A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Solution of the pulse width modulation problem using orthogonal polynomials and Korteweg-de Vries equations

The mathematical underpinning of the pulse width modulation (PWM) technique lies in the attempt to represent “accurately” harmonic waveforms using only square forms of a fixed height. The accuracy can be measured using many norms, but the quality of the approximation of the analog signal (a harmonic form) by a digital one (simple pulses of a fixed high voltage level) requires the elimination of high order harmonics in the error term. The most important practical problem is in “accurate” reproduction of sine-wave using the same number of pulses as the number of high harmonics eliminated. We describe in this paper a complete solution of the PWM problem using Padé approximations, orthogonal polynomials, and solitons. The main result of the paper is the characterization of discrete pulses answering the general PWM problem in terms of the manifold of all rational solutions to Korteweg-de Vries equations.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

RNA virus error catastrophe: Direct molecular test by using ribavirin

RNA viruses evolve rapidly. One source of this ability to rapidly change is the apparently high mutation frequency in RNA virus populations. A high mutation frequency is a central tenet of the quasispecies theory. A corollary of the quasispecies theory postulates that, given their high mutation frequency, animal RNA viruses may be susceptible to error catastrophe, where they undergo a sharp drop in viability after a modest increase in mutation frequency. We recently showed that the important broad-spectrum antiviral drug ribavirin (currently used to treat hepatitis C virus infections, among others) is an RNA virus mutagen, and we proposed that ribavirin's antiviral effect is by forcing RNA viruses into error catastrophe. However, a direct demonstration of error catastrophe has not been made for ribavirin or any RNA virus mutagen. Here we describe a direct demonstration of error catastrophe by using ribavirin as the mutagen and poliovirus as a model RNA virus. We demonstrate that ribavirin's antiviral activity is exerted directly through lethal mutagenesis of the viral genetic material. A 99.3% loss in viral genome infectivity is observed after a single round of virus infection in ribavirin concentrations sufficient to cause a 9.7-fold increase in mutagenesis. Compiling data on both the mutation levels and the specific infectivities of poliovirus genomes produced in the presence of ribavirin, we have constructed a graph of error catastrophe showing that normal poliovirus indeed exists at the edge of viability. These data suggest that RNA virus mutagens may represent a promising new class of antiviral drugs.

Expression of error-prone polymerases in BL2 cells activated for Ig somatic hypermutation

High affinity antibodies are generated in mice and humans by means of somatic hypermutation (SHM) of variable (V) regions of Ig genes. Mutations with rates of 10−5–10−3 per base pair per generation, about 106-fold above normal, are targeted primarily at V-region hot spots by unknown mechanisms. We have measured mRNA expression of DNA polymerases ι, η, and ζ by using cultured Burkitt's lymphoma (BL)2 cells. These cells exhibit 5–10-fold increases in heavy-chain V-region mutations targeted only predominantly to RGYW (R = A or G, Y = C or T, W = T or A) hot spots if costimulated with T cells and IgM crosslinking, the presumed in vivo requirements for SHM. An ∼4-fold increase pol ι mRNA occurs within 12 h when cocultured with T cells and surface IgM crosslinking. Induction of pols η and ζ occur with T cells, IgM crosslinking, or both stimuli. The fidelity of pol ι was measured at RGYW hot- and non-hot-spot sequences situated at nicks, gaps, and double-strand breaks. Pol ι formed T⋅G mispairs at a frequency of 10−2, consistent with SHM-generated C to T transitions, with a 3-fold increased error rate in hot- vs. non-hot-spot sequences for the single-nucleotide overhang. The T cell and IgM crosslinking-dependent induction of pol ι at 12 h may indicate an SHM “triggering” event has occurred. However, pols ι, η, and ζ are present under all conditions, suggesting that their presence is not sufficient to generate mutations because both T cell and IgM stimuli are required for SHM induction.

Roles of DNA polymerases V and II in SOS-induced error-prone and error-free repair in Escherichia coli

DNA polymerase V, composed of a heterotrimer of the DNA damage-inducible UmuC and UmuD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{2}^{^{\prime}}}}\end{equation*}\end{document} proteins, working in conjunction with RecA, single-stranded DNA (ssDNA)-binding protein (SSB), β sliding clamp, and γ clamp loading complex, are responsible for most SOS lesion-targeted mutations in Escherichia coli, by catalyzing translesion synthesis (TLS). DNA polymerase II, the product of the damage-inducible polB (dinA ) gene plays a pivotal role in replication-restart, a process that bypasses DNA damage in an error-free manner. Replication-restart takes place almost immediately after the DNA is damaged (≈2 min post-UV irradiation), whereas TLS occurs after pol V is induced ≈50 min later. We discuss recent data for pol V-catalyzed TLS and pol II-catalyzed replication-restart. Specific roles during TLS for pol V and each of its accessory factors have been recently determined. Although the precise molecular mechanism of pol II-dependent replication-restart remains to be elucidated, it has recently been shown to operate in conjunction with RecFOR and PriA proteins.

Motor learning by field approximation.

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.

Mutants in the Exo I motif of Escherichia coli dnaQ: defective proofreading and inviability due to error catastrophe.

The Escherichia coli dnaQ gene encodes the proofreading 3' exonuclease (epsilon subunit) of DNA polymerase III holoenzyme and is a critical determinant of chromosomal replication fidelity. We constructed by site-specific mutagenesis a mutant, dnaQ926, by changing two conserved amino acid residues (Asp-12-->Ala and Glu-14-->Ala) in the Exo I motif, which, by analogy to other proofreading exonucleases, is essential for the catalytic activity. When residing on a plasmid, dnaQ926 confers a strong, dominant mutator phenotype, suggesting that the protein, although deficient in exonuclease activity, still binds to the polymerase subunit (alpha subunit or dnaE gene product). When dnaQ926 was transferred to the chromosome, replacing the wild-type gene, the cells became inviable. However, viable dnaQ926 strains could be obtained if they contained one of the dnaE alleles previously characterized in our laboratory as antimutator alleles or if it carried a multicopy plasmid containing the E. coli mutL+ gene. These results suggest that loss of proofreading exonuclease activity in dnaQ926 is lethal due to excessive error rates (error catastrophe). Error catastrophe results from both the loss of proofreading and the subsequent saturation of DNA mismatch repair. The probability of lethality by excessive mutation is supported by calculations estimating the number of inactivating mutations in essential genes per chromosome replication.

A simple test of the vicarious trial-and-error hypothesis of hippocampal function.

Vicarious trial-and-error (VTE) is a term that Muenzinger and Tolman used to describe the rat's conflict-like behavior before responding to choice. Recently, VTE was proposed as a mechanism alternative to the concept of "cognitive map" in accounts of hippocampal function. That is, many phenomena of impaired learning and memory related to hippocampal interventions may be explained by behavioral first principles: reduced conflicting, incipient, pre-choice tendencies to approach and avoid. The nonspatial black-white discrimination learning and VTE behavior of the rat were investigated. Hippocampal-lesioned and sham-lesioned animals were trained for 25 days (20 trials per day) starting at 60 days of age. Each movement of the head from one discriminative stimulus to the other was counted as a VTE instance. Lesioned rats had fewer VTEs than sham controls, and the former learned much more slowly or never learned. After learning, VTE frequency declined. Male and female rats showed no significant differences in VTE behavior or discrimination learning.