On the characterization of energy networks of proteins

The construction of a realistic theoretical model of proteins is determinant for improving the computational simulations of their structural and functional aspects. Modeling proteins as a network of non-covalent connections between the atoms of amino acid residues has shown valuable insights into these macromolecules. The energy-related properties of protein structures are known to be very important in molecular dynamics. However, these same properties have been neglected when the protein structures are modeled as networks of atoms and amino acid residues. A new approach for the construction of protein models based on a network of atoms is presented. This method, based on interatomic interaction, takes into account the energy and geometric aspects of the protein structures that were not employed before, such as atomic occlusion inside the protein, the use of solvation, protein modeling and analysis, and the use of energy potentials to estimate the energies of interatomic non-covalent contacts. As a result, we achieved a more realistic network model of proteins. This model has the virtue of being more robust in face of different unknown variables that usually are arbitrarily estimated. We were able to determine the most connected residues of all the proteins studied, so that we are now in a better condition to study their structural role.     

Robustness in phenotypic plasticity and heterogeneity patterns enabled by EMT networks

Epithelial-mesenchymal plasticity (EMP) is a key arm of cancer metastasis and is observed across many contexts. Cells undergoing EMP can reversibly switch between three classes of phenotypes: epithelial (E), mesenchymal (M), and hybrid E/M. While a large number of multistable regulatory networks have been identified to be driving EMP in various contexts, the exact mechanisms and design principles that enable robustness in driving EMP across contexts are not yet fully understood. Here, we investigated dynamic and structural robustness in EMP networks with regard to phenotypic heterogeneity and plasticity. We use two different approaches to simulate these networks: a computationally inexpensive, parameter-independent continuous state space Boolean model, and an ODE-based parameter-agnostic framework (RACIPE), both of which yielded similar phenotypic distributions. While the latter approach is useful for measurements of plasticity, the former model enabled us to extensively investigate robustness in phenotypic heterogeneity. Using perturbations to network topology and by varying network parameters, we show that multistable EMP networks are structurally and dynamically more robust compared with their randomized counterparts, thereby highlighting their topological hallmarks. These features of robustness are governed by a balance of positive and negative feedback loops embedded in these networks. Using a combination of the number of negative and positive feedback loops weighted by their lengths, we identified a metric that can explain the structural and dynamical robustness of these networks. This metric enabled us to compare networks across multiple sizes, and the network principles thus obtained can be used to identify fragilities in large networks without simulating their dynamics. Our analysis highlights a network topology-based approach to quantify robustness in the phenotypic heterogeneity and plasticity emergent from EMP networks.     

Integrating multi-attribute similarity networks for robust representation of the protein space

MOTIVATION: A global view of the protein space is essential for functional and evolutionary analysis of proteins. In order to achieve this, a similarity network can be built using pairwise relationships among proteins. However, existing similarity networks employ a single similarity measure and therefore their utility depends highly on the quality of the selected measure. A more robust representation of the protein space can be realized if multiple sources of information are used. RESULTS: We propose a novel approach for analyzing multi-attribute similarity networks by combining random walks on graphs with Bayesian theory. A multi-attribute network is created by combining sequence and structure based similarity measures. For each attribute of the similarity network, one can compute a measure of affinity from a given protein to every other protein in the network using random walks. This process makes use of the implicit clustering information of the similarity network, and we show that it is superior to naive, local ranking methods. We then combine the computed affinities using a Bayesian framework. In particular, when we train a Bayesian model for automated classification of a novel protein, we achieve high classification accuracy and outperform single attribute networks. In addition, we demonstrate the effectiveness of our technique by comparison with a competing kernel-based information integration approach.     

Brain rhythms reveal a hierarchical network organization

Recordings of ongoing neural activity with EEG and MEG exhibit oscillations of specific frequencies over a non-oscillatory background. The oscillations appear in the power spectrum as a collection of frequency bands that are evenly spaced on a logarithmic scale, thereby preventing mutual entrainment and cross-talk. Over the last few years, experimental, computational and theoretical studies have made substantial progress on our understanding of the biophysical mechanisms underlying the generation of network oscillations and their interactions, with emphasis on the role of neuronal synchronization. In this paper we ask a very different question. Rather than investigating how brain rhythms emerge, or whether they are necessary for neural function, we focus on what they tell us about functional brain connectivity. We hypothesized that if we were able to construct abstract networks, or "virtual brains", whose dynamics were similar to EEG/MEG recordings, those networks would share structural features among themselves, and also with real brains. Applying mathematical techniques for inverse problems, we have reverse-engineered network architectures that generate characteristic dynamics of actual brains, including spindles and sharp waves, which appear in the power spectrum as frequency bands superimposed on a non-oscillatory background dominated by low frequencies. We show that all reconstructed networks display similar topological features (e.g. structural motifs) and dynamics. We have also reverse-engineered putative diseased brains (epileptic and schizophrenic), in which the oscillatory activity is altered in different ways, as reported in clinical studies. These reconstructed networks show consistent alterations of functional connectivity and dynamics. In particular, we show that the complexity of the network, quantified as proposed by Tononi, Sporns and Edelman, is a good indicator of brain fitness, since virtual brains modeling diseased states display lower complexity than virtual brains modeling normal neural function. We finally discuss the implications of our results for the neurobiology of health and disease.     

Inferring Intracellular Signal Transduction Circuitry from Molecular Perturbation Experiments

The development of network inference methodologies that accurately predict connectivity in dysregulated pathways may enable the rational selection of patient therapies. Accurately inferring an intracellular network from data remains a very challenging problem in molecular systems biology. Living cells integrate extremely robust circuits that exhibit significant heterogeneity, but still respond to external stimuli in predictable ways. This phenomenon allows us to introduce a network inference methodology that integrates measurements of protein activation from perturbation experiments. The methodology relies on logic-based networks to provide a predictive approximation of the transfer of signals in a network. The approach presented was validated in silico with a set of test networks and applied to investigate the epidermal growth factor receptor signaling of a breast epithelial cell line, MFC10A. In our analysis, we predict the potential signaling circuitry most likely responsible for the experimental readouts of several proteins in the mitogen-activated protein kinase and phosphatidylinositol-3 kinase pathways. The approach can also be used to identify additional necessary perturbation experiments to distinguish between a set of possible candidate networks.     

Integration of data-independent acquisition (DIA) with co-fractionation mass spectrometry (CF-MS) to enhance interactome mapping capabilities

Proteomics technologies are continually advancing, providing opportunities to develop stronger and more robust protein interaction networks (PINs). In part, this is due to the ever-growing number of high-throughput proteomics methods that are available. This review discusses how data-independent acquisition (DIA) and co-fractionation mass spectrometry (CF-MS) can be integrated to enhance interactome mapping abilities. Furthermore, integrating these two techniques can improve data quality and network generation through extended protein coverage, less missing data, and reduced noise. CF-DIA-MS shows promise in expanding our knowledge of interactomes, notably for non-model organisms (NMOs). CF-MS is a valuable technique on its own, but upon the integration of DIA, the potential to develop robust PINs increases, offering a unique approach for researchers to gain an in-depth understanding into the dynamics of numerous biological processes.     

Structural Analysis to Determine the Core of Hypoxia Response Network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network''s dynamics. The question that begs for an answer is how to identify the core that is representative of a network''s dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.     

Structure–stability relationships in networks combining mutualistic and antagonistic interactions

The relationship between the structure of ecological networks and community stability has been studied for decades. Recent developments highlighted that this relationship depended on whether interactions were antagonistic or mutualistic. Different structures promoting stability in different types of ecological networks, i.e. mutualistic or antagonistic, have been pointed out. However, these findings come from studies considering mutualistic and antagonistic interactions separately whereas we know that species are part of both types of networks simultaneously. Understanding the relationship between network structure and community stability, when mutualistic and antagonistic interactions are merged in a single network, thus appears as the next challenge to improve our understanding of the dynamics of natural communities. Using a theoretical approach, we test whether the structural characteristics known to promote stability in networks made of a single interaction type still hold for network merging mutualistic and antagonistic interactions. We show that the effects of diversity and connectance remain unchanged. But the effects of nestedness and modularity are strongly weakened in networks combining mutualistic and antagonistic interactions. By challenging the stabilizing mechanisms proposed for networks with a single interaction type, our study calls for new measures of structure for networks that integrate the diversity of interaction.     

Alpha-Helical Protein Networks Are Self-Protective and Flaw-Tolerant

Alpha-helix based protein networks as they appear in intermediate filaments in the cell’s cytoskeleton and the nuclear membrane robustly withstand large deformation of up to several hundred percent strain, despite the presence of structural imperfections or flaws. This performance is not achieved by most synthetic materials, which typically fail at much smaller deformation and show a great sensitivity to the existence of structural flaws. Here we report a series of molecular dynamics simulations with a simple coarse-grained multi-scale model of alpha-helical protein domains, explaining the structural and mechanistic basis for this observed behavior. We find that the characteristic properties of alpha-helix based protein networks are due to the particular nanomechanical properties of their protein constituents, enabling the formation of large dissipative yield regions around structural flaws, effectively protecting the protein network against catastrophic failure. We show that the key for these self protecting properties is a geometric transformation of the crack shape that significantly reduces the stress concentration at corners. Specifically, our analysis demonstrates that the failure strain of alpha-helix based protein networks is insensitive to the presence of structural flaws in the protein network, only marginally affecting their overall strength. Our findings may help to explain the ability of cells to undergo large deformation without catastrophic failure while providing significant mechanical resistance.     

How structure determines correlations in neuronal networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks.     

Construction and Analyses of Human Large-Scale Tissue Specific Networks

Construction and analyses of tissue specific networks is crucial to unveil the function and organizational structure of biological systems. As a direct method to detect protein dynamics, human proteome-wide expression data provide an valuable resource to investigate the tissue specificity of proteins and interactions. By integrating protein expression data with large-scale interaction network, we constructed 30 tissue/cell specific networks in human and analyzed their properties and functions. Rather than the tissue specificity of proteins, we mainly focused on the tissue specificity of interactions to distill tissue specific networks. Through comparing our tissue specific networks with those inferred from gene expression data, we found our networks have larger scales and higher reliability. Furthermore, we investigated the similar extent of multiple tissue specific networks, which proved that tissues with similar functions tend to contain more common interactions. Finally, we found that the tissue specific networks differed from the static network in multiple topological properties. The proteins in tissue specific networks are interacting looser and the hubs play more important roles than those in the static network.     

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.     

In search of the biological significance of modular structures in protein networks

Many complex networks such as computer and social networks exhibit modular structures, where links between nodes are much denser within modules than between modules. It is widely believed that cellular networks are also modular, reflecting the relative independence and coherence of different functional units in a cell. While many authors have claimed that observations from the yeast protein–protein interaction (PPI) network support the above hypothesis, the observed structural modularity may be an artifact because the current PPI data include interactions inferred from protein complexes through approaches that create modules (e.g., assigning pairwise interactions among all proteins in a complex). Here we analyze the yeast PPI network including protein complexes (PIC network) and excluding complexes (PEC network). We find that both PIC and PEC networks show a significantly greater structural modularity than that of randomly rewired networks. Nonetheless, there is little evidence that the structural modules correspond to functional units, particularly in the PEC network. More disturbingly, there is no evolutionary conservation among yeast, fly, and nematode modules at either the whole-module or protein-pair level. Neither is there a correlation between the evolutionary or phylogenetic conservation of a protein and the extent of its participation in various modules. Using computer simulation, we demonstrate that a higher-than-expected modularity can arise during network growth through a simple model of gene duplication, without natural selection for modularity. Taken together, our results suggest the intriguing possibility that the structural modules in the PPI network originated as an evolutionary byproduct without biological significance.     

Structural compliance: A new metric for protein flexibility

Proteins are the active players in performing essential molecular activities throughout biology, and their dynamics has been broadly demonstrated to relate to their mechanisms. The intrinsic fluctuations have often been used to represent their dynamics and then compared to the experimental B-factors. However, proteins do not move in a vacuum and their motions are modulated by solvent that can impose forces on the structure. In this paper, we introduce a new structural concept, which has been called the structural compliance, for the evaluation of the global and local deformability of the protein structure in response to intramolecular and solvent forces. Based on the application of pairwise pulling forces to a protein elastic network, this structural quantity has been computed and sometimes is even found to yield an improved correlation with the experimental B-factors, meaning that it may serve as a better metric for protein flexibility. The inverse of structural compliance, namely the structural stiffness, has also been defined, which shows a clear anticorrelation with the experimental data. Although the present applications are made to proteins, this approach can also be applied to other biomolecular structures such as RNA. This present study considers only elastic network models, but the approach could be applied further to conventional atomic molecular dynamics. Compliance is found to have a slightly better agreement with the experimental B-factors, perhaps reflecting its bias toward the effects of local perturbations, in contrast to mean square fluctuations. The code for calculating protein compliance and stiffness is freely accessible at https://jerniganlab.github.io/Software/PACKMAN/Tutorials/compliance .     

Boolean dynamics of genetic regulatory networks inferred from microarray time series data

MOTIVATION: Methods available for the inference of genetic regulatory networks strive to produce a single network, usually by optimizing some quantity to fit the experimental observations. In this article we investigate the possibility that multiple networks can be inferred, all resulting in similar dynamics. This idea is motivated by theoretical work which suggests that biological networks are robust and adaptable to change, and that the overall behavior of a genetic regulatory network might be captured in terms of dynamical basins of attraction. RESULTS: We have developed and implemented a method for inferring genetic regulatory networks for time series microarray data. Our method first clusters and discretizes the gene expression data using k-means and support vector regression. We then enumerate Boolean activation-inhibition networks to match the discretized data. Finally, the dynamics of the Boolean networks are examined. We have tested our method on two immunology microarray datasets: an IL-2-stimulated T cell response dataset and a LPS-stimulated macrophage response dataset. In both cases, we discovered that many networks matched the data, and that most of these networks had similar dynamics. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Computer-based screening of functional conformers of proteins

A long-standing goal in biology is to establish the link between function, structure, and dynamics of proteins. Considering that protein function at the molecular level is understood by the ability of proteins to bind to other molecules, the limited structural data of proteins in association with other bio-molecules represents a major hurdle to understanding protein function at the structural level. Recent reports show that protein function can be linked to protein structure and dynamics through network centrality analysis, suggesting that the structures of proteins bound to natural ligands may be inferred computationally. In the present work, a new method is described to discriminate protein conformations relevant to the specific recognition of a ligand. The method relies on a scoring system that matches critical residues with central residues in different structures of a given protein. Central residues are the most traversed residues with the same frequency in networks derived from protein structures. We tested our method in a set of 24 different proteins and more than 260,000 structures of these in the absence of a ligand or bound to it. To illustrate the usefulness of our method in the study of the structure/dynamics/function relationship of proteins, we analyzed mutants of the yeast TATA-binding protein with impaired DNA binding. Our results indicate that critical residues for an interaction are preferentially found as central residues of protein structures in complex with a ligand. Thus, our scoring system effectively distinguishes protein conformations relevant to the function of interest.     

Optimized Null Model for Protein Structure Networks

Much attention has recently been given to the statistical significance of topological features observed in biological networks. Here, we consider residue interaction graphs (RIGs) as network representations of protein structures with residues as nodes and inter-residue interactions as edges. Degree-preserving randomized models have been widely used for this purpose in biomolecular networks. However, such a single summary statistic of a network may not be detailed enough to capture the complex topological characteristics of protein structures and their network counterparts. Here, we investigate a variety of topological properties of RIGs to find a well fitting network null model for them. The RIGs are derived from a structurally diverse protein data set at various distance cut-offs and for different groups of interacting atoms. We compare the network structure of RIGs to several random graph models. We show that 3-dimensional geometric random graphs, that model spatial relationships between objects, provide the best fit to RIGs. We investigate the relationship between the strength of the fit and various protein structural features. We show that the fit depends on protein size, structural class, and thermostability, but not on quaternary structure. We apply our model to the identification of significantly over-represented structural building blocks, i.e., network motifs, in protein structure networks. As expected, choosing geometric graphs as a null model results in the most specific identification of motifs. Our geometric random graph model may facilitate further graph-based studies of protein conformation space and have important implications for protein structure comparison and prediction. The choice of a well-fitting null model is crucial for finding structural motifs that play an important role in protein folding, stability and function. To our knowledge, this is the first study that addresses the challenge of finding an optimized null model for RIGs, by comparing various RIG definitions against a series of network models.     

Unveiling protein functions through the dynamics of the interaction network

Protein interaction networks have become a tool to study biological processes, either for predicting molecular functions or for designing proper new drugs to regulate the main biological interactions. Furthermore, such networks are known to be organized in sub-networks of proteins contributing to the same cellular function. However, the protein function prediction is not accurate and each protein has traditionally been assigned to only one function by the network formalism. By considering the network of the physical interactions between proteins of the yeast together with a manual and single functional classification scheme, we introduce a method able to reveal important information on protein function, at both micro- and macro-scale. In particular, the inspection of the properties of oscillatory dynamics on top of the protein interaction network leads to the identification of misclassification problems in protein function assignments, as well as to unveil correct identification of protein functions. We also demonstrate that our approach can give a network representation of the meta-organization of biological processes by unraveling the interactions between different functional classes.