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PubMed1992

Kinetics and mechanism of cell membrane electrofusion.

A new quantitative approach to study cell membrane electrofusion has been developed. Erythrocyte ghosts were brought into close contact using dielectrophoresis and then treated with one square or even exponentially decaying fusogenic pulse. Individual fusion events were followed by lateral diffusion of the fluorescent lipid analogue 1,1'-dihexadecyl-3,3,3',3'-tetramethylindocarbocyanine perchlorate (Dil) from originally labeled to unlabeled adjacent ghosts. It was found that ghost fusion can be described as a first-order rate process with corresponding rate constants; a true fusion rate constant, k(f), for the square waveform pulse and an effective fusion rate constant, k(ef), for the exponential pulse. Compared with the fusion yield, the fusion rate constants are more fundamental characteristics of the fusion process and have implications for its mechanisms. Values of k(f) for rabbit and human erythrocyte ghosts were obtained at different electric field strength and temperatures. Arrhenius k(f) plots revealed that the activation energy of ghost electrofusion is in the range of 6-10 kT. Measurements were also made with the rabbit erythrocyte ghosts exposed to 42 degrees C for 10 min (to disrupt the spectrin network) or 0.1-1.0 mM uranyl acetate (to stabilize the bilayer lipid matrix of membranes). A correlation between the dependence of the fusion and previously published pore-formation rate constants for all experimental conditions suggests that the cell membrane electrofusion process involve pores formed during reversible electrical breakdown. A statistical analysis of fusion products (a) further supports the idea that electrofusion is a stochastic process and (b) shows that the probability of ghost electrofusion is independent of the presence of Dil as a label as well as the number of fused ghosts.

Animals↗
PubMed2003

Bivariate surrogate techniques: necessity, strengths, and caveats.

The concept of surrogates allows testing results from time series analysis against specified null hypotheses. In application to bivariate model dynamics we here compare different types of surrogates, each designed to test against a different null hypothesis, e.g., an underlying bivariate linear stochastic process. Two measures that aim at a characterization of interdependence between nonlinear deterministic dynamics were used as discriminating statistics. We analyze eight different stochastic and deterministic models not only to demonstrate the power of the surrogates, but also to reveal some pitfalls and limitations.

Journal Article↗
PubMed1987

Sequestration hypothesis of atherosclerosis.

Atherosclerosis of the human aorta has been studied by morphometric, chemical, and histochemical methods. Results of these separate approaches are converging upon a theory of pathogenesis. This theory begins with the standard view of a two stage process, intimal fibroplasia followed by atheronecrosis in the most thickened and aged places. The first stage, fibroplasia, can be described in terms of a stochastic process wherein smooth muscle cells, scattered in accordance with a Poison distribution, elaborate matrix materials over time, causing the realms of the cells to expand and to aggregate. The fusion of the expanded smooth muscle cell realms seems to mark the advent of necrosis. The second stage, atheronecrosis, can be described such that the probability of a necrotic core emerging at a site in a vessel is governed by the amount and the age of interstitial matrix materials at the site. Further evidence shows that the matrix materials tend to sequester lipids in greater than proportionate amounts as the intimal bulk increases. The sequestered perifibrous lipid is histochemically different from the lipids of the necrotic core, in that only the latter can be fixed with chromic acid. These results suggest that lipids undergo a qualitative change as well as a quantitative increase at the stage of impending necrosis. This qualitative change is governed by age, which raises the possibility that necrotizing toxicity accumulates in the sequestered lipid as it ages.

Adolescent↗
PubMed2003

Current mechanistic approaches to the chemoprevention of cancer.

The prevention of cancer is one of the most important public health and medical practices of the 21st century. We have made much progress in this new emerging field, but so much remains to be accomplished before widespread use and practice become common place. Cancer chemoprevention encompasses the concepts of inhibition, reversal, and retardation of the cancer process. This process, called carcinogenesis, requires 20-40 years to reach the endpoint called invasive cancer. It typically follows multiple, diverse and complex pathways in a stochastic process of clonal evolution. These pathways appear amenable to inhibition, reversal or retardation at various points. We must therefore identify key pathways in the evolution of the cancer cell that can be exploited to prevent this carcinogenesis process. Basic research is identifying many genetic lesions and epigenetic processes associated with the progression of precancer to invasive disease. Many of these early precancerous lesions favor cell division over quiescence and protect cells against apoptosis when signals are present. Many oncogenes are active during early development and are reactivated in adulthood by aberrant gene promoting errors. Normal regulatory genes are mutated, making them insensitive to normal regulatory signals. Tumor suppressor genes are deleted or mutated rendering them inactive. Thus there is a wide range of defects in cellular machinery which can lead to evolution of the cancer phenotype. Mistakes may not have to appear in a certain order for cells to progress along the cancer pathway. To conquer this diverse disease, we must attack multiple key pathways at once for a predetermined period of time. Thus, agent combination prevention strategies are essential to decrease cancer morbidity. Furthermore, each cancer type may require custom combination of prevention strategies to be successful.

Animals↗
PubMedDate not supplied

Deterministic model of ion channel flipping with fractal scaling of kinetic rates.

The flipping of ion channels in biological membranes has usually been modeled in terms of Markov transitions between open and closed states. The basic assumption of this approach is that channel flipping between open and closed states is an inherent stochastic process, due to random thermal fluctuations of units forming the channel protein. In this paper, we propose a different view of channel flipping, one not involving external stochastic causes. We consider the channel as a physical dynamic system, the unpredictable flipping of which is due to a deterministic mechanism which sustains a chaotic dynamics. In particular, we presume the changes in the channel conformation are due to delayed interaction between the ionic flow through the channel and the protein forming the channel. The model proposed here describes the channel by means of macroscopic physical quantities such as conductance, current, membrane, and reversal potentials and predicts open and closed dwell time distributions consisting of multiple exponential components and exhibiting power-law scaling over a wide range of time scales. The effective kinetic rate computed through use of simulation data shows fractal properties in good agreement with those seen experimentally. This mathematical model of the ion channel is physically consistent in terms of a plausible real system and may provide a novel key to understanding the complex behavior of the flipping process.

Electric Conductivity↗
PubMed2003

The identity by descent process along the chromosome.

The probabilities of the various possible identity by descent (IBD) states at a locus captures all the genealogical information for that locus for the set of individuals under consideration. Here we study the stochastic process of the IBD state as one moves across the genome of a set of individuals. In general it is no longer sufficient to specify the IBD state, one needs to increase the state space if one is to maintain the Markov property, as has been discussed by for instance McPeak and Sun [Am J Hum Genet 2000;66:1076-1094] and Browning and Browning [Theor Popul Biol 2002;62:1-8]. This paper discusses a general method of deriving the transition matrix for that Markov chain iteratively from one time point to a subsequent one. This method allows a considerable reduction in the size of the state space needed. The basic recursion is set out here and the application is illustrated by two specific examples.

Alleles↗
PubMed2006

Inferring steady state single-cell gene expression distributions from analysis of mesoscopic samples.

BACKGROUND: A great deal of interest has been generated by systems biology approaches that attempt to develop quantitative, predictive models of cellular processes. However, the starting point for all cellular gene expression, the transcription of RNA, has not been described and measured in a population of living cells. RESULTS: Here we present a simple model for transcript levels based on Poisson statistics and provide supporting experimental evidence for genes known to be expressed at high, moderate, and low levels. CONCLUSION: Although the model describes a microscopic process occurring at the level of an individual cell, the supporting data we provide uses a small number of cells where the echoes of the underlying stochastic processes can be seen. Not only do these data confirm our model, but this general strategy opens up a potential new approach, Mesoscopic Biology, that can be used to assess the natural variability of processes occurring at the cellular level in biological systems.

Base Sequence↗
PubMed2005

Genetic variation and migration in the Mexican free-tailed bat (Tadarida brasiliensis mexicana).

Incomplete lineage sorting can genetically link populations long after they have diverged, and will exert a more powerful influence on larger populations. The effects of this stochastic process can easily be confounded with those of gene flow, potentially leading to inaccurate estimates of dispersal capabilities or erroneous designation of evolutionarily significant units (ESUs). We have used phylogenetic, population genetic, and coalescent methods to examine genetic structuring in large populations of a widely dispersing bat species and to test hypotheses concerning the influences of coalescent stochasticity vs. gene flow. The Mexican free-tailed bat, Tadarida brasiliensis mexicana, exhibits variation in both migratory tendency and route over its range. Observations of the species' migratory behaviour have led to the description of behaviourally and geographically defined migratory groups, with the prediction that these groups compose structured gene pools. Here, we used mtDNA sequence analyses coupled with existing information from allozyme, banding, and natural history studies to evaluate hypotheses regarding the relationship between migration and genetic structure. Analyses of molecular variance revealed no significant genetic structuring of behaviourally distinct migratory groups. Demographic analyses were consistent with population growth, although the timing of population expansion events differs between migratory and nonmigratory populations. Hypotheses concerning the role of gene flow vs. incomplete lineage sorting on these data are explored using coalescent simulations. Our study demonstrates the importance of accounting for coalescent stochasticity in formulating phylogeographical hypotheses, and indicates that analyses that do not take such processes into account can lead to false conclusions regarding a species' phylogeographical history.

Analysis of Variance↗
PubMed2002

Statically transformed autoregressive process and surrogate data test for nonlinearity.

The key feature for the successful implementation of the surrogate data test for nonlinearity on a scalar time series is the generation of surrogate data that represent exactly the null hypothesis (statically transformed normal stochastic process), i.e., they possess the sample autocorrelation and amplitude distribution of the given data. A conceptual approach and algorithm for the generation of surrogate data is proposed, called the statically transformed autoregressive process (STAP). It identifies a normal autoregressive process and a monotonic static transform, so that the transformed realizations of this process fulfill exactly both conditions and do not suffer from bias in autocorrelation as the surrogate data generated by other algorithms. The appropriateness of STAP is demonstrated with simulated and real world data.

Journal Article↗
PubMed2005

The analysis of reaction norms for age and size at maturity using maturation rate models.

Reaction norms for age and size at maturity are being analyzed to answer important questions about the evolution of life histories. A new statistical method is developed in the framework of time-to-event data analysis, which circumvents shortcomings in currently available approaches. The method emphasizes the estimation of age- and size-dependent maturation rates. Individual probabilities of maturation during any given time interval follow by integrating maturation rate along the growth curve. The integration may be performed in different ways, over ages or sizes or both, corresponding to different assumptions on how individuals store the operational history of the maturation process. Data analysis amounts to fitting generalized nonlinear regression models to a maturation status variable. This technique has three main advantages over existing methods: (1) treating maturation as a stochastic process enables one to specify a rate of maturation; (2) age and size at which maturation occurs do not have to be observed exactly, and bias arising from approximations and interpolations is avoided; (3) ages at which sizes are measured and maturation status are observed can differ between individuals. An application to data on the springtail Folsomia candida is presented. Models with age-dependent integration of maturation rates were preferred. The analysis demonstrates a significant size dependence of the maturation rate but no age dependence.

Age Factors↗
PubMed1984

A non-stationary model of single evoked EEG activity and its estimation.

There are many different techniques of estimating evoked EEG activity. Each construction of an estimator depends on the model of the process generating the evoked activity. In this paper a model is proposed in which the evoked activity is a transient signal described by the so-called uniformly modulated stochastic process. The usual supposition, that the evoked activity does not depend on the background activity is replaced by the conditional independence of the spontaneous prestimulation and evoked activities. A linear filter with a time varying frequency transfer function is used to construct the estimator of the evoked activity. A statistical relationship between the spontaneous prestimulation and the background activities is considered and the single evoked activity estimator is proposed.

Electroencephalography↗
PubMed2005

Intratumor heterogeneity in blood perfusion in orthotopic human melanoma xenografts assessed by dynamic contrast-enhanced magnetic resonance imaging.

PURPOSE: To determine the intratumor heterogeneity in blood perfusion of orthotopic human melanoma xenografts by use of gadopentetate dimeglumine (Gd-DTPA)-based dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). MATERIALS AND METHODS: Orthotopic xenografts of an amelanotic human melanoma cell line (A-07) were scanned sagittally, coronally, and axially in three subsequent DCE-MRI sessions, using spoiled gradient recalled sequences, a voxel size of 0.31x0.62x2.0 mm3, and an interleaving acquisition method to avoid slice gaps. Tumor images of E . F (E is initial extraction fraction and F is perfusion) were produced by subjecting the DCE-MRI data to Kety analysis. E . F was used as a parameter for tumor blood perfusion, since E for Gd-DTPA is close to unity in A-07 tumors. RESULTS: All A-07 tumors subjected to investigation showed anisotropic radial heterogeneity in blood perfusion. The blood perfusion was low in the center of the tumors and increased toward the tumor periphery in the cranial, dorsal, caudal, and ventral directions, but not in the lateral and medial directions. In addition, 9 of 10 tumors showed blood perfusion hot spots in central or nonperipheral regions. The hot spots differed significantly between tumors in size, shape, location, and intensity, and appeared to be governed by stochastic processes. This heterogeneity superimposed the radial heterogeneity, but did not overshadow it in any tumor. CONCLUSION: Orthotopic human melanoma xenografts show significant intratumor heterogeneity in blood perfusion. This heterogeneity is made up of two distinctly different components, one stochastic and one nonstochastic radial component. The radial component is anisotropic and dominant and is superimposed by the stochastic component.

Animals↗
PubMed2003

Fluctuations of jamming coverage upon random sequential adsorption on homogeneous and heterogeneous media.

The fluctuations of the jamming coverage upon random sequential adsorption (RSA) are studied using both analytical and numerical techniques. Our main result shows that these fluctuations (characterized by sigma(thetaJ)) decay with the lattice size according to the power law sigma(thetaJ) proportional, variant L(-1/nu). The exponent nu depends on the dimensionality D of the substrate and the fractal dimension of the set where the RSA process actually takes place (df) according to nu=2/(2D-df). This theoretical result is confirmed by means of extensive numerical simulations applied to the RSA of dimers on homogeneous and stochastic fractal substrates. Furthermore, our predictions are in excellent agreement with different previous numerical results. It is also shown that, studying correlated stochastic processes, one can define various fluctuating quantities designed to capture either the underlying physics of individual processes or that of the whole system. So, subtle differences in the definitions may lead to dramatically different physical interpretations of the results. Here, this statement is demonstrated for the case of RSA of dimers on binary alloys.

Journal Article↗
PubMed2003

Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability.

In this paper, we derive analytic solutions of stochastic mutation-selection networks that describe early events of cancer formation. A main assumption is that cancer is initiated in tissue compartments, where only a relatively small number of cells are at risk of mutating into cells that escape from homeostatic regulation. In this case, the evolutionary dynamics can be approximated by a low-dimensional stochastic process with a linear Kolmogorov forward equation that can be solved analytically. Most of the time, the cell population is homogeneous with respect to relevant mutations. Occasionally, such homogeneous states are connected by 'stochastic tunnels'. We give a precise analysis of the existence of tunnels and calculate the rate of tunneling. Finally, we calculate the conditions for chromosomal instability (CIN) to precede inactivation of the first tumor suppressor gene. In this case, CIN is an early event and a driving force of cancer progression. The techniques developed in this paper can be used to study arbitrarily complex mutation-selection networks of the somatic evolution of cancer.

Cell Physiological Phenomena↗
PubMed2001

First-passage-time exponent for higher-order random walks: using Lévy flights.

We present a heuristic derivation of the first-passage-time exponent for the integral of a random walk [Y. G. Sinai, Theor. Math. Phys. 90, 219 (1992)]. Building on this derivation, we construct an estimation scheme to understand the first-passage-time exponent for the integral of the integral of a random walk, which is numerically observed to be 0.220+/-0.001. We discuss the implications of this estimation scheme for the nth integral of a random walk. For completeness, we also address the n=infinity case. Finally, we explore an application of these processes to an extended, elastic object being pulled through a random potential by a uniform applied force. In so doing, we demonstrate a time reparametrization freedom in the Langevin equation that maps nonlinear stochastic processes into linear ones.

Journal Article↗
PubMed2002

Evolutionary reconstruction of networks.

Can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system? In this model study, we present a Metropolis algorithm for reconstruction of graphs from their Laplacian spectra. Through a stochastic process of mutations and selection, evolving test networks converge to a reference graph. Applying the method to several examples of random graphs, clustered graphs, and small-world networks, we show that the proposed stochastic evolution allows exact reconstruction of relatively small networks and yields good approximations in the case of large sizes.

Journal Article↗
PubMed2004

Index for spatial heterogeneity in breast cancer.

Histopathological heterogeneity in cancer is a general concern. Breast carcinoma heterogeneity is now widely admitted as a source of histological grading imprecision and reproducibility problems. Classically, homogeneity is defined as equivalent to stationarity. A measure of heterogeneity based on asymptotic properties of spatial statistics is developed. Long-range dependences in heterogeneous spatial processes make estimation of the proposed heterogeneity measure unreliable. A robust estimator based on the wavelet transform is presented; this bypasses long-range dependences. The estimator extends previous works on one-dimensional stochastic processes to two dimensions as appropriate for histopathological analysis. As a side result, the estimator gives confidence intervals for the heterogeneity measure that enables the formulation and validation of testable hypothesis on the observed histopathological samples. This approach is applied to the characterization of breast cancer tumours. We show that the heterogeneity measure for various blocks of a single tumour is invariable, even when various blocks differ in size and in number of marked nuclei.

Breast Neoplasms↗
PubMed2004

Multilocus estimation of genetic structure within populations.

Spatial structure of genetic variation within populations is well measured by statistics based on the distribution of pairs of individual genotypes, and various such statistics have been widely used in experimental studies. However, the problem of uncharacterized correlations among statistics for different alleles has limited the applications of multiallelic, multilocus summary measures, since these had unknown sampling distributions. Usually multiple alleles and/or multiple loci are required in order to precisely measure spatial structures, and to provide precise indirect estimates of the amount of dispersal in samples of reasonable size. This article examines the correlations among pair-wise statistics, including Moran I-statistics and various measures of conditional kinship, for different alleles of a locus. First the correlations are mathematically derived for random spatial distributions, which allow averages over alleles and loci to be used as more powerful yet exact test statistics for the null hypothesis. Then extensive computer simulations are conducted to examine the correlations among values for different alleles under isolation by distance processes. For loci with more than three alleles, the results show that the correlations are remarkably and perhaps surprisingly small, establishing the principle that then alleles behave as nearly independent realizations of space-time stochastic processes. The results also show that the correlations are largely robust with respect to the degree of spatial structure, and they can be used in a straightforward manner to form confidence intervals for averages. The results allow a precise connection between observations in experimental studies and levels of dispersal in theoretical models.

Alleles↗