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PubMed1997

Dynamics of pore growth in membranes and membrane stability.

Pores can form and grow in biomembranes because of factors such as thermal fluctuation, transmembrane electrical potential, and cellular environment. We propose a new statistical physics model of the pore growth treated as a non-Markovian stochastic process, with a free energy barrier and memory friction from the membrane matrix treated as a quasi-two-dimensional viscoelastic and dielectric fluid continuum. On the basis of the modern theory of activated barrier crossing, an analytical expression for membrane lifetime and the phase diagram for membrane stability are obtained. The memory effect due to membrane viscoelasticity and the elasticity due to cytoskeletal network are found to induce sharp transitions to membrane stability against pore growth and compete with other factors to manifest rich dynamic transitions over the membrane lifetime.

Biophysical Phenomena↗
PubMed2006

Long-distance dispersal of plants.

Long-distance dispersal (LDD) of plants poses challenges to research because it involves rare events driven by complex and highly stochastic processes. The current surge of renewed interest in LDD, motivated by growing recognition of its critical importance for natural populations and communities and for humanity, promises an improved, quantitatively derived understanding of LDD. To gain deep insights into the patterns, mechanisms, causes, and consequences of LDD, we must look beyond the standard dispersal vectors and the mean trend of the distribution of dispersal distances. "Nonstandard" mechanisms such as extreme climatic events and generalized LDD vectors seem to hold the greatest explanatory power for the drastic deviations from the mean trend, deviations that make the nearly impossible LDD a reality.

Animals↗
PubMed2006

Spatial stochastic models for cancer initiation and progression.

The multistage carcinogenesis hypothesis has been formulated by a number of authors as a stochastic process. However, most previous models assumed "perfect mixing" in the population of cells, and included no information about spatial locations. In this work, we studied the role of spatial dynamics in carcinogenesis. We formulated a 1D spatial generalization of a constant population (Moran) birth-death process, and described the dynamics analytically. We found that in the spatial model, the probability of fixation of advantageous and disadvantageous mutants is lower, and the rate of generation of double-hit mutants (the so-called tunneling rate) is higher, compared to those for the space-free model. This means that the results previously obtained for space-free models give an underestimation for rates of cancer initiation in the case where the first event is the generation of a double-hit mutant, e.g. the inactivation of a tumor-suppressor gene.

Algorithms↗
PubMed1979

A stochastic compartment model of stomach cancer with correlated waiting time distributions.

The incidence and growth rate of stomach cancer in the US population is modelled, for each sex, as a partially observed, discrete state stochastic process. Explicit evaluation of the transition rates between the states of the model is made possible by identifying them as specific functions of the time spent within each state. The functions used in the model were selected from the medical and epidemiological literature. With the model it was found possible to obtain fits to the age distribution of deaths due to stomach cancer for white males in 1975 and for selected age ranges for white females. These results suggested that the natural history of stomach cancer is different for females above and below age 65.

Adult↗
PubMed1994

Hidden Markov model approach to skill learning and its application to telerobotics.

In this paper, we discuss the problem of how human skill can be represented as a parametric model using a hidden Markov model (HMM), and how an HMM-based skill model can be used to learn human skill. HMM is feasible to characterize a doubly stochastic process--measurable action and immeasurable mental states--that is involved in the skill learning. We formulated the learning problem as a multidimensional HMM and developed a testbed for a variety of skill learning applications. Based on "the most likely performance" criterion, the best action sequence can be selected from all previously measured action data by modeling the skill as an HMM. The proposed method has been implemented in the teleoperation control of space station robot system, and some important implementation issues have been discussed. The method allows a robot to learn human skill in certain tasks and to improve motion performance.

Algorithms↗
PubMed2006

Bayesian inference in a hidden stochastic two-compartment model for feline hematopoiesis.

In this paper, we describe a hidden two-compartment stochastic process used to model the kinetics of feline hematopoietic stem cells (HSCs) in continuous time. Because of the experimental design and data collection scheme, the inferential task presents numerous challenges. While the hematopoietic process evolves in continuous time, the observations are collected only at discrete irregular times and are a probabilistic function of the state of the process. In addition, the animals go through an experimental procedure such that their reserve of HSCs is severely depleted at the start of the observation period. This impedes any approximation of the hematopoietic process with a continuous state-space process (normal approximation of the transition probabilities would be inaccurate when the state of the process, i.e. the number of stem cells, is small). We implement a Markov chain Monte Carlo algorithm that allows us to estimate the posterior distribution of the parameters of the hematopoietic process while maintaining its state-space discrete (i.e. without using any approximation). We show the performance of the algorithm on simulated data. Finally, we apply the algorithm to data on multiple experimental cats and provide estimates of the rates of the fates of feline HSCs. The obtained estimates are in agreement with the estimates obtained with different methods published in the medical literature. However, the proposed approach makes a more efficient use of the data and hence the parameter estimates are much more accurate than the one obtained with the methods previously proposed.

Algorithms↗
PubMed2000

Active life expectancy estimates for the U.S. elderly population: a multidimensional continuous-mixture model of functional change applied to completed cohorts, 1982-1996.

An increment-decrement stochastic-process life table model that continuously mixes measures of functional change is developed to represent age transitions among highly refined disability states interacting simultaneously with mortality. The model is applied to data from the National Long Term Care Surveys of elderly persons in the years 1982 to 1996 to produce active life expectancy estimates based on completed-cohort life tables. At ages 65 and 85, comparisons with extant period estimates for 1990 show that our active life expectancy estimates are larger for both males and females than are extant period estimates based on coarse disability states.

Activities of Daily Living↗
PubMed1999

Optimized radiation therapy based on radiobiological objectives.

In the broad field of radiation therapy optimization, both simple and complex problems have their origins in the interaction of the radiation beams with the biological structures of normal and malignant tissues of the human body. Therefore, it is no great surprise that many treatment optimization problems are best handled by the use of well-designed radiobiological models. The classic way of quantifying dose-response relations for tumors and normal tissues as well as their cross-correlation with each other and their dependence on the underlying genetic and molecular biology of the cell are first briefly reviewed. Radiobiological objective functions, such as the probability of achieving complication-free cure and its expectation value under influence of stochastic processes during the course of treatment, are defined and shown to solve many of the problems of radiation therapy planning. Finally, it is shown through the use of these quantifiers that, simply by introducing biologically optimal intensity modulated dose delivery, the treatment outcome can be improved by about 20% or more in cases with a complex spread of the disease. Once radiobiological optimal plans have been developed, they can be approximated by ordinary physical planning, but the biological objective functions are still needed to have a figure of merit for the quality of the treatment.

Dose-Response Relationship, Radiation↗
PubMed2001

The evolution of postzygotic isolation: accumulating Dobzhansky-Muller incompatibilities.

Hybrid sterility and inviability often result from the accumulation of substitutions that, while functional on their normal genetic backgrounds, cause a loss of fitness when brought together in hybrids. Previous theory has shown that such Dobzhansky-Muller incompatibilities should accumulate at least as fast as the square of the number of substitutions separating two species, the so-called snowball effect. Here we explicitly describe the stochastic accumulation of these incompatibilities as a function of time. The accumulation of these incompatibilities involves three levels of stochasticity: (1) the number of substitutions separating two allopatric lineages at a given time; (2) the number of incompatibilities resulting from these substitutions; and (3) the fitness effects of individual incompatibilities. Previous analyses ignored the stochasticity of molecular evolution (level 1) as well as that due to the variable effects of incompatibilities (level 3). Here we approximate the full stochastic process characterizing the accumulation of hybrid incompatibilities between pairs of loci. We derive the distribution of the number of incompatibilities as a function of divergence time between allopatric taxa as well as the distribution of waiting times to speciation by postzygotic isolation. We provide simple approximations for the mean and variance of these waiting times. These results let us estimate. albeit crudely, the probability, p, that two diverged sites from different species will contribute to hybrid sterility or inviability. Our analyses of data from Drosophila and Bombina suggest that p is generally very small, on the order of 10(-6) or less.

Animals↗
PubMed1990

Eye-movement models for arithmetic and reading performance.

Three stochastic eye-movement models for arithmetic and reading performance have been proposed, one for arithmetic and two for reading. Each model characterizes a real-time stochastic process in terms of fixation durations and saccadic movement, but only direction and length of saccades are considered, not acceleration or velocity. Aspects of the models that are emphasized, partly because of their general neglect in the literature, are the probability distribution of fixation durations and the random walk of saccade directions. The distributions of fixation duration are approximately exponential, but systematic deviations can be accounted for in the models, even though the fit to data is not perfect. In the case of the arithmetic algorithms of addition and subtraction, the random walk of the normative model has only two possible moves. Data are also presented on backtracking, skipping and wandering eye movements, each of which has a significant relative frequency. The first reading model is called a minimal control model, because it does not take account of the effects of many local variables, e.g., word length, that have been extensively studied. The axioms on fixation duration for the minimal control model are the same as for the arithmetic model. Abstracting from the different arrangement of stimuli in arithmetic algorithms and in linear text, the axioms on saccadic motion for the two models are also essentially identical. The stochastic nature of both models is strongly supported by data on the independence of fixation durations from previous fixation durations. Additional detailed evidence is presented for the arithmetic model. To better account for a great variety of experimental results concerning significant effects on eye movements in reading, a text-dependent probabilistic model of reading is introduced. Significant local effects fall into three classes, identified as line, word and grammatical variables. The revised axioms embody five features of text known to be significant: (i) fixation duration depends on the number of letters in a word; (ii) a saccade is longer when a longer word is to the right; (iii) a saccade is longer when the current fixation is on a longer word; (iv) high-frequency fixation words have the highest probability of being skipped; (v) ambiguous or difficult grammatical structures increase backtracking.

Cognition↗
PubMed2005

Inferring network activity from synaptic noise.

During intense network activity in vivo, cortical neurons are in a high-conductance state, in which the membrane potential (V(m)) is subject to a tremendous fluctuating activity. Clearly, this "synaptic noise" contains information about the activity of the network, but there are presently no methods available to extract this information. We focus here on this problem from a computational neuroscience perspective, with the aim of drawing methods to analyze experimental data. We start from models of cortical neurons, in which high-conductance states stem from the random release of thousands of excitatory and inhibitory synapses. This highly complex system can be simplified by using global synaptic conductances described by effective stochastic processes. The advantage of this approach is that one can derive analytically a number of properties from the statistics of resulting V(m) fluctuations. For example, the global excitatory and inhibitory conductances can be extracted from synaptic noise, and can be related to the mean activity of presynaptic neurons. We show here that extracting the variances of excitatory and inhibitory synaptic conductances can provide estimates of the mean temporal correlation-or level of synchrony-among thousands of neurons in the network. Thus, "probing the network" through intracellular V(m) activity is possible and constitutes a promising approach, but it will require a continuous effort combining theory, computational models and intracellular physiology.

Animals↗
PubMed2005

Stochastic interplay between mutation and recombination during the acquisition of drug resistance mutations in human immunodeficiency virus type 1.

The emergence of drug resistance mutations in human immunodeficiency virus (HIV) has been a major setback in the treatment of infected patients. Besides the high mutation rate, recombination has been conjectured to have an important impact on the emergence of drug resistance. Population genetic theory suggests that in populations limited in size recombination may facilitate the acquisition of beneficial mutations. The viral population in an infected patient may indeed represent such a population limited in size, since current estimates of the effective population size range from 500 to 10(5). To address the effects of limited population size, we therefore expand a previously described deterministic population genetic model of HIV replication by incorporating the stochastic processes that occur in finite populations of infected cells. Using parameter estimates from the literature, we simulate the evolution of drug-resistant viral strains. The simulations show that recombination has only a minor effect on the rate of acquisition of drug resistance mutations in populations with effective population sizes as small as 1,000, since in these populations, viral strains typically fix beneficial mutations sequentially. However, for intermediate effective population sizes (10(4) to 10(5)), recombination can accelerate the evolution of drug resistance by up to 25%. Furthermore, a reduction in population size caused by drug therapy can be overcome by a higher viral mutation rate, leading to a faster evolution of drug resistance.

Anti-HIV Agents↗
PubMed1989

On the relationship between the menstrual cycle and the body weight and food intake of women.

Body weight and food intake of women are analyzed over the whole menstrual cycle. Over 68-94 days body weight and food intake of eight women and three men are recorded. For food intake, a diary self-report method is used. The beginning of each woman's menstrual cycle is also recorded. Body weight and food intake are regarded as stochastic processes. The theory of time series and spectral analysis is applied. As opposed to the males, in the spectra of seven females, there is a peak at a frequency with the period of the respective females' menstrual cycles. There are no further consistent differences. This sine wave reaches its maximum two to three days before menses. The data suggest that, as a first approximation, the body weight of women during a complete menstrual cycle can be described by a simple sine wave. For food intake, the spectra show hardly any differences between females and males. However, it is shown that the same sine wave as in body weight is also contained in the food intake of seven females, reaching its maximum about four days before menses.

Adult↗
PubMed1998

A comparison of smoothing techniques for CD4 data measured with error in a time-dependent Cox proportional hazards model.

The use of CD4+ T-lymphocyte counts as a covariate presents some unique challenges in survivorship analyses due to the variability of this marker. If one does not account for the measurement error component of this variability in some manner, the estimate of the relative risk parameter in a time-dependent Cox model is biased towards zero, and coverage levels of confidence intervals may be seriously incorrect. We use a two-stage approach to reduce the variability in the observed CD4 counts in order to obtain a more accurate estimate of the relative risk parameter and more valid summary statistics. In the first stage, population based smoothing methods derived from a random-effects model plus a stochastic process or individual based smoothing methods are used to replace the observed longitudinal CD4 counts with less variable imputes at each failure time. In the second stage, we use the imputes in a time-dependent Cox model to estimate the risk parameter and its associated summary statistics. We compare the smoothing methods in simulation studies and find that the use of these smoothing methods results in a substantial reduction in bias for the true risk parameter estimate, better efficiency, and more accurate coverage rates in confidence intervals. We apply our two-stage smoothing methods to the marker CD4 in the ACTG-019 clinical trial part B.

AIDS-Related Complex↗
PubMed2001

The effective size of fluctuating populations.

We consider a Wright-Fisher model whose population size is an autocorrelated stochastic process. Our interest is in the effects of autocorrelated fluctuations of the population size on the effective size. We define the inbreeding effective size and the variance effective size and show that these effective sizes are the same for this model. In the literature, it is said that the effective size is equal to the harmonic mean of population size when the size fluctuates. We will show, however, that the effective size is not the same as the harmonic mean of population size unless the fluctuations of population size are uncorrelated. The effective size is larger (resp. smaller) than the harmonic mean when the fluctuations of population size are positively (resp. negatively) autocorrelated. Further, we obtain some asymptotic expressions for effective size when the population size is very large and/or the autocorrelation of the fluctuation is very strong.

Animals↗
PubMed2000

Semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles.

We consider semiparametric regression for periodic longitudinal data. Parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect. The within-subject correlation is modeled using subject-specific random effects and a random stochastic process with a periodic variance function. We use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function, whose estimator is shown to be a periodic cubic smoothing spline. We use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components. We show that all model parameters can be easily obtained by fitting a linear mixed model. A common problem in the analysis of longitudinal data is to compare the time profiles of two groups, e.g., between treatment and placebo. We develop a scaled chi-squared test for the equality of two nonparametric time functions. The proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations.

Biometry↗
PubMed2005

Comparing internal models of the dynamics of the visual environment.

It is well known that the human postural control system responds to motion of the visual scene, but the implicit assumptions it makes about the visual environment and what quantities, if any, it estimates about the visual environment are unknown. This study compares the behavior of four models of the human postural control system to experimental data. Three include internal models that estimate the state of the visual environment, implicitly assuming its dynamics to be that of a linear stochastic process (respectively, a random walk, a general first-order process, and a general second-order process). In each case, all of the coefficients that describe the process are estimated by an adaptive scheme based on maximum likelihood. The fourth model does not estimate the state of the visual environment. It adjusts sensory weights to minimize the mean square of the control signal without making any specific assumptions about the dynamic properties of the environmental motion. We find that both having an internal model of the visual environment and its type make a significant difference in how the postural system responds to motion of the visual scene. Notably, the second-order process model outperforms the human postural system in its response to sinusoidal stimulation. Specifically, the second-order process model can correctly identify the frequency of the stimulus and completely compensate so that the motion of the visual scene has no effect on sway. In this case the postural control system extracts the same information from the visual modality as it does when the visual scene is stationary. The fourth model that does not simulate the motion of the visual environment is the only one that reproduces the experimentally observed result that, across different frequencies of sinusoidal stimulation, the gain with respect to the stimulus drops as the amplitude of the stimulus increases but the phase remains roughly constant. Our results suggest that the human postural control system does not estimate the state of the visual environment to respond to sinusoidal stimuli.

Algorithms↗
PubMed2000

Mean-field stochastic theory for species-rich assembled communities.

A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be formulated as a master equation describing a one-step stochastic process. The stationary distribution is obtained in closed form, and is shown to reduce to a log-series or log-normal distribution, depending on the values that the parameters describing the model take on. A hyperbolic relationship between the connectance of the matrix of interspecies interactions and the average number of species exists for a range of parameter values. The time evolution of the model at short and intermediate times is analyzed using van Kampen's approximation, which is valid when the number of individuals in the community is large. Good agreement with numerical simulations is found. The large time behavior, and the approach to the stationary state, is obtained by solving the equation for the generating function of the probability distribution. The analytical results which follow from the analysis are also in good agreement with direct simulations of the model.

Biophysical Phenomena↗