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.     

Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.     

Protein interaction networks in medicine and disease

The physical interaction of proteins is subject to intense investigation that has revealed that proteins are assembled into large densely connected networks. In this review, we will examine how signaling pathways can be combined to form higher order protein interaction networks. By using network graph theory, these interaction networks can be further analyzed for global organization, which has revealed unique aspects of the relationships between protein networks and complex biological phenotypes. Moreover, several studies have shown that the structure and dynamics of protein networks are disturbed in complex diseases such as cancer progression. These relationships suggest a novel paradigm for treatment of complex multigenic disease where the protein interaction network is the target of therapy more so than individual molecules within the network.     

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm''s locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.     

Recurrent fractal neural networks: a strategy for the exchange of local and global information processing in the brain

The regulation of biological networks relies significantly on convergent feedback signaling loops that render a global output locally accessible. Ideally, the recurrent connectivity within these systems is self-organized by a time-dependent phase-locking mechanism. This study analyzes recurrent fractal neural networks (RFNNs), which utilize a self-similar or fractal branching structure of dendrites and downstream networks for phase-locking of reciprocal feedback loops: output from outer branch nodes of the network tree enters inner branch nodes of the dendritic tree in single neurons. This structural organization enables RFNNs to amplify re-entrant input by over-the-threshold signal summation from feedback loops with equivalent signal traveling times. The columnar organization of pyramidal neurons in the neocortical layers V and III is discussed as the structural substrate for this network architecture. RFNNs self-organize spike trains and render the entire neural network output accessible to the dendritic tree of each neuron within this network. As the result of a contraction mapping operation, the local dendritic input pattern contains a downscaled version of the network output coding structure. RFNNs perform robust, fractal data compression, thus coping with a limited number of feedback loops for signal transport in convergent neural networks. This property is discussed as a significant step toward the solution of a fundamental problem in neuroscience: how is neuronal computation in separate neurons and remote brain areas unified as an instance of experience in consciousness? RFNNs are promising candidates for engaging neural networks into a coherent activity and provide a strategy for the exchange of global and local information processing in the human brain, thereby ensuring the completeness of a transformation from neuronal computation into conscious experience.     

Insights into the organization of biochemical regulatory networks using graph theory analyses

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.     

MCAM: multiple clustering analysis methodology for deriving hypotheses and insights from high-throughput proteomic datasets

Advances in proteomic technologies continue to substantially accelerate capability for generating experimental data on protein levels, states, and activities in biological samples. For example, studies on receptor tyrosine kinase signaling networks can now capture the phosphorylation state of hundreds to thousands of proteins across multiple conditions. However, little is known about the function of many of these protein modifications, or the enzymes responsible for modifying them. To address this challenge, we have developed an approach that enhances the power of clustering techniques to infer functional and regulatory meaning of protein states in cell signaling networks. We have created a new computational framework for applying clustering to biological data in order to overcome the typical dependence on specific a priori assumptions and expert knowledge concerning the technical aspects of clustering. Multiple clustering analysis methodology ('MCAM') employs an array of diverse data transformations, distance metrics, set sizes, and clustering algorithms, in a combinatorial fashion, to create a suite of clustering sets. These sets are then evaluated based on their ability to produce biological insights through statistical enrichment of metadata relating to knowledge concerning protein functions, kinase substrates, and sequence motifs. We applied MCAM to a set of dynamic phosphorylation measurements of the ERRB network to explore the relationships between algorithmic parameters and the biological meaning that could be inferred and report on interesting biological predictions. Further, we applied MCAM to multiple phosphoproteomic datasets for the ERBB network, which allowed us to compare independent and incomplete overlapping measurements of phosphorylation sites in the network. We report specific and global differences of the ERBB network stimulated with different ligands and with changes in HER2 expression. Overall, we offer MCAM as a broadly-applicable approach for analysis of proteomic data which may help increase the current understanding of molecular networks in a variety of biological problems.     

Fine-Scale Dissection of Functional Protein Network Organization by Statistical Network Analysis

Revealing organizational principles of biological networks is an important goal of systems biology. In this study, we sought to analyze the dynamic organizational principles within the protein interaction network by studying the characteristics of individual neighborhoods of proteins within the network based on their gene expression as well as protein-protein interaction patterns. By clustering proteins into distinct groups based on their neighborhood gene expression characteristics, we identify several significant trends in the dynamic organization of the protein interaction network. We show that proteins with distinct neighborhood gene expression characteristics are positioned in specific localities in the protein interaction network thereby playing specific roles in the dynamic network connectivity. Remarkably, our analysis reveals a neighborhood characteristic that corresponds to the most centrally located group of proteins within the network. Further, we show that the connectivity pattern displayed by this group is consistent with the notion of “rich club connectivity” in complex networks. Importantly, our findings are largely reproducible in networks constructed using independent and different datasets.     

Using Pareto optimality to explore the topology and dynamics of the human connectome

Graph theory has provided a key mathematical framework to analyse the architecture of human brain networks. This architecture embodies an inherently complex relationship between connection topology, the spatial arrangement of network elements, and the resulting network cost and functional performance. An exploration of these interacting factors and driving forces may reveal salient network features that are critically important for shaping and constraining the brain''s topological organization and its evolvability. Several studies have pointed to an economic balance between network cost and network efficiency with networks organized in an ‘economical’ small-world favouring high communication efficiency at a low wiring cost. In this study, we define and explore a network morphospace in order to characterize different aspects of communication efficiency in human brain networks. Using a multi-objective evolutionary approach that approximates a Pareto-optimal set within the morphospace, we investigate the capacity of anatomical brain networks to evolve towards topologies that exhibit optimal information processing features while preserving network cost. This approach allows us to investigate network topologies that emerge under specific selection pressures, thus providing some insight into the selectional forces that may have shaped the network architecture of existing human brains.     

Identification of Important Nodes in Directed Biological Networks: A Network Motif Approach

Identification of important nodes in complex networks has attracted an increasing attention over the last decade. Various measures have been proposed to characterize the importance of nodes in complex networks, such as the degree, betweenness and PageRank. Different measures consider different aspects of complex networks. Although there are numerous results reported on undirected complex networks, few results have been reported on directed biological networks. Based on network motifs and principal component analysis (PCA), this paper aims at introducing a new measure to characterize node importance in directed biological networks. Investigations on five real-world biological networks indicate that the proposed method can robustly identify actually important nodes in different networks, such as finding command interneurons, global regulators and non-hub but evolutionary conserved actually important nodes in biological networks. Receiver Operating Characteristic (ROC) curves for the five networks indicate remarkable prediction accuracy of the proposed measure. The proposed index provides an alternative complex network metric. Potential implications of the related investigations include identifying network control and regulation targets, biological networks modeling and analysis, as well as networked medicine.     

The Index-Based Subgraph Matching Algorithm with General Symmetries (ISMAGS): Exploiting Symmetry for Faster Subgraph Enumeration

Subgraph matching algorithms are used to find and enumerate specific interconnection structures in networks. By enumerating these specific structures/subgraphs, the fundamental properties of the network can be derived. More specifically in biological networks, subgraph matching algorithms are used to discover network motifs, specific patterns occurring more often than expected by chance. Finding these network motifs yields information on the underlying biological relations modelled by the network. In this work, we present the Index-based Subgraph Matching Algorithm with General Symmetries (ISMAGS), an improved version of the Index-based Subgraph Matching Algorithm (ISMA). ISMA quickly finds all instances of a predefined motif in a network by intelligently exploring the search space and taking into account easily identifiable symmetric structures. However, more complex symmetries (possibly involving switching multiple nodes) are not taken into account, resulting in superfluous output. ISMAGS overcomes this problem by using a customised symmetry analysis phase to detect all symmetric structures in the network motif subgraphs. These structures are then converted to symmetry-breaking constraints used to prune the search space and speed up calculations. The performance of the algorithm was tested on several types of networks (biological, social and computer networks) for various subgraphs with a varying degree of symmetry. For subgraphs with complex (multi-node) symmetric structures, high speed-up factors are obtained as the search space is pruned by the symmetry-breaking constraints. For subgraphs with no or simple symmetric structures, ISMAGS still reduces computation times by optimising set operations. Moreover, the calculated list of subgraph instances is minimal as it contains no instances that differ by only a subgraph symmetry. An implementation of the algorithm is freely available at https://github.com/mhoubraken/ISMAGS.     

Distinctive topologies of partner-switching signaling networks correlate with their physiological roles

Regulatory networks controlling bacterial gene expression often evolve from common origins and share homologous proteins and similar network motifs. However, when functioning in different physiological contexts, these motifs may be re-arranged with different topologies that significantly affect network performance. Here we analyze two related signaling networks in the bacterium Bacillus subtilis in order to assess the consequences of their different topologies, with the aim of formulating design principles applicable to other systems. These two networks control the activities of the general stress response factor sigma(B) and the first sporulation-specific factor sigma(F). Both networks have at their core a "partner-switching" mechanism, in which an anti-sigma factor forms alternate complexes either with the sigma factor, holding it inactive, or with an anti-anti-sigma factor, thereby freeing sigma. However, clear differences in network structure are apparent: the anti-sigma factor for sigma(F) forms a long-lived, "dead-end" complex with its anti-anti-sigma factor and ADP, whereas the genes encoding sigma(B) and its network partners lie in a sigma(B)-controlled operon, resulting in positive and negative feedback loops. We constructed mathematical models of both networks and examined which features were critical for the performance of each design. The sigma(F) model predicts that the self-enhancing formation of the dead-end complex transforms the network into a largely irreversible hysteretic switch; the simulations reported here also demonstrate that hysteresis and slow turn off kinetics are the only two system properties associated with this complex formation. By contrast, the sigma(B) model predicts that the positive and negative feedback loops produce graded, reversible behavior with high regulatory capacity and fast response time. Our models demonstrate how alterations in network design result in different system properties that correlate with regulatory demands. These design principles agree with the known or suspected roles of similar networks in diverse bacteria.     

Information processing in social insect networks

Investigating local-scale interactions within a network makes it possible to test hypotheses about the mechanisms of global network connectivity and to ask whether there are general rules underlying network function across systems. Here we use motif analysis to determine whether the interactions within social insect colonies resemble the patterns exhibited by other animal associations or if they exhibit characteristics of biological regulatory systems. Colonies exhibit a predominance of feed-forward interaction motifs, in contrast to the densely interconnected clique patterns that characterize human interaction and animal social networks. The regulatory motif signature supports the hypothesis that social insect colonies are shaped by selection for network patterns that integrate colony functionality at the group rather than individual level, and demonstrates the utility of this approach for analysis of selection effects on complex systems across biological levels of organization.     

Toward a classification of isodynamic feed-forward motifs

A preceding study analysed how the topology of network motifs affects the overall rate of the underlying biochemical processes. Surprisingly, it was shown that topologically non-isomorphic motifs can still be isodynamic in the sense that they exhibit the exact same performance rate. Because of the high prevalence of feed-forward functional modules in biological networks, one may hypothesize that evolution tends to favour motifs with faster dynamics. As a step towards ranking the efficiency of feed-forward network motifs, we use a linear flow model to prove theorems establishing that certain classes of motifs are isodynamic. In partitioning the class of all motifs on n nodes into equivalence classes based upon their dynamics, we establish a basis for comparing the efficiency/performance rates of different motifs. The potential biological importance of the theorems is briefly discussed and is the subject of an ongoing large-scale project.     

Dynamic network rewiring determines temporal regulatory functions in Drosophila melanogaster development processes

The identification of network motifs has been widely considered as a significant step towards uncovering the design principles of biomolecular regulatory networks. To date, time‐invariant networks have been considered. However, such approaches cannot be used to reveal time‐specific biological traits due to the dynamic nature of biological systems, and hence may not be applicable to development, where temporal regulation of gene expression is an indispensable characteristic. We propose a concept of a “temporal sequence of network motifs”, a sequence of network motifs in active sub‐networks constructed over time, and investigate significant network motifs in the active temporal sub‐networks of Drosophila melanogaster . Based on this concept, we find a temporal sequence of network motifs which changes according to developmental stages and thereby cannot be identified from the whole static network. Moreover, we show that the temporal sequence of network motifs corresponding to each developmental stage can be used to describe pivotal developmental events.