in vivo PleC-CcaS chimeric histidine kinase reporter assay and demonstrated using this method that PodJ leverages its intrinsically disordered region to bind to PleC’s PAS sensory domain and regulate PleC-CcaS signaling. Regulation of the PleC-CcaS was most robust when PodJ was concentrated at the cell poles and was dependent on the allosteric coupling between PleC-CcaS’s PAS sensory domain and its downstream histidine kinase domain. In conclusion, our in vitro biochemical studies suggest that PodJ phase separation may be coupled to changes in PleC enzymatic function. We propose that this coupling of phase separation and allosteric regulation may be a generalizable phenomenon among enzymes associated with biomolecular condensates.     

Bone morphogenetic protein 6–mediated crosstalk between endothelial cells and hepatocytes recapitulates the iron-sensing pathway in vitro

Liver sinusoidal endothelial cell–derived bone morphogenetic protein 6 (BMP6) and the BMP6–small mothers against decapentaplegic homolog (SMAD) signaling pathway are essential for the expression of hepcidin, the secretion of which is considered the systemic master switch of iron homeostasis. However, there are continued controversies related to the strong and direct suppressive effect of iron on hepatocellular hepcidin in vitro in contrast to in vivo conditions. Here, we directly studied the crosstalk between endothelial cells (ECs) and hepatocytes using in vitro coculture models that mimic hepcidin signaling in vivo. Huh7 cells were directly cocultured with ECs, and EC conditioned media (CM) were also used to culture Huh7 cells and primary mouse hepatocytes. To explore the reactions of ECs to surrounding iron, they were grown in the presence of ferric ammonium citrate and heme, two iron-containing molecules. We found that both direct coculture with ECs and EC-CM significantly increased hepcidin expression in Huh7 cells. The upstream SMAD pathway, including phosphorylated SMAD1/5/8, SMAD1, and inhibitor of DNA binding 1, was induced by EC-CM, promoting hepcidin expression. Efficient blockage of this EC-mediated hepcidin upregulation by an inhibitor of the BMP6 receptor ALK receptor tyrosine kinase 2/3 or BMP6 siRNA identified BMP6 as a major hepcidin regulator in this coculture system, which highly fits the model of hepcidin regulation by iron in vivo. In addition, EC-derived BMP6 and hepcidin were highly sensitive to levels of not only ferric iron but also heme as low as 500 nM. We here establish a hepatocyte–endothelial coculture system to fully recapitulate iron regulation by hepcidin using EC-derived BMP6.     

Characterization of interactions within the Igα/Igβ transmembrane domains of the human B-cell receptor provides insights into receptor assembly

The B-cell receptor (BCR), a complex comprised of a membrane-associated immunoglobulin and the Igα/β heterodimer, is one of the most important immune receptors in humans and controls B-cell development, activity, selection, and death. BCR signaling plays key roles in autoimmune diseases and lymphoproliferative disorders, yet, despite the clinical significance of this protein complex, key regions (i.e., the transmembrane domains) have yet to be structurally characterized. The mechanism for BCR signaling also remains unclear and has been variously described by the mutually exclusive cross-linking and dissociation activation models. Common to these models is the significance of local plasma membrane composition, which implies that interactions between BCR transmembrane domains (TMDs) play a role in receptor functionality. Here we used an in vivo assay of TMD oligomerization called GALLEX alongside spectroscopic and computational methods to characterize the structures and interactions of human Igα and Igβ TMDs in detergent micelles and natural membranes. We observed weak self-association of the Igβ TMD and strong self-association of the Igα TMD, which scanning mutagenesis revealed was entirely stabilized by an E–X₁₀–P motif. We also demonstrated strong heterotypic interactions between the Igα and Igβ TMDs both in vitro and in vivo, which scanning mutagenesis and computational models suggest is multiconfigurational but can accommodate distinct interaction sites for self-interactions and heterotypic interactions of the Igα TMD. Taken together, these results demonstrate that the TMDs of the human BCR are sites of strong protein–protein interactions that may direct BCR assembly, endoplasmic reticulum retention, and immune signaling.     

Modeling species-specific diacylglycerol dynamics in the RAW 264.7 macrophage

A mathematical model of the G protein signaling pathway in RAW 264.7 macrophages downstream of P2Y₆ receptors activated by the ubiquitous signaling nucleotide uridine 5’-diphosphate is developed. The model, which is based on time-course measurements of inositol trisphosphate, cytosolic calcium, and diacylglycerol, focuses particularly on differential dynamics of multiple chemical species of diacylglycerol. When using the canonical pathway representation, the model predicted that key interactions were missing from the current network structure. Indeed, the model suggested that accurate depiction of experimental observations required an additional branch to the signaling pathway. An intracellular pool of diacylglycerol is immediately phosphorylated upon stimulation of an extracellular receptor for uridine 5’-diphosphate and subsequently used to aid replenishment of phosphatidylinositol. As a result of sensitivity analysis of the model parameters, key predictions can be made regarding which of these parameters are the most sensitive to perturbations and are therefore most responsible for output uncertainty.     

RegnANN: Reverse Engineering Gene Networks using Artificial Neural Networks

RegnANN is a novel method for reverse engineering gene networks based on an ensemble of multilayer perceptrons. The algorithm builds a regressor for each gene in the network, estimating its neighborhood independently. The overall network is obtained by joining all the neighborhoods. RegnANN makes no assumptions about the nature of the relationships between the variables, potentially capturing high-order and non linear dependencies between expression patterns. The evaluation focuses on synthetic data mimicking plausible submodules of larger networks and on biological data consisting of submodules of Escherichia coli. We consider Barabasi and Erdös-Rényi topologies together with two methods for data generation. We verify the effect of factors such as network size and amount of data to the accuracy of the inference algorithm. The accuracy scores obtained with RegnANN is methodically compared with the performance of three reference algorithms: ARACNE, CLR and KELLER. Our evaluation indicates that RegnANN compares favorably with the inference methods tested. The robustness of RegnANN, its ability to discover second order correlations and the agreement between results obtained with this new methods on both synthetic and biological data are promising and they stimulate its application to a wider range of problems.     

Regulation of DNA-binding activity of the Staphylococcus aureus catabolite control protein A by copper (II)-mediated oxidation

Catabolite control protein A (CcpA) of the human pathogen Staphylococcus aureus is an essential DNA regulator for carbon catabolite repression and virulence, which facilitates bacterial survival and adaptation to a changing environment. Here, we report that copper (II) signaling mediates the DNA-binding capability of CcpA in vitro and in vivo. Copper (II) catalyzes the oxidation of two cysteine residues (Cys216 and Cys242) in CcpA to form intermolecular disulfide bonds between two CcpA dimers, which results in the formation and dissociation of a CcpA tetramer of CcpA from its cognate DNA promoter. We further demonstrate that the two cysteine residues on CcpA are important for S. aureus to resist host innate immunity, indicating that S. aureus CcpA senses the redox-active copper (II) ions as a natural signal to cope with environmental stress. Together, these findings reveal a novel regulatory mechanism for CcpA activity through copper (II)-mediated oxidation.     

Ghrelin protects against lipopolysaccharide-induced acute respiratory distress syndrome through the PI3K/AKT pathway

Pulmonary endothelial barrier dysfunction is a major pathophysiology observed in acute respiratory distress syndrome (ARDS). Ghrelin, a key regulator of metabolism, has been shown to play protective roles in the respiratory system. However, its effects on lipopolysaccharide (LPS)-induced pulmonary endothelial barrier injury are unknown. In this study, the effects of ghrelin on LPS-induced ARDS and endothelial cell injury were evaluated in vivo and in vitro. In vivo, mice treated with LPS (3 mg/kg intranasal application) were used to establish the ARDS model. Annexin V/propidium iodide apoptosis assay, scratch-wound assay, tube formation assay, transwell permeability assay, and Western blotting experiment were performed to reveal in vitro effects and underlying mechanisms of ghrelin on endothelial barrier function. Our results showed that ghrelin had protective effects on LPS-induced ARDS and endothelial barrier disruption by inhibiting apoptosis, promoting cell migration and tube formation, and activating the PI3K/AKT signaling pathway. Furthermore, ghrelin stabilized LPS-induced endothelial barrier function by decreasing endothelial permeability and increasing the expression of the intercellular junction protein vascular endothelial cadherin. LY294002, a specific inhibitor of the PI3K pathway, reversed the protective effects of ghrelin on the endothelial cell barrier. In conclusion, our findings indicated that ghrelin protected against LPS-induced ARDS by impairing the pulmonary endothelial barrier partly through activating the PI3K/AKT pathway. Thus, ghrelin may be a valuable therapeutic strategy for the prevention or treatment of ARDS.     

DREAM4: Combining genetic and dynamic information to identify biological networks and dynamical models

Background

Current technologies have lead to the availability of multiple genomic data types in sufficient quantity and quality to serve as a basis for automatic global network inference. Accordingly, there are currently a large variety of network inference methods that learn regulatory networks to varying degrees of detail. These methods have different strengths and weaknesses and thus can be complementary. However, combining different methods in a mutually reinforcing manner remains a challenge.

Methodology

We investigate how three scalable methods can be combined into a useful network inference pipeline. The first is a novel t-test–based method that relies on a comprehensive steady-state knock-out dataset to rank regulatory interactions. The remaining two are previously published mutual information and ordinary differential equation based methods (tlCLR and Inferelator 1.0, respectively) that use both time-series and steady-state data to rank regulatory interactions; the latter has the added advantage of also inferring dynamic models of gene regulation which can be used to predict the system''s response to new perturbations.

Conclusion/Significance

Our t-test based method proved powerful at ranking regulatory interactions, tying for first out of methods in the DREAM4 100-gene in-silico network inference challenge. We demonstrate complementarity between this method and the two methods that take advantage of time-series data by combining the three into a pipeline whose ability to rank regulatory interactions is markedly improved compared to either method alone. Moreover, the pipeline is able to accurately predict the response of the system to new conditions (in this case new double knock-out genetic perturbations). Our evaluation of the performance of multiple methods for network inference suggests avenues for future methods development and provides simple considerations for genomic experimental design. Our code is publicly available at http://err.bio.nyu.edu/inferelator/.