Diffusion Model Based Spectral Clustering for Protein-Protein Interaction Networks

Background

A goal of systems biology is to analyze large-scale molecular networks including gene expressions and protein-protein interactions, revealing the relationships between network structures and their biological functions. Dividing a protein-protein interaction (PPI) network into naturally grouped parts is an essential way to investigate the relationship between topology of networks and their functions. However, clear modular decomposition is often hard due to the heterogeneous or scale-free properties of PPI networks.

Methodology/Principal Findings

To address this problem, we propose a diffusion model-based spectral clustering algorithm, which analytically solves the cluster structure of PPI networks as a problem of random walks in the diffusion process in them. To cope with the heterogeneity of the networks, the power factor is introduced to adjust the diffusion matrix by weighting the transition (adjacency) matrix according to a node degree matrix. This algorithm is named adjustable diffusion matrix-based spectral clustering (ADMSC). To demonstrate the feasibility of ADMSC, we apply it to decomposition of a yeast PPI network, identifying biologically significant clusters with approximately equal size. Compared with other established algorithms, ADMSC facilitates clear and fast decomposition of PPI networks.

Conclusions/Significance

ADMSC is proposed by introducing the power factor that adjusts the diffusion matrix to the heterogeneity of the PPI networks. ADMSC effectively partitions PPI networks into biologically significant clusters with almost equal sizes, while being very fast, robust and appealing simple.     

A systematic survey of centrality measures for protein-protein interaction networks

Background

Numerous centrality measures have been introduced to identify “central” nodes in large networks. The availability of a wide range of measures for ranking influential nodes leaves the user to decide which measure may best suit the analysis of a given network. The choice of a suitable measure is furthermore complicated by the impact of the network topology on ranking influential nodes by centrality measures. To approach this problem systematically, we examined the centrality profile of nodes of yeast protein-protein interaction networks (PPINs) in order to detect which centrality measure is succeeding in predicting influential proteins. We studied how different topological network features are reflected in a large set of commonly used centrality measures.

Results

We used yeast PPINs to compare 27 common of centrality measures. The measures characterize and assort influential nodes of the networks. We applied principal component analysis (PCA) and hierarchical clustering and found that the most informative measures depend on the network’s topology. Interestingly, some measures had a high level of contribution in comparison to others in all PPINs, namely Latora closeness, Decay, Lin, Freeman closeness, Diffusion, Residual closeness and Average distance centralities.

Conclusions

The choice of a suitable set of centrality measures is crucial for inferring important functional properties of a network. We concluded that undertaking data reduction using unsupervised machine learning methods helps to choose appropriate variables (centrality measures). Hence, we proposed identifying the contribution proportions of the centrality measures with PCA as a prerequisite step of network analysis before inferring functional consequences, e.g., essentiality of a node.

     

Performance of Fast Routing Algorithms in Large Optical Switches Built on the Vertical Stacking of Banyan Structures

Vertical stacking of multiple optical banyan networks is a novel scheme for building banyan-based nonblocking optical switches. The resulting network, namely vertically stacked optical banyan (VSOB) network, preserves the properties of small depth and absolutely loss uniformity but loses the nice self-routing capability of banyan networks. To guarantee a high switching speed, routing in VSOB network needs special attentions so that paths can be established as fast as possible. The best known global routing algorithm for an N×N nonblocking VSOB network has the time complexity of O(NlogN), which will introduce an unacceptable long delay in path establishment for a large size optical switch. In this paper, we propose two fast routing algorithms for the VSOB network based on the idea of inputs grouping. The two algorithms, namely plane fixed routing (PFR) algorithm and partially random routing (PRR) algorithm, have the time complexities of O(logN) and O( ) respectively, and FR algorithm can actually turn a VSOB network into a self-routing one. Extensive simulation based on a network simulator indicates that for large VSOB networks our new algorithms can achieve a reasonably low blocking probability while guarantee a very high switching speed.     

Detecting overlapping protein complexes in PPI networks based on robustness

Background

Recently, large data sets of protein-protein interactions (PPI) which can be modeled as PPI networks are generated through high-throughput methods. And locally dense regions in PPI networks are very likely to be protein complexes. Since protein complexes play a key role in many biological processes, detecting protein complexes in PPI networks is one of important tasks in post-genomic era. However, PPI networks are often incomplete and noisy, which builds barriers to mining protein complexes.

Results

We propose a new and effective algorithm based on robustness to detect overlapping clusters as protein complexes in PPI networks. And in order to improve the accuracy of resulting clusters, our algorithm tries to reduce bad effects brought by noise in PPI networks. And in our algorithm, each new cluster begins from a seed and is expanded through adding qualified nodes from the cluster's neighbourhood nodes. Besides, in our algorithm, a new distance measurement method between a cluster K and a node in the neighbours of K is proposed as well. The performance of our algorithm is evaluated by applying it on two PPI networks which are Gavin network and Database of Interacting Proteins (DIP). The results show that our algorithm is better than Markov clustering algorithm (MCL), Clique Percolation method (CPM) and core-attachment based method (CoAch) in terms of F-measure, co-localization and Gene Ontology (GO) semantic similarity.

Conclusions

Our algorithm detects locally dense regions or clusters as protein complexes. The results show that protein complexes generated by our algorithm have better quality than those generated by some previous classic methods. Therefore, our algorithm is effective and useful.

     

Antifouling activity of seaweed extracts on the green alga Enteromorpha prolifera and the mussel Mytilus edulis

Twenty-seven species of common seaweeds from the coast of Korea havebeen screened for antifouling activity. The seaweed extracts were tested inlaboratory assays against the marine fouling green alga Enteromorphaprolifera and the blue mussel Mytilus edulis. Tissue growth, sporesettlement, zygote formation and germlings of the E. prolifera wereinhibited by methanol extracts of the seaweed Ishige sinicola (= I. foliacea) and Sargassum horneri. Spore settlement was stronglyinhibited by using extract concentrations as low as 30 g mL^-1with I. sinicola and 120 g mL^-1 with S. horneri. The repulsive activity of the foot of the mussel was completely inhibited bymethanol extracts of I. sinicola and Scytosiphon lomentaria atconcentrations of 40 g per 10 L drop supplied to eachmussel. These extracts also showed strong antifouling activities onlarval settlement with, respectively, no or only 6% of the spat settlingwhen a test concentration of 0.8 mg mL^-1 was used. This work isthe first stage towards the development of novel antifouling agents frommarine macroalgae.     

Ontology integration to identify protein complex in protein interaction networks

Background

Protein complexes can be identified from the protein interaction networks derived from experimental data sets. However, these analyses are challenging because of the presence of unreliable interactions and the complex connectivity of the network. The integration of protein-protein interactions with the data from other sources can be leveraged for improving the effectiveness of protein complexes detection algorithms.

Methods

We have developed novel semantic similarity method, which use Gene Ontology (GO) annotations to measure the reliability of protein-protein interactions. The protein interaction networks can be converted into a weighted graph representation by assigning the reliability values to each interaction as a weight. Following the approach of that of the previously proposed clustering algorithm IPCA which expands clusters starting from seeded vertices, we present a clustering algorithm OIIP based on the new weighted Protein-Protein interaction networks for identifying protein complexes.

Results

The algorithm OIIP is applied to the protein interaction network of Sacchromyces cerevisiae and identifies many well known complexes. Experimental results show that the algorithm OIIP has higher F-measure and accuracy compared to other competing approaches.

     

GraphCrunch 2: Software tool for network modeling,alignment and clustering

Background  

Recent advancements in experimental biotechnology have produced large amounts of protein-protein interaction (PPI) data. The topology of PPI networks is believed to have a strong link to their function. Hence, the abundance of PPI data for many organisms stimulates the development of computational techniques for the modeling, comparison, alignment, and clustering of networks. In addition, finding representative models for PPI networks will improve our understanding of the cell just as a model of gravity has helped us understand planetary motion. To decide if a model is representative, we need quantitative comparisons of model networks to real ones. However, exact network comparison is computationally intractable and therefore several heuristics have been used instead. Some of these heuristics are easily computable "network properties," such as the degree distribution, or the clustering coefficient. An important special case of network comparison is the network alignment problem. Analogous to sequence alignment, this problem asks to find the "best" mapping between regions in two networks. It is expected that network alignment might have as strong an impact on our understanding of biology as sequence alignment has had. Topology-based clustering of nodes in PPI networks is another example of an important network analysis problem that can uncover relationships between interaction patterns and phenotype.     

A distributed clustering algorithm for large-scale dynamic networks

We propose an algorithm that builds and maintains clusters over a network subject to mobility. This algorithm is fully decentralized and makes all the different clusters grow concurrently. The algorithm uses circulating tokens that collect data and move according to a random walk traversal scheme. Their task consists in (i) creating a cluster with the nodes it discovers and (ii) managing the cluster expansion; all decisions affecting the cluster are taken only by a node that owns the token. The size of each cluster is maintained higher than m nodes (m is a parameter of the algorithm). The obtained clustering is locally optimal in the sense that, with only a local view of each clusters, it computes the largest possible number of clusters (i.e. the sizes of the clusters are as close to m as possible). This algorithm is designed as a decentralized control algorithm for large scale networks and is mobility-adaptive: after a series of topological changes, the algorithm converges to a clustering. This recomputation only affects nodes in clusters where topological changes happened, and in adjacent clusters.     

Clustering of resting state networks

Background

The goal of the study was to demonstrate a hierarchical structure of resting state activity in the healthy brain using a data-driven clustering algorithm.

Methodology/Principal Findings

The fuzzy-c-means clustering algorithm was applied to resting state fMRI data in cortical and subcortical gray matter from two groups acquired separately, one of 17 healthy individuals and the second of 21 healthy individuals. Different numbers of clusters and different starting conditions were used. A cluster dispersion measure determined the optimal numbers of clusters. An inner product metric provided a measure of similarity between different clusters. The two cluster result found the task-negative and task-positive systems. The cluster dispersion measure was minimized with seven and eleven clusters. Each of the clusters in the seven and eleven cluster result was associated with either the task-negative or task-positive system. Applying the algorithm to find seven clusters recovered previously described resting state networks, including the default mode network, frontoparietal control network, ventral and dorsal attention networks, somatomotor, visual, and language networks. The language and ventral attention networks had significant subcortical involvement. This parcellation was consistently found in a large majority of algorithm runs under different conditions and was robust to different methods of initialization.

Conclusions/Significance

The clustering of resting state activity using different optimal numbers of clusters identified resting state networks comparable to previously obtained results. This work reinforces the observation that resting state networks are hierarchically organized.     

Characterization of functional and structural integrity in experimental focal epilepsy: reduced network efficiency coincides with white matter changes

Background

Although focal epilepsies are increasingly recognized to affect multiple and remote neural systems, the underlying spatiotemporal pattern and the relationships between recurrent spontaneous seizures, global functional connectivity, and structural integrity remain largely unknown.

Methodology/Principal Findings

Here we utilized serial resting-state functional MRI, graph-theoretical analysis of complex brain networks and diffusion tensor imaging to characterize the evolution of global network topology, functional connectivity and structural changes in the interictal brain in relation to focal epilepsy in a rat model. Epileptic networks exhibited a more regular functional topology than controls, indicated by a significant increase in shortest path length and clustering coefficient. Interhemispheric functional connectivity in epileptic brains decreased, while intrahemispheric functional connectivity increased. Widespread reductions of fractional anisotropy were found in white matter regions not restricted to the vicinity of the epileptic focus, including the corpus callosum.

Conclusions/Significance

Our longitudinal study on the pathogenesis of network dynamics in epileptic brains reveals that, despite the locality of the epileptogenic area, epileptic brains differ in their global network topology, connectivity and structural integrity from healthy brains.     

Counting motifs in dynamic networks

Background

A network motif is a sub-network that occurs frequently in a given network. Detection of such motifs is important since they uncover functions and local properties of the given biological network. Finding motifs is however a computationally challenging task as it requires solving the costly subgraph isomorphism problem. Moreover, the topology of biological networks change over time. These changing networks are called dynamic biological networks. As the network evolves, frequency of each motif in the network also changes. Computing the frequency of a given motif from scratch in a dynamic network as the network topology evolves is infeasible, particularly for large and fast evolving networks.

Results

In this article, we design and develop a scalable method for counting the number of motifs in a dynamic biological network. Our method incrementally updates the frequency of each motif as the underlying network’s topology evolves. Our experiments demonstrate that our method can update the frequency of each motif in orders of magnitude faster than counting the motif embeddings every time the network changes. If the network evolves more frequently, the margin with which our method outperforms the existing static methods, increases.

Conclusions

We evaluated our method extensively using synthetic and real datasets, and show that our method is highly accurate(≥?96%) and that it can be scaled to large dense networks. The results on real data demonstrate the utility of our method in revealing interesting insights on the evolution of biological processes.

     

Effect of 241-Am on bone fibroblasts

Conclusion The results indicate that the fibroblast colony forming cell is radiosensitive for-irradiation from the radionuclide^241Am. This implies that the CFU-f must be localized within the range of the-rays.The quantitative response of the CFU-f on the-irradiation does not allow to draw the firm conclusion that the CFU-f is a possible target cell for bone-cancer induction. Only radioresistant CFU-f keep the potentiality of bone-cancer induction. This leads to the hypothesis, that the radio-resistant (and even increasing) CFU-f population in femur shaft, distal, and proximal epiphyses and sternum could be most interesting to follow and to check for qualitative changes that could give information about the toxicological properties of²⁴¹Am in connection with the carcinogenic induction in this cell line.     

A framework to find the logic backbone of a biological network

Background

Cellular behaviors are governed by interaction networks among biomolecules, for example gene regulatory and signal transduction networks. An often used dynamic modeling framework for these networks, Boolean modeling, can obtain their attractors (which correspond to cell types and behaviors) and their trajectories from an initial state (e.g. a resting state) to the attractors, for example in response to an external signal. The existing methods however do not elucidate the causal relationships between distant nodes in the network.

Results

In this work, we propose a simple logic framework, based on categorizing causal relationships as sufficient or necessary, as a complement to Boolean networks. We identify and explore the properties of complex subnetworks that are distillable into a single logic relationship. We also identify cyclic subnetworks that ensure the stabilization of the state of participating nodes regardless of the rest of the network. We identify the logic backbone of biomolecular networks, consisting of external signals, self-sustaining cyclic subnetworks (stable motifs), and output nodes. Furthermore, we use the logic framework to identify crucial nodes whose override can drive the system from one steady state to another. We apply these techniques to two biological networks: the epithelial-to-mesenchymal transition network corresponding to a developmental process exploited in tumor invasion, and the network of abscisic acid induced stomatal closure in plants. We find interesting subnetworks with logical implications in these networks. Using these subgraphs and motifs, we efficiently reduce both networks to succinct backbone structures.

Conclusions

The logic representation identifies the causal relationships between distant nodes and subnetworks. This knowledge can form the basis of network control or used in the reverse engineering of networks.

     

Seed selection strategy in global network alignment without destroying the entire structures of functional modules

Background

Network alignment is one of the most common biological network comparison methods. Aligning protein-protein interaction (PPI) networks of different species is of great important to detect evolutionary conserved pathways or protein complexes across species through the identification of conserved interactions, and to improve our insight into biological systems. Global network alignment (GNA) problem is NP-complete, for which only heuristic methods have been proposed so far. Generally, the current GNA methods fall into global heuristic seed-and-extend approaches. These methods can not get the best overall consistent alignment between networks for the opinionated local seed. Furthermore These methods are lost in maximizing the number of aligned edges between two networks without considering the original structures of functional modules.

Methods

We present a novel seed selection strategy for global network alignment by constructing the pairs of hub nodes of networks to be aligned into multiple seeds. Beginning from every hub seed and using the membership similarity of nodes to quantify to what extent the nodes can participate in functional modules associated with current seed topologically we align the networks by modules. By this way we can maintain the functional modules are not damaged during the heuristic alignment process. And our method is efficient in resolving the fatal problem of most conventional algorithms that the initialization selected seeds have a direct influence on the alignment result. The similarity measures between network nodes (e.g., proteins) include sequence similarity, centrality similarity, and dynamic membership similarity and our algorithm can be called Multiple Hubs-based Alignment (MHA).

Results

When applying our seed selection strategy to several pairs of real PPI networks, it is observed that our method is working to strike a balance, extending the conserved interactions while maintaining the functional modules unchanged. In the case study, we assess the effectiveness of MHA on the alignment of the yeast and fly PPI networks. Our method outperforms state-of-the-art algorithms at detecting conserved functional modules and retrieves in particular 86% more conserved interactions than IsoRank.

Conclusions

We believe that our seed selection strategy will lead us to obtain more topologically and biologically similar alignment result. And it can be used as the reference and complement of other heuristic methods to seek more meaningful alignment results.

     

A novel method of spectral clustering in attributed networks by constructing parameter-free affinity matrix

The most basic and significant issue in complex network analysis is community detection, which is a branch of machine learning. Most current community detection approaches, only consider a network's topology structures, which lose the potential to use node attribute information. In attributed networks, both topological structure and node attributed are important features for community detection. In recent years, the spectral clustering algorithm has received much interest as one of the best performing algorithms in the subcategory of dimensionality reduction. This algorithm applies the eigenvalues of the affinity matrix to map data to low-dimensional space. In the present paper, a new version of the spectral cluster, named Attributed Spectral Clustering (ASC), is applied for attributed graphs that the identified communities have structural cohesiveness and attribute homogeneity. Since the performance of spectral clustering heavily depends on the goodness of the affinity matrix, the ASC algorithm will use the Topological and Attribute Random Walk Affinity Matrix (TARWAM) as a new affinity matrix to calculate the similarity between nodes. TARWAM utilizes the biased random walk to integrate network topology and attribute information. It can improve the similarity degree among the pairs of nodes in the same density region of the attributed network, without the need for parameter tuning. The proposed approach has been compared to other primary and new attributed graph clustering algorithms based on synthetic and real datasets. The experimental results show that the proposed approach is more effective and accurate compared to other state-of-the-art attributed graph clustering techniques.

     

The Reticular Cell Network: A Robust Backbone for Immune Responses

Lymph nodes are meeting points for circulating immune cells. A network of reticular cells that ensheathe a mesh of collagen fibers crisscrosses the tissue in each lymph node. This reticular cell network distributes key molecules and provides a structure for immune cells to move around on. During infections, the network can suffer damage. A new study has now investigated the network’s structure in detail, using methods from graph theory. The study showed that the network is remarkably robust to damage: it can still support immune responses even when half of the reticular cells are destroyed. This is a further important example of how network connectivity achieves tolerance to failure, a property shared with other important biological and nonbiological networks.Lymph nodes are critical sites for immune cells to connect, exchange information, and initiate responses to foreign invaders. More than 90% of the cells in each lymph node—the T and B lymphocytes of the adaptive immune system—only reside there temporarily and are constantly moving around as they search for foreign substances (antigen). When there is no infection, T and B cells migrate within distinct regions. But lymph node architecture changes dramatically when antigen is found, and an immune response is mounted. New blood vessels grow and recruit vast numbers of lymphocytes from the blood circulation. Antigen-specific cells divide and mature into “effector” immune cells. The combination of these two processes—increased influx of cells from outside and proliferation within—can make a lymph node grow 10-fold within only a few days [1]. Accordingly, the structural backbone supporting lymph node function cannot be too rigid; otherwise, it would impede this rapid organ expansion. This structural backbone is provided by a network of fibroblastic reticular cells (FRCs) [2], which secrete a form of collagen (type III alpha 1) that produces reticular fibers—thin, threadlike structures with a diameter of less than 1 μm. Reticular fibers cross-link and form a spider web–like structure. The FRCs surrounding this structure form the reticular cell network (Fig 1), which was first observed in the 1930s [3]. Interestingly, experiments in which the FRCs were destroyed showed that the collagen fiber network remained intact [4].Open in a separate windowFig 1Structure of the reticular cell network.The reticular cell network is formed by fibroblastic reticular cells (FRCs) whose cell membranes ensheathe a core of collagen fibers that acts as a conduit system for the distribution of small molecules [5]. In most other tissues, collagen fibers instead reside outside cell membranes, where they form the extracellular matrix. Inset: graph structure representing the FRCs in the depicted network as “nodes” (circles) and the direct connections between them as “edges” (lines). Shape and length of the fibers are not represented in the graph.Reticular cell networks do not only support lymph node structure; they are also important players in the immune response. Small molecules from the tissue environment or from pathogens, such as viral protein fragments, can be distributed within the lymph node through the conduit system formed by the reticular fibers [5]. Some cytokines and chemokines that are vital for effective T cell migration—and the nitric oxide that inhibits T cell proliferation [6]—are even produced by the FRCs themselves. Moreover, the network is thought of as a “road system” for lymphocyte migration [7]: in 2006, a seminal study found that lymphocytes roaming through lymph nodes were in contact with network fibers most of the time [8]. A few years before, it had become possible to observe lymphocyte migration in vivo by means of two-photon microscopy [9]. Movies from these experiments strikingly demonstrated that individual cells were taking very different paths, engaging in what appeared to be a “random walk.” But these movies did not show the structures surrounding the migrating cells, which created an impression of motion in empty space. Appreciating the role of the reticular cell network in this pattern of motion [8] suggested that the complex cell trajectories reflect the architecture of the network along which the cells walk.Given its important functions, it is surprising how little we know about the structure of the reticular cell network—compared to, for instance, our wealth of knowledge on neuron connectivity in the brain. In part this is because the reticular cells are hard to visualize. In vivo techniques like two-photon imaging do not provide sufficient resolution to reliably capture the fine-threaded mesh. Instead, thin tissue sections are stained with fluorescent antibodies that bind to the reticular fibers and are imaged with high-resolution confocal microscopy to reveal the network structure. One study [10] applied this method to determine basic parameters such as branch length and the size of gaps between fibers. Here, we discuss a recent study by Novkovic et al. [11] that took a different approach to investigating properties of the reticular cell network structure: they applied methods from graph theory.Graph theory is a classic subject in mathematics that is often traced back to Leonhard Euler’s stroll through 18th-century Königsberg, Prussia. Euler could not find a circular route that crossed each of the city’s seven bridges exactly once, and wondered how he could prove that such a route does not exist. He realized that this problem could be phrased in terms of a simple diagram containing points (parts of the city) and lines between them (bridges). Further detail, such as the layout of city’s streets, was irrelevant. This was the birth of graph theory—the study of objects consisting of points (nodes) connected by lines (edges). Graph theory has diverse applications ranging from logistics to molecular biology. Since the beginning of this century, there has been a strong interest in applying graph theory to understand the structure of networks that occur in nature—including biological networks, such as neurons in the brain, and more recently, social networks like friendships on Facebook. Various mathematical models of network structures have been developed in an attempt to understand network properties that are relevant in different contexts, such as the speed at which information spreads or the amount of damage that a network can tolerate before breaking into disconnected parts. Three well-known network topologies are random, small-world, and scale-free networks (Box 1). Novkovic et al. modeled reticular cell networks as graphs by considering each FRC to be a node and the fiber connections between FRCs to be edges (Fig 1).

Box 1. Graph Theory and the Robustness of Real Networks

After the publication of several landmark papers on network topology at the end of the previous century, the science of complex networks has grown explosively. One of these papers described “small-world” networks [16] and demonstrated that several natural networks have the amazing property that the average length of shortest paths between arbitrary nodes is unexpectedly small (making it a “small world”), even if most of the network nodes are clustered (that is, when neighbors of neighbors tend to be neighbors). The Barabasi group published a series of papers describing “scale-free” networks [17,18] and demonstrated that scale-free networks are extremely robust to random deletions of nodes—the vast majority of the nodes can be deleted before the network falls apart [15]. In scale-free networks, the number of edges per node is distributed according to a power law, implying that most nodes have very few connections, and a few nodes are hubs having very many connections. Thus, the topology of complex networks can be scale-free, small-world, or neither, such as with random networks [19]. Novkovic et al. [11] describe the clustering of the edges of neighbors and the average shortest path–length between arbitrary nodes, finding that reticular cell networks have small-world properties. Whether or not these networks have scale-free properties is not explicitly examined in the paper, but given that they are embedded in a three-dimensional space, that they “already” lose functionality when about 50% of the FRCs are ablated, and that the number of connected protrusions per FRC is not distributed according to a power law (see the data underlying their Figure 2g), reticular cell networks are not likely to be scale-free. Thus, the enhanced robustness of reticular cell networks is most likely due to their high local connectivity: Networks lose functionality when they fall apart in disconnected components, and high clustering means that the graph is unlikely to split apart when a single node is removed, because the neighbors of that node tend to stay connected [14]. Additionally, since the reticular cell network has a spatial structure (unlike the internet or the Facebook social network), its high degree of clustering is probably due to the preferential attachment to nearby FRCs when the network develops, which agrees well with Novkovic et al.’s recent classification as a small-world network with lattice-like properties [11].Some virus infections are known to damage reticular cell networks [12], either through infection of the FRCs or as a bystander effect of inflammation. It is therefore important to understand to what extent the network structure is able to survive partial destruction. Novkovic et al. first approached this question by performing computer simulations, in which they randomly removed FRC nodes from the networks they had reconstructed from microscopy images. They found that they had to remove at least half of the nodes to break the network apart into disconnected parts. To study the effect of damage on the reticular cell network in vivo rather than in silico, Novkovic et al. used an experimental technique called conditional cell ablation. In this technique, a gene encoding the diphtheria toxin receptor (DTR) is inserted after a specific promoter that leads it to be expressed in a particular cell type of interest. Administration of diphtheria toxin kills DTR-expressing cells, leaving other cells unaffected. By expressing DTR under the control of the FRC-specific Ccl19 promoter, Novkovic et al. were able to selectively destroy the reticular cell network and then watch it grow back over time. Regrowth took about four weeks, and the resulting network properties were no different from a network formed naturally during development. Thus, it seems that the reticular cell network structure is imprinted and reemerges even after severe damage. This finding ties in nicely with previous data from the same group [13], showing that reticular cell networks form even in the absence of lymphotoxin-beta receptor, an otherwise key player in many aspects of lymphoid tissue development. Together, these data make a compelling case that network formation is a robust fundamental trait of FRCs.Next, Novkovic et al. varied the dose of diphtheria toxin such that only a fraction of FRCs were destroyed, effectively removing a random subset of the network nodes. They measured in two ways how FRC loss affects the immune system: they tracked T cell migration using two-photon microscopy and they determined the amount of antiviral T cells produced by the mice after an infection. Remarkably, as predicted by their computer simulations, lymph nodes appeared capable of tolerating the loss of up to half of FRCs with little effect on either T cell migration or the numbers of activated antiviral T cells. Only when more than half of the FRCs were destroyed did T cell motion slow down significantly and the mice were no longer able to mount effective antiviral immune responses. Such a tolerance of damage is impressive—for comparison, consider what would happen if one were to close half of London’s subway stations!Robustness to damage is of interest for many different networks, from power grids to the internet [14]. In particular, the “scale-free” architecture that features rare, strongly connected “hub” nodes is highly robust to random damage [15]. Novkovic et al. did not address whether the reticular cell network is scale-free, but it is likely that it isn’t (Box 1). Instead, the network’s robustness probably arises from its high degree of clustering, which means that the neighbors of each node are likely to be themselves also neighbors. If a node is removed from a clustered network, then there is still likely a short detour available by going through two of the neighbors. Therefore, one would have to randomly remove a large fraction of the nodes before the network structure breaks down. High clustering in the network could be a consequence of the fact that multiple fibers extend from each FRC and establish connections to many FRCs in its vicinity. A question not yet addressed by Novkovic et al. is how robust reticular cell networks would be to nonrandom damage, such as a locally spreading viral infection. In fact, scale-free networks are drastically more vulnerable to targeted rather than random damage: the United States flight network can come to a grinding halt by closing a few hub airports [15]. Less is known about the robustness to nonrandom damage for other network architectures, and the findings by Novkovic et al. motivate future research in this direction.Novkovic et al. did not yet explicitly identify all mechanisms that hamper T cell responses when more than half of the FRCs are depleted. But given the reticular cell network’s many different functions, this could occur in several ways. For instance, severe depletion might prevent the secretion of important molecules, halt the migration of T cells, prevent the anchoring of antigen-presenting dendritic cells (DCs) on the network, or cause structural disarray in the tissue. In addition to the effects on T cell migration, Novkovic et al. also showed that the amount of DCs in fact decreased when FRCs were depleted, emphasizing that several mechanisms are likely at play. Disentangling these mechanisms will require substantial additional research efforts.The current reticular cell network reconstruction by Novkovic et al. is based on thin tissue slices. It will be exciting to study the network architecture when it can be visualized in the whole organ. Some aspects of the network may then look different. For instance, those FRCs that are near the border of a slice will have their degree of connectivity underestimated, as not all of their neighbors in the network can be seen. Further refinements of the network analysis may also consider that reticular fibers are real physical objects situated in a three-dimensional space (unlike abstract connections such as friendships). Migrating T cells may travel quicker via a short, straight fiber than on a long, curved one, but the network graph does not make this distinction. More generally, it would be interesting to understand conceptually how reticular cell networks help foster immune cell migration. While at first it appears obvious that having a “road system” should make it easier for cells to roam lymph node tissue, three different theoretical studies have in fact all concluded that effective T cell migration should also be possible in the absence of a network [20–22]. A related question is whether T cells are constrained to move only on the network or are merely using it for loose guidance. For instance, could migrating T cells be in contact with two or more network fibers at once or with none at all? This would make the relationship between cell migration and network structure more complex than the graph structure alone suggests.There is also some evidence that T cells can migrate according to what is called a Lévy walk [23]—a kind of random walk where frequent short steps are interspersed with few very long steps, a search strategy that appears to occur frequently in nature (though this is debated [24]). While there is so far no evidence that T cells perform a Lévy walk when roaming the lymph node [25], this may be in part due to limitations of two-photon imaging, and one could speculate that reticular cell networks might in fact be constructed in a way that facilitates this or another efficient kind of “search strategy.” Resolving this question will require substantial improvements in imaging technology, allowing individual T cells to be tracked across an entire lymph node.No doubt further studies will address these and other questions, and provide further insights on how reticular cell networks benefit immune responses. Such advances may help us design better treatments against infections that damage the network. It may also help us understand how we can best administer vaccines or tumor immune therapy treatments in a way that ensures optimal delivery to immune cells in the lymph node. As is nicely illustrated by the study of Novkovic et al., mathematical methods may well play key roles in this quest.