SSMBS: a web server to locate sequentially separated motifs in biological sequences

The identification of sequence (amino acids or nucleotides) motifs in a particular order in biological sequences has proved to be of interest. This paper describes a computing server, SSMBS, which can locate anddisplay the occurrences of user-defined biologically important sequence motifs (a maximum of five) present in a specific order in protein and nucleotide sequences. While the server can efficiently locate motifs specified using regular expressions, it can also find occurrences of long and complex motifs. The computation is carried out by an algorithm developed using the concepts of quantifiers in regular expressions. The web server is available to users around the clock at http://dicsoft1.physics.iisc.ernet.in/ssmbs/.

Recognition and alignment of homologous DNA sequences between minichromosomes and single-stranded DNA promoted by RecA protein

The incorporation of DNA into nucleosomes and higher-order forms of chromatin in vivo creates difficulties with respect to its accessibility for cellular functions such as transcription, replication, repair and recombination. To understand the role of chromatin structure in the process of homologous recombination, we have studied the interaction of nucleoprotein filaments, comprised of RecA protein and ssDNA, with minichromosomes. Using this paradigm, we have addressed how chromatin structure affects the search for homologous DNA sequences, and attempted to distinguish between two mutually exclusive models of DNA-DNA pairing mechanisms. Paradoxically, we found that the search for homologous sequences, as monitored by unwinding of homologous or heterologous duplex DNA, was facilitated by nucleosomes, with no discernible effect on homologous pairing. More importantly, unwinding of minichromosomes required the interaction of nucleoprotein filaments and led to the accumulation of circular duplex DNA sensitive to nuclease P1. Competition experiments indicated that chromatin templates and naked DNA served as equally efficient targets for homologous pairing. These and other findings suggest that nucleosomes do not impede but rather facilitate the search for homologous sequences and establish, in accordance with one proposed model, that unwinding of duplex DNA precedes alignment of homologous sequences at the level of chromatin. The potential application of this model to investigate the role of chromosomal proteins in the alignment of homologous sequences in the context of cellular recombination is considered.

A Method to Find Sequentially Separated Motifs in Biological Sequences (SSMBS)

Sequence motifs occurring in a particular order in proteins or DNA have been proved to be of biological interest. In this paper, a new method to locate the occurrences of up to five user-defined motifs in a specified order in large proteins and in nucleotide sequence databases is proposed. It has been designed using the concept of quantifiers in regular expressions and linked lists for data storage. The application of this method includes the extraction of relevant consensus regions from biological sequences. This might be useful in clustering of protein families as well as to study the correlation between positions of motifs and their functional sites in DNA sequences.

Expanding the Peptide beta-Turn in alpha gamma Hybrid Sequences: 12 Atom Hydrogen Bonded Helical and Hairpin Turns

Hybrid peptide segments containing contiguous alpha and gamma amino acid residues can form C-12 hydrogen bonded turns which may be considered as backbone expanded analogues of C-10 beta-turns) found in alpha alpha segments. Exploration of the regular hydrogen bonded conformations accessible for hybrid alpha gamma sequences is facilitated by the use of a stereochemically constrained gamma amino acid residue gabapentin (1-aminomethylcyclohexaneacetic acid, Gpn), in which the two torsion angles about C-gamma-C-beta (theta(1)) and C-beta-C-alpha (theta(2)) are predominantly restricted to gauche conformations. The crystal structures of the octapeptides Boc-Gpn-Aib-Gpn-Aib-Gpn-Aib-Gpn-Aib-OMe (1) and Boc-Leu-Phe-Val-Aib-Gpn-Leu-Phe-Val-OMe (2) reveal two distinct conformations for the Aib-Gpn segment. Peptide 1 forms a continuous helix over the Aib(2)-Aib(6) segment, while the peptide 2 forms beta-hairpin structure stabilized by four cross-strand hydrogen bonds with the Aib-Gpn segment forming a nonhelical C-12 turn. The robustness of the helix in peptide 1 in solution is demonstrated by NMR methods. Peptide 2 is conformationally fragile in solution with evidence of beta-hairpin conformations being obtained in methanol. Theoretical calculations permit delineation of the various C-12 hydrogen bonded structures which are energetically feasible in alpha gamma and gamma alpha sequences.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Low correlation sequences over AM-PSK and QAM alphabets

A construction for a family of sequences over the 8-ary AM-PSK constellation that has maximum nontrivial correlation magnitude bounded as theta(max) less than or similar to root N is presented here. The famfly is asymptotically optimal with respect to the Welch bound on maximum magnitude of correlation. The 8-ary AM-PSK constellation is a subset of the 16-QAM constellation. We also construct two families of sequences over 16-QAM with theta(max) less than or similar to root 2 root N. These families are constructed by interleaving sets of sequences. A construction for a famBy of low-correlation sequences over QAM alphabet of size 2(2m) is presented with maximum nontrivial normalized correlation parameter bounded above by less than or similar to a root N, where N is the period of the sequences in the family and where a ranges from 1.61 in the case of 16-QAM modulation to 2.76 for large m. When used in a CDMA setting, the family will permit each user to modulate the code sequence with 2m bits of data. Interestingly, the construction permits users on the reverse link of the CDMA channel to communicate using varying data rates by switching between sequence famflies; associated to different values of the parameter m. Other features of the sequence families are improved Euclidean distance between different data symbols in comparison with PSK signaling and compatibility of the QAM sequence families with sequences belonging to the large quaternary sequence families {S(p)}.

Isoperimetric Problem and Meta-fibonacci Sequences

Let G = (V,E) be a simple, finite, undirected graph. For S ⊆ V, let $\delta(S,G) = \{ (u,v) \in E : u \in S \mbox { and } v \in V-S \}$ and $\phi(S,G) = \{ v \in V -S: \exists u \in S$ , such that (u,v) ∈ E} be the edge and vertex boundary of S, respectively. Given an integer i, 1 ≤ i ≤ ∣ V ∣, the edge and vertex isoperimetric value at i is defined as b e (i,G) =  min S ⊆ V; |S| = i |δ(S,G)| and b v (i,G) =  min S ⊆ V; |S| = i |φ(S,G)|, respectively. The edge (vertex) isoperimetric problem is to determine the value of b e (i, G) (b v (i, G)) for each i, 1 ≤ i ≤ |V|. If we have the further restriction that the set S should induce a connected subgraph of G, then the corresponding variation of the isoperimetric problem is known as the connected isoperimetric problem. The connected edge (vertex) isoperimetric values are defined in a corresponding way. It turns out that the connected edge isoperimetric and the connected vertex isoperimetric values are equal at each i, 1 ≤ i ≤ |V|, if G is a tree. Therefore we use the notation b c (i, T) to denote the connected edge (vertex) isoperimetric value of T at i. Hofstadter had introduced the interesting concept of meta-fibonacci sequences in his famous book “Gödel, Escher, Bach. An Eternal Golden Braid”. The sequence he introduced is known as the Hofstadter sequences and most of the problems he raised regarding this sequence is still open. Since then mathematicians studied many other closely related meta-fibonacci sequences such as Tanny sequences, Conway sequences, Conolly sequences etc. Let T 2 be an infinite complete binary tree. In this paper we related the connected isoperimetric problem on T 2 with the Tanny sequences which is defined by the recurrence relation a(i) = a(i − 1 − a(i − 1)) + a(i − 2 − a(i − 2)), a(0) = a(1) = a(2) = 1. In particular, we show that b c (i, T 2) = i + 2 − 2a(i), for each i ≥ 1. We also propose efficient polynomial time algorithms to find vertex isoperimetric values at i of bounded pathwidth and bounded treewidth graphs.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

Network flow-control using asynchronous stochastic approximation

We propose several stochastic approximation implementations for related algorithms in flow-control of communication networks. First, a discrete-time implementation of Kelly's primal flow-control algorithm is proposed. Convergence with probability 1 is shown, even in the presence of communication delays and stochastic effects seen in link congestion indications. This ensues from an analysis of the flow-control algorithm using the asynchronous stochastic approximation (ASA) framework. Two relevant enhancements are then pursued: a) an implementation of the primal algorithm using second-order information, and b) an implementation where edge-routers rectify misbehaving flows. Next, discretetime implementations of Kelly's dual algorithm and primaldual algorithm are proposed. Simulation results a) verifying the proposed algorithms and, b) comparing the stability properties are presented.

A quantum stochastic Lie-Trotter product formula

A Trotter product formula is established for unitary quantum stochastic processes governed by quantum stochastic differential equations with constant bounded coefficients.

Stochastic simulations of the origins and implications of long-tailed distributions in gene expression

Gene expression noise results in protein number distributions ranging from long-tailed to Gaussian. We show how long-tailed distributions arise from a stochastic model of the constituent chemical reactions and suggest that, in conjunction with cooperative switches, they lead to more sensitive selection of a subpopulation of cells with high protein number than is possible with Gaussian distributions. Single-cell-tracking experiments are presented to validate some of the assumptions of the stochastic simulations. We also examine the effect of DNA looping on the shape of protein distributions. We further show that when switches are incorporated in the regulation of a gene via a feedback loop, the distributions can become bimodal. This might explain the bimodal distribution of certain morphogens during early embryogenesis.

Polypeptide Helices in Hybrid Peptide Sequences

A new class of polypeptide helices in hybrid sequences containing alpha-, beta-, and gamma-residues is described. The molecular conformations in crystals determined for the synthetic peptides Boc-Leu-Phe-Val-Aib-beta Phe-Leu-Phe-Val-OMe 1 (beta Phe: (S)-beta(3)-homophenylalanine) and Boc-Aib-Gpn-AibGpn-OM2(Gpn:1-(aminomethyl)cycl hexaneacetic acid) reveal expanded helical turns in the hybrid sequences (alpha alpha beta)(n) and (ay), In 1, a repetitive helical structure composed Of C-14 hydrogen-bonded units is observed, whereas 2 provides an example of a repetitive C-12 hydrogen-bonded structure. Using experimentally determined backbone torsion angles for the hydrogen-bonded units formed by hybrid sequences, we have generated energetically favorable hybrid helices. Conformational parameters are provided for C-11, C-12, C-13, C-14, and C-15 helices in hybrid sequences.

Multiple conformational states in crystals and in solution in alpha gamma hybrid peptides. Fragility of the C-12 helix in short sequences

The conformational properties of foldamers generated from alpha gamma hybrid peptide sequences have been probed in the model sequence Boc-Aib-Gpn-Aib-Gpn-NHMe. The choice of alpha-aminoisobutyryl (Aib) and gabapentin (Gpn) residues greatly restricts sterically accessible coil formational space. This model sequence was anticipated to be a short segment of the alpha gamma C-12 helix, stabilized by three successive 4 -> 1 hydrogen bonds, corresponding to a backbone-expanded analogue of the alpha polypeptide 3(10)-helix. Unexpectedly, three distinct crystalline polymorphs were characterized in the solid state by X-ray diffraction. In one form, two successive C-12 hydrogen bonds were obtained at the N-terminus, while a novel C-17 hydrogen-bonded gamma alpha gamma turn was observed at the C-terminus. In the other two polymorphs, isolated C-9 and C-7 hydrogen-bonded turns were observed at Gpn (2) and Gpn (4). Isolated C-12 and C-9 turns were also crystallographically established in the peptides Boc-Aib-Gpn-Aib-OMe and Boc-Gpn-Aib-NHMe, respectively. Selective line broadening of NH resonances and the observation of medium range NH(i)<-> NH(i+2) NOEs established the presence of conformational heterogeneity for the tetrapeptide in CDCl3 solution. The NMR results are consistent with the limited population of the continuous C-12 helix conformation. Lengthening of the (alpha gamma)(n) sequences in the nonapeptides Boc-Aib-Gpn-Aib-Gpn-Aib-Gpn-Aib-Gpn-Xxx (Xxx = Aib, Leu) resulted in the observation of all of the sequential NOEs characteristic of an alpha gamma C-12 helix. These results establish that conformational fragility is manifested in short hybrid alpha gamma sequences despite the choice of conformationally constrained residues, while stable helices are formed on chain extension.

Optimal threshold policies for admission control in communication networks via discrete parameter stochastic approximation

The problem of admission control of packets in communication networks is studied in the continuous time queueing framework under different classes of service and delayed information feedback. We develop and use a variant of a simulation based two timescale simultaneous perturbation stochastic approximation (SPSA) algorithm for finding an optimal feedback policy within the class of threshold type policies. Even though SPSA has originally been designed for continuous parameter optimization, its variant for the discrete parameter case is seen to work well. We give a proof of the hypothesis needed to show convergence of the algorithm on our setting along with a sketch of the convergence analysis. Extensive numerical experiments with the algorithm are illustrated for different parameter specifications. In particular, we study the effect of feedback delays on the system performance.

Hybrid moving block bootstrap for stochastic simulation of multi-site multi-season streamflows

The Hybrid approach introduced by the authors for at-site modeling of annual and periodic streamflows in earlier works is extended to simulate multi-site multi-season streamflows. It bears significance in integrated river basin planning studies. This hybrid model involves: (i) partial pre-whitening of standardized multi-season streamflows at each site using a parsimonious linear periodic model; (ii) contemporaneous resampling of the resulting residuals with an appropriate block size, using moving block bootstrap (non-parametric, NP) technique; and (iii) post-blackening the bootstrapped innovation series at each site, by adding the corresponding parametric model component for the site, to obtain generated streamflows at each of the sites. It gains significantly by effectively utilizing the merits of both parametric and NP models. It is able to reproduce various statistics, including the dependence relationships at both spatial and temporal levels without using any normalizing transformations and/or adjustment procedures. The potential of the hybrid model in reproducing a wide variety of statistics including the run characteristics, is demonstrated through an application for multi-site streamflow generation in the Upper Cauvery river basin, Southern India. (C) 2004 Elsevier B.V. All rights reserved.