Unravelling the functional interaction structure of a cellular network from temporal slope information of experimental data

Due to the unavoidable nonbiological variations accompanying many experiments, it is imperative to consider a way of unravelling the functional interaction structure of a cellular network (e.g. signalling cascades or gene networks) by using the qualitative information of time-series experimental data instead of computation through the measured absolute values. In this spirit, we propose a very simple but effective method of identifying the functional interaction structure of a cellular network based on temporal ascending or descending slope information from given time-series measurements. From this method, we can gain insight into the acceptable measurement error ranges in order to estimate the correct functional interaction structure and we can also find guidance for a new experimental design to complement the insufficient information of a given experimental dataset. We developed experimental sign equations, making use of the temporal slope sign information from time-series experimental data, without a specific assumption on parameter perturbations for each network node. Based on these equations, we further describe the available specific information from each part of experimental data in detail and show the functional interaction structure obtained by integrating such information. In this procedure, we use only simple algebra on sign changes without complicated computations on the measured absolute values of the experimental data. The result is, however, verified through rigorous mathematical definitions and proofs. The present method provides us with information about the acceptable measurement error ranges for correct estimation of the functional interaction structure and it further leads to a new experimental design to complement the given experimental data by informing us about additional specific sampling points to be chosen for further required information.     

How to reconstruct a large genetic network from n gene perturbations in fewer than n(2) easy steps.

MOTIVATION: The reconstruction of genetic networks is the holy grail of functional genomics. Its core task is to identify the causal structure of a gene network, that is, to distinguish direct from indirect regulatory interactions among gene products. In other words, to reconstruct a genetic network is to identify, for each network gene, which other genes and their activity the gene influences directly. Crucial to this task are perturbations of gene activity. Genomic technology permits large-scale experiments perturbing the activity of many genes and assessing the effect of each perturbation on all other genes in a genome. However, such experiments cannot distinguish between direct and indirect effects of a genetic perturbation. RESULTS: I present an algorithm to reconstruct direct regulatory interactions in gene networks from the results of gene perturbation experiments. The algorithm is based on a graph representation of genetic networks and applies to networks of arbitrary size and complexity. Algorithmic complexity in both storage and time is low, less than O(n(2)). In practice, the algorithm can reconstruct networks of several thousand genes in mere CPU seconds on a desktop workstation. AVAILABILITY: A perl implementation of the algorithm is given in the Appendix. CONTACT: wagnera@unm.edu     

Plato's Cave Algorithm: Inferring Functional Signaling Networks from Early Gene Expression Shadows

Improving the ability to reverse engineer biochemical networks is a major goal of systems biology. Lesions in signaling networks lead to alterations in gene expression, which in principle should allow network reconstruction. However, the information about the activity levels of signaling proteins conveyed in overall gene expression is limited by the complexity of gene expression dynamics and of regulatory network topology. Two observations provide the basis for overcoming this limitation: a. genes induced without de-novo protein synthesis (early genes) show a linear accumulation of product in the first hour after the change in the cell''s state; b. The signaling components in the network largely function in the linear range of their stimulus-response curves. Therefore, unlike most genes or most time points, expression profiles of early genes at an early time point provide direct biochemical assays that represent the activity levels of upstream signaling components. Such expression data provide the basis for an efficient algorithm (Plato''s Cave algorithm; PLACA) to reverse engineer functional signaling networks. Unlike conventional reverse engineering algorithms that use steady state values, PLACA uses stimulated early gene expression measurements associated with systematic perturbations of signaling components, without measuring the signaling components themselves. Besides the reverse engineered network, PLACA also identifies the genes detecting the functional interaction, thereby facilitating validation of the predicted functional network. Using simulated datasets, the algorithm is shown to be robust to experimental noise. Using experimental data obtained from gonadotropes, PLACA reverse engineered the interaction network of six perturbed signaling components. The network recapitulated many known interactions and identified novel functional interactions that were validated by further experiment. PLACA uses the results of experiments that are feasible for any signaling network to predict the functional topology of the network and to identify novel relationships.     

Bayesian analysis of signaling networks governing embryonic stem cell fate decisions

MOTIVATION: Signaling events that direct mouse embryonic stem (ES) cell self-renewal and differentiation are complex and accordingly difficult to understand in an integrated manner. We address this problem by adapting a Bayesian network learning algorithm to model proteomic signaling data for ES cell fate responses to external cues. Using this model we were able to characterize the signaling pathway influences as quantitative, logic-circuit type interactions. Our experimental dataset includes measurements for 28 signaling protein phosphorylation states across 16 different factorial combinations of cytokine and matrix stimuli as reported previously. RESULTS: The Bayesian network modeling approach allows us to uncover previously reported signaling activities related to mouse ES cell self-renewal, such as the roles of LIF and STAT3 in maintaining undifferentiated ES cell populations. Furthermore, the network predicts novel influences such as between ERK phosphorylation and differentiation, or RAF phosphorylation and differentiated cell proliferation. Visualization of the influences detected by the Bayesian network provides intuition about the underlying physiology of the signaling pathways. We demonstrate that the Bayesian networks can capture the linear, nonlinear and multistate logic interactions that connect extracellular cues, intracellular signals and consequent cell functional responses.     

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.     

Models from experiments: combinatorial drug perturbations of cancer cells

We present a novel method for deriving network models from molecular profiles of perturbed cellular systems. The network models aim to predict quantitative outcomes of combinatorial perturbations, such as drug pair treatments or multiple genetic alterations. Mathematically, we represent the system by a set of nodes, representing molecular concentrations or cellular processes, a perturbation vector and an interaction matrix. After perturbation, the system evolves in time according to differential equations with built‐in nonlinearity, similar to Hopfield networks, capable of representing epistasis and saturation effects. For a particular set of experiments, we derive the interaction matrix by minimizing a composite error function, aiming at accuracy of prediction and simplicity of network structure. To evaluate the predictive potential of the method, we performed 21 drug pair treatment experiments in a human breast cancer cell line (MCF7) with observation of phospho‐proteins and cell cycle markers. The best derived network model rediscovered known interactions and contained interesting predictions. Possible applications include the discovery of regulatory interactions, the design of targeted combination therapies and the engineering of molecular biological networks.     

Model identification of signal transduction networks from data using a state regulator problem

Advances in molecular biology provide an opportunity to develop detailed models of biological processes that can be used to obtain an integrated understanding of the system. However, development of useful models from the available knowledge of the system and experimental observations still remains a daunting task. In this work, a model identification strategy for complex biological networks is proposed. The approach includes a state regulator problem (SRP) that provides estimates of all the component concentrations and the reaction rates of the network using the available measurements. The full set of the estimates is utilised for model parameter identification for the network of known topology. An a priori model complexity test that indicates the feasibility of performance of the proposed algorithm is developed. Fisher information matrix (FIM) theory is used to address model identifiability issues. Two signalling pathway case studies, the caspase function in apoptosis and the MAP kinase cascade system, are considered. The MAP kinase cascade, with measurements restricted to protein complex concentrations, fails the a priori test and the SRP estimates are poor as expected. The apoptosis network structure used in this work has moderate complexity and is suitable for application of the proposed tools. Using a measurement set of seven protein concentrations, accurate estimates for all unknowns are obtained. Furthermore, the effects of measurement sampling frequency and quality of information in the measurement set on the performance of the identified model are described.     

Complexity management in visualizing protein interaction networks

MOTIVATION: Protein-protein interaction networks often consist of thousands of nodes or more. This severely limits the utility of many graph drawing tools because they become too slow for an interactive analysis of the networks and because they produce cluttered drawings with many edge crossings. RESULTS: A new layout algorithm with complexity management operations in visualizing a large-scale protein interaction network was developed and implemented in a program called InterViewer3. InterViewer3 simplifies a complex network by collapsing a group of nodes with the same interacting partners into a composite node and by replacing a clique with a star-shaped subgraph. The experimental results demonstrated that InterViewer3 is one order of magnitude faster than the other drawing programs and that its complexity management is successful.     

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.     

Complexity of multitrophic interactions in a grassland ecosystem depends on plant species diversity

1.?We studied the theoretical prediction that a loss of plant species richness has a strong impact on community interactions among all trophic levels and tested whether decreased plant species diversity results in a less complex structure and reduced interactions in ecological networks. 2.?Using plant species-specific biomass and arthropod abundance data from experimental grassland plots (Jena Experiment), we constructed multitrophic functional group interaction webs to compare communities based on 4 and 16 plant species. 427 insect and spider species were classified into 13 functional groups. These functional groups represent the nodes of ecological networks. Direct and indirect interactions among them were assessed using partial Mantel tests. Interaction web complexity was quantified using three measures of network structure: connectance, interaction diversity and interaction strength. 3.?Compared with high plant diversity plots, interaction webs based on low plant diversity plots showed reduced complexity in terms of total connectance, interaction diversity and mean interaction strength. Plant diversity effects obviously cascade up the food web and modify interactions across all trophic levels. The strongest effects occurred in interactions between adjacent trophic levels (i.e. predominantly trophic interactions), while significant interactions among plant and carnivore functional groups, as well as horizontal interactions (i.e. interactions between functional groups of the same trophic level), showed rather inconsistent responses and were generally rarer. 4.?Reduced interaction diversity has the potential to decrease and destabilize ecosystem processes. Therefore, we conclude that the loss of basal producer species leads to more simple structured, less and more loosely connected species assemblages, which in turn are very likely to decrease ecosystem functioning, community robustness and tolerance to disturbance. Our results suggest that the functioning of the entire ecological community is critically linked to the diversity of its component plants species.     

Difference in gene duplicability may explain the difference in overall structure of protein-protein interaction networks among eukaryotes

Background  

A protein-protein interaction network (PIN) was suggested to be a disassortative network, in which interactions between high- and low-degree nodes are favored while hub-hub interactions are suppressed. It was postulated that a disassortative structure minimizes unfavorable cross-talks between different hub-centric functional modules and was positively selected in evolution. However, by re-examining yeast PIN data, several researchers reported that the disassortative structure observed in a PIN might be an experimental artifact. Therefore, the existence of a disassortative structure and its possible evolutionary mechanism remains unclear.     

Pruning artificial neural networks using neural complexity measures

This paper describes a new method for pruning artificial neural networks, using a measure of the neural complexity of the neural network. This measure is used to determine the connections that should be pruned. The measure computes the information-theoretic complexity of a neural network, which is similar to, yet different from previous research on pruning. The method proposed here shows how overly large and complex networks can be reduced in size, whilst retaining learnt behaviour and fitness. The technique proposed here helps to discover a network topology that matches the complexity of the problem it is meant to solve. This novel pruning technique is tested in a robot control domain, simulating a racecar. It is shown, that the proposed pruning method is a significant improvement over the most commonly used pruning method Magnitude Based Pruning. Furthermore, some of the pruned networks prove to be faster learners than the benchmark network that they originate from. This means that this pruning method can also help to unleash hidden potential in a network, because the learning time decreases substantially for a pruned a network, due to the reduction of dimensionality of the network.     

Ensemble learning of genetic networks from time-series expression data

MOTIVATION: Inferring genetic networks from time-series expression data has been a great deal of interest. In most cases, however, the number of genes exceeds that of data points which, in principle, makes it impossible to recover the underlying networks. To address the dimensionality problem, we apply the subset selection method to a linear system of difference equations. Previous approaches assign the single most likely combination of regulators to each target gene, which often causes over-fitting of the small number of data. RESULTS: Here, we propose a new algorithm, named LEARNe, which merges the predictions from all the combinations of regulators that have a certain level of likelihood. LEARNe provides more accurate and robust predictions than previous methods for the structure of genetic networks under the linear system model. We tested LEARNe for reconstructing the SOS regulatory network of Escherichia coli and the cell cycle regulatory network of yeast from real experimental data, where LEARNe also exhibited better performances than previous methods. AVAILABILITY: The MATLAB codes are available upon request from the authors.     

Quantitative network signal combinations downstream of TCR activation can predict IL-2 production response

Proximal signaling events activated by TCR-peptide/MHC (TCR-pMHC) binding have been the focus of intense ongoing study, but understanding how the consequent downstream signaling networks integrate to govern ultimate avidity-appropriate TCR-pMHC T cell responses remains a crucial next challenge. We hypothesized that a quantitative combination of key downstream network signals across multiple pathways must encode the information generated by TCR activation, providing the basis for a quantitative model capable of interpreting and predicting T cell functional responses. To this end, we measured 11 protein nodes across six downstream pathways, along five time points from 10 min to 4 h, in a 1B6 T cell hybridoma stimulated by a set of three myelin proteolipid protein 139-151 altered peptide ligands. A multivariate regression model generated from this data compendium successfully comprehends the various IL-2 production responses and moreover successfully predicts a priori the response to an additional peptide treatment, demonstrating that TCR binding information is quantitatively encoded in the downstream network. Individual node and/or time point measurements less effectively accounted for the IL-2 responses, indicating that signals must be integrated dynamically across multiple pathways to adequately represent the encoded TCR signaling information. Of further importance, the model also successfully predicted a priori direct experimental tests of the effects of individual and combined inhibitors of the MEK/ERK and PI3K/Akt pathways on this T cell response. Together, our findings show how multipathway network signals downstream of TCR activation quantitatively integrate to translate pMHC stimuli into functional cell responses.     

Refinement of protein-protein complexes in contact map space with metadynamics simulations

Accurate protein-protein complex prediction, to atomic detail, is a challenging problem. For flexible docking cases, current state-of-the-art docking methods are limited in their ability to exhaustively search the high dimensionality of the problem space. In this study, to obtain more accurate models, an investigation into the local optimization of initial docked solutions is presented with respect to a reference crystal structure. We show how physics-based refinement of protein-protein complexes in contact map space (CMS), within a metadynamics protocol, can be performed. The method uses 5 times replicated 10 ns simulations for sampling and ranks the generated conformational snapshots with ZRANK to identify an ensemble of n snapshots for final model building. Furthermore, we investigated whether the reconstructed free energy surface (FES), or a combination of both FES and ZRANK, referred to as CS_α, can help to reduce snapshot ranking error.     

Condition-dependent functional connectivity: syntax networks in bilinguals

This paper introduces a method to study the variation of brain functional connectivity networks with respect to experimental conditions in fMRI data. It is related to the psychophysiological interaction technique introduced by Friston et al. and extends to networks of correlation modulation (CM networks). Extended networks containing several dozens of nodes are determined in which the links correspond to consistent correlation modulation across subjects. In addition, we assess inter-subject variability and determine networks in which the condition-dependent functional interactions can be explained by a subject-dependent variable. We applied the technique to data from a study on syntactical production in bilinguals and analysed functional interactions differentially across tasks (word reading or sentence production) and across languages. We find an extended network of consistent functional interaction modulation across tasks, whereas the network comparing languages shows fewer links. Interestingly, there is evidence for a specific network in which the differences in functional interaction across subjects can be explained by differences in the subjects' syntactical proficiency. Specifically, we find that regions, including ones that have previously been shown to be involved in syntax and in language production, such as the left inferior frontal gyrus, putamen, insula, precentral gyrus, as well as the supplementary motor area, are more functionally linked during sentence production in the second, compared with the first, language in syntactically more proficient bilinguals than in syntactically less proficient ones. Our approach extends conventional activation analyses to the notion of networks, emphasizing functional interactions between regions independently of whether or not they are activated. On the one hand, it gives rise to testable hypotheses and allows an interpretation of the results in terms of the previous literature, and on the other hand, it provides a basis for studying the structure of functional interactions as a whole, and hence represents a further step towards the notion of large-scale networks in functional imaging.     

Detecting and Removing Inconsistencies between Experimental Data and Signaling Network Topologies Using Integer Linear Programming on Interaction Graphs

Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely available toolbox SigNetTrainer making it an appealing approach for various applications.