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At least 433 records · Page 24Linked to original sources
PubMed2006

Voltage noise influences action potential duration in cardiac myocytes.

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current-voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current-voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.

Action Potentials↗
PubMedDate not supplied

An algorithmic synthesis of the deterministic and stochastic paradigms via computer intensive methods.

In this paper, an approach to synthesizing the deterministic and stochastic paradigms, via computer intensive methods, is presented within the framework of a stochastic model of a HIV/AIDS epidemic in a population of homosexuals. Because of dependence among members of a population, the problem of determining threshold conditions was approached by systematically embedding a system of differential equations in a stochastic process and determining if the Jacobian matrix of this system is stable or not stable, when evaluated at a disease free equilibrium. It has been shown in numerous Monte Carlo simulation experiments that if this matrix is not stable, then an epidemic will develop in a population with positive probability, following the introduction of infectives into a population of susceptibles. This technique was used to search for points in the parameter space such that an epidemic would develop in a population of susceptibles, following the entrance of one or more infectious recruits during any time interval with small probability. Such recurrent rare events are of interest in the studying the emergence of new diseases, involving the transmission of a virus from a species that has evolved resistance to it to another species that lacks resistance.

Acquired Immunodeficiency Syndrome↗
PubMed1998

The emergence of drug-resistant malaria.

Stochastic processes play a vital role in the early stages of the evolution of drug-resistant malaria. We present a simple and flexible method for investigating these processes and understanding how they affect the emergence of drug-resistant malaria. Qualitatively different predictions can be made depending on the biological and epidemiological factors which prevail in the field. Intense intra-host competition between co-infecting clones, low numbers of genes required to encode resistance, and high drug usage all encourage the emergence of drug resistance. Drug-resistant forms present at the time drug application starts are less likely to survive than those which arise subsequently; survival of the former largely depends on how rapidly malaria population size stabilizes after drug application. In particular, whether resistance is more likely to emerge in areas of high or low transmission depends on malaria intra-host dynamics, the level of drug usage, the population regulation of malaria, and the number of genes required to encode resistance. These factors are discussed in relation to the practical implementation of drug control programmes.

Drug Resistance↗
PubMed1991

A mathematical model of vaccination against HIV to prevent the development of AIDS.

Vaccination and post-exposure immunization against the human immunodeficiency viruses (HIV-1 and HIV-2) faces the problem of the extensive genetic and antigenic variability of these viruses. This raises the question of what fraction of all possible antigen strains of the virus must be recognized by the immune response to a vaccine to prevent development of acquired immunodeficiency disease (AIDS). The success of a vaccine can depend on the variability of the target epitopes. The different HIV variants must be suppressed faster than new escape mutants can be produced. In this paper the antigenic variation of HIV during an individual infection is described by a stochastic process. The central assumption is that antigenic drift is important for the virus to survive immunological attack and to establish a persistent infection that leads to the development of AIDS after a long incubation period. The mathematical analysis reveals that the fraction of antigenic variants recognized by the immune response, that is induced by a successful immunogen, must exceed 1-1/R, where R is the diversification rate of the virus population. This means that if each HIV strain can produce, on average, five new escape mutants, then more than 80% of the possible variants must be covered by the immunogen. A generic result of the model is that, no matter how immunogenic a vaccine is, it will fail if it does not enhance immune attack against a sufficiently large fraction of strains. Furthermore, it is shown that the timing of the application of post-exposure immunization is important.

AIDS Vaccines↗
PubMed1987

Dynamic heterogeneity: characterization of two cell lines derived from experimental lung metastases of mouse KHT fibrosarcoma.

We have recently demonstrated that KHT fibrosarcoma variant cells that form experimental metastases are generated by a stochastic process at high effective rates (approximately 10(-5)/cell/generation). The metastatic variant cells are unstable and are rapidly lost with an effective rate of reversion of approximately 10(-1)/cell/generation. In this study, we have examined the dynamics of generation of metastatic variant cells for two lines of KHT cells derived from individual experimental lung metastases in a single step selection. When grown in vitro, the KHT35-L1 cell population maintained a highly metastatic phenotype whereas the KHT3-L1c cell population reverted to a poorly metastatic phenotype. Our results indicate that there is an approximately 10-fold higher effective rate of generation of metastatic variant cells for KHT35-L1 cells relative to KHT3-L1c cells. Thus, a higher effective rate of generation of metastatic variants accompanies a stably expressed metastatic ability in fibrosarcoma cells and, as we have previously reported, in melanoma cells.

Animals↗
PubMed2002

Functional mixed effects models.

In this article, a new class of functional models in which smoothing splines are used to model fixed effects as well as random effects is introduced. The linear mixed effects models are extended to nonparametric mixed effects models by introducing functional random effects, which are modeled as realizations of zero-mean stochastic processes. The fixed functional effects and the random functional effects are modeled in the same functional space, which guarantee the population-average and subject-specific curves have the same smoothness property. These models inherit the flexibility of the linear mixed effects models in handling complex designs and correlation structures, can include continuous covariates as well as dummy factors in both the fixed or random design matrices, and include the nested curves models as special cases. Two estimation procedures are proposed. The first estimation procedure exploits the connection between linear mixed effects models and smoothing splines and can be fitted using existing software. The second procedure is a sequential estimation procedure using Kalman filtering. This algorithm avoids inversion of large dimensional matrices and therefore can be applied to large data sets. A generalized maximum likelihood (GML) ratio test is proposed for inference and model selection. An application to comparison of cortisol profiles is used as an illustration.

Bayes Theorem↗
PubMed1994

All-night sleep EEG and artificial stochastic control signals have similar correlation dimensions.

EEG signals have been considered to be generated either by stochastic processes or by non-linear deterministic systems exhibiting chaotic behavior. To address this problem, the correlation dimension of the EEG was computed and compared to the correlation dimension of an artificial signal with identical power spectrum. By using a new type of personal super computer we were able for the first time to calculate the correlation dimension for the sleep episode of an entire night as well as for the corresponding artificial signal. The correlation dimension was high in episodes of rapid eye movement (REM) sleep, declined progressively within each non-REM sleep episode, and reached a low level at times when EEG slow waves (0.75-4.5 Hz) were dominant. The correlation dimension of the artificial signal and the EEG changed largely in parallel, although on average the values of the artificial signal were 7.3% higher. These results do not support the hypothesis that the sleep EEG is generated by a chaotic attractor.

Adult↗
PubMed1998

Investigations of the problems of assessing aflatoxin levels in peanuts.

In this study, a number of probability distributions that have been used to model the occurrence of aflatoxin in peanuts are compared. Two distributions, the compound gamma and the negative binomial, are shown to have special appeal in that both can be justified by reasoning from the fundamental biological and stochastic processes that generate the aflatoxin. Since method of moments and maximum likelihood give consistent estimates of parameters in both models, practical considerations suggest using the former. One hundred twenty data sets, each consisting of fifty observations, were not sufficient to provide goodness-of-fit tests to establish either as superior to the other as a model. Both models fit the data well, appreciably better than other models examined. An attractive aspect of the compound gamma and the negative binomial distributions is that, as a consequence of their theoretical underpinnings, both involve parameters that have meaningful interpretations. In the compound gamma, the alpha parameter reflects the shape of the kernel-to-kernel aflatoxin content distribution, the lambda parameter reflects the number (or frequency) of contaminated kernels in the sample, and the beta parameter is a scale parameter. In the negative binomial, the two parameters can be used as measures of mean or location and shape.

Aflatoxins↗
PubMed2005

Delay-induced stochastic oscillations in gene regulation.

The small number of reactant molecules involved in gene regulation can lead to significant fluctuations in intracellular mRNA and protein concentrations, and there have been numerous recent studies devoted to the consequences of such noise at the regulatory level. Theoretical and computational work on stochastic gene expression has tended to focus on instantaneous transcriptional and translational events, whereas the role of realistic delay times in these stochastic processes has received little attention. Here, we explore the combined effects of time delay and intrinsic noise on gene regulation. Beginning with a set of biochemical reactions, some of which are delayed, we deduce a truncated master equation for the reactive system and derive an analytical expression for the correlation function and power spectrum. We develop a generalized Gillespie algorithm that accounts for the non-Markovian properties of random biochemical events with delay and compare our analytical findings with simulations. We show how time delay in gene expression can cause a system to be oscillatory even when its deterministic counterpart exhibits no oscillations. We demonstrate how such delay-induced instabilities can compromise the ability of a negative feedback loop to reduce the deleterious effects of noise. Given the prevalence of negative feedback in gene regulation, our findings may lead to new insights related to expression variability at the whole-genome scale.

Algorithms↗
PubMed1995

A stochastic model for multistage tumorigenesis in developing and adult mice.

A stochastic process model for one-, two-, and three-stage malignant transformation has been developed for embryonic and adult mice. The model has been used to study the influence of mutation rate, number of stages required for transformation, and number of stem cells at risk on the kinetics of spontaneous appearance of malignant tumors. As expected, tumors appeared earlier with fewer required mutational stages, higher mutation rate, and greater number of stem cells at risk. However, a notable observation was that tumor latency was more strongly influenced by number of stages and by stem cell number at lower mutation rates than at higher rates. This implies that tumor latency may be a less useful observation when the spontaneous mutation rate is high. In the future, the model will be applied to analysis of tumorigenesis experiments in transgenic mice with p53 genetic abnormalities, subjected to irradiation or chemical tumorigenesis at different stages of development.

Animals↗
PubMed2003

An assessment of preferential attachment as a mechanism for human sexual network formation.

Recent research into the properties of human sexual-contact networks has suggested that the degree distribution of the contact graph exhibits power-law scaling. One notable property of this power-law scaling is that the epidemic threshold for the population disappears when the scaling exponent rho is in the range 2 < rho < or = 3. This property is of fundamental significance for the control of sexually transmitted diseases (STDs) such as HIV/AIDS since it implies that an STD can persist regardless of its transmissibility. A stochastic process, known as preferential attachment, that yields one form of power-law scaling has been suggested to underlie the scaling of sexual degree distributions. The limiting distribution of this preferential attachment process is the Yule distribution, which we fit using maximum likelihood to local network data from samples of three populations: (i) the Rakai district, Uganda; (ii) Sweden; and (iii) the USA. For all local networks but one, our interval estimates of the scaling parameters are in the range where epidemic thresholds exist. The estimate of the exponent for male networks in the USA is close to 3, but the preferential attachment model is a very poor fit to these data. We conclude that the epidemic thresholds implied by this model exist in both single-sex and two-sex epidemic model formulations. A strong conclusion that we derive from these results is that public health interventions aimed at reducing the transmissibility of STD pathogens, such as implementing condom use or high-activity anti-retroviral therapy, have the potential to bring a population below the epidemic transition, even in populations exhibiting large degrees of behavioural heterogeneity.

Female↗
PubMed2004

A neutral model of transcriptome evolution.

Microarray technologies allow the identification of large numbers of expression differences within and between species. Although environmental and physiological stimuli are clearly responsible for changes in the expression levels of many genes, it is not known whether the majority of changes of gene expression fixed during evolution between species and between various tissues within a species are caused by Darwinian selection or by stochastic processes. We find the following: (1) expression differences between species accumulate approximately linearly with time; (2) gene expression variation among individuals within a species correlates positively with expression divergence between species; (3) rates of expression divergence between species do not differ significantly between intact genes and expressed pseudogenes; (4) expression differences between brain regions within a species have accumulated approximately linearly with time since these regions emerged during evolution. These results suggest that the majority of expression differences observed between species are selectively neutral or nearly neutral and likely to be of little or no functional significance. Therefore, the identification of gene expression differences between species fixed by selection should be based on null hypotheses assuming functional neutrality. Furthermore, it may be possible to apply a molecular clock based on expression differences to infer the evolutionary history of tissues.

Animals↗
PubMed2005

Classification using functional data analysis for temporal gene expression data.

MOTIVATION: Temporal gene expression profiles provide an important characterization of gene function, as biological systems are predominantly developmental and dynamic. We propose a method of classifying collections of temporal gene expression curves in which individual expression profiles are modeled as independent realizations of a stochastic process. The method uses a recently developed functional logistic regression tool based on functional principal components, aimed at classifying gene expression curves into known gene groups. The number of eigenfunctions in the classifier can be chosen by leave-one-out cross-validation with the aim of minimizing the classification error. RESULTS: We demonstrate that this methodology provides low-error-rate classification for both yeast cell-cycle gene expression profiles and Dictyostelium cell-type specific gene expression patterns. It also works well in simulations. We compare our functional principal components approach with a B-spline implementation of functional discriminant analysis for the yeast cell-cycle data and simulations. This indicates comparative advantages of our approach which uses fewer eigenfunctions/base functions. The proposed methodology is promising for the analysis of temporal gene expression data and beyond. AVAILABILITY: MATLAB programs are available upon request.

Algorithms↗
PubMed1997

Tumor dormancy and cell signaling. V. Regrowth of the BCL1 tumor after dormancy is established.

The majority of BALB/c mice immunized with the BCL1 lymphoma-derived idiotype (Id+) IgM and subsequently challenged with BCL1 tumor cells develop a state of tumor dormancy. The vast majority of dormant lymphoma cells are in cell cycle arrest, but there are also residual replicating cells. In the present studies, we attempted to define features of both the dormant lymphoma cells and the host that lead to escape from dormancy. Escape from dormancy occurs at a steady rate over a 2-year period, suggesting that it is a stochastic process. We found that, in the majority of mice, escape was due to the emergence of genetic variants that were no longer susceptible to the anti-Id-mediated induction of dormancy. Ten percent of these variants were Id-; the remainder were Id+ but could grow in the presence of anti-Id antibodies, suggesting that there were mutations in molecules involved in one or more mIg-mediated negative-signaling pathways. In two of five such escapees, alterations in either Syk, HS1, and/or Lyn were observed. In a small percentage of mice, a low titer of circulating anti-Id antibody before tumor challenge correlated with a subsequent, more rapid loss of dormancy.

Adaptor Proteins, Signal Transducing↗
PubMed1993

Autoregressive modeling of epicardial electrograms during ventricular fibrillation.

During ventricular fibrillation (VF), electrograms from bipolar epicardial electrodes generally appear to have little organization or structure. We sought to identify any well defined organization or structure in these signals by determining if they could be modeled as an autoregressive stochastic process with a white noise excitation during the short time period (6.5-8 s) typically used by automatic implantable defibrillators. The autoregressive model is then used to synthesize VF signals using a white noise excitation with the same probability distribution function as the estimated excitation determined from the autoregressive model for that particular true VF episode. Both the original and ten synthesized VF signals for each patient are then compared using root mean square (rms) amplitude, the number of zero crossings per second, the amplitude distribution of the signals, the rate, and percent variation of rate. The results of examining the synthesized VF waveforms indicate that the rms amplitudes are similar to the true VF waveforms. While the synthesized VF signals had higher rate, more regular RR intervals, more zero crossings per second, and spent less time at baseline than the VF signal from which they were generated, these differences are generally not significant (p > or = 0.05). The use of such synthesized VF signals may allow more thorough testing of VF detection algorithms than is possible with the present limited libraries of human VF recordings.

Defibrillators, Implantable↗
PubMed2001

Forecasting herd structure and milk production for production risk management.

Substantial increases in milk price volatility have resulted from changes in federal dairy policies. For a dairy farm, however, monthly gross milk receipts are a function of unit price and quantity produced. Both can vary substantially over time. Therefore, to be effective, risk management strategies must address milk and input price volatility (price risk management) and fluctuations in milk production per cow and cow numbers (production risk management). Herd milk production through time can be modeled as a discrete stochastic process using finite Markov chains. Cows at time t = 0 are assigned to homogeneous production cells in four-dimensional arrays with coordinates determined by parity (1, 2, 3), week in milk (1, ..., 104), pregnancy status (0, 1), and week pregnant (1, ..., 40). The processes of aging, pregnancy, involuntary cull, voluntary cull, abortion, dry-off, and freshening from week i-1 to week i are accounted for, using nonstationary transition probabilities. Bayesian estimates of transition probabilities are derived from historical herd data, assuming that individual outcomes are from Bernoulli distributions. The values of parameters theta(i) for the Bernoulli distributions are unknown but have prior distributions that follow beta distributions with parameters alpha(i) and beta(i) estimated from historical data. Herd observations are then used to generate posterior distributions of theta(i), also from beta distributions. Projecting from one week to the next is accomplished by moving virtual animals from one production cell to the next based on the transition probability assigned to that path. Summing production estimates and variances of all independent cells provides for an expected herd production with an associated variance. As expected, the forecast variance increases with time, reflecting increased uncertainty of distant projections. Model validation presents an interesting problem because future observations used for validation are under human control and are not independent of the forecast.

Animal Husbandry↗
PubMed2005

A stochastic model to analyze clonal data on multi-type cell populations.

This article presents a stochastic model designed to analyze experimental data on the development of cell clones composed of two (or more) distinct types of cells. The proposed model is an extension of the traditional multi-type Bellman-Harris branching stochastic process allowing for nonidentical time-to-transformation distributions defined for different cell types. A simulated pseudo likelihood method has been developed for the parametric statistical inference from experimental data on cell clones under the proposed model. The method uses simulation-based approximations of the means and the variance-covariance matrices of cell counts. The proposed estimator for the vector of unknown parameters is strongly consistent and asymptotically normal under mild regularity conditions, while its variance-covariance matrix is estimated by the parametric bootstrap. A Monte Carlo Wald test is proposed for the test of hypotheses. Finite sample properties of the estimator have been studied by computer simulations. The model and associated methods of parametric inference have been applied to the analysis of proliferation and differentiation of cultured O-2A progenitor cells that play a key role in the development of the central nervous system. It follows from this analysis that the time to division of the progenitor cell and the time to its differentiation (into an oligodendrocyte) are not identically distributed. This biological finding suggests that a molecular event determining the type of cell transformation is more likely to occur at the start rather than at the end of the mitotic cycle.

Biometry↗
PubMed2005

An episode-based framework for analyzing health care expenditures: an application of reward renewal models.

OBJECTIVE: To illustrate an episode-based framework for analyzing health care expenditures based on reward renewal models, a stochastic process used in engineering for describing processes that cycle on and off with "rewards" (or costs) occurring at the end of each cycle. DATA SOURCES/STUDY SETTING: Data used in the illustration were collected as part of an evaluation of a national initiative to improve mental health services for children and youth. Participants were enrolled in a longitudinal study at a demonstration site and in a comparison community between 1997 and 1999. The illustration involves analyses of mental health expenditures at the two sites and of the dynamics of service use behind those expenditures. DATA COLLECTION/EXTRACTION METHODS: Services data were derived from management information systems as well as patient records at inpatient facilities in the two communities. These data cover services received between 1997 and 2003. The analysis focuses on the year following study entry. PRINCIPAL FINDINGS: Between-site differences in expenditures reflect complex between-site differences in the timing of service use. In particular, children at the demonstration stayed in treatment longer but were less likely to return for treatment later. In contrast, children at the comparison site experienced substantially less continuity of care. Costs per day of treatment within an episode were comparable at the two sites. CONCLUSIONS: Reward renewal models offer a promising means for integrating research on service episodes and the dynamics of service use with that on health care expenditures.

Adolescent↗