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.

Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

Regular and stochastic dynamics in the real quadratic family

We prove the Regulat or Stochastic Conjecture for the real quadratic family which asserts that almost every real quadratic map Pc, c ∈ [−2, 1/4], has either an attracting cycle or an absolutely continuous invariant measure.

Stochastic processes strongly influence HIV-1 evolution during suboptimal protease-inhibitor therapy

It has long been assumed that HIV-1 evolution is best described by deterministic evolutionary models because of the large population size. Recently, however, it was suggested that the effective population size (Ne) may be rather small, thereby allowing chance to influence evolution, a situation best described by a stochastic evolutionary model. To gain experimental evidence supporting one of the evolutionary models, we investigated whether the development of resistance to the protease inhibitor ritonavir affected the evolution of the env gene. Sequential serum samples from five patients treated with ritonavir were used for analysis of the protease gene and the V3 domain of the env gene. Multiple reverse transcription–PCR products were cloned, sequenced, and used to construct phylogenetic trees and to calculate the genetic variation and Ne. Genotypic resistance to ritonavir developed in all five patients, but each patient displayed a unique combination of mutations, indicating a stochastic element in the development of ritonavir resistance. Furthermore, development of resistance induced clear bottleneck effects in the env gene. The mean intrasample genetic variation, which ranged from 1.2% to 5.7% before treatment, decreased significantly (P < 0.025) during treatment. In agreement with these findings, Ne was estimated to be very small (500–15,000) compared with the total HIV-1 RNA copy number. This study combines three independent observations, strong population bottlenecking, small Ne, and selection of different combinations of protease-resistance mutations, all of which indicate that HIV-1 evolution is best described by a stochastic evolutionary model.

Gene dosage and stochastic effects determine the severity and direction of uniparental ribosomal RNA gene silencing (nucleolar dominance) in Arabidopsis allopolyploids

Nucleolar dominance is an epigenetic phenomenon in which one parental set of ribosomal RNA (rRNA) genes is silenced in an interspecific hybrid. In natural Arabidopsis suecica, an allotetraploid (amphidiploid) hybrid of Arabidopsis thaliana and Cardaminopsis arenosa, the A. thaliana rRNA genes are repressed. Interestingly, A. thaliana rRNA gene silencing is variable in synthetic Arabidopsis suecica F1 hybrids. Two generations are needed for A. thaliana rRNA genes to be silenced in all lines, revealing a species-biased direction but stochastic onset to nucleolar dominance. Backcrossing synthetic A. suecica to tetraploid A. thaliana yielded progeny with active A. thaliana rRNA genes and, in some cases, silenced C. arenosa rRNA genes, showing that the direction of dominance can be switched. The hypothesis that naturally dominant rRNA genes have a superior binding affinity for a limiting transcription factor is inconsistent with dominance switching. Inactivation of a species-specific transcription factor is argued against by showing that A. thaliana and C. arenosa rRNA genes can be expressed transiently in the other species. Transfected A. thaliana genes are also active in A. suecica protoplasts in which chromosomal A. thaliana genes are repressed. Collectively, these data suggest that nucleolar dominance is a chromosomal phenomenon that results in coordinate or cooperative silencing of rRNA genes.

Models for stochastic climate prediction

There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate prediction. Here several idealized models for stochastic climate modeling are introduced and analyzed through unambiguous mathematical theory. This analysis demonstrates the potential need for more sophisticated models beyond stable linear Langevin equations. The new phenomena include the emergence of both unstable linear Langevin stochastic models for the climate mean and the need to incorporate both suitable nonlinear effects and multiplicative noise in stochastic models under appropriate circumstances. The strategy for stochastic climate modeling that emerges from this analysis is illustrated on an idealized example involving truncated barotropic flow on a beta-plane with topography and a mean flow. In this example, the effect of the original 57 degrees of freedom is well represented by a theoretically predicted stochastic model with only 3 degrees of freedom.

Modeling stochastic gene expression: Implications for haploinsufficiency

There is increasing recognition that stochastic processes regulate highly predictable patterns of gene expression in developing organisms, but the implications of stochastic gene expression for understanding haploinsufficiency remain largely unexplored. We have used simulations of stochastic gene expression to illustrate that gene copy number and expression deactivation rates are important variables in achieving predictable outcomes. In gene expression systems with non-zero expression deactivation rates, diploid systems had a higher probability of uninterrupted gene expression than haploid systems and were more successful at maintaining gene product above a very low threshold. Systems with relatively rapid expression deactivation rates (unstable gene expression) had more predictable responses to a gradient of inducer than systems with slow or zero expression deactivation rates (stable gene expression), and diploid systems were more predictable than haploid, with or without dosage compensation. We suggest that null mutations of a single allele in a diploid organism could decrease the probability of gene expression and present the hypothesis that some haploinsufficiency syndromes might result from an increased susceptibility to stochastic delays of gene initiation or interruptions of gene expression.

Phospholipase Cβ4 is specifically involved in climbing fiber synapse elimination in the developing cerebellum

Elimination of excess climbing fiber (CF)–Purkinje cell synapses during cerebellar development involves a signaling pathway that includes type 1 metabotropic glutamate receptor, Gαq, and the γ isoform of protein kinase C. To identify phospholipase C (PLC) isoforms involved in this process, we generated mice deficient in PLCβ4, one of two major isoforms expressed in Purkinje cells. PLCβ4 mutant mice are viable but exhibit locomotor ataxia. Their cerebellar histology, parallel fiber synapse formation, and basic electrophysiology appear normal. However, developmental elimination of multiple CF innervation clearly is impaired in the rostral portion of the cerebellar vermis, in which PLCβ4 mRNA is predominantly expressed. By contrast, CF synapse elimination is normal in the caudal cerebellum, in which low levels of PLCβ4 mRNA but reciprocally high levels of PLCβ3 mRNA are found. These results indicate that PLCβ4 transduces signals that are required for CF synapse elimination in the rostral cerebellum.

Impaired motor coordination and persistent multiple climbing fiber innervation of cerebellar Purkinje cells in mice lacking Gαq

Mice lacking the α-subunit of the heterotrimeric guanine nucleotide binding protein Gq (Gαq) are viable but suffer from ataxia with typical signs of motor discoordination. The anatomy of the cerebellum is not overtly disturbed, and excitatory synaptic transmission from parallel fibers to cerebellar Purkinje cells (PCs) and from climbing fibers (CFs) to PCs is functional. However, about 40% of adult Gαq mutant PCs remain multiply innervated by CFs because of a defect in regression of supernumerary CFs in the third postnatal week. Evidence is provided suggesting that Gαq is part of a signaling pathway that is involved in the elimination of multiple CF innervation during this period.

Brandon/Hill selected list of print books and journals for the small medical library*

After thirty-six years of biennial updates, the authors take great pride in being able to publish the nineteenth version (2001) of the “Brandon/Hill Selected List of Print Books and Journals for the Small Medical Library.” This list of 630 books and 143 journals is intended as a selection guide for health sciences libraries or similar facilities. It can also function as a core collection for a library consortium. Books and journals are categorized by subject; the book list is followed by an author/editor index, and the subject list of journals, by an alphabetical title listing. Due to continuing requests from librarians, a “minimal core list” consisting of 81 titles has been pulled out from the 217 asterisked (*) initial-purchase books and marked with daggers (†*) before the asterisks. To purchase the entire collection of 630 books and to pay for 143 2001 journal subscriptions would require $124,000. The cost of only the asterisked items, books and journals, totals $55,000. The “minimal core list” book collection costs approximately $14,300.

Stochastic game theory: For playing games, not just for doing theory

Recent theoretical advances have dramatically increased the relevance of game theory for predicting human behavior in interactive situations. By relaxing the classical assumptions of perfect rationality and perfect foresight, we obtain much improved explanations of initial decisions, dynamic patterns of learning and adjustment, and equilibrium steady-state distributions.

Brandon/Hill selected list of print books and journals in allied health*

This list of 424 books and 77 journals is intended as a selection guide for print literature to be used in a library supporting allied health educational programs or allied health personnel in either an academic or health care setting. Because of the impossibility of covering the large number and wide variety of allied health professions and occupations, the recommended publications are focused primarily on the educational programs listed and recognized by the American Medical Association and other accrediting bodies. Books and journals are categorized by subject; the book list is followed by an author/editor index, and the subject list of journals by an alphabetical title listing. Items suggested for initial purchase (167 books and 31 journals) are indicated by asterisks. To purchase the entire collection of books and journals (2000 subscriptions) would require an expenditure of about $31,970. The cost of only the asterisked items totals $12,515.