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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↗

Persistence of a continuous stochastic process with discrete-time sampling.

We introduce the concept of "discrete-time persistence," which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T=n Delta T. For a Gaussian Markov process with relaxation rate mu, we show that the persistence (no crossing) probability decays as [rho(a)](n) for large n, where a = exp(-mu Delta T), and we compute rho(a) to high precision. We also define the concept of "alternating persistence," which corresponds to a<0. For a>1, corresponding to motion in an unstable potential (mu<0), there is a nonzero probability of having no zero-crossings in infinite time, and we show how to calculate it.

Journal Article↗

Path-integral formulation of stochastic processes for exclusive particle systems

We present a systematic formalism to derive a path-integral formulation for hard-core particle systems far from equilibrium. Writing the master equation for a stochastic process of the system in terms of the annihilation and creation operators with mixed commutation relations, we find the Kramers-Moyal coefficients for the corresponding Fokker-Planck equation (FPE), and the stochastic differential equation (SDE) is derived by connecting these coefficients in the FPE to those in the SDE. Finally, the SDE is mapped onto field theory using the path integral, giving the field-theoretic action, which may be analyzed by the renormalization group method. We apply this formalism to a two-species reaction-diffusion system with drift, finding a universal decay exponent for the long-time behavior of the average concentration of particles in arbitrary dimension.

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Coarse-grained stochastic processes for microscopic lattice systems.

Diverse scientific disciplines ranging from materials science to catalysis to biomolecular dynamics to climate modeling involve nonlinear interactions across a large range of physically significant length scales. Here a class of coarse-grained stochastic processes and corresponding Monte Carlo simulation methods, describing computationally feasible mesoscopic length scales, are derived directly from microscopic lattice systems. It is demonstrated below that the coarse-grained stochastic models can capture large-scale structures while retaining significant microscopic information. The requirement of detailed balance is used as a systematic design principle to guarantee correct noise fluctuations for the coarse-grained model. The coarse-grained stochastic algorithms provide large computational savings without increasing programming complexity or computer time per executive event compared to microscopic Monte Carlo simulations.

Algorithms↗

Average shape of a fluctuation: universality in excursions of stochastic processes.

We study the average shape of a fluctuation of a time series x(t), which is the average value (T) before x(t) first returns at time T to its initial value x(0). For large classes of stochastic processes, we find that a scaling law of the form (T) = T(alpha)f(t/T) is obeyed. The scaling function f(s) is, to a large extent, independent of the details of the single increment distribution, while it encodes relevant statistical information on the presence and nature of temporal correlations in the process. We discuss the relevance of these results for Barkhausen noise in magnetic systems.

Journal Article↗

Debilitation's aftermath: stochastic process models of mortality.

A stochastic differential equation model is developed to clarify the interaction of debilitation, recuperation, selection, and aging. The model yields various insights about the lingering mortality consequences of disasters such as wars, famines, and epidemics that may weaken the survivors. A key result is that debilitation and selection are interdependent: debilitation that increases population heterogeneity will result in subsequent selection; selection, by altering the distribution of population heterogeneity, will influence the impact of debilitating events.

Aging↗

Stochastic processes of particle trapping and detrapping by a wave in a magnetized plasma.

This paper presents some relevant numerical simulations of the three-dimensional evolution of a monochromatic lower hybrid wave interacting at the Landau resonance with a Maxwellian electron beam in a magnetized plasma. A statistical study of the stochastic trapping-detrapping transitions performed by a large set of quasiresonant test particles moving self-consistently in the wave's potential has been carried out using dynamical criteria based on simple physical arguments. The paper allows us to explain the role of the stochastic processes at work in the wave-particle interactions and to shed light on their influence on the dynamical evolution of the system over a long range of time.

Journal Article↗

Diffusion approximation of the stochastic process of microtubule assembly.

Microtubules are protein polymers that guide intracellular motility. Stochastic switching of a microtubule between states of elongation, shortening, and pause is described in detail by the dynamic instability (DI) model. Recently we have described the dynamics of microtubules phenomenologically as generalized diffusion of their ends. Genesis of the diffusion dynamics and accuracy of diffusion model are studied in this work. It is shown that wandering of the end of a microtubule undergoing DI asymptotically approaches the Wiener diffusion process. Accuracy of the diffusion approximation is evaluated by comparing its predictions with results of simulation of DI. Stationary distributions of microtubule length and life-time that are predicted by both models differ qualitatively between two cell types considered. However, predictions of the diffusion model are in each case practically identical to predictions of the DI model being also consistent with experimental data. The peculiar stochastic process of microtubule assembly thus converges at cell scale to a kind of widespread-in-nature diffusion process. This result is considered an example of qualitative change in dynamical properties in transition from the molecular to cellular level of biological organization. Additionally, it suggests employment of diffusion process theory in studying functions of microtubules in the cell.

Animals↗

Stochastic process of equilibrium fluctuations of a system with long-range interactions.

The relaxation towards equilibrium of systems with long-range interactions is not yet understood. As a step towards such a comprehension, we propose the study of dynamical equilibrium fluctuations in a model system with long-range interaction. We compute analytically, from the microscopic dynamics, the autocorrelation function of the order parameter. From this result, we derive analytically a Fokker-Planck equation which describes the stochastic process of the impulsion of a single particle in an equilibrium bath. The diffusion coefficient is explicitly computed.

Journal Article↗

Stochastic processes in nano-biomachines revealed by single molecule detection.

Proteins and their assemblies are in the size of nanometers and are exposed to thermal disturbances. Many molecular processes in these nano-biomachines are stochastic, reflecting the fact that the input energy level is comparable to that of thermal energy. These stochastic properties have been revealed by recently developed single molecule detection techniques. The movement of molecular motors, myosin, and kinesin, has been suggested to be thermally driven. Random thermal movement is biased using the energy of the ATP hydrolysis. Thus, the molecular motors may harness thermal energy. This unique mechanism may be important in understanding the operation of the biosystems.

Adenosine Triphosphate↗

Noise in hysteretic systems and stochastic processes on graphs

It is shown that the theory of stochastic diffusion processes on graphs is a natural tool for the analysis of noise in hysteretic systems. In particular, by using this theory, analytical expressions for stationary characteristics of random outputs of some hysteretic systems are derived.

Journal Article↗

Stochastic processes and conformal invariance.

We discuss a one-dimensional model of a fluctuating interface with a dynamic exponent z=1. The events that occur are adsorption, which is local, and desorption which is nonlocal and may take place over regions of the order of the system size. In the thermodynamic limit, the time dependence of the system is given by characters of the c=0 logarithmic conformal field theory of percolation. This implies in a rigorous way, a connection between logarithmic conformal field theory and stochastic processes. The finite-size scaling behavior of the average height, interface width and other observables are obtained. The avalanches produced during desorption are analyzed and we show that the probability distribution of the avalanche sizes obeys finite-size scaling with new critical exponents.

Journal Article↗

Branching stochastic processes with immigration in analysis of renewing cell populations.

This paper considers the utility of a new class of stochastic branching processes with non-homogeneous immigration in modeling complex renewing cell systems. Such systems typically include the population of stem cells that provides an inexhaustible supply of cells necessary for maintaining the cellular composition of a tissue. A stem cell may be induced to transform (differentiate) into a progenitor cell. Progenitor cells retain the ability to proliferate and their function is believed to provide a quick proliferative response to an increased demand for cells in the population. There may be several sub-types of progenitor cells. Terminally differentiated cells do not divide under normal conditions; they are responsible for maintaining tissue-specific functions. Recent advancements in experimental techniques offer considerable scope for quantitative studies of in vivo cell kinetics based on stochastic modeling of renewing cell populations. However, no ready-made theory is currently available to take full advantage of these advancements. This paper introduces such a theory with a special focus on its feasibility in biological applications.

Cell Death↗

Single cell origin of multilineage colonies in culture. Evidence that differentiation of multipotent progenitors and restriction of proliferative potential of monopotent progenitors are stochastic processes.

In this paper, we report analysis of differentiation in human hemopoietic colonies derived from a single cell. Cord blood mononulear cells and panned My-10 antigen-positive bone marrow and cord blood cells were plated in methylcellulose medium containing erythropoietin and conditioned medium. Initially, we performed mapping studies to identify candidate colony-forming cells. Subsequently, using a micromanipulator, we transferred single cells individually to 35-mm dishes for analysis of colony formation. Cellular composition of the colony was determined by identifying all of the cells in the May-Grunwald-Giemsa stained preparation. Of 150 single candidate cells replated, 63 produced colonies. The incidences of single lineage colonies included 19 erythroid, 17 monocyte-macrophage, and 9 eosinophil colonies. There were 18 mixed hemopoietic colonies consisting of cells in two, three, four, and five lineages in varying combinations. In some instances, we noted the predominance of one lineage and the presence of very small populations of cells in a second or third lineage. These results provide evidence for the single-cell origin of human multilineage hemopoietic colonies, and are consistent with the stochastic model of stem cell differentiation in man. They also indicate that restriction of the proliferative potential of committed progenitors is a stochastic process.

Bone Marrow Cells↗

Applying the saddlepoint approximation to bivariate stochastic processes.

The problem of moment closure is central to the study of multitype stochastic population dynamics since equations for moments up to a given order will generally involve higher-order moments. To obtain a Normal approximation, the standard approach is to replace third- and higher-order moments by zero, which may be severely restrictive on the structure of the p.d.f. The purpose of this paper is therefore to extend the univariate truncated saddlepoint procedure to multivariate scenarios. This has several key advantages: no distributional assumptions are required; it works regardless of the moment order deemed appropriate; and, we obtain an algebraic form for the associated p.d.f. irrespective of whether or not we have complete knowledge of the cumulants. The latter is especially important, since no families of distributions currently exist which embrace all cumulants up to any given order. In general the algorithm converges swiftly to the required p.d.f.; analysis of a severe test case illustrates its current operational limit.

Algorithms↗

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↗

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↗