Stability of Noisy Metropolis-Hastings

Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that they target marginally the correct invariant distribution. However, the pseudo-marginal Markov chain can exhibit poor mixing and slow convergence towards its target. As an alternative, a subtly different Markov chain can be simulated, where better mixing is possible but the exactness property is sacrificed. This is the noisy algorithm, initially conceptualised as Monte Carlo within Metropolis (MCWM), which has also been studied but to a lesser extent. The present article provides a further characterisation of the noisy algorithm, with a focus on fundamental stability properties like positive recurrence and geometric ergodicity. Sufficient conditions for inheriting geometric ergodicity from a standard Metropolis-Hastings chain are given, as well as convergence of the invariant distribution towards the true target distribution

Global consensus Monte Carlo

To conduct Bayesian inference with large data sets, it is often convenient or necessary to distribute the data across multiple machines. We consider a likelihood function expressed as a product of terms, each associated with a subset of the data. Inspired by global variable consensus optimisation, we introduce an instrumental hierarchical model associating auxiliary statistical parameters with each term, which are conditionally independent given the top-level parameters. One of these top-level parameters controls the unconditional strength of association between the auxiliary parameters. This model leads to a distributed MCMC algorithm on an extended state space yielding approximations of posterior expectations. A trade-off between computational tractability and fidelity to the original model can be controlled by changing the association strength in the instrumental model. We further propose the use of a SMC sampler with a sequence of association strengths, allowing both the automatic determination of appropriate strengths and for a bias correction technique to be applied. In contrast to similar distributed Monte Carlo algorithms, this approach requires few distributional assumptions. The performance of the algorithms is illustrated with a number of simulated examples

Non-Natural Nucleotides As Probes For The Mechanism And Fidelity Of DNA Polymerases

DNA is a remarkable macromolecule that functions primarily as the carrier of the genetic information of organisms ranging from viruses to bacteria to eukaryotes. The ability of DNA polymerases to efficiently and accurately replicate genetic material represents one of the most fundamental yet complex biological processes found in nature. The central dogma of DNA polymerization is that the efficiency and fidelity of this biological process is dependent upon proper hydrogen-bonding interactions between an incoming nucleotide and its templating partner. However, the foundation of this dogma has been recently challenged by the demonstration that DNA polymerases can effectively and, in some cases, selectively incorporate non-natural nucleotides lacking classic hydrogen-bonding capabilities into DNA. In this review, we describe the results of several laboratories that have employed a variety of non-natural nucleotide analogs to decipher the molecular mechanism of DNA polymerization. The use of various non-natural nucleotides has lead to the development of several different models that can explain how efficient DNA synthesis can occur in the absence of hydrogen-bonding interactions. These models include the influence of steric fit and shape complementarity, hydrophobicity and solvation energies, base-stacking capabilities, and negative selection as alternatives to rules invoking simple recognition of hydrogen-bonding patterns. Discussions are also provided regarding how the kinetics of primer extension and exonuclease proofreading activities associated with high-fidelity DNA polymerases are influenced by the absence of hydrogen-bonding functional groups exhibited by non-natural nucleotides

Adenosine Triphosphate-Dependent Degradation of A Fluorescent λ N Substrate Mimic by Lon Protease

Escherichia coli Lon exhibits a varying degree of energy requirement toward hydrolysis of different substrates. Efficient degradation of protein substrates requires the binding and hydrolysis of ATP such that the intrinsic ATPase of Lon is enhanced during protein degradation. Degradation of synthetic tetrapeptides, by contrast, is achieved solely by ATP binding with concomitant inhibition of the ATPase activity. In this study, a synthetic peptide (FRETN 89-98), containing residues 89–98 of λ N protein and a fluorescence donor (anthranilamide) and quencher (3-nitrotyrosine), has been examined for ATP-dependent degradation by E. coli and human Lon proteases. The cleavage profile of FRETN 89-98 by E. coli Lon resembles that of λ N degradation. Both the peptide and protein substrates are specifically cleaved between Cys93 and Ser94 with concomitant stimulation of Lon\u27s ATPase activity. Furthermore, the degradation of FRETN 89-98 is supported by ATP and AMPPNP but not ATPγS nor AMPPCP. FRETN 89-98 hydrolysis is eight times more efficient in the presence of 0.5 mM ATP compared to 0.5 mM AMPPNP at 86 μM peptide. The ATP-dependent hydrolysis of FRETN 89-98 displays sigmodial kinetics. The kcat, [S]0.5, and the Hill coefficient of FRETN 89-98 degradation are 3.2 ± 0.3 s−1, 106 ± 21 μM, and 1.6 respectively

Fluorescent Analysis of Translesion DNA Synthesis by Using A Novel, Non-natural Nucleotide Analogue

The replication of damaged DNA is a promutagenic process that can lead to disease development. This report evaluates the dynamics of nucleotide incorporation opposite an abasic site, a commonly formed DNA lesion, by using two fluorescent nucleotide analogues, 2-aminopurine deoxyribose triphosphate (2-APTP) and 5-phenylindole deoxyribose triphosphate (5-PhITP). In both cases, the kinetics of incorporation were compared by using a 32 P-radiolabel extension assay versus a fluorescence-quenching assay. Although 2-APTP is efficiently incorporated opposite a templating nucleobase (thymine), the kinetics for incorporation opposite an abasic site are significantly slower. The lower catalytic efficiency hinders its use as a probe to study translesion DNA synthesis. In contrast, the rate constant for the incorporation of 5-PhITP opposite the DNA lesion is 100-fold faster than that for 2- APTP. Nearly identical kinetic parameters are obtained from fluorescence quenching or the 32 P-radiolabel assay. Surprisingly, distinct differences in the kinetics of 5-PhITP incorporation opposite the DNA lesion are detected when using either bacteriophage T4 DNA polymerase or the Escherichia coli Klenow fragment. These differences suggest that the dynamics of nucleotide incorporation opposite an abasic site are polymerase-dependent. Collectively, these data indicate that 5-PhITP can be used to perform real time analyses of translesion DNA synthesis as well as to functionally probe differences in polymerase function

Measurement of Sivers Asymmetries for Di-jets in \sqrt{s}=200 GeV pp Collisions at STAR

Measurement of the transverse spin dependence of the di-jet opening angle in pp collisions at sqrt{s}=200 GeV has been performed by the STAR collaboration. An analyzing power consistent with zero has been observed over a broad range in pseudorapidity sum of the two jets with respect to the polarized beam direction. A non-zero (Sivers) correlation between transverse momentum direction of partons in the initial state and transverse spin orientation of the parent proton has been previously observed in semi-inclusive deep inelastic scattering (SIDIS). The present measurements are much smaller than deduced from predictions made for STAR di-jets based on non-zero quark Sivers functions deduced from SIDIS, and furthermore indicate that gluon Sivers asymmetries are comparably small.Comment: 4 pages, 3 figures, talk presented at SPIN 2006, Kyoto, October 200