Nita Parekh

A new numerical scheme for the Fisher equation

In the context of the one-dimensional Fisher equation (1937) the authors study a new numerical scheme for reaction-diffusion equations (proposed by Oono and Puri (1987)). They find that this scheme enables a reasonable simulation of the Fisher equation at high values of the time increment, where conventional schemes are not applicable. For lower values of the time increment, the new scheme compares favourably with conventional schemes.

Synchronization and control of spatiotemporal chaos using time-series data from local regions

In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series data for driving along with simultaneous self-adaptation of the control parameter representative control goals like suppressing spatiotemporal chaos and synchronization of spatiotemporally chaotic dynamics have been discussed. (c) 1998 American Institute of Physics.

Non-algebraic domain growth in random magnets: a cell dynamical approach

The authors develop a novel numerical approach, based on a computationally efficient cell dynamical system (CDS) model, for studying the kinetics of ordering in systems (described by a non-conserved order parameter) with quenched disorder, evolving from unstable initial states. They use this model to study the kinetics of domain growth in a coarse-grained version of the random exchange Ising model. Their numerical data strongly indicate quantitative agreement with the theoretically predicted asymptotic growth law over a limited range of disorder amplitudes. They also compare their observations with those in laboratory experiments and make important predictions regarding dynamical scaling in these systems.

NAPS: Network Analysis of Protein Structures

Traditionally, protein structures have been analysed by the secondary structure architecture and fold arrangement. An alternative approach that has shown promise is modelling proteins as a network of non-covalent interactions between amino acid residues. The network representation of proteins provide a systems approach to topological analysis of complex three-dimensional structures irrespective of secondary structure and fold type and provide insights into structure-function relationship. We have developed a web server for network based analysis of protein structures, NAPS, that facilitates quantitative and qualitative (visual) analysis of residue–residue interactions in: single chains, protein complex, modelled protein structures and trajectories (e.g. from molecular dynamics simulations). The user can specify atom type for network construction, distance range (in Å) and minimal amino acid separation along the sequence. NAPS provides users selection of node(s) and its neighbourhood based on centrality measures, physicochemical properties of amino acids or cluster of well-connected residues (k-cliques) for further analysis. Visual analysis of interacting domains and protein chains, and shortest path lengths between pair of residues are additional features that aid in functional analysis. NAPS support various analyses and visualization views for identifying functional residues, provide insight into mechanisms of protein folding, domain-domain and protein–protein interactions for understanding communication within and between proteins. URL:http://bioinf.iiit.ac.in/NAPS/.

Controllability of spatiotemporal systems using constant pinnings

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 variable dependent. Thus complete controllability (i.e., control and anti-control) of dynamics in these spatially extended systems having coupled multi-variable processes does not only depend on the sign and strength of the perturbation, but also on the specific variable being pinned. This also implies that external manipulation of state variables in natural systems can lead to quite different responses depending at the level of action of the perturbation.

Non-algebraic domain growth in binary alloys with quenched disorder

The authors present detailed numerical results from a computationally efficient cell dynamical system model of domain growth in binary alloys with quenched disorder. Their numerical results suggest that the domain growth law for the disordered case is compatible with (R)(t) approximately (1nt)x, where x has a weak dependence on the disorder amplitude. However, it is possible that their simulations do not access the true asymptotic regime. They also find that the scaled structure factor for the disordered case is independent of the amplitude of disorder and is the same as that for the pure system.

Functional characterization of drought-responsive modules and genes in Oryza sativa: a network-based approach.

Drought is one of the major environmental stress conditions affecting the yield of rice across the globe. Unraveling the functional roles of the drought-responsive genes and their underlying molecular mechanisms will provide important leads to improve the yield of rice. Co-expression relationships derived from condition-dependent gene expression data is an effective way to identify the functional associations between genes that are part of the same biological process and may be under similar transcriptional control. For this purpose, vast amount of freely available transcriptomic data may be used. In this study, we consider gene expression data for different tissues and developmental stages in response to drought stress. We analyze the network of co-expressed genes to identify drought-responsive genes modules in a tissue and stage-specific manner based on differential expression and gene enrichment analysis. Taking cues from the systems-level behavior of these modules, we propose two approaches to identify clusters of tightly co-expressed/co-regulated genes. Using graph-centrality measures and differential gene expression, we identify biologically informative genes that lack any functional annotation. We show that using orthologous information from other plant species, the conserved co-expression patterns of the uncharacterized genes can be identified. Presence of a conserved neighborhood enables us to extrapolate functional annotation. Alternatively, we show that single ‘guide-gene’ approach can help in understanding tissue-specific transcriptional regulation of uncharacterized genes. Finally, we confirm the predicted roles of uncharacterized genes by the analysis of conserved cis-elements and explain the possible roles of these genes toward drought tolerance.

Identifying tandem Ankyrin repeats in protein structures

BackgroundTandem repetition of structural motifs in proteins is frequently observed across all forms of life. Topology of repeating unit and its frequency of occurrence are associated to a wide range of structural and functional roles in diverse proteins, and defects in repeat proteins have been associated with a number of diseases. It is thus desirable to accurately identify specific repeat type and its copy number. Weak evolutionary constraints on repeat units and insertions/deletions between them make their identification difficult at the sequence level and structure based approaches are desired. The proposed graph spectral approach is based on protein structure represented as a graph for detecting one of the most frequently observed structural repeats, Ankyrin repeat.ResultsIt has been shown in a large number of studies that 3-dimensional topology of a protein structure is well captured by a graph, making it possible to analyze a complex protein structure as a mathematical entity. In this study we show that eigen spectra profile of a protein structure graph exhibits a unique repetitive profile for contiguous repeating units enabling the detection of the repeat region and the repeat type. The proposed approach uses a non-redundant set of 58 Ankyrin proteins to define rules for the detection of Ankyrin repeat motifs. It is evaluated on a set of 370 proteins comprising 125 known Ankyrin proteins and remaining non-solenoid proteins and the prediction compared with UniProt annotation, sequence-based approach, RADAR, and structure-based approach, ConSole. To show the efficacy of the approach, we analyzed the complete PDB structural database and identified 641 previously unrecognized Ankyrin repeat proteins. We observe a unique eigen spectra profile for different repeat types and show that the method can be easily extended to detect other repeat types. It is implemented as a web server, AnkPred. It is freely available at ‘bioinf.iiit.ac.in/AnkPred’.ConclusionsAnkPred provides an elegant and computationally efficient graph-based approach for detecting Ankyrin structural repeats in proteins. By analyzing the eigen spectra of the protein structure graph and secondary structure information, characteristic features of a known repeat family are identified. This method is especially useful in correctly identifying new members of a repeat family.

IGIPT - Integrated genomic island prediction tool.

IGIPT is a web-based integrated platform for the identification of genomic islands (GIs). It incorporates thirteen parametric measures based on anomalous nucleotide composition on a single platform, thus improving the predictive power of a horizontally acquired region, since it is known that no single measure can absolutely predict a horizontally transferred region. The tool filters putative GIs based on standard deviation from genomic average and also provides raw output in MS excel format for further analysis. To facilitate the identification of various structural features, viz., tRNA integration sites, repeats, etc. in the vicinity of GIs, the tool provides option to extract the predicted regions and its flanking regions. Availability The database is available for free at http://bioinf.iiit.ac.in/IGIPT/

Analysis and characterization of complex spatio-temporal patterns in nonlinear reaction-diffusion systems

Two important classes of spatio-temporal patterns, namely, spatio-temporal chaos and self-replicating patterns, for a representative three variable autocatalytic reaction mechanism coupled with diffusion has been studied. The characterization of these patterns has been carried out in terms of Lyapunov exponents and dimension density. The results show a linear scaling as a function of sub-system size for the Lyapunov dimension and entropy while the Lyapunov dimension density was found to rapidly saturate. The possibility of synchronizing the spatio-temporal dynamics by analyzing the conditional Lyapunov exponents of sub-systems was also observed.