Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “Stochastic Processes”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,783 records · Page 99Linked to original sources
PubMed2003

Analysis of the distributed computing approach applied to the folding of a small beta peptide.

In the recently proposed distributed computing approach to protein folding a very large number of short independent simulations is performed. Using this method, folding events on a time scale orders of magnitude shorter than the experimental one have been reported. However, it has also been observed that the folding process is not an elementary kinetic step and that the presence of initial lag phases can bias short simulations toward atypical pathways. We study here a 20-residue three-stranded antiparallel beta-sheet peptide whose equilibrium properties can be characterized by atomistic molecular dynamics simulations. We found that the folding rate of this peptide is estimated correctly by the distributed computing approach when trajectories > approximately 1/100 of the equilibrium folding time are considered. We also found that the fastest folding events occur through high-energy pathways, which are unlikely under equilibrium conditions. These very fast folding pathways do not relax within the equilibrium denatured state that is stabilized by the transient presence of both native and non-native interactions, and they are characterized by the nearly simultaneous formation of the two beta-hairpins and a very small number of non-native contacts.

Computer Simulation↗
PubMed2000

A quantitative evaluation of SAGE.

Serial Analysis of Gene Expression (SAGE) is an innovative technique that offers the potential of cataloging both the identity and relative frequencies of mRNA transcripts in a given poly(A(+)) RNA preparation. Although it is a very effective approach for determining the expression of mRNA populations, there are significant biases in the observed results that are inherent in the experimental process. These are caused by sampling error, sequencing error, nonuniqueness, and nonrandomness of tag sequences. The quantitative information desired from SAGE experiments consists of estimates of the number of genes and the frequency distribution of transcript copy numbers. Of additional concern is the extent to which a given tag sequence can be assumed to be unique to its gene. The present study takes these mathematical biases into account and presents a basis for maximum likelihood estimation of gene number and transcript copy frequencies given a set of experimental results. These estimates of the true state of genomic expression are markedly different from those based directly on the observations from the underlying experiments. It also is shown that while in many cases it is probable that a given tag sequence is unique within the genome, in larger genomes this cannot be safely assumed.

Computer Simulation↗
PubMed2006

Emergence of protein fold families through rational design.

Diverse proteins with similar structures are grouped into families of homologs and analogs, if their sequence similarity is higher or lower, respectively, than 20%-30%. It was suggested that protein homologs and analogs originate from a common ancestor and diverge in their distinct evolutionary time scales, emerging as a consequence of the physical properties of the protein sequence space. Although a number of studies have determined key signatures of protein family organization, the sequence-structure factors that differentiate the two evolution-related protein families remain unknown. Here, we stipulate that subtle structural changes, which appear due to accumulating mutations in the homologous families, lead to distinct packing of the protein core and, thus, novel compositions of core residues. The latter process leads to the formation of distinct families of homologs. We propose that such differentiation results in the formation of analogous families. To test our postulate, we developed a molecular modeling and design toolkit, Medusa, to computationally design protein sequences that correspond to the same fold family. We find that analogous proteins emerge when a backbone structure deviates only 1-2 angstroms root-mean-square deviation from the original structure. For close homologs, core residues are highly conserved. However, when the overall sequence similarity drops to approximately 25%-30%, the composition of core residues starts to diverge, thereby forming novel families of protein homologs. This direct observation of the formation of protein homologs within a specific fold family supports our hypothesis. The conservation of amino acids in designed sequences recapitulates that of the naturally occurring sequences, thereby validating our computational design methodology.

Computational Biology↗
PubMed2005

Robust time delay estimation of bioelectric signals using least absolute deviation neural network.

The time delay estimation (TDE) is an important issue in modern signal processing and it has found extensive applications in the spatial propagation feature extraction of biomedical signals as well. Due to the extreme complexity and variability of the underlying systems, biomedical signals are usually nonstationary, unstable and even chaotic. Furthermore, due to the limitations of the measurement environments, biomedical signals are often noise-contaminated. Therefore, the TDE of biomedical signals is a challenging issue. A new TDE algorithm based on the least absolute deviation neural network (LADNN) and its application experiments are presented in this paper. The LADNN is the neural implementation of the least absolute deviation (LAD) optimization model, also called unconstrained minimum L1-norm model, with a theoretically proven global convergence. In the proposed LADNN-based TDE algorithm, a given signal is modeled using the moving average (MA) model. The MA parameters are estimated by using the LADNN and the time delay corresponds to the time index at which the MA coefficients have a peak. Due to the excellent features of L1-norm model superior to Lp-norm (p > 1) models in non-Gaussian noise environments or even in chaos, especially for signals that contain sharp transitions (such as biomedical signals with spiky series or motion artifacts) or chaotic dynamic processes, the LADNN-based TDE is more robust than the existing TDE algorithms based on wavelet-domain correlation and those based on higher-order spectra (HOS). Unlike these conventional methods, especially the current state-of-the-art HOS-based TDE, the LADNN-based method is free of the assumption that the signal is non-Gaussian and the noises are Gaussian and, thus, it is more applicable in real situations. Simulation experiments under three different noise environments, Gaussian, non-Gaussian and chaotic, are conducted to compare the proposed TDE method with the existing HOS-based method. Real application experiment is conducted to extract time delay information between every two adjacent channels of gastric myoelectrical activity (GMA) to assess the spatial propagation characteristics of GMA during different phases of the migrating myoelectrical complex (MMC).

Algorithms↗
PubMed2002

Algorithm for vector autoregressive model parameter estimation using an orthogonalization procedure.

We review the derivation of the fast orthogonal search algorithm, first proposed by Korenberg, with emphasis on its application to the problem of estimating coefficient matrices of vector autoregressive models. New aspects of the algorithm not previously considered are examined. One of these is the application of the algorithm to estimate coefficient matrices of a vector autoregressive process with time-varying coefficients when multiple realizations of the said process are available. Computer simulations were also performed to characterize the statistical properties of the estimates. The results show that even for shorter time series the algorithm works well and obtains good estimates of the time-varying parameters. Statistical characterization indicates that the standard deviation of the estimates decreases as 1 square root N (N being the length of the time series), a typical behavior of least-squares estimators. Another key aspect of the approach, which has previously been considered, is its direct extension to the parameter estimation of vector nonlinear autoregressive models. Nonlinear terms can be added to the model and the same algorithm can be applied to effectively estimate their associated parameters. Using chaotic time series generated from the Lorenz equations, the algorithm produces a model that captures the nonlinear structure of the data and exhibits the same chaotic attractor as that of the original system.

Algorithms↗
PubMed1998

Waiting with and without recombination: the time to production of a double mutant.

R.A. Fisher and H.J. Muller argued in the 1930s that a major evolutionary advantage of recombination is that it allows favorable mutations to be combined within an individual even when they first appear in different individuals. This effect is evaluated in a two-locus, two-allele model by calculating the average waiting time until a new genotypic combination first appears in a haploid population. Three approximations are developed and compared with Monte Carlo simulations of the Wright-Fisher process of random genetic drift in a finite population. First, a crude method, based on the deterministic accumulation of single mutants, produces a waiting time of 1/square root of N mu(2) with no recombination and [formula: see text] with recombination between the two loci, where mu is the mutation rate, N is the haploid population size, and R is the recombination rate. Second, the waiting time is calculated as the expected value of a heterogeneous geometric distribution obtained from a branching process approximation. This gives accurate estimates for small values of N mu large. The estimates for small values of N mu are considerably lower than the simulated values. Finally, diffusion analysis of the Wright-Fisher process provides accurate estimates for N mu small, and the time scales of the diffusion process show a difference between R = 0 and for R >> 0 of the same order of magnitude as seen in the deterministic analysis. In the absence of recombination, accurate approximations to the waiting time are obtained by using the branching process for high N mu and the diffusion approximation for low N mu. For low N mu the waiting time is well approximated by 1/the square root of 8N2 mu(3). With R >> 0, the following dependence on N mu is observed: For N mu > 1 the waiting time is virtually independent of recombination and is well described by the branching process approximation. For N mu approximately equal to 1 the waiting time is well described by a simplified diffusion approximation that assumes symmetry in the frequencies of single mutants. For N mu << 1 the waiting time is well described by the diffusion approximation allowing asymmetry in the frequencies of single mutants. Recombination lowers the waiting time until a new genotypic combination first appears, but the effect is small compared to that of the mutation rate and population size. For large N mu, recombination has a negligible effect, and its effect is strongest for small N mu, in which case the waiting time approaches a fixed fraction of the waiting time for R = 0. Free recombination lowers the waiting time to about 45% of the waiting time for absolute linkage for small N mu. Selection has little effect on the importance of recombination in general.

Biological Evolution↗
PubMed2002

The distribution of particles in the plane dispersed by a simple 3-dimensional diffusion process.

Populations of particles dispersed in the 2-dimensional plane from a single point-source may be grouped as focus expansion patterns, with an exponentially decreasing density, and more diffuse patterns with thicker tails. Exponentially decreasing distributions are often modelled as the result of 2-dimensional diffusion processes acting to disperse the particles, while thick-tailed distributions tend to be modelled by purely descriptive distributions. Models based on the Cauchy distribution have been suggested, but these have not been related to diffusion modelling. However, the distribution of particles dispersed from a point source by a 3-dimensional Brownian motion that incorporates a constant drift, under the condition that the particle starts at a given height and is stopped when it reaches the xy plane (zero height) may be shown to result in both slim-tailed exponentially decreasing densities, and thick-tailed polynomially decreasing densities with infinite mean travel distance from the source, depending on parameter values. The drift in the third coordinate represents gravitation, while the drift in the first and second represents a (constant) wind. Conditions for the density having exponentially decreasing tails is derived in terms of gravitation and wind, with a special emphasis on applications to light-weighted particles such as fungal spores.

Diffusion↗
PubMed2006

Mutation, selection, and ancestry in branching models: a variational approach.

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. We then focus on the case when the type is determined by a sequence of letters (like nucleotides or matches/mismatches relative to a reference sequence), and we ask how much of the above competition can still be seen by observing only the letter composition (as given by the frequencies of the various letters within the sequence). If mutation and reproduction rates can be approximated in a smooth way, the fitness of letter compositions resulting from the interplay of reproduction and mutation is determined in the limit as the number of sequence sites tends to infinity. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. In this model, the fitness of letter compositions is worked out explicitly. In certain cases, their competition leads to a phase transition.

Animals↗
PubMed2006

Unravelling gene networks from noisy under-determined experimental perturbation data.

Systems biology aims to study the properties of biological systems in terms of the properties of their molecular constituents. This occurs frequently by a process of mathematical modelling. The first step in this modelling process is to unravel the interaction structure of biological systems from experimental data. Previously, an algorithm for gene network inference from gene expression perturbation data was proposed. Here, the algorithm is extended by using regression with subset selection. The performance of the algorithm is extensively evaluated on a set of data produced with gene network models at different levels of simulated experimental noise. Regression with subset selection outperforms the previously stated matrix inverse approach in the presence of experimental noise. Furthermore, this regression approach enables us to deal with under-determination, that is, when not all genes are perturbed. The results on incomplete data sets show that the new method performs well at higher number of perturbations, even when noise levels are high. At lower number of perturbations, although still being able to recover the majority of the connections, less confidence can be placed in the recovered edges.

Cell Physiological Phenomena↗
PubMed2002

Ratio statistics of gene expression levels and applications to microarray data analysis.

MOTIVATION: Expression-based analysis for large families of genes has recently become possible owing to the development of cDNA microarrays, which allow simultaneous measurement of transcript levels for thousands of genes. For each spot on a microarray, signals in two channels must be extracted from their backgrounds. This requires algorithms to extract signals arising from tagged mRNA hybridized to arrayed cDNA locations and algorithms to determine the significance of signal ratios. RESULTS: This paper focuses on estimation of signal ratios from the two channels, and the significance of those ratios. The key issue is the determination of whether a ratio is significantly high or low in order to conclude whether the gene is upregulated or downregulated. The paper builds on an earlier study that involved a hypothesis test based on a ratio statistic under the supposition that the measured fluorescent intensities subsequent to image processing can be assumed to reflect the signal intensities. Here, a refined hypothesis test is considered in which the measured intensities forming the ratio are assumed to be combinations of signal and background. The new method involves a signal-to-noise ratio, and for a high signal-to-noise ratio the new test reduces (with close approximation) to the original test. The effect of low signal-to-noise ratio on the ratio statistics constitutes the main theme of the paper. Finally, and in this vein, a quality metric is formulated for spots. This measure can be used to decide whether or not a spot ratio should be deleted, or to adjust various measurements to reflect confidence in the quality of the measurement. CONTACT: e-dougherty@tamu.edu

Cell Line↗
PubMed2006

Standardization of edge magnitude in color images.

Edge detection is a useful task in low-level image processing. The efficiency of many image processing and computer vision tasks depends on the perfection of detecting meaningful edges. To get a meaningful edge, thresholding is almost inevitable in any edge detection algorithm. Many algorithms reported in the literature adopt ad hoc schemes for this purpose. These algorithms require the threshold values to be supplied and tuned by the user. There are many high-level tasks in computer vision which are to be performed without human intervention. Thus, there is a need to develop a scheme where a single set of threshold values would give acceptable results for many color images. In this paper, an attempt has been made to devise such an algorithm. Statistical variability of partial derivatives at each pixel is used to obtain standardized edge magnitude and is thresholded using two threshold values. The advantage of standardization is evident from the results obtained.

Algorithms↗
PubMed2004

Signaling in small subcellular volumes. II. Stochastic and diffusion effects on synaptic network properties.

The synaptic signaling network is capable of sophisticated cellular computations. These include the ability to respond selectively to different patterns of input, and to sustain changes in response over long periods. The small volume of the synapse complicates the analysis of signaling because the chemical environment is strongly affected by diffusion and stochasticity. This study is based on an updated version of a previously proposed synaptic signaling circuit (Bhalla and Iyengar, 1999) and analyzes three network computation properties in small volumes: bistability, thresholding, and pattern selectivity. Simulations show that although there are diffusive regimes in which bistability may persist, chemical noise at small volumes overwhelms bistability. In the deterministic situation, the network exhibits a sharp threshold for transition between lower and upper stable states. This transition is broadened and individual runs partition between lower and upper states, when stochasticity is considered. The third network property, pattern selectivity, is severely degraded at synaptic volumes. However, there are regimes in which a process similar to stochastic resonance operates and amplifies pattern selectivity. These results imply that simple scaling of signaling conditions to femtoliter volumes is unlikely, and microenvironments, such as reaction complex formation, may be essential for reliable small-volume signaling.

Calcium↗
PubMed2003

High resolution processing techniques for ultrasound doppler velocimetry in the presence of colored noise. Part II: Multiplephase pipe-flow velocity measurement.

This paper presents an application of continuous wave ultrasound Doppler velocity measurements to two-phase flow in pipes. In many petroleum wells, the multiphase flow is separated into two phases: the first is a liquid phase and the second is a gas phase with small scatterers. The problem of multiphase velocity profile measurements has not been satisfactorily solved by classical approaches due to the multiphase nature of the fluid and the presence of colored noise, which introduces a significant bias in classical frequency estimators. We propose the use of high resolution frequency techniques to overcome the classical limitations. Direct estimation of Doppler frequency then obtained using either time frequency maximum frequency or arguments of poles of the parametric model that identifies the Doppler part of the signal is discussed. The tests made with synthetic Doppler signals and two-phase flow have demonstrated the excellent performance of the high resolution techniques based on reassignment and parametric techniques.

Algorithms↗
PubMed1989

The motile response of alveolar macrophages. An experimental study using single-cell and cell population approaches.

In this report, we studied the applicability of a random walk model of individual cell motility in predicting the motile behavior of alveolar macrophage populations under agarose. The migration of a population of cells in the absence of a chemotactic or chemokinetic gradient can be characterized by the random motility coefficient, mu, which is analogous to a particle diffusion coefficient. Random walk theory relates this latter coefficient to particle speed and collision time (equivalent to the time between changes in particle direction). By analogy, according to a similar random walk theory for cell migration, mu for a cell population is a function of the speed and persistence time (with direction changes governed by cell behavioral processes rather than by collisions) of individual cells. To test the model, normal guinea pig alveolar macrophages were incubated in the presence or absence of uniform concentrations of the chemotactic tripeptide formyl-norleucyl leucyl phenylalanine (FNLLP) to elicit different levels of motile activity. Mu was calculated from cell population density profiles obtained by fixing and staining cultures after 2, 3, or 4 days. In parallel experiments, individual cell speeds and persistence times were measured from 1-h, time-lapse video microscopy recordings. The value of mu calculated from single-cell measurements was in good agreement with that from population studies for stimulated random migration (at 10(-7) to 10(-11) M FNLLP), but not in the absence of stimulant. Overall, these results support the applicability of the random walk model of individual cell migration to randomly migrating alveolar macrophage populations.

Animals↗
PubMed2006

Intracellular demography and the dynamics of Salmonella enterica infections.

An understanding of within-host dynamics of pathogen interactions with eukaryotic cells can shape the development of effective preventive measures and drug regimes. Such investigations have been hampered by the difficulty of identifying and observing directly, within live tissues, the multiple key variables that underlay infection processes. Fluorescence microscopy data on intracellular distributions of Salmonella enterica serovar Typhimurium (S. Typhimurium) show that, while the number of infected cells increases with time, the distribution of bacteria between cells is stationary (though highly skewed). Here, we report a simple model framework for the intensity of intracellular infection that links the quasi-stationary distribution of bacteria to bacterial and cellular demography. This enables us to reject the hypothesis that the skewed distribution is generated by intrinsic cellular heterogeneities, and to derive specific predictions on the within-cell dynamics of Salmonella division and host-cell lysis. For within-cell pathogens in general, we show that within-cell dynamics have implications across pathogen dynamics, evolution, and control, and we develop novel generic guidelines for the design of antibacterial combination therapies and the management of antibiotic resistance.

Animals↗
PubMed1998

Within-host transmission strategies of transovarial, feminizing parasites of Gammarus duebeni.

The amphipod Gammarus duebeni harbours several species of vertically transmitted microsporidian parasites. G. Duebeni were collected from 3 localities in the UK. Animals from Budle Bay, Northumberland, were infected with Octosporea effeminans, and those from Millport, Isle of Cumbrae and Fenham Flats, Northumberland were infected with microsporidia of the genus Nosema. We derived expected distributions of parasites per host embryonic cell by modelling parasite transmission as a multitype, Galton-Watson branching process. Parasite prevalence (proportion of females infected) was significantly heterogeneous among localities. Parasite burden in zygotes was much higher for females infected with Nosema than in animals infected with O. effeminans. There was no significant difference between localities in the number of Nosema in the zygotes. Comparison of models and data from 64-cell host embryos showed that the distributions of parasites per cell were consistent with the hypothesis that sorting of parasites into daughter cells is biased for at least 1 cell lineage. Host embryos infected with O. effeminans could expect to contain a growing number of parasites in each cell generation within such biased cell lineages; similar estimates for Nosema predict a decline in the number of parasites per cell within a biased lineage. We discuss the possibility that the 2 species of parasite may be employing different strategies in order to ensure transmission to the next host generation.

Animals↗
PubMed2003

Gene finding with a hidden Markov model of genome structure and evolution.

MOTIVATION: A growing number of genomes are sequenced. The differences in evolutionary pattern between functional regions can thus be observed genome-wide in a whole set of organisms. The diverse evolutionary pattern of different functional regions can be exploited in the process of genomic annotation. The modelling of evolution by the existing comparative gene finders leaves room for improvement. RESULTS: A probabilistic model of both genome structure and evolution is designed. This type of model is called an Evolutionary Hidden Markov Model (EHMM), being composed of an HMM and a set of region-specific evolutionary models based on a phylogenetic tree. All parameters can be estimated by maximum likelihood, including the phylogenetic tree. It can handle any number of aligned genomes, using their phylogenetic tree to model the evolutionary correlations. The time complexity of all algorithms used for handling the model are linear in alignment length and genome number. The model is applied to the problem of gene finding. The benefit of modelling sequence evolution is demonstrated both in a range of simulations and on a set of orthologous human/mouse gene pairs. AVAILABILITY: Free availability over the Internet on www server: http://www.birc.dk/Software/evogene.

Algorithms↗
PubMed2001

Skewed X inactivation in X-linked disorders.

X chromosome inactivation is a process by which the dosage of proteins transcribed from genes on the X chromosome is equalized between males (XY) and females (XX) through the silencing of most genes on one of the two X chromosomes in females. Although the choice of which of the two X's is inactivated is entirely random, not all women have a 50:50 ratio of cells with one or the other X chromosomes active. A number of different mechanisms lead to extremely skewed ratios and this can result in expression of the phenotype of X-linked recessive disorders in females. Nonrandom X inactivation patterns are also associated with selective female survival in male-lethal X-linked dominant disorders or with variable severity of the phenotype in women carrying X-linked dominant mutations. These features are important for the study and gene identification of X-linked disorders and for counseling of affected families.

Diseases in Twins↗