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PubMed2006

On the attenuation and amplification of molecular noise in genetic regulatory networks.

BACKGROUND: Noise has many important roles in cellular genetic regulatory functions at the nanomolar scale. At present, no good theory exists for identifying all possible mechanisms of genetic regulatory networks to attenuate the molecular noise to achieve regulatory ability or to amplify the molecular noise to randomize outcomes to the advantage of diversity. Therefore, the noise filtering of genetic regulatory network is an important topic for gene networks under intrinsic fluctuation and extrinsic noise. RESULTS: Based on stochastic dynamic regulation equation, the intrinsic fluctuation in reaction rates is modeled as a state-dependent stochastic process, which will influence the stability of gene regulatory network, especially, with low concentrations of reacting species. Then the mechanisms of genetic regulatory network to attenuate or amplify extrinsic fluctuation are revealed from the nonlinear stochastic filtering point of view. Furthermore, a simple measure of attenuation level or amplification level of extrinsic noise for genetic regulatory networks is also introduced by nonlinear robust filtering method. Based on the global linearization scheme, a convenient method is introduced to measure noise attenuation or amplification for each gene of the nonlinear stochastic regulatory network by solving a set of filtering problems, which correspond to a set of linearized stochastic regulatory networks. Finally, by the proposed methods, several simulation examples of genetic regulatory networks are given to measure their robust stability under intrinsic fluctuations, and to estimate the genes' attenuation and amplification levels under extrinsic noises. CONCLUSION: In this study, a stochastic nonlinear dynamic model is developed for genetic regulatory networks under intrinsic fluctuation and extrinsic noise. By the method we proposed, we could determine the robust stability under intrinsic fluctuations and identify the genes that are significantly affected by extrinsic noises, which we call the weak structure of the network. This method will be potential for robust gene circuit design in future, on which a drug design could be based.

Animals↗

PubMed2004

Mapping spatial persistent large deviations of nonequilibrium surface growth processes onto the temporal persistent large deviations of stochastic random walk processes.

Spatial persistent large deviations probability of surface growth processes governed by the Edwards-Wilkinson dynamics, Px(x,s), with -1< or =s< or =1 is mapped isomorphically onto the temporal persistent large deviations probability Pt(t,s) associated with the stochastic Markovian random walk problem. We show using numerical simulations that the infinite family of spatial persistent large deviations exponents thetax(s) characterizing the power-law decay of Px(x,s ) agrees, as predicted on theoretical grounds by Phys. Rev. Lett. 86, 3700 (2001)], with the numerical measurements of thetat(s), the continuous family of exponents characterizing the long-time power law behavior of Pt(t,s). We also discuss the simulations of the spatial persistence probability corresponding to a discrete model in the Mullins-Herring universality class, where our discrete simulations do not agree well with the theoretical predictions perhaps because of the severe finite-size corrections which are known to strongly inhibit the manifestation of the asymptotic continuum behavior in discrete models involving large values of the dynamical exponent and the associated extremely slow convergence to the asymptotic regime.

Journal Article↗

PubMed1989

The propagation of uncertainty in human mortality processes operating in stochastic environments.

This paper presents a model describing how the uncertainty due to influential exogenous processes combines with stochasticity intrinsic to physiological aging processes and propagates through time to generate uncertainty about the future physiological state of the population. Variance expressions are derived for (a) the future values of the physiological variables under the assumption that external factors evolve under a linear stochastic diffusion process, and (b) the cohort survival functions and cohort life expectancies which reflect the uncertainty in the future values of the physiological variables. The model implies that a major component of uncertainty in forecasts of the physiological characteristics of a closed cohort is due to differential rates of survival associated with different realizations of the external process. This suggests that the limits to forecasting may be different in physiological systems subject to systematic mortality than in physical systems such as weather where the concepts of closed cohorts and of mortality selection have no simple analog.

Aging↗

PubMed1999

Dynamic stochastic synapses as computational units.

In most neural network models, synapses are treated as static weights that change only with the slow time scales of learning. It is well known, however, that synapses are highly dynamic and show use-dependent plasticity over a wide range of time scales. Moreover, synaptic transmission is an inherently stochastic process: a spike arriving at a presynaptic terminal triggers the release of a vesicle of neurotransmitter from a release site with a probability that can be much less than one. We consider a simple model for dynamic stochastic synapses that can easily be integrated into common models for networks of integrate-and-fire neurons (spiking neurons). The parameters of this model have direct interpretations in terms of synaptic physiology. We investigate the consequences of the model for computing with individual spikes and demonstrate through rigorous theoretical results that the computational power of the network is increased through the use of dynamic synapses.

Action Potentials↗

PubMed2006

Mean value and fluctuations in a model of diffusion in porous media.

We consider a stochastic model for the diffusion in a porous media. For a case where the average satisfies an anomalous diffusion equation, we investigate the behavior of the realizations around the mean value. The most relevant result of our work is that, although the concentration corresponding to each realization diffuses normally for large times, it experiences large deviations from the mean value during intermediate times. As a consequence, the experimental measurements will always depart from the average value of the realizations (with respect to the stochastic process) for unpredictable times.

Algorithms↗

PubMed1994

Selection against deleterious mutations and the maintenance of biparental sex.

The mutational deterministic hypothesis postulates an advantage to sexual over asexual reproduction when mutation rates are on the order of 1.0 per genome per generation, provided that selection takes the form of a synergistic epistasis. While the efficacy of this mechanism has been investigated for infinite populations, its ability to protect sex in finite populations exhibiting stochastic dynamics remains untested. Stochastic processes have the potential to undermine protection for sex in two ways: (1) asexual lineages derived from sexual ancestors may, by chance, be founded by individuals bearing fewer than the equilibrium mean number of mutations, and (2) once established, such lineages will undergo random perturbations in the rates at which they grow and accumulate mutations. In the present study, I show using computer simulation that sexual populations of as many as 10,000 individuals are susceptible to invasion by asexual lineages for mutation rates higher than predicted under the mutational deterministic hypothesis. My simulations differ from previous investigations in that they model the progress of asexual lineages into sexual populations as both stochastic and deterministic processes for various mutation rates, selection regimes, and population sizes. It is suggested that ecological factors, such as parasitism or release from competition, could interact with selection against deleterious mutations to protect sex. To provide the sole explanation for sex, however, may require that selection against deleterious mutations be accompanied by mutation rates on the order of 2.0 per genome per generation.

Animals↗

PubMed2006

Going from bad to worse: a stochastic model of transitions in deficit accumulation, in relation to mortality.

As people age, they accumulate deficits. The more deficits they accumulate, the greater their vulnerability, which can be expressed as the probability to accumulate even more deficits, or to die. The probability of death is known to be exponentially related to the number of deficits. Using data from elderly (aged 65 + years) participants in the Canadian Study of Health and Aging (n = 9008), we investigated the relationship between the number of deficits and the change in the number of deficits over two successive 5 year intervals. We show that the probabilities of changes in the number of deficits, in relation to baseline, are well fitted (R(2) > 0.98) by a simple distribution, with two parameters. The model suggests a maximum to deficit accumulation, and illustrates no level of deficit accumulation at which there is a net gain in fitness. Age-related deficit accumulation is highly characteristic, and can be modeled as a stochastic process with readily interpretable parameters.

Aged↗

PubMed1990

Non-stationary analysis of electromyographic activity prior to a ballistic voluntary contraction.

The electromyogram (EMG) in a ballistic voluntary action of muscle after a slight sustained contraction shows a short period of decrease or disappearance of the activity prior to the onset of phasic discharge. The EMG of elbow extensor (triceps brachii) prior to phasic discharge was analyzed as a non-stationary stochastic process. The distribution of the EMG amplitude began to change from 100 ms before the phasic discharge. The statistical test showed that the EMG activity became non-Gaussian from 30 to 50 ms before the phasic discharge. The standard deviation of the EMG showed a decreasing tendency from 80 to 100 ms prior to the phasic discharge. The statistical evidence for the EMG depression was also confirmed in fourth and sixth order coefficients of the orthogonal expansion of the probability density function. These results suggested that the EMG process profoundly changed its statistical characteristics just before the phasic discharge.

Action Potentials↗

PubMed2002

Genealogical trees, coalescent theory and the analysis of genetic polymorphisms.

Improvements in genotyping technologies have led to the increased use of genetic polymorphism for inference about population phenomena, such as migration and selection. Such inference presents a challenge, because polymorphism data reflect a unique, complex, non-repeatable evolutionary history. Traditional analysis methods do not take this into account. A stochastic process known as the 'coalescent' presents a coherent statistical framework for analysis of genetic polymorphisms.

Animals↗

PubMedDate not supplied

Determination of threshold conditions for a non-linear stochastic partnership model for heterosexually transmitted diseases with stages.

When comparing the performance of a stochastic model of an epidemic at two points in a parameter space, a threshold is said to have been crossed when at one point an epidemic develops with positive probability; while at the other there is a tendency for an epidemic to become extinct. The approach used to find thresholds in this paper was to embed a system of ordinary non-linear differential equations in a stochastic process, accommodating the formation and dissolution of marital partnerships in a heterosexual population, extra-marital sexual contacts, and diseases such as HIV/AIDS with stages. A symbolic representation of the Jacobian matrix of this system was derived. To determine whether this matrix was stable or non-stable at a particular parameter point, the Jacobian was evaluated at a disease-free equilibrium and its eigenvalues were computed. The stability or non-stability of the matrix was then determined by checking if all real parts of the eigenvalues were negative. By writing software to repeat this process for a selected set of points in the parameter space, it was possible to develop search engines for finding points in the parameter space where thresholds were crossed. The results of a set of Monte Carlo simulation experiments were reported which suggest that, by combining the stochastic and deterministic paradigms within a single formulation, it was possible to obtain more informative interpretations of simulation experiments than if attention were confined solely to either paradigm.

Acquired Immunodeficiency Syndrome↗

PubMed2001

Pink-noise behaviour of biosystems.

Pink (1/f) noise is one of the most common behaviours of biosystems. Our present paper is devoted to clarify the origin of this interesting phenomenon. It is shown that the stationary random stochastic processes under self-similar conditions (as we have in living objects) generate pink noise independently of the kind and number of variables.

Biophysics↗

PubMed1980

Intraclonal variation in proliferative potential of human diploid fibroblasts: stochastic mechanism for cellular aging.

At several points during the growth of a clone of human embryonic lung fibroblasts in vitro, 100 to 200 cells were removed at random and the proliferative potential of each cell was determined. At each sample point, a wide variation in remaining population doubling ability was observed among the individual cells and the distributions of doubling potentials were distinctly bimodal. Furthermore, the two cells arising from a single mitosis differed in their ability to proliferate by as many as eight population doublings (256-fold in the number of cells produced). The results suggest that a stochastic process is responsible for determining the limited proliferative potential of human embryonic lung fibroblasts.

Cell Division↗

PubMed2026

Climate and soil shape Daqu wheat quality and seed microbiome via rhizosphere taxa and microbial assembly.

The grain quality and seed microbiome of Daqu wheat are fundamental determinants of Daqu fermentation performance; however, the mechanisms by which cultivation environments influence these traits via rhizosphere microbial communities remain unclear. Bacterial and fungal communities across the bulk soil-rhizosphere-seed continuum of three wheat cultivars grown in four ecoregions were characterized using absolute quantitative amplicon sequencing. The rhizosphere microbiome was treated as a central intermediary, while the response variables were seed microbial diversity and grain-quality traits, including starch content, protein content, and grain hardness. Twelve physicochemical properties of soil and 11 climatic factors were integrated into a multidimensional association framework. Environmental conditions exerted stronger influences on both seed quality traits and microbial diversity than cultivar identity. Distinct regional signatures were also evident in rhizosphere microbiomes, with environmental gradients explaining community variation more effectively than geographic distance. Bacterial communities exhibited greater sensitivity to environmental fluctuations than fungi. Mantel analyses identified available nitrogen, precipitation, and atmospheric pressure as significant drivers of core rhizosphere taxa (P < 0.05). iCAMP revealed that stochastic processes predominantly governed rhizosphere bacterial assembly, whereas stochastic and deterministic mechanisms jointly shaped fungal assembly. Partial least squares path modeling further uncovered a rhizosphere-mediated environment-seed cascade, wherein sunlight intensity and duration, atmospheric pressure, and soil nitrogen directly or indirectly affected seed wet gluten content, grain hardness, and seed microbial diversity through their influences on rhizosphere microbiota. Rhizosphere bacterial diversity was negatively associated with seed bacterial diversity (path coefficient = -0.118, P < 0.05), indicating that rhizosphere communities may shape seed endophytic bacterial assemblages via environmental filtering and competitive interactions. Collectively, these findings elucidate how environments shape the quality and seed microbiomes of Daqu wheat, providing scientific guidance for optimal site selection and the standardized production of high-quality brewing wheat for industrial Baijiu.

Triticum↗

PubMed2002

A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks.

Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.

Journal Article↗

PubMed2002

Epigenetic regulation of an IAP retrotransposon in the aging mouse: progressive demethylation and de-silencing of the element by its repetitive induction.

The recent insertion of a murine intracisternal A-particle (IAP) retrotransposon within one of the introns of a housekeeping gene, the circadian m.nocturnin gene, revealed a singular expression profile, both throughout the daytime and the mouse life span. Measurement of the levels of transcripts from this element by quantitative real-time RT-PCR, in organs of 1-24-month-old mice, disclosed that the inserted element--which is part of a large family of otherwise severely repressed mobile elements--becomes active upon aging, specifically in the liver where the m.nocturnin housekeeping gene is expressed in a circadian manner and induces a circadian expression of the IAP sequence. This age-dependent induction is cell-autonomous, as it persists in hepatocytes in primary culture. We further show, using methylation-sensitive enzymes, a correlation between the life-time kinetics of this process and a liver-specific demethylation of the IAP promoter. These results strongly support a model whereby the progressive demethylation and turning on of the IAP sequence is the sole result of the transient, daily activation-throughout the mouse life span--of its promoter. This phenomenon, which develops on a timescale of months to years in the aging mouse, might reveal a general epigenetic--and stochastic--process, which could account for a large series of events associated with cell and animal aging.

Aging↗

PubMed1999

Microgeographical distribution of two chromosomal races of house mice in Tunisia: pattern and origin of habitat partitioning.

Two chromosomal races of the house mouse occur in Tunisia, a standard morph (40St) found all over the country, and a derived morph (22Rb) occurring only in central Tunisia. In this region, habitat partitioning between the two morphs was investigated by a microgeographical analysis of their distribution, assessing habitat characteristics and demographic parameters. Results showed that the 22Rb mice always occurred in the oldest sections of towns (medinas), often extending to more recent surrounding neighbourhoods where the 40St morph was most abundant. The latter was never trapped within the medinas. The transition between the two morphs was located within cities in the more recent areas, the hybrid zone being estimated at less than 0.5 km in width by a clinal analysis of chromosomal data. Although differences between habitats exist, almost no demographic differences were found between populations of the two morphs when they occurred in the same or in different habitats. Two hypotheses are discussed to account for the origin of habitat partitioning. The first relies on competitive exclusion of the 40St mice from the medinas by the derived 22Rb mice; the second is based on stochastic processes related to historical evolution of Tunisian urban communities.

Animals↗

PubMed2006

Optimization of a stochastically simulated gene network model via simulated annealing.

By rearranging naturally occurring genetic components, gene networks can be created that display novel functions. When designing these networks, the kinetic parameters describing DNA/protein binding are of great importance, as these parameters strongly influence the behavior of the resulting gene network. This article presents an optimization method based on simulated annealing to locate combinations of kinetic parameters that produce a desired behavior in a genetic network. Since gene expression is an inherently stochastic process, the simulation component of simulated annealing optimization is conducted using an accurate multiscale simulation algorithm to calculate an ensemble of network trajectories at each iteration of the simulated annealing algorithm. Using the three-gene repressilator of Elowitz and Leibler as an example, we show that gene network optimizations can be conducted using a mechanistically realistic model integrated stochastically. The repressilator is optimized to give oscillations of an arbitrary specified period. These optimized designs may then provide a starting-point for the selection of genetic components needed to realize an in vivo system.

Algorithms↗

PubMed1995

Nonrandom frequency patterns of synonymous substitutions in homologous mammalian genes.

All 69 homologous coding sequences that are currently available in four mammalian orders were aligned and the synonymous positions of quartet and duet (fourfold and twofold degenerate) codons were divided into three classes (that will be called conserved, intermediate, and variable) according to whether they show no change, one change, or more than one change, respectively. We observed (1) that the frequencies of conserved, intermediate, and variable positions of quartet and duet codons are different in different genes; (2) that the frequencies of the three classes are significantly different from expectations based on a random substitution process in the majority of genes (especially for GC-rich genes) for quartet codons and in a minority of genes for doublet codons; and (3) that the frequencies of the three classes of positions of quartet codons are correlated with those of duet codons, the conserved positions of quartet and duet codons being, in addition, correlated with the degree of amino acid conservation. Our main conclusions are that synonymous substitution frequencies: (1) are gene-specific; (2) are not simply the result of a stochastic process in which nucleotide substitutions accumulate at random, over time; and (3) are correlated in quartet and duet codons.

Animals↗