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PubMed1992

Extending the stochastic two-stage model of carcinogenesis to include self-regulation of the nonmalignant cell population.

One of the challenges of introducing greater biological realism into stochastic models of cancer induction is to find a way to represent the homeostatic control of the normal cell population over its own size without complicating the analysis too much to obtain useful results. Current two-stage models of carcinogenesis typically ignore homeostatic control. Instead, a deterministic growth path is specified for the population of "normal" cells, while the population of "initiated" cells is assumed to grow randomly according to a birth-death process with random immigrations from the normal population. This paper introduces a simple model of homeostatically controlled cell division for mature tissues, in which the size of the nonmalignant population remains essentially constant over time. Growth of the nonmalignant cell population (normal and initiated cells) is restricted by allowing cells to divide only to fill the "openings" left by cells that die or differentiate, thus maintaining the constant size of the nonmalignant cell population. The fundamental technical insight from this model is that random walks, rather than birth-and-death processes, are the appropriate stochastic processes for describing the kinetics of the initiated cell population. Qualitative and analytic results are presented, drawn from the mathematical theories of random walks and diffusion processes, that describe the probability of spontaneous extinction and the size distribution of surviving initiated populations when the death/differentiation rates of normal and initiated cells are known. The constraint that the nonmalignant population size must remain approximately constant leads to much simpler analytic formulas and approximations, flowing directly from random walk theory, than in previous birth-death models.(ABSTRACT TRUNCATED AT 250 WORDS)

Cell Death↗
PubMed1999

Models for forecasting chronic disease processes in adult and elderly populations: effects of stochasticity.

BACKGROUND: Forecasting the population health burden of chronic diseases requires models consistent with the relation, over time and in an uncertain environment, of risk factors and diseases at the individual level. There is now sufficient longitudinal data, and scientific understanding, of some chronic diseases to construct detailed process-models to better predict their population health burden and more realistically describe the effects of interventions. A crucial clement in constructing models is the way in which stochastic influences are described, e.g. are they allowed to interact over time with deterministic model features? METHODS: A review of statistical and forecasting models aimed to establish what ancillary data and scientific insights are necessary to describe multivariate stochastic health processes and their response to interventions. For circulatory diseases and cancer there exists sufficient longitudinal data and biological insight to construct stochastic multivariate process models. For other diseases, biological knowledge is less complete and there are fewer data sets where multiple risk factors are assessed longitudinally. Forecasting models for those diseases will then rely more heavily on theoretical assumptions about disease behaviour.

Chronic Disease↗
PubMed1988

Number of visits to a state in a random walk, before absorption, and related topics.

Equations are derived for the probability of n visits to a given state during the course of a random walk on a finite diagram that starts from a specified state and ends with absorption. By deriving the mean number of visits in two different ways, certain conjectures or theorems are encountered that connect properties of different but related diagrams in an interesting way. Other subjects included are (i) number of one-way transitions between two states before absorption; (ii) time dependence of the rate of cycle completions before absorption; and (iii) the relation of this work to the "return process" of Karlin and Taylor.

Absorption↗
PubMed1992

Applicability of the convection-diffusion mechanism for modeling migration of 137Cs and 90Sr in the soil.

The convection-diffusion equation is analyzed as a basis for modeling the migration of radionuclides. To describe the experimental data adequately within the framework of the diffusion-convection equation, it is necessary to introduce migration parameters which increase as the radionuclides penetrate further down through the soil layer and decrease as the observation time lengthens. The assumption that sorption processes in the migration of 137Cs and 90Sr are linear seems to be unjustified. The stochastic model helps us to overcome the main problems of the diffusion-convection approach, but it needs to be tested on a wider range of experimental material.

Cesium Radioisotopes↗
PubMed1999

A processive single-headed motor: kinesin superfamily protein KIF1A.

A single kinesin molecule can move "processively" along a microtubule for more than 1 micrometer before detaching from it. The prevailing explanation for this processive movement is the "walking model," which envisions that each of two motor domains (heads) of the kinesin molecule binds coordinately to the microtubule. This implies that each kinesin molecule must have two heads to "walk" and that a single-headed kinesin could not move processively. Here, a motor-domain construct of KIF1A, a single-headed kinesin superfamily protein, was shown to move processively along the microtubule for more than 1 micrometer. The movement along the microtubules was stochastic and fitted a biased Brownian-movement model.

Adenosine Triphosphate↗
PubMed2001

Behavioral stochastic resonance: how a noisy army betrays its outpost.

Juvenile paddlefish prey upon single zooplankton by detecting a weak electric signature resulting from its feeding and swimming motions. Moreover, it has recently been shown that paddlefish make use of stochastic resonance near the threshold for prey detection: a process termed behavioral stochastic resonance. But this process depends upon an external source of electric noise. A swarm of plankton, for example, Daphnia, can provide this noise. Assuming that juvenile paddlefish attack single Daphnia as outliers in the vicinity of the swarm, making use of noise from the swarm, we calculate the spatial distribution of the average phase locking period for the subthreshold signals acting at the paddlefish rostrum. Numeric evaluation of analytic formulas supports the notion of a noise-induced widening of the capture area quantitatively.

Algorithms↗
PubMed2000

Early HIV infection in vivo: branching-process model for studying timing of immune responses and drug therapy.

We propose a stochastic, branching-process model of early events in vivo in human or simian immunodeficiency virus (HIV or SIV) infection and study the influence that the time of appearance of virus-specific antibodies or cytotoxic cells, or of administration of antiretroviral drugs, has on the probability of progression to a chronic infection. In some biological scenarios, our model predicts that a few days' delay in response or intervention would make little difference, while in others it would be highly deleterious. We show that prophylactic efficacy does not require perfect efficiency at neutralizing infectious virus. Data from a trial of PMPA, a potent antiretroviral drug, as post-exposure therapy for SIV infection in macaques, reported by C.-C. Tsai, P. Emau, K.E. Follis, T.W. Beck, R. E. Beneveniste, N. Bischofberger, J.D. Lifson, W.R. Morton (J. Virol. 72 (1998) 4265), provides a test of the model. We show that their observations are consistent with a branching-process without invoking supplementary viral- or host-variability. Finally, most animal trials of antiviral drugs or vaccines use very high viral inoculums; our model demonstrates that in such experiments we risk greatly underestimating the efficacy of these agents.

Adenine↗
PubMed2002

Wavelet analysis of nonequilibrium ionic currents in human heart sodium channel (hH1a).

Nonequilibrium response spectroscopy (NRS), the technique of using rapidly fluctuating voltage pulses in the study of ion channels, is applied here. NRS is known to drive an ensemble of ion channels far from equilibrium where, it has been argued, new details of ion channel kinetics can be studied under nonequilibrium conditions. In this paper, a single-pulse NRS technique with custom-designed waveforms built from wavelets is used. The pulses are designed to produce different responses from two competing models of a human heart isoform of the sodium channel (hH1a). Experimental data using this new type of pulses are obtained through whole-cell recordings from mammalian cells (HEK 293). Wavelet analysis of the model response and the experimental data is introduced to show how these NRS pulses can aid in distinguishing the better of the two models and thus introduces another important application of this new technique.

Cell Line↗
PubMed1986

The Markov process as a general method for nonparametric analysis of right-censored medical data.

The product limit method of Kaplan and Meier for estimating survival functions and the logrank test of Mantel are widely employed for analysis of longitudinal medical data. Developed for analysis of one-time events such as death, survival analysis is also commonly adapted to more complex states such as loss of vision or cancer remission by restricting analysis to first occurrences. The nonparametric discrete time nonhomogeneous Markov process is proposed as a better model for any applications of the latter type. This simple stochastic model allows for an arbitrary number of possible states and for transitions in any direction. Maximum likelihood estimators are easily computed for the stochastic model and are identical to the product-limit estimates in the special case represented by the Kaplan-Meier model. The logrank test extends to evaluation of differences between populations with respect to any specified transition.

Actuarial Analysis↗
PubMed2005

Noise-induced cooperative behavior in a multicell system.

MOTIVATION: All cell components exhibit intracellular noise on account of random births and deaths of individual molecules, and extracellular noise because of environment perturbations. Gene regulation in particular, is an inherently noisy process with transcriptional control, alternative splicing, translation, diffusion and chemical modification reactions, all of which involve stochastic fluctuations. Such stochastic noises may not only affect the dynamics of the entire system but may also be exploited by living organisms to actively facilitate certain functions, such as cooperative behavior and communication. RESULTS: We have provided a general model and an analytic tool to examine the cooperative behavior of a multicell system with both intracellular and extracellular stochastic fluctuations. A multicell system with a synthetic gene network is adopted to demonstrate the effects of noises and coupling on collective dynamics. These results establish not only a theoretical foundation but also a quantitative basis for understanding essential roles of noises on cooperative dynamics, such as synchronization and communication among cells.

Adaptation, Physiological↗
PubMed2005

Encoding frequency modulation to improve cochlear implant performance in noise.

Different from traditional Fourier analysis, a signal can be decomposed into amplitude and frequency modulation components. The speech processing strategy in most modern cochlear implants only extracts and encodes amplitude modulation in a limited number of frequency bands. While amplitude modulation encoding has allowed cochlear implant users to achieve good speech recognition in quiet, their performance in noise is severely compromised. Here, we propose a novel speech processing strategy that encodes both amplitude and frequency modulations in order to improve cochlear implant performance in noise. By removing the center frequency from the subband signals and additionally limiting the frequency modulation's range and rate, the present strategy transforms the fast-varying temporal fine structure into a slowly varying frequency modulation signal. As a first step, we evaluated the potential contribution of additional frequency modulation to speech recognition in noise via acoustic simulations of the cochlear implant. We found that while amplitude modulation from a limited number of spectral bands is sufficient to support speech recognition in quiet, frequency modulation is needed to support speech recognition in noise. In particular, improvement by as much as 71 percentage points was observed for sentence recognition in the presence of a competing voice. The present result strongly suggests that frequency modulation be extracted and encoded to improve cochlear implant performance in realistic listening situations. We have proposed several implementation methods to stimulate further investigation. Index Terms-Amplitude modulation, cochlear implant, fine structure, frequency modulation, signal processing, speech recognition, temporal envelope.

Algorithms↗
PubMed1996

A model of stochastic activity of neurone in some types of Gaussian input processes.

A new approach to computer modelling of neuronal stochastic activity is described. The output dynamic activity which depends on the types and the number of input synapses, weights of the synaptic efficacy, the absolute refractory phase duration and threshold level is evaluated on this model in some types of Gaussian input processes. The behaviour of this model for one excitatory and one inhibitory synapse is described in dependence on the changes of excitation weight. The neuronal behaviour presented depends on the number of interspike intervals and the excitation weight and interspike interval density distribution. A novel concept of the e-curve is being introduced, which shows the dependence of the number of output interspike intervals on the weight of excitation on a stable inhibition level, the absolute refractory phase value and the threshold level. The properties of e-curves are discussed. Furthermore, examples of transformations of input stochastic processes are mentioned from the aspect of density distribution changes of interspike intervals.

Computer Simulation↗
PubMed1998

A nonparametric approach to a survival study with surrogate endpoints.

A nonparametric estimator for the joint distribution of a survival time and surrogate response time, which may occur earlier during follow-up, is presented. In the absence of the surrogate response variable, the estimator reduces to the Kaplan Meier nonparametric estimator for the survival time alone. The estimator derived in this paper is done so in a particular novel way using an exchangeable process (reinforced random walks) to model individual observations. The methodology introduced in the paper is readily extended to modelling multiple state processes.

Humans↗
PubMed2001

Modeling spiking behavior of neurons with time-dependent Poisson processes.

Three kinds of interval statistics, as represented by the coefficient of variation, the skewness coefficient, and the correlation coefficient of consecutive intervals, are evaluated for three kinds of time-dependent Poisson processes: pulse regulated, sinusoidally regulated, and doubly stochastic. Among these three processes, the sinusoidally regulated and doubly stochastic Poisson processes, in the case when the spike rate varies slowly compared with the mean interval between spikes, are found to be consistent with the three statistical coefficients exhibited by data recorded from neurons in the prefrontal cortex of monkeys.

Animals↗
PubMed2006

The evolutionary emergence of pandemic influenza.

Pandemic influenza remains a serious public health threat and the processes involved in the evolutionary emergence of pandemic influenza strains remain incompletely understood. Here, we develop a stochastic model for the evolutionary emergence of pandemic influenza, and use it to address three main questions. (i) What is the minimum annual number of avian influenza virus infections required in humans to explain the historical rate of pandemic emergence? (ii) Are such avian influenza infections in humans more likely to give rise to pandemic strains if they are driven by repeated cross-species introductions, or by low-level transmission of avian influenza viruses between humans? (iii) What are the most effective interventions for reducing the probability that an influenza strain with pandemic potential will evolve? Our results suggest that if evolutionary emergence of past pandemics has occurred primarily through viral reassortment in humans, then thousands of avian influenza virus infections in humans must have occurred each year for the past 250 years. Analyses also show that if there is epidemiologically significant variation among avian influenza virus genotypes, then avian virus outbreaks stemming from repeated cross-species transmission events result in a greater likelihood of a pandemic strain evolving than those caused by low-level transmission between humans. Finally, public health interventions aimed at reducing the duration of avian virus infections in humans give the greatest reduction in the probability that a pandemic strain will evolve.

Animals↗
PubMed2001

Effects of correlated and independent noise on signal processing in neuronal systems.

Stochastic resonance has recently received considerable attention demonstrating that noise can play a constructive role in signal processing. We investigate the effects of input noise on sensory processing via numerical simulation when they are independent of each other or spatially correlated in a globally coupled neuronal network. The network exhibits a coherent behavior in the absence of stimulation. Such ongoing activity has a remarkable influence on neuronal responses to stimuli. In the presence of a subthreshold periodic signal, the activity averaged over neurons can convey precise information about the stimulus in the case of independent noise. On the other hand, when the noise is correlated among the neurons, the average response is nearly as noisy and variable as the responses of the individual neurons. Thus, the spatially correlated noise diminishes the beneficial effects of pooling, although it can evoke synchronous firings of neurons. These suggest that response variability in cortical activity may be closely related to the correlation in input noise.

Action Potentials↗
PubMed2006

Field theories and exact stochastic equations for interacting particle systems.

We consider the dynamics of interacting particles with reaction and diffusion. Starting from the underlying discrete stochastic jump process we derive a general field theory describing the dynamics of the density field, which we relate to an exact stochastic equation on the density field. We show how our field theory maps onto the original Doi-Peliti formalism, allowing us to clarify further the issue of the "imaginary" Langevin noise that appears in the context of reaction-diffusion processes. Our procedure applies to a wide class of problems and is related to large deviation functional techniques developed recently to describe fluctuations of nonequilibrium systems in the hydrodynamic limit.

Journal Article↗