Evolutionary connection between the catalytic subunits of DNA-dependent RNA polymerases and eukaryotic RNA-dependent RNA polymerases and the origin of RNA polymerases

BACKGROUND: The eukaryotic RNA-dependent RNA polymerase (RDRP) is involved in the amplification of regulatory microRNAs during post-transcriptional gene silencing. This enzyme is highly conserved in most eukaryotes but is missing in archaea and bacteria. No evolutionary relationship between RDRP and other polymerases has been reported so far, hence the origin of this eukaryote-specific polymerase remains a mystery. RESULTS: Using extensive sequence profile searches, we identified bacteriophage homologs of the eukaryotic RDRP. The comparison of the eukaryotic RDRP and their homologs from bacteriophages led to the delineation of the conserved portion of these enzymes, which is predicted to harbor the catalytic site. Further, detailed sequence comparison, aided by examination of the crystal structure of the DNA-dependent RNA polymerase (DDRP), showed that the RDRP and the β' subunit of DDRP (and its orthologs in archaea and eukaryotes) contain a conserved double-psi β-barrel (DPBB) domain. This DPBB domain contains the signature motif DbDGD (b is a bulky residue), which is conserved in all RDRPs and DDRPs and contributes to catalysis via a coordinated divalent cation. Apart from the DPBB domain, no similarity was detected between RDRP and DDRP, which leaves open two scenarios for the origin of RDRP: i) RDRP evolved at the onset of the evolution of eukaryotes via a duplication of the DDRP β' subunit followed by dramatic divergence that obliterated the sequence similarity outside the core catalytic domain and ii) the primordial RDRP, which consisted primarily of the DPBB domain, evolved from a common ancestor with the DDRP at a very early stage of evolution, during the RNA world era. The latter hypothesis implies that RDRP had been subsequently eliminated from cellular life forms and might have been reintroduced into the eukaryotic genomes through a bacteriophage. Sequence and structure analysis of the DDRP led to further insights into the evolution of RNA polymerases. In addition to the β' subunit, β subunit of DDRP also contains a DPBB domain, which is, however, distorted by large inserts and does not harbor a counterpart of the DbDGD motif. The DPBB domains of the two DDRP subunits together form the catalytic cleft, with the domain from the β' subunit supplying the metal-coordinating DbDGD motif and the one from the β subunit providing two lysine residues involved in catalysis. Given that the two DPBB domains of DDRP contribute completely different sets of active residues to the catalytic center, it is hypothesized that the ultimate ancestor of RNA polymerases functioned as a homodimer of a generic, RNA-binding DPBB domain. This ancestral protein probably did not have catalytic activity and served as a cofactor for a ribozyme RNA polymerase. Subsequent evolution of DDRP and RDRP involved accretion of distinct sets of additional domains. In the DDRPs, these included a RNA-binding Zn-ribbon, an AT-hook-like module and a sandwich-barrel hybrid motif (SBHM) domain. Further, lineage-specific accretion of SBHM domains and other, DDRP-specific domains is observed in bacterial DDRPs. In contrast, the orthologs of the β' subunit in archaea and eukaryotes contains a four-stranded α + β domain that is shared with the α-subunit of bacterial DDRP, eukaryotic DDRP subunit RBP11, translation factor eIF1 and type II topoisomerases. The additional domains of the RDRPs remain to be characterized. CONCLUSIONS: Eukaryotic RNA-dependent RNA polymerases share the catalytic double-psi β-barrel domain, containing a signature metal-coordinating motif, with the universally conserved β' subunit of DNA-dependent RNA polymerases. Beyond this core catalytic domain, the two classes of RNA polymerases do not have common domains, suggesting early divergence from a common ancestor, with subsequent independent domain accretion. The β-subunit of DDRP contains another, highly diverged DPBB domain. The presence of two distinct DPBB domains in two subunits of DDRP is compatible with the hypothesis that the ultimate ancestor of RNA polymerases was a RNA-binding DPBB domain that had no catalytic activity but rather functioned as a homodimeric cofactor for a ribozyme polymerase

Entropy of Constant Curvature Black Holes in General Relativity

We consider the thermodynamic properties of the constant curvature black hole solution recently found by Banados. We show that it is possible to compute the entropy and the quasilocal thermodynamics of the spacetime using the Einstein-Hilbert action of General Relativity. The constant curvature black hole has some unusual properties which have not been seen in other black hole spacetimes. The entropy of the black hole is not associated with the event horizon; rather it is associated with the region between the event horizon and the observer. Further, surfaces of constant internal energy are not isotherms so the first law of thermodynamics exists only in an integral form. These properties arise from the unusual topology of the Euclidean black hole instanton.Comment: 4 pages LaTeX2e (RevTeX), 2 PostScript figures. Small corrections in the text and the reference

A stochastic-Lagrangian particle system for the Navier-Stokes equations

This paper is based on a formulation of the Navier-Stokes equations developed by P. Constantin and the first author (\texttt{arxiv:math.PR/0511067}, to appear), where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. In this paper, we take $N$ copies of the above process (each based on independent Wiener processes), and replace the expected value with $\frac{1}{N}$ times the sum over these $N$ copies. (We remark that our formulation requires one to keep track of $N$ stochastic flows of diffeomorphisms, and not just the motion of $N$ particles.) We prove that in two dimensions, this system of interacting diffeomorphisms has (time) global solutions with initial data in the space \holderspace{1}{\alpha} which consists of differentiable functions whose first derivative is $\alpha$ H\"older continuous (see Section \ref{sGexist} for the precise definition). Further, we show that as $N \to \infty$ the system converges to the solution of Navier-Stokes equations on any finite interval $[0,T]$. However for fixed $N$, we prove that this system retains roughly $O(\frac{1}{N})$ times its original energy as $t \to \infty$. Hence the limit $N \to \infty$ and $T\to \infty$ do not commute. For general flows, we only provide a lower bound to this effect. In the special case of shear flows, we compute the behaviour as $t \to \infty$ explicitly.Comment: v3: Typo fixes, and a few stylistic changes. 17 pages, 2 figure

Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame

The equations of motion of compact binary systems and their associated Lagrangian formulation have been derived in previous works at the third post-Newtonian (3PN) approximation of general relativity in harmonic coordinates. In the present work we investigate the binary's relative dynamics in the center-of-mass frame (center of mass located at the origin of the coordinates). We obtain the 3PN-accurate expressions of the center-of-mass positions and equations of the relative binary motion. We show that the equations derive from a Lagrangian (neglecting the radiation reaction), from which we deduce the conserved center-of-mass energy and angular momentum at the 3PN order. The harmonic-coordinates center-of-mass Lagrangian is equivalent, {\it via} a contact transformation of the particles' variables, to the center-of-mass Hamiltonian in ADM coordinates that is known from the post-Newtonian ADM-Hamiltonian formalism. As an application we investigate the dynamical stability of circular binary orbits at the 3PN order.Comment: 31 pages, to appear in Classical and Quantum Gravit

Origin and evolution of the archaeo-eukaryotic primase superfamily and related palm-domain proteins: structural insights and new members

We report an in-depth computational study of the protein sequences and structures of the superfamily of archaeo-eukaryotic primases (AEPs). This analysis greatly expands the range of diversity of the AEPs and reveals the unique active site shared by all members of this superfamily. In particular, it is shown that eukaryotic nucleo-cytoplasmic large DNA viruses, including poxviruses, asfarviruses, iridoviruses, phycodnaviruses and the mimivirus, encode AEPs of a distinct family, which also includes the herpesvirus primases whose relationship to AEPs has not been recognized previously. Many eukaryotic genomes, including chordates and plants, encode previously uncharacterized homologs of these predicted viral primases, which might be involved in novel DNA repair pathways. At a deeper level of evolutionary connections, structural comparisons indicate that AEPs, the nucleases involved in the initiation of rolling circle replication in plasmids and viruses, and origin-binding domains of papilloma and polyoma viruses evolved from a common ancestral protein that might have been involved in a protein-priming mechanism of initiation of DNA replication. Contextual analysis of multidomain protein architectures and gene neighborhoods in prokaryotes and viruses reveals remarkable parallels between AEPs and the unrelated DnaG-type primases, in particular, tight associations with the same repertoire of helicases. These observations point to a functional equivalence of the two classes of primases, which seem to have repeatedly displaced each other in various extrachromosomal replicons

Decay of charged scalar field around a black hole: quasinormal modes of R-N, R-N-AdS and dilaton black holes

It is well known that the charged scalar perturbations of the Reissner-Nordstrom metric will decay slower at very late times than the neutral ones, thereby dominating in the late time signal. We show that at the stage of quasinormal ringing, on the contrary, the neutral perturbations will decay slower for RN, RNAdS and dilaton black holes. The QN frequencies of the nearly extreme RN black hole have the same imaginary parts (damping times) for charged and neutral perturbations. An explanation of this fact is not clear but, possibly, is connected with the Choptuik scaling.Comment: 10 pages, LaTeX, 4 figures, considerable changes made and wrong interpretation of computations correcte