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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↗

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↗

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↗

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↗

PubMed1986

Dependent competing risks: a stochastic process model.

Analyses of human mortality data classified according to cause of death frequently are based on competing risk theory. In particular, the times to death for different causes often are assumed to be independent. In this paper, a competing risk model with a weaker assumption of conditional independence of the times to death, given an assumed stochastic covariate process, is developed and applied to cause specific mortality data from the Framingham Heart Study. The results generated under this conditional independence model are compared with analogous results under the standard marginal independence model. Under the assumption that this conditional independence model is valid, the comparison suggests that the standard model overestimates by 4% the effect on life expectancy at age 30 due to the hypothetical elimination of cancer and by 7% the effect for cardiovascular/cerebrovascular disease. By age 80 the overestimates were 11% for cancer and 16% for heart disease. These results suggest the importance of avoiding the marginal independence assumption when appropriate data are available--especially when focusing on mortality at advanced ages.

Adolescent↗

PubMed1989

Cellular senescence involves stochastic processes causing loss of expression of differentiated function genes: transfection with SV40 as a means for dissociating effects of senescence on growth and on differentiated function gene expression.

In the accompanying work we demonstrated that the decline in expression of steroid 17 alpha-hydroxylase in mass cultures and clones of adrenocortical cells is the result of a stochastic switching process which yields mixtures of expressing and nonexpressing cells. There is an apparent positive correlation between the replicative potential of adrenocortical cell cultures and the number of cells in the culture that can express 17 alpha-hydroxylase. We investigated this by extending the cells' replicative potential by transfecting them with cloned SV40 virus. Cells from a senescent subclone, with very limited remaining replicative potential, were transfected. The cell population showed a progressive increase in growth rate and gave rise to a line of cells that expressed T antigen and which was apparently immortalized. Induction of mRNA for 17 alpha-hydroxylase by cyclic AMP was absent in this line of cells, as it was in the senescent cells prior to transfection. The cells remained responsive to gene induction by cyclic AMP as evidenced by increases in mRNA and activity for cholesterol side-chain cleavage. The absence of 17 alpha-hydroxylase expression in this line was not the result of interference by SV40 T antigen. When early passage cells were transfected with pSV3neo, which contains the early region of SV40 and neo, and were selected with G418, SV40 T antigen-expressing lines were derived which showed high levels of expression of 17 alpha-hydroxylase after induction with cyclic AMP. These cells maintained high levels of expression of 17 alpha-hydroxylase through four successive recloning events, over a period of replication much longer than that achievable by nontransfected cells. Thus, transfection by SV40 can be used to dissociate effects of senescence on growth and differentiated gene expression. T antigen expression selectively affects growth, but preserves the state of expression of a differentiated function gene as it was prior to transfection.

Adrenal Cortex↗

PubMed1978