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.     

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.     

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.     

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/.     

Identification of an endocytosis motif in an intracellular loop of Wntless protein, essential for its recycling and the control of Wnt protein signaling

The secretion of Wnt signaling proteins is dependent upon the transmembrane sorting receptor, Wntless (Wls), which recycles between the trans-Golgi network and the cell surface. Loss of Wls results in impairment of Wnt secretion and defects in development and homeostasis in Drosophila, Caenorhabditis elegans, and the mouse. The sorting signals for the internalization and trafficking of Wls have not been defined. Here, we demonstrate that Wls internalization requires clathrin and dynamin I, components of the clathrin-mediated endocytosis pathway. Moreover, we have identified a conserved YXXφ endocytosis motif in the third intracellular loop of the multipass membrane protein Wls. Mutation of the tyrosine-based motif YEGL to AEGL (Y425A) resulted in the accumulation of human mutant Wls on the cell surface of transfected HeLa cells. The cell surface accumulation of Wls^AEGL was rescued by the insertion of a classical YXXφ motif in the cytoplasmic tail. Significantly, a Drosophila Wls^AEGL mutant displayed a wing notch phenotype, with reduced Wnt secretion and signaling. These findings demonstrate that YXXφ endocytosis motifs can occur in the intracellular loops of multipass membrane proteins and, moreover, provide direct evidence that the trafficking of Wls is required for efficient secretion of Wnt signaling proteins.     

Petri Nets with Fuzzy Logic (PNFL): Reverse Engineering and Parametrization

Background

The recent DREAM4 blind assessment provided a particularly realistic and challenging setting for network reverse engineering methods. The in silico part of DREAM4 solicited the inference of cycle-rich gene regulatory networks from heterogeneous, noisy expression data including time courses as well as knockout, knockdown and multifactorial perturbations.

Methodology and Principal Findings

We inferred and parametrized simulation models based on Petri Nets with Fuzzy Logic (PNFL). This completely automated approach correctly reconstructed networks with cycles as well as oscillating network motifs. PNFL was evaluated as the best performer on DREAM4 in silico networks of size 10 with an area under the precision-recall curve (AUPR) of 81%. Besides topology, we inferred a range of additional mechanistic details with good reliability, e.g. distinguishing activation from inhibition as well as dependent from independent regulation. Our models also performed well on new experimental conditions such as double knockout mutations that were not included in the provided datasets.

Conclusions

The inference of biological networks substantially benefits from methods that are expressive enough to deal with diverse datasets in a unified way. At the same time, overly complex approaches could generate multiple different models that explain the data equally well. PNFL appears to strike the balance between expressive power and complexity. This also applies to the intuitive representation of PNFL models combining a straightforward graphical notation with colloquial fuzzy parameters.     

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.     

Probability density functions for axial ratios of sectioning profiles of anisotropically arranged elliptical microvessels

The article theoretically regards probability density functions (PDFs) for axial ratio (X/Y) of sectioning profiles of elliptical microvessels (MVs) arranged with anisotropy in a biological tissue volume. A technique for the PDF_X/Y calculations in anisotropy of the elliptical MVs is described. The essence of this technique is introducing anisotropy in PDF(α,φ), i.e. the function of the joint distribution of the polar and planar angles α and φ, which define mutual orientation of the elliptical MVs and sectioning planes. With the aid of this technique, the anisotropy cases are studied with PDF(α,φ) given by pair combinations of the following distributions: (i) a uniform distribution of the angles α and/or φ, (ii) the angle α distribution with , and (iii) Gaussian distributions of the α or φ values. Specifically, PDF_X/Y curves are obtained for MVs with the true, or three-dimensional, axial ratio X₀/Y₀=2.0, and the anisotropy effects on the X/Y expected frequencies are analysed. Conclusions of this analysis, the PDF_X/Y calculation technique, and the PDF_X/Y curves obtained are useful for stereological reconstruction of anisotropically organised microcirculatory networks, with an ellipticity of their MVs being taken into consideration.     

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.     

Formation of VEGF isoform-specific spatial distributions governing angiogenesis: computational analysis

Background

Cellular interaction networks can be used to analyze the effects on cell signaling and other functional consequences of perturbations to cellular physiology. Thus, several methods have been used to reconstitute interaction networks from multiple published datasets. However, the structure and performance of these networks depends on both the quality and the unbiased nature of the original data. Due to the inherent bias against membrane proteins in protein-protein interaction (PPI) data, interaction networks can be compromised particularly if they are to be used in conjunction with drug screening efforts, since most drug-targets are membrane proteins.

Results

To overcome the experimental bias against PPIs involving membrane-associated proteins we used a probabilistic approach based on a hypergeometric distribution followed by logistic regression to simultaneously optimize the weights of different sources of interaction data. The resulting less biased genome-scale network constructed for the budding yeast Saccharomyces cerevisiae revealed that the starvation pathway is a distinct subnetwork of autophagy and retrieved a more integrated network of unfolded protein response genes. We also observed that the centrality-lethality rule depends on the content of membrane proteins in networks.

Conclusions

We show here that the bias against membrane proteins can and should be corrected in order to have a better representation of the interactions and topological properties of protein interaction networks.     

Estimating the capacity for improvement in risk prediction with a marker

Consider a set of baseline predictors X to predict a binaryoutcome D and let Y be a novel marker or predictor. This paperis concerned with evaluating the performance of the augmentedrisk model P(D = 1|Y,X) compared with the baseline model P(D= 1|X). The diagnostic likelihood ratio, DLR_X(y), quantifiesthe change in risk obtained with knowledge of Y = y for a subjectwith baseline risk factors X. The notion is commonly used inclinical medicine to quantify the increment in risk predictiondue to Y. It is contrasted here with the notion of covariate-adjustedeffect of Y in the augmented risk model. We also propose methodsfor making inference about DLR_X(y). Case–control studydesigns are accommodated. The methods provide a mechanism toinvestigate if the predictive information in Y varies with baselinecovariates. In addition, we show that when combined with a baselinerisk model and information about the population distributionof Y given X, covariate-specific predictiveness curves can beestimated. These curves are useful to an individual in decidingif ascertainment of Y is likely to be informative or not forhim. We illustrate with data from 2 studies: one is a studyof the performance of hearing screening tests for infants, andthe other concerns the value of serum creatinine in diagnosingrenal artery stenosis.     

Decision tree modeling predicts effects of inhibiting contractility signaling on cell motility

Background

Mathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking.

Results

Herein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks.

Conclusion

CellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use.     

Co-Inheritance Analysis within the Domains of Life Substantially Improves Network Inference by Phylogenetic Profiling

Phylogenetic profiling, a network inference method based on gene inheritance profiles, has been widely used to construct functional gene networks in microbes. However, its utility for network inference in higher eukaryotes has been limited. An improved algorithm with an in-depth understanding of pathway evolution may overcome this limitation. In this study, we investigated the effects of taxonomic structures on co-inheritance analysis using 2,144 reference species in four query species: Escherichia coli, Saccharomyces cerevisiae, Arabidopsis thaliana, and Homo sapiens. We observed three clusters of reference species based on a principal component analysis of the phylogenetic profiles, which correspond to the three domains of life—Archaea, Bacteria, and Eukaryota—suggesting that pathways inherit primarily within specific domains or lower-ranked taxonomic groups during speciation. Hence, the co-inheritance pattern within a taxonomic group may be eroded by confounding inheritance patterns from irrelevant taxonomic groups. We demonstrated that co-inheritance analysis within domains substantially improved network inference not only in microbe species but also in the higher eukaryotes, including humans. Although we observed two sub-domain clusters of reference species within Eukaryota, co-inheritance analysis within these sub-domain taxonomic groups only marginally improved network inference. Therefore, we conclude that co-inheritance analysis within domains is the optimal approach to network inference with the given reference species. The construction of a series of human gene networks with increasing sample sizes of the reference species for each domain revealed that the size of the high-accuracy networks increased as additional reference species genomes were included, suggesting that within-domain co-inheritance analysis will continue to expand human gene networks as genomes of additional species are sequenced. Taken together, we propose that co-inheritance analysis within the domains of life will greatly potentiate the use of the expected onslaught of sequenced genomes in the study of molecular pathways in higher eukaryotes.     

Four-Dimensional Spatial Nanometry of Single Particles in Living Cells Using Polarized Quantum Rods

Single particle tracking is widely used to study protein movement with high spatiotemporal resolution both in vitro and in cells. Quantum dots, which are semiconductor nanoparticles, have recently been employed in single particle tracking because of their intense and stable fluorescence. Although single particles inside cells have been tracked in three spatial dimensions (X, Y, Z), measurement of the angular orientation of a molecule being tracked would significantly enhance our understanding of the molecule’s function. In this study, we synthesized highly polarized, rod-shaped quantum dots (Qrods) and developed a coating method that optimizes the Qrods for biological imaging. We describe a Qrod-based single particle tracking technique that blends optical nanometry with nanomaterial science to simultaneously measure the three-dimensional and angular movements of molecules. Using Qrods, we spatially tracked a membrane receptor in living cells in four dimensions with precision close to the single-digit range in nanometers and degrees.     

Four-Dimensional Spatial Nanometry of Single Particles in Living Cells Using Polarized Quantum Rods

Single particle tracking is widely used to study protein movement with high spatiotemporal resolution both in vitro and in cells. Quantum dots, which are semiconductor nanoparticles, have recently been employed in single particle tracking because of their intense and stable fluorescence. Although single particles inside cells have been tracked in three spatial dimensions (X, Y, Z), measurement of the angular orientation of a molecule being tracked would significantly enhance our understanding of the molecule’s function. In this study, we synthesized highly polarized, rod-shaped quantum dots (Qrods) and developed a coating method that optimizes the Qrods for biological imaging. We describe a Qrod-based single particle tracking technique that blends optical nanometry with nanomaterial science to simultaneously measure the three-dimensional and angular movements of molecules. Using Qrods, we spatially tracked a membrane receptor in living cells in four dimensions with precision close to the single-digit range in nanometers and degrees.     

Steady-State Kinetic Modeling Constrains Cellular Resting States and Dynamic Behavior

A defining characteristic of living cells is the ability to respond dynamically to external stimuli while maintaining homeostasis under resting conditions. Capturing both of these features in a single kinetic model is difficult because the model must be able to reproduce both behaviors using the same set of molecular components. Here, we show how combining small, well-defined steady-state networks provides an efficient means of constructing large-scale kinetic models that exhibit realistic resting and dynamic behaviors. By requiring each kinetic module to be homeostatic (at steady state under resting conditions), the method proceeds by (i) computing steady-state solutions to a system of ordinary differential equations for each module, (ii) applying principal component analysis to each set of solutions to capture the steady-state solution space of each module network, and (iii) combining optimal search directions from all modules to form a global steady-state space that is searched for accurate simulation of the time-dependent behavior of the whole system upon perturbation. Importantly, this stepwise approach retains the nonlinear rate expressions that govern each reaction in the system and enforces constraints on the range of allowable concentration states for the full-scale model. These constraints not only reduce the computational cost of fitting experimental time-series data but can also provide insight into limitations on system concentrations and architecture. To demonstrate application of the method, we show how small kinetic perturbations in a modular model of platelet P2Y₁ signaling can cause widespread compensatory effects on cellular resting states.