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At least 19 recordsLinked to original sources
PubMed1989

Absence of effect in stochastic processes: its influence on test validation and test use.

Negativity in stochastic processes presents problems in interpretation because it is never possible to attain an absolutely adequate assurance of safety with such processes. Thus, it is extremely difficult to have complete confidence in the utility of validation studies of new methods in comparison to those that are accepted to be well established, especially when these processes are stochastic in the statistical sense of this term. The regulatory scientist who must make decisions on the basis of available evidence, therefore, has to make a number of assumptions in dealing with negativity. It is important to review the validity and usefulness of these assumptions from time to time to ensure that they cannot be replaced by improved methodology in the light of new scientific knowledge.

Animals↗
PubMed1981

Probability of neuronal spike initiation as a curve-crossing problem for Gaussian stochastic processes.

Probability of neuronal spike initiation was considered within the framework of a simple stochastic model. The time of spike occurrence was defined as the first time of crossing of a stochastic process and a determined time function. This problem has been investigated in the case of a stationary Gaussian stochastic process and a linear time function. An integral equation obtained for the probability density function of the first time crossing was numerically solved by means of computer calculations. The model was applied to the analysis of temporal pattern of spike activity evoked in the cat spinal motoneurones by depolarizing current injected through the recording microelectrode.

Animals↗
PubMed1986

A stochastic process determines the time at which cell division begins in Escherichia coli.

The theoretical distributions of cell masses in exponential cultures of bacteria were derived for both total cells and cells having formed a constriction in preparation for division. The parameters used for this derivation include the mass doubling time, tau, the T-period, and 3 statistical parameters (h, sigma 1, sigma 2) which describe the variability of the cell cycle. The theoretical distributions were compared with observed distributions from E. coli B/rA growing in glucose minimal medium (45 min doubling time) to determine whether a stochastic process in the division pathway affects the time of initiation of constriction or the duration of the constriction process. The results indicate that the stochastic process determines the onset rather than the completion of constriction and that the timing of this process is coupled (6% variability, = sigma 1) to a given cell mass. The values obtained for the duration of the T-period, T = 9.3 min, and for a half-life parameter associated with the stochastic process, h = 4.3 min, agree with previously reported data.

Cell Division↗
PubMed1991

Transient behavior of a stochastic process for screening progressive diseases.

This paper extends a mathematical model developed by the authors for describing the stochastic process underlying the etiology of non-contagious progressive diseases. For a population with no prior history of scheduled screening, the number of undetected and detected diseased individuals in the population under an established screening policy is used to calculate the expected total screening cost at any given time during the transient period of the associated stochastic process. A graphical representation of our model shows the status of different subgroups of a particular age group at any time T, and provides a clear summary of the expected number of individuals whose disease remains undetected.

Mass Screening↗
PubMed1985

Mortality and aging in a heterogeneous population: a stochastic process model with observed and unobserved variables.

Various multivariate stochastic process models have been developed to represent human physiological aging and mortality. These efforts are extended by considering the effects of observed and unobserved state variables on the age trajectory of physiological parameters. This is done by deriving the Kolmogorov-Fokker-Planck equations describing the distribution of the unobserved state variables conditional on the history of the observed state variables. Given some assumptions, it is proved that the distribution is Gaussian. Strategies for estimating the parameters of the distribution are suggested based on an extension of the theory of Kalman filters to include systematic mortality selection. Various empirical applications of the model to studies of human aging and mortality as well as to other types of "failure" processes in heterogeneous populations are discussed.

Aging↗
PubMed1982

Model analysis of the frequency of neuronal action potentials in the case of Gaussian input stochastic processes.

The authors describe the effects of changes in excitatory and inhibitory synapse weight on the number of spikes generated in the presence of constant absolute refractory phase and threshold level values. Input stochastic processes with Gaussian distributions were presumed. The problem was resolved in a hybrid computer model of stochastic neuronal activity. The results are given in the form of "e-curves", "i-curves" and gradient fields. It was shown that, in a set of paired values of the two weights, zones could be found in which the number of generated spikes depended mainly on just one of them. It was also shown that, in a given neurone with a fixed synapse morphology, the effect of the individual synapses on the number of generated spikes altered with changes in input stochastic processes to the synapses.

Action Potentials↗
PubMed1984

[Carcinogenesis, embryogenesis and aging from the view point of the assessment of cell proliferation and differentiation as a stochastic process].

An approach to cell proliferation and differentiation as to stochastic processes is described. The rate constants of cell population transitions to subsequent epigenetic states are interpreted as indicating instability of initial states. The duration of embryogenesis, the rate of loss of the ability to proliferation (a result of final differentiation) by the initial cell cultures, the error accumulation rate in the genetic cell apparatus (including both the genome itself and its interactions with the chromatin components) which determines the rate of ageing and the rate of the tumour incidence rise in particular, are all connected via the level of instability of the epigenetic states of cells. It is supposed that the differentiation mechanism of multicellular organisms originated from mechanisms of intragenome recombinational rearrangements of unicellular ones. A hypothetic scheme for basic processes occurring during cell differentiation is proposed accounting for the dual character of oncogenes necessary for differentiation but able to block it under definite conditions.

Aging↗
PubMed1995

Excitotoxicity as a stochastic process.

1. Neuronal death following excitotoxic insult appears to be a stochastic process involving transition through an intermediate biochemical state. 2. Hydrogen ion accumulation in the hours after toxic glutamate exposure may indicate that this transition has occurred.

Animals↗
PubMed1989

Bone metastasis as a non-stochastic process.

Bone metastasis may be considered a non-stochastic process, since the blood flow in bone is lower than that in other organs and most cancers do not have a tendency to metastasize to bone in in vivo experiments. Furthermore, the experimental model of bone metastasis, based on the ligation of major venous flow, can not explain the wide-spread bone metastasis which is commonly observed in clinical cases. These observations may be explained by the hypothesis that tumor cells have a phenotype for translocating to specific tissues and that tumor cell growth is controlled by the microenvironmental factors in situ.

Animals↗
PubMed1994

Computer simulation of cell growth governed by stochastic processes: application to clonal growth cancer models.

Cancer is a multistage process in which cell proliferation determines the growth of cells within stages and is associated with the transition of cells from one stage to the next. The usual model for cancer risk assessment, the linearized multistage model, does not explicitly include cell proliferation. More realistic cancer models are needed to reduce uncertainty in cancer risk assessment and to provide basic insights into the quantitative roles of cell proliferation and mutation. This report describes a simulation model for the transition of cells from one stage to the next and for clonal growth within stages. The model is intended to facilitate the use of experimental data on cell replication and preneoplastic lesions in risk assessment. When a population of cells is small its growth may be governed by stochastic processes. Such a population may disappear by chance even when the probability of cell division on a given time interval exceeds the probability of cell death. Procedures for estimating cell proliferation and mutation parameters from data for use in risk assessment should account for this random aspect of growth. The present model describes cell growth governed by stochastic processes, is consistent with earlier analytical expressions for such growth (Dewanjii et al., Risk Anal. 9, 179, 1989), and is flexible with respect to time-dependent data. A data set for spontaneous basophilic clones in male F344 rats (Popp et al., Fundam. Appl. Toxicol. 5, 314, 1985) is analyzed and predictions are made for (a) the probability of mutation to the basophilic genotype per division of a normal hepatocyte (3.5 x 10(-8)), (b) number of basophilic clones too small to be detected, and (c) number of basophilic clones that disappear by chance. This work illustrates the potential of computer simulation for quantitative analysis of the roles of cell division, cell death, and mutation in cancer.

Animals↗
PubMed1995

The effects of health histories on stochastic process models of aging and mortality.

A model of human health history and aging, based on a multivariate stochastic process with both continuous diffusion and discrete jump components, is presented. Discrete changes generate non-Gaussian diffusion with time varying continuous state distributions. An approach to calculating transition rates in dynamically heterogeneous populations, which generalizes the conditional averaging of hazard rates done in "fixed frailty" population models, is presented to describe health processes with multiple jumps. Conditional semi-invariants are used to approximate the conditional p.d.f. of the unobserved health history components. This is useful in analyzing the age dependence of mortality and health changes at advanced age (e.g., 95+) where homeostatic controls weaken, and physiological dynamics and survival manifest nonlinear behavior.

Aging↗
PubMed1981

Plasticity of dendritic spine formation: a state-dependent stochastic process.

This study proposes that plasticity of dendritic spine formation may be modeled as distribution patterns imbedded in a spine length-dependent and density-dependent stochastic process. Modeling the jewel fish tectal interneuron revealed a critical 10-36 micron region where spine length plasticity was predicted to be most detectable. This hypothesis was tested by comparing neurons sampled from jewel fish reared for 4 years in a crowded environment (1 fish/5.64 l) with uncrowded controls (1 fish/25 l). The interaction between fish groups and the location of spine length differences was significant (p less than 0.01) within the basal 10-30 micron dendritic segment. Spine head widths were also significantly smaller (p less than 0.01) in the crowded fish over the entire dendrite. These findings suggest two modes of neuronal plasticity: (1) plasticity of spine length during formation, and (2) plasticity in spine head width after the spine is formed.

Animals↗
PubMed1980

[Dynamics of systems with induced cell proliferation within the framework of a branching stochastic process model. I. The number of cell generations induced to proliferate].

The probabilistic description of cell generation numbers in the populations induced to proliferate is considered on the basis of the model of branching age-dependent stochastic process. The recurrent formulas for generating functions (and moments) are derived for the following process which are of interest for the analysis of induced proliferation in closed cell populations: the number of cells in n-th generation horn up to the moment of observation, and the number of cell in n-th generation existing at a given moment.

Cell Division↗
PubMed1987

A stochastic process approach to the development of atheroma.

This study aims at formulating a dynamic model of particle sedimentation as applied to lipoprotein deposition during atheroma progression. The basic assumption is that all particles are identical and that the number of sedimented particles is relatively great. It is hypothised that sedimentation of a given particle is random; according to the theory of stochastic processes, the probability of a certain number of particles to sediment or deposit changes with time. The stochastic approach may explain some aspects of atherosclerosis development, i.e. its progression or regression.

Animals↗
PubMed1990

Mutational order: a major stochastic process in evolution.

Computer simulations in which selection acts on a quantitative character show that the randomness of mutations can contribute significantly to evolutionary divergence between populations. In different populations, different advantageous mutations occur, and are selected to fixation, so that the populations diverge even when they are initially identical, and are subject to identical selection. This stochastic process is distinct from random genetic drift. In some circumstances (large populations or strong selection, or both) mutational order can be greatly more important than random drift in bringing about divergence. It can generate a 'disconnection' between evolution at the phenotypic and genotypic levels, and can give rise to a rough 'molecular clock', albeit episodic, that is driven by selection. In the absence of selection, mutational order has little or no effect.

Biological Evolution↗
PubMed1991

Simulation of stochastic processes in motile crossbridge systems.

The underlying stochastic nature of many models of the actomyosin interaction should result in fluctuations in both force and shortening velocity. In classical experimental approaches involving intact or glycerinated muscle preparations these fluctuations are too small to resolve owing to the large numbers of crossbridges involved. However, new experimental techniques allow mechanical measurements to be made in systems in which small numbers of myosin heads act on a single actin filament, or small numbers of kinesin molecules act on a single tubulin filament. In these systems, stochastic effects should be evident. To understand better the nature of the expected stochastic effects, we have used computer simulation to investigate the fluctuations predicted by the original model for muscle crossbridge mechanics proposed by A.F. Huxley. We consider three situations: (1) the translation of actin or tubulin filaments by myosin or kinesin motors immobilized on a fixed substrate, (2) the production of tension by ensembles of immobilized myosin which involve the displacement of an elastic load, and (3) the fluctuations in axial displacement of a single, bipolar myosin thick filament interacting with actin filaments as in a sarcomere. In all three cases, fluctuations are clearly evident in simulations involving small numbers of motors. For case (1), we show that translation velocities can vary with crossbridge density. Whether one motor translates a filament faster, slower or at the same speed as many motors depends on the relative magnitudes of the attachment and detachment rate functions. Analytical expressions are provided to quantitate this relationship. For case (2), we show that fluctuations predicted assuming perfectly isometric conditions differ form those observed when the 'isometric state' is achieved against an elastic load. 'Elastic damping' of the fluctuations in the system results from the presence of many attached motors. In case (3) we show that in spite of the presence of stochastic fluctuations which can destabilize the uniformity of filament overlap in a sarcomere, the magnitude of thick filament displacement is less than might be anticipated over time periods of in vivo contraction. Taken together, these simulations allow one to better interpret experimental data in terms of current models of motor function.

Actin Cytoskeleton↗
PubMed1989

Cellular senescence involves stochastic processes causing loss of expression of differentiated function genes: visualization by in situ hybridization for steroid 17 alpha-hydroxylase in bovine adrenocortical cells.

When grown for long periods in culture, bovine adrenocortical cells lose the expression of a differentiated function gene, steroid 17 alpha-hydroxylase. Previously, we documented a decline in 17 alpha-hydroxylase mRNA with increasing culture passage level after induction with cyclic AMP (P. J. Hornsby et al., 1987, Proc. Natl. Acad. Sci. USA 84, 1580). We used in situ hybridization to investigate the loss of expression of this gene during cellular senescence at an individual cell level. In primary cultures, cells were uniformly positive for hybridization with cDNA for 17 alpha-hydroxylase after cyclic AMP induction. After two passages, cultures comprised a mixture of hybridizing and nonhybridizing cells. Cells appeared either to hybridize at a level comparable to that in primary cultures or to be nonhybridizing. When in situ hybridization was combined with immunofluorescence, cells positive for immunofluorescence were also positive for hybridization. Senescing mass cultures showed decreasing numbers of positive cells, and after 30 passages cultures comprised entirely nonhybridizing cells. Thus, the previously observed decline in overall 17 alpha-hydroxylase mRNA levels results from a decline in the fraction of expressing cells in the culture, and the rate of loss of expressing cells is in agreement with the rate of loss of total 17 alpha-hydroxylase mRNA. Primary clones, even when isolated at an early stage of clonal expansion, had mixtures of subclones of hybridizing and nonhybridizing cells. On recloning, hybridizing subclones usually produced uniformly nonhybridizing sub-subclones. Some subclones within primary clones had a morphology associated with replicative senescence (flattened cells with sparse intercellular contacts), yet had high numbers of hybridizing cells. We conclude that, in both mass and clonal populations, cells initially expressing 17 alpha-hydroxylase rapidly give rise to clones of nonexpressing cells. Such cells are continually derived by a stochastic process from cells originally expressing the gene.

Adrenal Cortex↗