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.

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.

A model of ocular dominance column development by competition for trophic factor

Recent experimental evidence has shown that application of certain neurotrophic factors (NTs) to the developing primary visual cortex prevents the development of ocular dominance (OD) columns. One interpretation of this result is that afferents from the lateral geniculate nucleus compete for postsynaptic trophic factor in an activity-dependent manner. Application of excess trophic factor eliminates this competition, thereby preventing OD column formation. We present a model of OD column development, incorporating Hebbian synaptic modification and activity-driven competition for NT, which accounts for both normal OD column development as well as the prevention of that development when competition is removed. In the “control” situation, when available NT is below a critical amount, OD columns form normally. These columns form without weight normalization procedures and in the presence of positive inter-eye correlations. In the “experimental” case, OD column development is prevented in a local neighborhood in which excess NT has been added. Our model proposes a biologically plausible mechanism for competition between neural populations that is motivated by several pieces of experimental data, thereby accounting for both normal and experimentally perturbed conditions.

Subplate neuron ablation alters neurotrophin expression and ocular dominance column formation

Ocular dominance column formation in visual cortex depends on both the presence of subplate neurons and the endogenous expression of neurotrophins. Here we show that deletion of subplate neurons, which supply glutamatergic inputs to visual cortex, leads to a paradoxical increase in brain-derived neurotrophic factor mRNA in the same region of visual cortex in which ocular dominance columns are absent. Subplate neuron ablation also increases glutamic acid decarboxylase-67 levels, indicating an alteration in cortical inhibition. These observations imply a role for this special class of neurons in modulating activity-dependent competition by regulating levels of neurotrophins and excitability within a developing cortical circuit.

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.

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.

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.

Pars triangularis asymmetry and language dominance.

The pars triangular is a portion of Broca's area. The convolutions that form the inferior and caudal extent of the pars triangularis include the anterior horizontal and anterior ascending rami of the sylvian fissure, respectively. To learn if there are anatomic asymmetries of the pars triangularis, these convolutions were measured on volumetric magnetic resonance imaging scans of 11 patients who had undergone selective hemispheric anesthesia (Wada testing) to determine hemispheric speech and language lateralization. Of the 10 patients with language lateralized to the left hemisphere, 9 had a leftward asymmetry of the pars triangularis. The 1 patient with language lateralized to the right hemisphere had a significant rightward asymmetry of the pars triangularis. Our data suggest that asymmetries of the pars triangularis may be related to speech-language lateralization.

Dominance of one bacterial phylotype at a Mid-Atlantic Ridge hydrothermal vent site.

Microbial community structure in natural environments has remained largely unexplored yet is generally considered to be complex. It is shown here that in a Mid-Atlantic Ridge hydrothermal vent habitat, where food webs depend on prokaryotic primary production, the surface microbial community consists largely of only one bacterial phylogenetic type (phylotype) as indicated by the dominance of a single 16S rRNA sequence. The main part of its population occurs as an ectosymbiont on the dominant animals, the shrimp Rimicaris exoculata, where it grows as a monoculture within the carapace and on the extremities. However, the same bacteria are also the major microbial component of the free-living substrate community. Phylogenetically, this type forms a distinct branch within the epsilon-Proteobacteria. This is different from all previously studied chemoautotrophic endo- and ectosymbioses from hydrothermal vents and other sulfidic habitats in which all the bacterial members cluster within the gamma-Proteobacteria.