Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

A matrix identity and perturbation expressions

An identity expressing formally the diagonal and off-diagonal elements of an inverse of a matrix is deduced employing operator techniques. Several well-known perturbation expressions for the self-energy are deduced as special cases. A new approximation and other applications following from the above formalism are briefly indicated through illustrations from a perturbed harmonic oscillator, chemisorption approximations and Kelly's result in the problem of electron correlation.

A taxonomic mystery for more than 180 years: the identity and systematic position of Brachysaura minor (HARDWICKE & GRAY, 1827)

Brachysaura is a monotypic genus of agamid lizard found in the Indian subcontinent; the identity and systematic position of B. minor has been long debated, and it has at times been subsumed into Agama, Charasia and Laudakia, with some authors suggesting affinities to Calotes. We constructed nuclear and mitochondrial phylogenetic trees including Brachysaura and allied agamid genera to resolve its phylogenetic position. We also compared osteology and external morphology with the genera Agama, Calotes and Laudakia. Hemipenial morphology was compared with Calotes and some other agamids from South Asia. Both nuclear and mitochondrial phylogenies demonstrate that Brachysaura is nested within the widespread South and Southeast Asian genus Calotes, with which it also shares certain external morphological, osteological and hemipenial characters. Adaptations to ground dwelling in Brachysaura minor has resulted in unique modifications to its body plan, which is likely why generic allocation has been long confused. This study also highlights the need for an integrated systematic approach to resolve taxonomic ambiguity in Asian agamids.

Extrapolation and series acceleration procedures: Hard spheres and discs as illustrations

Three new procedures - in the context of estimation of virial coefficients and summation of the partial virial series for hard discs and hard spheres - are proposed. They are based on the parametrised Euler transformation, a novel resummation, identity and the ε-convergence methods respectively. A comparison with other estimates (molecular dynamics, graph theory and empirical methods) reveals satisfactory agreement.

Mutational analysis of active-site residues in the Mycobacterium leprae RecA intein, a LAGLIDADG homing endonuclease: Asp(122) and Asp(193) are crucial to the double-stranded DNA cleavage activity whereas Asp(218) is not

Mycobacterium leprae recA harbors an in-frame insertion sequence that encodes an intein homing endonuclease (PI-MleI). Most inteins (intein endonucleases) possess two conserved LAGLIDADG (DOD) motifs at their ctive center. A common feature of LAGLIDADG-type homing endonucleases is that they recognize and cleave the same or very similar DNA sequences. However, PI-MleI is distinctive from other members of the family of LAGLIDADG-type HEases for its modular structure with functionally separable domains for DNA-binding and cleavage, each with distinct sequence preferences. Sequence alignment analyses of PI-MleI revealed three putative LAGLIDADG motifs; however, there is conflicting bioinformatics data in regard to their identity and specific location within the intein polypeptide. To resolve this conflict and to determine the active-site residues essential for DNA target site recognition and double-stranded DNA cleavage, we performed site-directed mutagenesis of presumptive catalytic residues in the LAGLIDADG motifs. Analysis of target DNA recognition and kinetic parameters of the wild-type PI-MleI and its variants disclosed that the two amino acid residues, Asp(122) (in Block C) and Asp(193) (in functional Block E), are crucial to the double-stranded DNA endonuclease activity, whereas Asp(218) (in pseudo-Block E) is not. However, despite the reduced catalytic activity, the PI-MleI variants, like the wild-type PI-MleI, generated a footprint of the same length around the insertion site. The D122T variant showed significantly reduced catalytic activity, and D122A and D193A mutations although failed to affect their DNA-binding affinities, but abolished the double-stranded DNA cleavage activity. On the other hand, D122C variant showed approximately twofold higher double-stranded DNA cleavage activity, compared with the wild-type PI-MleI. These results provide compelling evidence that Asp(122) and Asp(193) in DOD motif I and II, respectively, are bona fide active-site residues essential for DNA cleavage activity. The implications of these results are discussed in this report.

Cloning, expression, purification, and biochemical characterisation of the FIC motif containing protein of Mycobacterium tuberculosis

The role of FIC (Filamentation induced by cAMP)(2) domain containing proteins in the regulation of many vital pathways, mostly through the transfer of NMPs from NTPs to specific target proteins (NMPylation), in microorganisms, higher eukaryotes, and plants is emerging. The identity and function of FIC domain containing protein of the human pathogen, Mycobacterium tuberculosis, remains unknown. In this regard, M. tuberculosis fic gene (Mtfic) was cloned, overexpressed, and purified to homogeneity for its biochemical characterisation. It has the characteristic FIC motif, HPFREGNGRSTR (HPFxxGNGRxxR), spanning 144th to 155th residue. Neither the His-tagged nor the GST-tagged MtFic protein, overexpressed in Escherichia coil, nor expression of Mtfic in Mycobacterium smegmatis, yielded the protein in the soluble fraction. However, the maltose binding protein (MBP) tagged MtFic (MBP-MtFic) could be obtained partly in the soluble fraction. The cloned, overexpressed, and purified recombinant MBP-MtFic showed conversion of ATP, GTP, CTP, and UTP into AMP. GMP, CMP, and UMP, respectively. Sequence alignment with several FIC motif containing proteins, complemented with homology modeling on the FIC motif containing protein, VbhT of Bartonella schoenbuchensis as the template, showed conservation and interaction of residues constituting the FIC domain. Site-specific mutagenesis of the His144, or Glu148, or Asn150 of the FIC motif, or of Arg87 residue that constitutes the FIC domain, or complete deletion of the FIC motif, abolished the NTP to NMP conversion activity. The design of NMP formation assay using the recombinant, soluble MtFic would enable identification of its target substrate for NMPylation. (C) 2012 Elsevier Inc. All rights reserved.

Fractional Hilbert transform extensions and associated analytic signal construction

The analytic signal (AS) was proposed by Gabor as a complex signal corresponding to a given real signal. The AS has a one-sided spectrum and gives rise to meaningful spectral averages. The Hilbert transform (HT) is a key component in Gabor's AS construction. We generalize the construction methodology by employing the fractional Hilbert transform (FrHT), without going through the standard fractional Fourier transform (FrFT) route. We discuss some properties of the fractional Hilbert operator and show how decomposition of the operator in terms of the identity and the standard Hilbert operators enables the construction of a family of analytic signals. We show that these analytic signals also satisfy Bedrosian-type properties and that their time-frequency localization properties are unaltered. We also propose a generalized-phase AS (GPAS) using a generalized-phase Hilbert transform (GPHT). We show that the GPHT shares many properties of the FrHT, in particular, selective highlighting of singularities, and a connection with Lie groups. We also investigate the duality between analyticity and causality concepts to arrive at a representation of causal signals in terms of the FrHT and GPHT. On the application front, we develop a secure multi-key single-sideband (SSB) modulation scheme and analyze its performance in noise and sensitivity to security key perturbations. (C) 2013 Elsevier B.V. All rights reserved.

Evolutionary and structural analyses of heterodimeric proteins composed of subunits with same fold

Heterodimeric proteins with homologous subunits of same fold are involved in various biological processes. The objective of this study is to understand the evolution of structural and functional features of such heterodimers. Using a non-redundant dataset of 70 such heterodimers of known 3D structure and an independent dataset of 173 heterodimers from yeast, we note that the mean sequence identity between interacting homologous subunits is only 23-24% suggesting that, generally, highly diverged paralogues assemble to form such a heterodimer. We also note that the functional roles of interacting subunits/domains are generally quite different. This suggests that, though the interacting subunits/domains are homologous, the high evolutionary divergence characterize their high functional divergence which contributes to a gross function for the heterodimer considered as a whole. The inverse relationship between sequence identity and RMSD of interacting homologues in heterodimers is not followed. We also addressed the question of formation of homodimers of the subunits of heterodimers by generating models of fictitious homodimers on the basis of the 3D structures of the heterodimers. Interaction energies associated with these homodimers suggests that, in overwhelming majority of the cases, such homodimers are unlikely to be stable. Majority of the homologues of heterodimers of known structures form heterodimers (51.8%) and a small proportion (14.6%) form homodimers. Comparison of 3D structures of heterodimers with homologous homodimers suggests that interfacial nature of residues is not well conserved. In over 90% of the cases we note that the interacting subunits of heterodimers are co-localized in the cell. Proteins 2015; 83:1766-1786. (c) 2015 Wiley Periodicals, Inc.