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

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

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

Prokaryotic Genomes undergo various mutational events during the course of genome evolution through a variety of processes including Horizontal Gene Transfer. These regions of about 10 - 100 Kb in length are called Genomic Islands and presence of such regions offers selective advantage to the organism and may aid in the organism's growth, survival (saprophytic or symbiotic mode) or display of pathogenicity. Earlier analysis on horizontally transferred regions has shown significant variations from the average genomic values in their GC content, codon preferences and dinucleotide bias. We have developed a web-based tool identifying genomic islands in prokaryotic genomes (GIPro) based on various measures, viz., GC content (total and at individual codon positions), dinculeotide biases, and biases in codon and amino acid usage, carried out in a sliding window analysis along the length of the genome. The regions that deviate by n standard deviations (n - user defined, default value 2) from the average genome values for at least two measures are identified as probable genomic islands by the tool. GIPro can also be used for comparison of user defined regions / gene sets to confirm whether both belong to the same genome or have differences in their dinucleotide or codon usage biases as a result of horizontal transfer.

Abstract

Identifying tandem repeats in the proteome of any organism is important not only for understanding the structure and function of the proteins but also for analyzing the association of abnormal expansion of repeat regions with disorders We have developed an efficient tool for identifying Peptide Periodic Repeats (PEPPER) in protein sequences. The tool has three in-built modules: In the first module, initial screening of the protein sequence by a uni-dimensional vector equivalent to the dot-matrix is used to identify all possible repeat regions. In the second module, a sliding window analysis of the putative repeat region using a K-tuple identifies the period and the possible pattern of the repeat. In the third module, wraparound dynamic programming (WDP) algorithm is implemented to obtain the exact repeat boundaries. If the protein sequence does not contain tandem repeat region, then the second and third steps of the algorithm are skipped making it computationally efficient for database search compared to the other existing algorithms. We report up to three possible multiple-periodicities in a given repeat region. The tool reports the consensus repeat pattern, the complete repeat region, the score and alignment of the consensus with the repeat region along with percentage mismatch/indels. A preliminary comparison of our results with the TRIPS database of protein tandem repeats showed that our program not only identifies all the repeats in the TRIPS database, but we were also able to re-annotate a few incorrectly annotated repeats and found few new repeats no reported in the TRIPS database. PEPPER provides the user the facility to change parameter values for identifying small or approximate tandem repeats. A database of repeats can be built by the user for his set of protein sequences on the fly with PEPPER.

Abstract

About 14% of the protein sequences in the Swissprot database contain repetitive region, viz., tandem repeats, multiple copies of motifs/profiles, multiple copies of domain. And eukaryotic proteins are more likely to have repeats than Bacteria and Archaea. Our main focus is only on tandem repeats. Tandem repeat can be defined as contiguous repeat pattern of two or more copies. These copies can be exact or approximate. Many proteins with these repeat are involved in functions like transcription, translation, protein-protein interaction. Proteins with tandem repeats are involved in various neurodegenerative diseases like Huntington's disease. These proteins are also found to occur in sequences which are poorly conserved in evolution. We have developed a database of tandem repeats in protein sequences: Protein Tandem Repeats DataBase(PTRDB). The data for this database is extracted using our in-house tool PEPPER, a tool for identifying PEPtide PEriodic Repeats. This database is built on SwissProt (ver 51.7). PTRDB have 3145 proteins with 4713 tandem repeats. 77.74% are found in Eukaryota, 16.63% in Bacteria and 0.67% in Archaea. About 5% of proteins in this database are associated with disease. We have classified the database organism wise. This database can be queried by various attributes like SwissProt ID, organism name, PDBID, repeat pattern, repeat length, keyword and copy number. It gives the detail information of tandem repeats like SwissProt ID (hyperlinked to SwissProt to give Fasta sequence), organism name, PDBID (hyperlinked to PDB), one line description of the protein, gene name, protein name, taxonomy ID (hyperlinked to EBI), Family information (hyperlinked to Pfam), Description of associated disease, OMIM ID, scoring matrix with gap extension for the repeat, repeat pattern with alignment score, copy number, repeat length, start point, end point, alignment of repeat pattern with repeat region, secondary structure information of the repeat region. With the increasing abundance of tandem protein repeats in various proteomes this database will be increasingly important in proteome comparison.

Abstract

Recently much attention is being focused on the analysis of the three dimensional structure of proteins using graph and network concepts. The simplest protein network graph is constructed by defining the amino acids as nodes and the edges drawn between amino acids (within a threshold) which attempt to capture not only covalent but also non-covalent interactions. Analysis of the topological details of proteins with known structures, such as clustering of specific types of amino acids important for structure, folding and function, is of great value and is an active field of research. Since structures of a large number of proteins is now available, automatic methods of analysis are required to analyze them and recently, the tools from graph theory are being explored for such analysis. Here, we propose to use graph properties and their spectral analysis for identifying patterns in protein structures, in particular, structural repeats or motifs. These repeats are not easily detectable at the sequence level because of low conservation or high divergence between independent repeated units. The importance of such repeats in understanding biological function resides not only in their high frequency among known sequences, but also in their abilities to confer multiple binding and structural roles on proteins, e.g., zinc finger domain, a constituent of transcription factors involved in DNA binding, where the composition and copy number of individual tandem repeats confers selectivity and activity of DNA binding. This functional versatility is apparent not only among different repeat types, but also for similar repeats from the same family. Our understanding of repeats, with respect to their structures, functions, and evolution, therefore represents a considerable challenge. Our analysis of the degree distribution and spectral analysis of a set of proteins from various repeat families show that the repeat regions exhibit similar connectivity patterns in the graph. The network property, Betweenness, was found to identify accurately the repeat boundaries in protein families. Thus, this approach can help in identifying repeated motifs in proteins which are difficult to identify at the sequence level.

Abstract

The ultimate goal of molecular cell biology is to understand the physiology of living cells in terms of the information that is encoded in the genome of the cell and we would like to address the question how computational biology can help in achieving this goal. Genes coding for proteins is a very important pattern recognition problem in bioinformatics and this lecture focuses on some computational issues in gene identification.

Abstract

Most natural spatiotemporal systems are an organized ensemble of dynamical subsystems whose behaviour is regulated by nonlinearly coupled multi-variable processes. The response of each of these variables and/or combinations of them to any single or composite external perturbation can influence its spatiotemporal behaviour in a complex and non-intuitive manner. This paper attempts to study the dynamical response of two coupled map lattice systems having local dynamics described by (a) coupled discrete maps, and (b) coupled differential equations, to external perturbation (or “pinning”) applied to each variable individually or simultaneously. We show that the response of different variables to external pinning is quite different. Our results indicate that, though this pinning approach is useful in controlling complex dynamics both globally and locally, enhancing complexity in dynamics (“anti-control”) is …