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.

High-frequency, spin-label EPR of nonaxial lipid ordering and motion in cholesterol-containing membranes

The EPR spectra of spin-labeled lipid chains in fully hydrated bilayer membranes of dimyristoyl phosphatidylcholine containing 40 mol % of cholesterol have been studied in the liquid-ordered phase at a microwave radiation frequency of 94 GHz. At such high field strengths, the spectra should be optimally sensitive to lateral chain ordering that is expected in the formation of in-plane domains. The high-field EPR spectra from random dispersions of the cholesterol-containing membranes display very little axial averaging of the nitroxide g-tensor anisotropy for lipids spin labeled toward the carboxyl end of the sn-2 chain (down to the 8-C atom). For these positions of labeling, anisotropic 14N-hyperfine splittings are resolved in the gzz and gyy regions of the nonaxial EPR spectra. For positions of labeling further down the lipid chain, toward the terminal methyl group, the axial averaging of the spectral features systematically increases and is complete at the 14-C atom position. Concomitantly, the time-averaged 〈Azz〉 element of the 14N-hyperfine tensor decreases, indicating that the axial rotation at the terminal methyl end of the chains arises from correlated torsional motions about the bonds of the chain backbone, the dynamics of which also give rise to a differential line broadening of the 14N-hyperfine manifolds in the gzz region of the spectrum. These results provide an indication of the way in which lateral ordering of lipid chains in membranes is induced by cholesterol.

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.

Molecular ordering of the Fas-apoptotic pathway: The Fas/APO-1 protease Mch5 is a CrmA-inhibitable protease that activates multiple Ced-3/ICE-like cysteine proteases

The Fas/APO-1-receptor associated cysteine protease Mch5 (MACH/FLICE) is believed to be the enzyme responsible for activating a protease cascade after Fas-receptor ligation, leading to cell death. The Fas-apoptotic pathway is potently inhibited by the cowpox serpin CrmA, suggesting that Mch5 could be the target of this serpin. Bacterial expression of proMch5 generated a mature enzyme composed of two subunits, which are derived from the precursor proenzyme by processing at Asp-227, Asp-233, Asp-391, and Asp-401. We demonstrate that recombinant Mch5 is able to process/activate all known ICE/Ced-3-like cysteine proteases and is potently inhibited by CrmA. This contrasts with the observation that Mch4, the second FADD-related cysteine protease that is also able to process/activate all known ICE/Ced-3-like cysteine proteases, is poorly inhibited by CrmA. These data suggest that Mch5 is the most upstream protease that receives the activation signal from the Fas-receptor to initiate the apoptotic protease cascade that leads to activation of ICE-like proteases (TX, ICE, and ICE-relIII), Ced-3-like proteases (CPP32, Mch2, Mch3, Mch4, and Mch6), and the ICH-1 protease. On the other hand, Mch4 could be a second upstream protease that is responsible for activation of the same protease cascade in CrmA-insensitive apoptotic pathways.

Temperature, ordering, and equilibrium with time-dependent confining forces

The concepts of temperature and equilibrium are not well defined in systems of particles with time-varying external forces. An example is a radio frequency ion trap, with the ions laser cooled into an ordered solid, characteristic of sub-mK temperatures, whereas the kinetic energies associated with the fast coherent motion in the trap are up to 7 orders of magnitude higher. Simulations with 1,000 ions reach equilibrium between the degrees of freedom when only aperiodic displacements (secular motion) are considered. The coupling of the periodic driven motion associated with the confinement to the nonperiodic random motion of the ions is very small at low temperatures and increases quadratically with temperature.

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.

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.

Characterization and functional ordering of Slu7p and Prp17p during the second step of pre-mRNA splicing in yeast.

Temperature-sensitive alleles in four genes (slu7-1, prp16-2, prp17-1, and prp18-1) are known to confer a specific block to the second chemical step of pre-mRNA splicing in vivo in the yeast Saccharomyces cerevisiae. Previous studies showed that Prp16p and Prp18p are required solely for the second step in vitro. The RNA-dependent ATPase, Prp16p, functions at a stage in splicing when ATP is required, whereas Prp18p functions at an ATP-independent stage. Here we use immunodepletion to show that the roles of Slu7p and Prp17p are also confined to the second step of splicing. We find that extracts depleted of Prp17p require both Prp17p and ATP for slicing complementation, whereas extracts depleted of Slu7p require only the addition of Slu7p. These different ATP requirements suggest that Prp16p and Prp17p function before Prp18p and Slu7p. Although SLU7 encodes an essential gene product, we find that a null allele of prp17 is temperature-sensitive for growth and has a partial splicing defect in vitro. Finally, high-copy suppression experiments indicate functional interactions between PRP16 and PRP17, PRP16 and SLU7, and SLU7 and PRP18. Taken together, the results suggest that these four factors may function within a multi-component complex that has both an ATP-dependent and an ATP-independent role in the second step of pre-mRNA splicing.