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Results for “Stochastic Processes”

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PubMed1998

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.

Acquired Immunodeficiency Syndrome↗
PubMed1984

Sensitivity of membranes to their environment. Role of stochastic processes.

Ionic flow through biomembranes often exhibits a sensitivity to the environment, which is difficult to explain by classical theory, that usually assumes that the free energy available to change the membrane permeability results from the environmental change acting directly on the permeability control mechanism. This implies, for example, that a change delta V in the trans-membrane potential can produce a maximum free energy change, delta V X q, on a gate (control mechanism) carrying a charge q. The analysis presented here shows that when stochastic fluctuations are considered, under suitable conditions (gate cycle times rapid compared with the field relaxation time within a channel), the change in free energy is limited, not by the magnitude of the stimulus, but by the electrochemical potential difference across the membrane, which may be very much greater. Conformational channel gates probably relax more slowly than the field within the channel; this would preclude appreciable direct amplification of the stimulus. It is shown, however, that the effect of impermeable cations such as Ca++ is to restore the amplification of the stimulus through its interaction with the electric field. The analysis predicts that the effect of Ca++ should be primarily to affect the number of channels that are open, while only slightly affecting the conductivity of an open channel.

Animals↗
PubMedDate not supplied

Models of the interaction of mortality and the evolution of risk factor distribution: a general stochastic process formulation.

Generally analyses of longitudinal studies of chronic disease risks do not directly model the change with time of risk factor values and the interactions of those changes with risk levels. Failure to account for such process characteristics can lead to incorrect inferences about the specific effects of risk factors on mortality, the inability to accurately forecast the future risk of the cohort, and inaccurate statements about the effects of specific risk factor interventions on mortality. We present a model which does describe such a process and show how it can be estimated from longitudinal studies. We also illustrate the effects of certain risk factor process features on the evolution of disease risk data from males in the Framingham, Massachusetts study.

Actuarial Analysis↗
PubMed1985

Changes in self-renewal potential of human leukemic cells (K562): a bidirectional stochastic process.

Daughter cells arising from a single cell division in the leukemic cell line K562 have equivalent self-renewal potential with respect to their ability to form clones in semisolid medium. However, individual cells isolated from these clones in sequence have vastly different abilities in their self-renewal potentials. Thus, cells originating from a clone with any particular self-renewal potential exhibit the full range of self-renewal potentials--from highly renewing to none renewing, cells. These results show that self-renewal potential in the K562 cell line is a random, reversible and partially noninherited characteristic. It is suggested that the stochastic variability of the intraclonal self-renewal potential of K562 progeny cells either reflects the initial expression of a differentiation program or the expression of the predeterministic portion of the normal myelopoietic differentiation pathway.

Cell Differentiation↗
PubMed2002

Stochastic processes defining sensitivity and variability of internally calibrated quantitative NASBA-based viral load assays.

For quantitative assessment of virus particles in patient plasma samples various assays are commercially available. Typical performance characteristics for such assays are sensitivity, precision and the range of linearity. In order to assess these properties it is common practice to divide the range of inputs into subranges in order to apply different statistical models to evaluate these properties separately. We developed a general statistical model for internally calibrated amplification based viral load assays that combines these statistical properties in one powerful analysis. Based on the model an unambiguous definition of the lower limit of the linear range can be given. The proposed method of analysis was illustrated by a successful application to data generated by the NucliSens EasyQ HIV-1 assay.

HIV-1↗
PubMed2002

General statistics of stochastic process of gene expression in eukaryotic cells.

Thousands of genes are expressed at such very low levels (< or =1 copy per cell) that global gene expression analysis of rarer transcripts remains problematic. Ambiguity in identification of rarer transcripts creates considerable uncertainty in fundamental questions such as the total number of genes expressed in an organism and the biological significance of rarer transcripts. Knowing the distribution of the true number of genes expressed at each level and the corresponding gene expression level probability function (GELPF) could help resolve these uncertainties. We found that all observed large-scale gene expression data sets in yeast, mouse, and human cells follow a Pareto-like distribution model skewed by many low-abundance transcripts. A novel stochastic model of the gene expression process predicts the universality of the GELPF both across different cell types within a multicellular organism and across different organisms. This model allows us to predict the frequency distribution of all gene expression levels within a single cell and to estimate the number of expressed genes in a single cell and in a population of cells. A random "basal" transcription mechanism for protein-coding genes in all or almost all eukaryotic cell types is predicted. This fundamental mechanism might enhance the expression of rarely expressed genes and, thus, provide a basic level of phenotypic diversity, adaptability, and random monoallelic expression in cell populations.

Animals↗
PubMed1991

A model of ion channel kinetics using deterministic chaotic rather than stochastic processes.

Models of ion channel kinetics have previously assumed that the switching between the open and closed states is an intrinsically random process. Here, we present an alternative model based on a deterministic process. This model is a piecewise linear iterated map. We calculate the dwell time distributions, autocorrelation function, and power spectrum of this map. We also explore non-linear generalizations of this map. The chaotic nature of our model implies that its long-term behavior mimics the stochastic properties of a random process. In particular, the linear map produces an exponential probability distribution of dwell times in the open and closed states, the same as that produced by the two-state, closed in equilibrium open, Markov model. We show how deterministic and random models can be distinguished by their different phase space portraits. A test of some experimental data seems to favor the deterministic model, but further experimental evidence is needed for an unequivocal decision.

Animals↗
PubMed1981

Manifestation of carcinogenesis as a stochastic process on the basis of an altered mitochondrial genome.

Computer calculations are used to show the feasibility of a concept which explains the manifestation of a pathological cell function from a latent state by the phenomenon of extrachromosomal inheritance (through the mitochondrial genome) in mammalian cells. A hypothesis is submitted in which this principle is applied to the process of carcinogenesis. According to this concept, the manifestation of a tumor cell--after the initiation stage--entirely depends on stochastic events, i.e., random distribution of mitochondria during cell divisions, with an accumulation of the lesion in a few out of many cells. We feel that this concept comprises a better explanation of many characteristics and peculiarities of the phenomenon of carcinogenesis than do attempts which explain tumor formation as a phenomenon caused by mutation in a nuclear genome. A consideration of the principles presented automatically leads to a number of specific consequences with regard to carcinogenesis. Some of these consequences are discussed. They include: 1. the process of malignant transformation should not be irreversible for all the cells of a progeny; 2. the number of mitochondria in a cell type should be inversely correlated to tumor frequency; 3. the latent period should mainly be determined by the cell division rate and the "extent" of the initiating event; 4. susceptibility to carcinogenesis may be substantially higher if the number of mitochondria per cell line is increasing or decreasing, i.e., during the embryonic and fetal periods; 5. heterogeneous types of cells may arise from a single "initiated" cell, and 6. the process of malignant transformation should not necessarily be confined to one generation of the species. In addition, experimental approaches to support the submitted concept are suggested.

Animals↗
PubMed1998

Assessing hepatitis A virus epidemic stochastic process in eight cities in China in 1990.

BACKGROUND: In The People's Republic of China in 1990, the age-specific seroprevalence of hepatitis A was investigated in eight large cities. METHODS: A stochastic model, the two-state Markov chain, was applied to hepatitis A virus seroprevalence data by age group. An age-specific risk rate, Markov Risk Rate (MRR), and its weighted sum, Total MRR, are defined and used as novel measure indices to prioritize age groups for allocating vaccine or to decide in which cities vaccine should be used to prevent hepatitis A. RESULTS: In 1990, the MRR1- in Xi'an, Jinan, Ha'erbin and Huhehaote, and the MRR10- in Chongqing were over 40. The MRR10- in Xi'an, Nanjing, Jinan and Ha'erbin and the MRR20- in Chongqing and Nanjing were over 20. The Total MRR in Chongqing and Ha'erbin were over 160, which was higher than the warning value. CONCLUSIONS: All age groups whose MRR was over 20 are strongly recommended to be vaccinated first. Chongqing and Ha'erbin are cities at high risk of a hepatitis A virus epidemic in the 1990s and therefore should be under close surveillance.

Adolescent↗
PubMed2002

Anomalous pulse delay in microwave propagation: A stochastic process interpretation.

An experiment involving microwave propagation in the near-field region with two horn antennas demonstrated a superluminal behavior which is strongly dependent on the frequency. The models previously proposed are found to be inadequate for interpreting the results. An attempt is made within the framework of a stochastic model, which can be improved by a path-integral analysis.

Journal Article↗
PubMed1996

Evidence that hematopoiesis may be a stochastic process in vivo.

To study the behavior of hematopoietic stem cells in vivo, hematopoiesis was simulated by assuming that all stem cell decisions (that is, replication, apoptosis, initiation of a differentiation/maturation program) were determined by chance. Predicted outcomes from simulated experiments were compared with data obtained in autologous marrow transplantation studies of glucose 6-phosphate dehydrogenase (G6PD) heterozygous female Safari cats. With this approach, we prove that stochastic differentiation can result in the wide spectrum of discrete outcomes observed in vivo, and that clonal dominance can occur by chance. As the analyses also suggest that the frequency of feline hematopoietic stem cells is only 6 per 10(7) nucleated marrow cells, and that sem cells do not replicate on average more frequently than once every three weeks, these large-animal data challenge clinical strategies for marrow transplantation and gene therapy.

Animals↗
PubMed1969

Computer simulation of stochastic processes through model-sampling (Monte Carlo) techniques.

A simple Monte Carlo simulation program is outlined which can be used for the investigation of random-walk problems, for example in diffusion, or the movement of tracers in the blood circulation. The results given by the simulation are compared with those predicted by well-established theory, and it is shown how the model can be expanded to deal with drift, and with reflexion from or adsorption at a boundary.

Journal Article↗