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PubMed1991

Quantitative assay for morphogenesis indicates the role of extracellular matrix components and G proteins.

A quantitative assay for morphogenesis is described that involves counting the organizing centers (swirling patterns) formed by many cultured fibroblasts. Organizing centers, which are found in vivo, represent one of the smallest units of morphogenesis. We show that macroscopically visible organizing centers form by the merger of smaller organizing centers. Parallel orientation of cells on plastic substrata requires cell-cell contact, but organizing centers can develop without cell-cell contact on collagen gels. On collagen gels, the orientation of collagen fibers determines the orientation of cells with respect to one another. Although organizing centers resemble fingerprints, we have shown that a stochastic process determines the spatial orientation of organizing centers. Treatment of transformed cell lines with agents that increase cAMP levels or alter the activity of guanine nucleotide binding proteins resulted in the generation of organizing centers. Cholesterol precursors involved in protein isoprenylation were found to be potent reverse-transformation agents that could alter the two-dimensional morphogenesis of cells. The simple assay described should permit the analysis of morphogenesis at the molecular and cellular levels.

Animals↗
PubMed1991

Approximate entropy as a measure of system complexity.

Techniques to determine changing system complexity from data are evaluated. Convergence of a frequently used correlation dimension algorithm to a finite value does not necessarily imply an underlying deterministic model or chaos. Analysis of a recently developed family of formulas and statistics, approximate entropy (ApEn), suggests that ApEn can classify complex systems, given at least 1000 data values in diverse settings that include both deterministic chaotic and stochastic processes. The capability to discern changing complexity from such a relatively small amount of data holds promise for applications of ApEn in a variety of contexts.

Journal Article↗
PubMed1992

Approximating Markov chains.

A common framework of finite state approximating Markov chains is developed for discrete time deterministic and stochastic processes. Two types of approximating chains are introduced: (i) those based on stationary conditional probabilities (time averaging) and (ii) transient, based on the percentage of the Lebesgue measure of the image of cells intersecting any given cell. For general dynamical systems, stationary measures for both approximating chains converge weakly to stationary measures for the true process as partition width converges to 0. From governing equations, transient chains and resultant approximations of all n-time unit probabilities can be computed analytically, despite typically singular true-process stationary measures (no density function). Transition probabilities between cells account explicitly for correlation between successive time increments. For dynamical systems defined by uniformly convergent maps on a compact set (e.g., logistic, Henon maps), there also is weak continuity with a control parameter. Thus all moments are continuous with parameter change, across bifurcations and chaotic regimes. Approximate entropy is seen as the information-theoretic rate of entropy for approximating Markov chains and is suggested as a parameter for turbulence; a discontinuity in the Kolmogorov-Sinai entropy implies that in the physical world, some measure of coarse graining in a mixing parameter is required.

Journal Article↗
PubMed1995

Rectification and signal averaging of weak electric fields by biological cells.

Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity. Under certain circumstances, the excess noise leads to an increase in the signal-to-noise ratio in a manner similar to processes labeled "stochastic resonance." Numerical results indicate that it is difficult to reconcile biological effects with low field strengths.

Animals↗
PubMed1997

The capital-asset-pricing model and arbitrage pricing theory: a unification.

We present a model of a financial market in which naive diversification, based simply on portfolio size and obtained as a consequence of the law of large numbers, is distinguished from efficient diversification, based on mean-variance analysis. This distinction yields a valuation formula involving only the essential risk embodied in an asset's return, where the overall risk can be decomposed into a systematic and an unsystematic part, as in the arbitrage pricing theory; and the systematic component further decomposed into an essential and an inessential part, as in the capital-asset-pricing model. The two theories are thus unified, and their individual asset-pricing formulas shown to be equivalent to the pervasive economic principle of no arbitrage. The factors in the model are endogenously chosen by a procedure analogous to the Karhunen-Loéve expansion of continuous time stochastic processes; it has an optimality property justifying the use of a relatively small number of them to describe the underlying correlational structures. Our idealized limit model is based on a continuum of assets indexed by a hyperfinite Loeb measure space, and it is asymptotically implementable in a setting with a large but finite number of assets. Because the difficulties in the formulation of the law of large numbers with a standard continuum of random variables are well known, the model uncovers some basic phenomena not amenable to classical methods, and whose approximate counterparts are not already, or even readily, apparent in the asymptotic setting.

Journal Article↗
PubMed1998

Time course of reactions controlled and gated by intramolecular dynamics of proteins: predictions of the model of random walk on fractal lattices.

Computer simulations of random walk on the Sierpinski gasket and percolation clusters demonstrate that the short, initial condition-dependent stage of protein involving reactions can dominate the progress of the reaction over the main stage described by the standard kinetics. This phenomenon takes place if the intramolecular conformational transition dynamics modeled by the stochastic process is slow enough and the initial conformational substate of the protein already belongs to the transition state of the reaction. Both conditions are realized in two kinds of experiments: small ligand rebinding to protein after laser flash photolysis and direct recording of single protein channel activity. The model considered suggests simple analytical formulae that can explain the time behavior of the processes observed and its variation with temperature. The initial condition-dependent stage, and not the stage described by the standard kinetics, is expected as responsible for the coupling of component reactions in the complete catalytic cycles and more complex processes of biological free energy transduction.

Journal Article↗
PubMed2004

Early single cell bifurcation of pro- and antiapoptotic states during oxidative stress.

In a population of cells undergoing oxidative stress, an individual cell either succumbs to apoptotic cell death or maintains homeostasis and survives. Exposure of PC-12-D(2)R cells to 200 microm hydrogen peroxide (H(2)O(2)) induces apoptosis in about half of cells after 24 h. After 1-h exposure to 200 microm H(2)O(2), both antiapoptotic extracellular regulated kinase (ERK) phosphorylation and pro-apoptotic Ser-15-p53 phosphorylation are observed. Microarray and real-time PCR assays of gene expression after H(2)O(2) exposure identified several transcripts, including egr1, that are rapidly induced downstream of ERK. Single cell analysis of egr1 induction and of phospho-ERK and phospho-p53 formation revealed the presence of two distinct cellular programs. Whereas the proportion of cells activating ERK versus p53 at 1 h depended on H(2)O(2) concentration, individual cells showed exclusively either phospho-p53 formation or activation of ERK and egr1 induction. Exposure to H(2)O(2) for 1 h also elicited these two non-overlapping cellular responses in both dopaminergic SN4741 cells and differentiated postmitotic PC-12-D(2)R cells. Repressing p53 with pifithrin-alpha or small interfering RNA increased ERK phosphorylation by H(2)O(2), indicating that p53-dependent suppression of ERK activity may contribute to the bi-stable single cell responses observed. By 24 h, the subset of cells in which ERK activity was suppressed exhibit caspase 3 activation and the nuclear condensation characteristic of apoptosis. These studies suggest that the individual cell rapidly and stochastically processes the oxidative stress stimulus, leading to an all-or-none cytoprotective or pro-apoptotic signaling response.

Animals↗
PubMedDate not supplied

Sources of influence on rate of cognitive change over time in Swedish twins: an application of latent growth models.

The use of latent growth models to examine influence on individual differences on ability level versus rate of change were examined for measures of fluid ability, memory, and perceptual speed in a sample of twins from the Swedish Adoption/Twin Study of Aging. Results indicated a larger amount of individual variation for average ability level (i.e., intercept) than rate of change (i.e., slope) for all three traits: Block Design, Thurstone's Picture Memory, and Symbol Digit. Generally, genetic influences were of greater importance to individual variation in ability level whereas variation for rate of change exhibited a larger environmental component. These findings support theories of increasing environmental influences with age. When genetic and environmental sources of covariation between educational attainment and pulmonary function with latent growth parameters were considered, the sources of covariation between the latent cognitive growth model parameters (i.e., intercept and slope) and both covariates were primarily genetic for ability level (intercepts) but environmental for rate of change (slopes). Such findings suggest that the forces important to timing or entry into cognitive decline may reflect stochastic processes or external environmental factors, primarily nonshared, that may differentially hasten cognitive decline in twins. These same forces may overlap with those that influence higher or lower educational attainment or those leading to better or worse pulmonary functioning.

Adult↗
PubMed2001

Distribution of the number of clonogens surviving fractionated radiotherapy: a long-standing problem revisited.

PURPOSE: A long-standing problem is addressed: what form of the probability distribution for the number of clonogenic tumor cells remaining after fractionated radiotherapy should be used in the analysis aimed at evaluating the efficacy of cancer treatment? Over a period of years, a lack of theoretical results leading to a closed-form analytic expression for this distribution, even under very simplistic models of cell kinetics in the course of fractionated radiotherapy, was the most critical deterrent to the development of relevant methods of data analysis. MATERIALS AND METHODS: Rigorous mathematical results associated with a model of fractionated irradiation of tumors based on the iterated birth and death stochastic process are discussed. RESULTS: A formula is presented for the exact distribution of the number of clonogenic tumor cells at the end of treatment. It is shown that, under certain conditions, this distribution can be approximated by a Poisson distribution. An explicit formula for the parameter of the limiting Poisson distribution is given and sample computations aimed at evaluation of the convergence rate are reported. Another useful limit that retains a dose-response relationship in the distribution of the number of clonogens has been found. Practical implications of the key theoretical findings are discussed in the context of survival data analysis. CONCLUSIONS: This study answers some challenging theoretical questions that have been under discussion over a number of years. The results presented in this work provide mechanistic motivation for parametric regression models designed to analyze data on the efficacy of radiation therapy.

Humans↗
PubMed1999

Protein folding as a nonlinear nonequilibrium thermodynamic process.

Biofurcational theory of protein folding is developed describing the process of formation of protein native structure as a sequence of non-equilibrium irreversible fluctuations, specific for a particular protein. The model gives explanation to all characteristic features of the folding process: stochastic mechanism, short time and precision of proteins self-assembling. A constructive role of entropy in the formation of a highly ordered structure out of disorder is discussed. A numerical method of a priori calculations of polypeptide structures basing on principles of bifractional folding model is presented.

Entropy↗
PubMed1993

A task-based statistical model of a worker's exposure distribution: Part I--Description of the model.

The authors present a task-based model to describe a single worker's exposures to a single airborne chemical toxicant. The model accounts for variability in short-term time-weighted average (TWA) exposure values within a task, and for variability in arithmetic mean exposure levels between tasks. For a given workday, the 8-hour TWA value is equated with the sample mean of an appropriate number of short-term TWAs arising from stratified random sampling of short-term TWAs with proportional allocation by task. The model accounts for autocorrelation in the stochastic process that generates successive short-term TWA values. Due to the underlying random process, a given type of workday with regard to the set of task times has an associated distribution of 8-hour TWA values; the variance of this distribution increases with increasing autocorrelation in the time series of short-term TWAs. A worker's total distribution of 8-hour TWAs is a mixture of these day-specific distributions weighted by the relative frequency of each type of workday; the variance of the total distribution increases with greater day-to-day variability in the array of task times.

Air Pollutants, Occupational↗
PubMed2000

Modeling pharmacokinetic data using heavy-tailed multivariate distributions.

Pharmacokinetic studies of drug and metabolite concentrations in the blood are usually conducted as crossover trials, especially in Phases I and II. A longitudinal series of measurements is collected on each subject within each period. Dependence among such observations, within and between periods, will generally be fairly complex, requiring two levels of variance components, for the subjects and for the periods within subjects, and an autocorrelation within periods as well as a time-varying variance. Until now, the standard way in which this has been modeled is using a multivariate normal distribution. Here, we introduce procedures for simultaneously handling these various types of dependence in a wider class of distributions called the multivariate power exponential and Student t families. They can have the heavy tails required for handling the extreme observations that may occur in such contexts. We also consider various forms of serial dependence among the observations and find that they provide more improvement to our models than do the variance components. An integrated Ornstein-Uhlenbeck (IOU) stochastic process fits much better to our data set than the conventional continuous first-order autoregression, CAR(1). We apply these models to a Phase I study of the drug, flosequinan, and its metabolite.

Clinical Trials, Phase I as Topic↗
PubMed1986

Commitment to expression of the metalloendopeptidases, collagenase and stromelysin: relationship of inducing events to changes in cytoskeletal architecture.

Agents that alter the morphology of rabbit synovial fibroblasts induce synthesis of the metalloendopeptidases, collagenase and stromelysin. We studied the relationship of cytoskeletal changes to the commitment to expression of these metalloendopeptidases. Cells treated with cytochalasin B (CB) or 12-O-tetradecanoylphorbol-13-acetate rounded, and only cells that had lost their stress fibers expressed collagenase and stromelysin, as determined by immunofluorescence. We concentrated on the effects of CB because of its rapid reversibility. When CB was added for 1-24 h, then removed, the cells respread within 30-60 min. The minimum period of CB treatment that committed cells to the subsequent synthesis of collagenase and stromelysin was 3 h. After initial treatment with 2 micrograms/ml CB for 3-24 h, or with various concentrations of CB (0-2 micrograms/ml) for 24 h, both enzyme activity and biosynthesis of the proenzymes showed a graded increase when measured at 24 h. Even after treatment with 2 micrograms/ml CB for only 3 h, greater than 85% of all cells were positive for both collagenase and stromelysin when cells were monitored by immunofluorescence. In contrast, when the dependence of collagenase and stromelysin expression on the inducing concentration of CB was examined, there was a dose-dependent increase in the number of cells positive for collagenase and stromelysin, as determined by immunofluorescence. Thus, at low concentrations of CB (less than 0.5 micrograms/ml), a heterogeneous population response was observed. These results suggest that the commitment of fibroblasts to induction of the metalloproteinases is a stochastic process in which a second signal that correlates with the disruption of the actin cytoskeleton may be rate-limiting for collagenase and stromelysin gene expression.

Actins↗
PubMed1982

Freeze-fracture cytochemistry: partition of glycophorin in freeze-fractured human erythrocyte membranes.

Thin-section and critical-point-dried fracture-labeled preparations are used to determine the distribution and partition of glycophorin-associated wheat germ agglutinin (WGA) binding sites over protoplasmic and exoplasmic faces of freeze-fractured human erythrocyte membranes. Most wheat germ agglutinin binding sites are found over exoplasmic faces. Label is sparse over the protoplasmic faces. These results contrast with previous observations of the partition of band 3 component where biochemical analysis and fracture-label of concanavalin A (Con A) binding sites show preferential partition of this transmembrane protein with the protoplasmic face. Presence of characteristic proportions of WGA and Con A binding sites over each fracture face is interpreted to indicate the operation of a stochastic process during freeze-fracture. This process appears modulated by the relative expression of each transmembrane protein at either surface as well as by their association to components of the erythrocyte membrane skeleton.

Erythrocyte Membrane↗
PubMed1991

Human B cell clones can be induced to proliferate and to switch to IgE and IgG4 synthesis by interleukin 4 and a signal provided by activated CD4+ T cell clones.

In the present study, it is demonstrated that cloned surface IgM-positive human B cells can be induced to proliferate and to switch with high frequencies to IgG4 and IgE production after a contact-mediated signal provided by T cell clones and interleukin 4 (IL-4). This T cell signal is antigen nonspecific and is provided by activated CD4+ cells, whereas activated CD8+ or resting CD4+ T cell clones are ineffective. 15-35% of the B cell clones cultured with cloned CD4+ T cells and IL-4 produced antibodies; 35-45% of those wells in which antibodies were produced contained IgE and IgG4. In addition to B cell clones that produced IgG4 or IgE only, B cell clones producing multiple isotypes were observed. Simultaneous production of IgG4 and IgE, IgM, IgE, and IgM, or IgG4 and IgE was detected, suggesting that during clonal expansion switching might occur in successive steps from IgM to IgG4 and IgE. In addition, production of only IgM, IgG4, and IgE during clonal expansion indicates that this isotype switching is directed by the way a B cell is stimulated and that it is not a stochastic process.

Antibodies, Monoclonal↗
PubMed1994

Role of kit-ligand in proliferation and suppression of apoptosis in mast cells: basis for radiosensitivity of white spotting and steel mutant mice.

The receptor tyrosine kinase Kit and its cognate ligand KL/steel factor are encoded at the white spotting (W) and Steel (Sl) loci of the mouse, respectively. Mutations at both the W and the Sl loci affect hematopoiesis including the stem cell hierarchy, erythropoiesis, and mast cells, as well as gametogenesis and melanogenesis. In addition, mutant mice display an increased sensitivity to lethal doses of irradiation. The role of KL/c-kit in cell proliferation and survival under conditions of growth factor-deprivation and gamma-irradiation was studied by using bone marrow-derived mast cells (BMMC) as a model. Whereas apoptosis induced by growth factor deprivation in BMMC is a stochastic process and follows zero order kinetics, gamma-irradiation-induced apoptosis is an inductive process and follows higher order kinetics. In agreement with these results, gamma-irradiation-induced apoptosis in BMMC was shown to be dependent on p53 whereas apoptosis induced by deprivation is partly dependent on p53, implying that there are other mechanisms mediating apoptosis in KL-deprived BMMC. In the presence and in the absence of serum, KL stimulated proliferation by promoting cell cycle progression. The presence of KL was required only during the early part of the G1 phase for entry into the S phase. At concentrations lower than those required for proliferation, KL suppressed apoptosis induced by both growth factor-deprivation and gamma-irradiation, and internucleosomal DNA fragmentation characteristic of apoptosis. The ability of KL to suppress apoptosis was independent of the phase of the cell cycle in which the cells were irradiated and suppression of apoptosis was a prerequisite for subsequent cell cycle progression. Moreover, addition of KL to gamma-irradiated and growth factor-deprived cells could be delayed for up to 1 h after irradiation or removal of growth factors when cells became irreversibly committed to apoptosis. KL and IL-3 induce suppression of apoptosis in mast cells by different mechanisms based on the observations of induction of bcl-2 gene expression by IL-3 but not by KL. It is proposed that the increased sensitivity of W and Sl mutant mice to lethal irradiation results from paucity of the apoptosis suppressing and proliferative effects of KL.

Animals↗
PubMed2003

Loss of the pro-apoptotic BH3-only Bcl-2 family member Bim inhibits BCR stimulation-induced apoptosis and deletion of autoreactive B cells.

During development, the stochastic process assembling the genes encoding antigen receptors invariably generates B and T lymphocytes that can recognize self-antigens. Several mechanisms have evolved to prevent the activation of these cells and the concomitant development of autoimmune disease. One such mechanism is the induction of apoptosis in developing or mature B cells by engagement of the B cell antigen receptor (BCR) in the absence of T cell help. Here we report that B lymphocytes lacking the pro-apoptotic Bcl-2 family member Bim are refractory to apoptosis induced by BCR ligation in vitro. The loss of Bim also inhibited deletion of autoreactive B cells in vivo in two transgenic systems of B cell tolerance. Bim loss prevented deletion of autoreactive B cells induced by soluble self-antigen and promoted accumulation of self-reactive B cells developing in the presence of membrane-bound self-antigen, although their numbers were considerably lower compared with antigen-free mice. Mechanistically, we determined that BCR ligation promoted interaction of Bim with Bcl-2, inhibiting its survival function. These findings demonstrate that Bim is a critical player in BCR-mediated apoptosis and in B lymphocyte deletion.

Animals↗