Abstract

Abstract. Here we present a simple method based on graph spectral properties to automatically partition multi-domain proteins into individual domains. The identification of structural domains in proteins is based on the assumption that the interactions between the amino acids are higher within a domain than across the domains. These interactions and the topological details of protein structures can be effectively captured by the protein contact graph, constructed by considering each amino acid as a node with an edge drawn between two nodes if the C alpha atoms of the amino acids are within 7. Here we show that Newmans community detection approach in social networks can be used to identify domains in protein structures. We have implemented this approach on protein contact networks and analyze the eigenvectors of the largest eigenvalue of modularity matrix, which is a modified form of the Adjacency matrix, using a quality function called modularity to identify optimal divisions of the network into domains. The proposed approach works even when the domains are formed with amino acids not occurring sequentially along the polypeptide chain and no a priori information regarding the number of nodes is required.

Abstract

In most real world networks the connectivity topology between individual entities is not governed by regular, nearest neighbour interactions but also includes long range interactions, e.g., small-world topology of interacting neurons, scale-free behaviour of gene regulatory networks, etc. In this study we have analyzed the synchronization and control of the dynamics in such networks having non-regular topology, viz., small-world, random and scale-free topologies, compared to that in regular networks modeled on coupled map lattices. For the analysis, logistic map, which exhibits rich dynamical behaviour, is modeled on each node and connectivity between the nodes is defined based on the Watt-Strogatz model for small-world and random networks and Albert-Barabasi model for the scale-free network. The synchronization and control of the complex dynamics is analyzed for varying coupling strengths and connectivity delays in the four network topologies. We observe that the synchronization of the network depends on the connection topology and also on connection delays, with poor synchronization observed in regular and small-world networks compared to random and scale-free topology. The connection delays between constituent units are capable of sustaining complex dynamical behaviour not seen in the undelayed system.

Abstract

The synchronization and control of dynamical systems on a regular lattice has been extensively studied. However, it has been observed that the underlying topology of a real-system need not always be regular, e.g., the brain has been observed to have a connection structure with small-world properties. Thus, non-standard topologies with long-range connections (i.e., non-local diffusion) are not uncommon in real-life systems and may provide different kinds of spatiotemporal dynamics depending on the extent of non-local diffusion. This led us to investigate the spatiotemporal dynamics of coupled logistic map on four different topological networks, viz., regular, small-world, random and scale-free. In particular, we are interested in the synchronization and control of the spatiotemporal dynamics. It has been shown earlier that the transmission delays between constituent units are capable of sustaining complex dynamical behavior, a phenomenon not observed in the undelayed systems. In fact, the synchronization of the dynamics is observed for a much larger parameter space when the underlying topology is scale-free or random. In our earlier work on the control of spatiotemporal dynamics, we have shown the effect of externally applied perturbation or 'pinning' on regular network. By varying the strength and sign of the pinning strength we were able to target the system to any desired dynamical state. Here we investigate the effect of pinning the dynamics on various topologies. Using graph centrality measures, viz., degree, betweenness and closeness for pinning the nodes, our preliminary results suggest that high betweenness nodes perform better in controlling the spatiotemporal dynamics with as few as 10% of nodes required for pinning in case of system exhibiting weak chaotic dynamics. This study has important practical applications in the control of dynamical diseases such as epileptic seizures and bursts on a small-world brain topology.

Abstract

Here we present a simple method based on graph spectral properties to automatically partition multi-domain proteins into individual domains. The identification of structural domains in proteins is based on the assumption that the interactions between the amino acids are higher within a domain than across the domains. These interactions and the topological details of protein structures can be effectively captured by the protein contact graph, constructed by considering each amino acid as a node with an edge drawn between two nodes if the Cα atoms of the amino acids are within 7Å. Here we show that Newman’s community detection approach in social networks can be used to identify domains in protein structures. We have implemented this approach on protein contact networks and analyze the eigenvectors of the largest eigenvalue of modularity matrix, which is a modified form of the Adjacency matrix, using a quality function called “modularity” to identify optimal divisions of the network into domains. The proposed approach works even when the domains are formed with amino acids not occurring sequentially along the polypeptide chain and no a priori information regarding the number of nodes is required.

Abstract

Here we apply the graph-theoretic concept of Betweenness centrality to a class of protein repeats, e.g., Armadillo (ARM) and HEAT. The Betweenness of a node represents how often a node is traversed on the shortest path between all pairs of nodes i, j in the network and thus gives the contribution of each node in the network. These repeats are not easily detectable at the sequence level because of low conservation between independent repeated units, e.g., HEAT repeats are known to have less than 13% identity. Their identification at the structure level typically involves self structure-structure comparison, which can be computationally very intensive. Our analysis of a set of proteins from ARM and HEAT repeat family shows that the repeat regions exhibit similar connectivity patterns for the repeating units. Since it is generally accepted that in many networks, the larger the degree of a node, the larger the chance that many of the shortest paths will pass through this node, computing vertex Betweenness provides a simple and elegant approach for identifying tandem structural repeats in proteins.

Abstract

We describe improved mechanisms to accurately clas-sify days when news for topics receive unexpectedly high amount of coverage. We further investigate the factors which influence this classification using ‘Pres-idential Elections’ as the topic of interest. This help sin bringing out useful trends and relations between days with hot topics by varying variables like history window size,van-ratio etc. We also propose a statisti-cal scheme to approximate major events related to the topic. We then try to approximate the chain of event srelated to the major events. This can support a news alert service and also serve the purpose of automati-cally tracking news which follow up major events.