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At least 973 records · Page 54Linked to original sources
PubMed1998

Molecular evolution modeled as a fractal Poisson process in agreement with mammalian sequence comparisons.

The fractal doubly stochastic Poisson process (FDSPP) model of molecular evolution, like other doubly stochastic Poisson models, agrees with the high estimates for the index of dispersion found from sequence comparisons. Unlike certain previous models, the FDSPP also predicts a positive geometric correlation between the index of dispersion and the mean number of substitutions. Such a relationship is statistically proven herein using comparisons between 49 mammalian genes. There is no characteristic rate associated with molecular evolution according to this model, but there is a scaling relationship in rates according to a fractal dimension of evolution. The FDSPP is a suitable replacement for the homogeneous Poisson process in tests of the lineage dependence of rates and in estimating confidence intervals for divergence times. As opposed to other fractal models, this model can be interpreted in terms of Darwinian selection and drift.

Animals↗
PubMed1986

On a stochastic integral of a branching process.

This paper is concerned with the properties of a stochastic integral which arises in the study of a modified Markov branching process. Explicit expressions are found for the mean and the limit distribution of the integral.

Animals↗
PubMed1997

Threshold parameters for a simple stochastic partnership model of sexually transmitted diseases formulated as a two-type CMJ process.

A simple stochastic model describing an epidemic of a sexually transmitted disease, accommodating the formation and dissolution of partnerships, was formulated within a two-type Crump-Mode-Jagers (CMJ) process in continuous time. A submodel, describing the formation and dissolution of partnerships, was formulated in terms of a semi-Markov process with a finite state space and death as an absorbing state. This model was then linked to a two-type CMJ process through offspring distributions. Numerical values of threshold parameters greater than one suggests that either the epidemic dies out with a probability significantly different form zero or it spreads explosively in the population.

Female↗
PubMed2005

AgentCell: a digital single-cell assay for bacterial chemotaxis.

MOTIVATION: In recent years, single-cell biology has focused on the relationship between the stochastic nature of molecular interactions and variability of cellular behavior. To describe this relationship, it is necessary to develop new computational approaches at the single-cell level. RESULTS: We have developed AgentCell, a model using agent-based technology to study the relationship between stochastic intracellular processes and behavior of individual cells. As a test-bed for our approach we use bacterial chemotaxis, one of the best characterized biological systems. In this model, each bacterium is an agent equipped with its own chemotaxis network, motors and flagella. Swimming cells are free to move in a 3D environment. Digital chemotaxis assays reproduce experimental data obtained from both single cells and bacterial populations.

Algorithms↗
PubMed2001

Stochastic radial basis functions.

Stochastic signal processing can implement gaussian activation functions for radial basis function networks, using stochastic counters. The statistics of neural inputs which control the increment and decrement operations of the counter are governed by Bernoulli distributions. The transfer functions relating the input and output pulse probabilities can closely approximate gaussian activation functions which improve with the number of states in the counter. The means and variances of these gaussian approximations can be controlled by varying the output combinational logic function of the binary counter variables.

Binomial Distribution↗
PubMed2001

Physiology of myeloproliferation.

The current dogma about polycythemia vera (PV) is that one or more genetic mutations in a hematopoietic stem cell (HSC) cause abnormal proliferation and differentiation of the progeny of that stem cell. This model ignores two fundamental characteristics of biologic systems that must be considered if regulation is to be understood: first, at a molecular level, biochemical processes are intrinsically stochastic; and second, ontogeny and hematopoiesis are branching processes-with one cell dividing into two cells, and so on. Why is it important to add an understanding of the stochastic, branching nature of HSC function to a description of the genes and gene products only? Why not just say one understands the regulation of normal hematopoiesis, or PV, when all the genes and gene products actively transcribed have been identified? The answer is that within a branching, stochastic process, one mutation can cause more than one outcome (phenotype) in the future. There will be one or more related outcomes that will be highly likely and others that will be less likely. Although most patients will have similar phenotypes, some will differ, but not because they have different underlying mutations. Mathematics will probably play an increasingly important role in describing and analyzing the regulation that occurs as the genetic program of HSC is expressed within a clone over time. Semin Hematol 38(suppl 2):5-9.

Clone Cells↗
PubMed1986

[Eye movements in sleep: towards a model].

The study of the REM-process by means of the oculomotor frequencies has shown that it is a stochastic point process. Therefore, the techniques utilized to quantify the time-dependency of this process were used. The structure of occurrence of REM's quantified by transition probability matrixes evidenced a two-state first order semi-Markov process. The oculo-motor configurations of REM-sleep revealed two independent entities, their number and their relative frequencies. This conclusion was used as a working hypothesis for the Spacelab 1 sleep-recording experiment in zero-gravity. The results confirmed the underlying hypothesis.

Adolescent↗
PubMed1990

Spatial and vacancy effects on the stabilising mechanisms of two-dimensional free growth.

A Monte-Carlo simulation technique is introduced to study the spatial considerations of cellular distribution that affect the overall asynchronous process of population growth. The stochastic nature of cellular characteristics such as mitotic time, loss rate and direction of growth is considered. The fluctuation of these values from one generation to the next and from one cell to the other, is illustrated. Cells are assumed to grow in a two-dimensional honeycomb-like network such that a central cell is always surrounded with six equally distant sites. The modes of cellular growth are controlled mainly and simply by the existence of a definite number of neighbouring vacancies. An IBM-compatible PC-AT computer was used and a program written in Pascal is employed to simulate and follow up the growth of a single stem cell in a 40,000-sites network. The results of the proposed stochastic model illustrate the importance of the spatial interaction among growing cellular modes such that vacancies act as local sensors for a negative feedback mechanism regulating the overall growth pattern. The role of the resting mode (G0) in stabilising the overall growth pattern is discussed.

Cell Count↗
PubMed1997

Estimation of the diffusion-limited rate of microtubule assembly.

Microtubule assembly is a complex process with individual microtubules alternating stochastically between extended periods of assembly and disassembly, a phenomenon known as dynamic instability. Since the discovery of dynamic instability, molecular models of assembly have generally assumed that tubulin incorporation into the microtubule lattice is primarily reaction-limited. Recently this assumption has been challenged and the importance of diffusion in microtubule assembly dynamics asserted on the basis of scaling arguments, with tubulin gradients predicted to extend over length scales exceeding a cell diameter, approximately 50 microns. To assess whether individual microtubules in vivo assemble at diffusion-limited rates and to predict the theoretical upper limit on the assembly rate, a steady-state mean-field model for the concentration of tubulin about a growing microtubule tip was developed. Using published parameter values for microtubule assembly in vivo (growth rate = 7 microns/min, diffusivity = 6 x 10(-12) m2/s, tubulin concentration = 10 microM), the model predicted that the tubulin concentration at the microtubule tip was approximately 89% of the concentration far from the tip, indicating that microtubule self-assembly is not diffusion-limited. Furthermore, the gradients extended less than approximately 50 nm (the equivalent of about two microtubule diameters) from the microtubule tip, a distance much less than a cell diameter. In addition, a general relation was developed to predict the diffusion-limited assembly rate from the diffusivity and bulk tubulin concentration. Using this relation, it was estimated that the maximum theoretical assembly rate is approximately 65 microns/min, above which tubulin can no longer diffuse rapidly enough to support faster growth.

Animals↗
PubMed2005

Regulation of odorant receptors: one allele at a time.

The odorant receptors (ORs) make up the largest gene family in mammals. Each olfactory sensory neuron chooses just one OR from the more than 1000 possibilities encoded in the genome and transcribes it from just one allele. This process generates great neuronal diversity and forms the basis for the development and logic of the olfactory circuit between the nose and the brain. The mechanism behind this monoallelic regulation has been the subject of intense speculation and increasing experimental investigation, yet remains enigmatic. Recent genetic experiments have brought the outlines of the process into sharper relief, identifying a feedback mechanism in which the first odorant receptor expressed, generates a signal that stabilizes its choice, thus maintaining singular selection. In the absence of this signal, the olfactory neuron re-enters the selection process and switches to choose an alternate OR. Irreversible genetic changes in the nuclei of olfactory neurons do not accompany OR selection, which must therefore be initiated by an epigenetic process that may involve a stochastic mechanism.

Alleles↗
PubMed2004

Stochastic resonance and sensory information processing: a tutorial and review of application.

OBJECTIVE: To review the stochastic resonance phenomena observed in sensory systems and to describe how a random process ('noise') added to a subthreshold stimulus can enhance sensory information processing and perception. RESULTS: Nonlinear systems need a threshold, subthreshold information bearing stimulus and 'noise' for stochastic resonance phenomena to occur. These three ingredients are ubiquitous in nature and man-made systems, which accounts for the observation of stochastic resonance in fields and conditions ranging from physics and engineering to biology and medicine. The stochastic resonance paradigm is compatible with single-neuron models or synaptic and channels properties and applies to neuronal assemblies activated by sensory inputs and perceptual processes as well. Here we review a few of the landmark experiments (including psychophysics, electrophysiology, fMRI, human vision, hearing and tactile functions, animal behavior, single/multiunit activity recordings). Models and experiments show a peculiar consistency with known neuronal and brain physiology. A number of naturally occurring 'noise' sources in the brain (e.g. synaptic transmission, channel gating, ion concentrations, membrane conductance) possibly accounting for stochastic resonance phenomena are also reviewed. Evidence is given suggesting a possible role of stochastic resonance in brain function, including detection of weak signals, synchronization and coherence among neuronal assemblies, phase resetting, 'carrier' signals, animal avoidance and feeding behaviors. CONCLUSIONS: Stochastic resonance is a ubiquitous and conspicuous phenomenon compatible with neural models and theories of brain function. The available evidence suggests cautious interpretation, but justifies research and should encourage neuroscientists and clinical neurophysiologists to explore stochastic resonance in biology and medical science.

Animals↗
PubMed2002

Process-dissociation procedure: a testable model for considering assumptions about the stochastic relation between consciously controlled and automatic processes.

This paper presents an extension of the process-dissociation procedure with wordstem completion, which makes possible the measurement of the stochastic relationship between consciously controlled and automatic processes. By means of an indirect wordstem completion test, the conditional probabilities of conscious remembering with and without automatic processes can be successfully determined. A multinomial model for the evaluation of this extended process-dissociation procedure is presented. This model makes the distinction between voluntary and involuntary conscious memory processes possible and has been applied to two experiments discussed in this paper. The results show that the assumption of stochastic independence is often violated, albeit not as strongly as predicted by the redundancy or exclusivity model variants. Two conscious processes were found, voluntary and involuntary conscious memory processes, each with a different probability of occurrence.

Attention↗
PubMed1999

Extinction in Fragmented Habitats Predicted from Stochastic Birth-death Processes with Density Dependence.

Habitat loss, the reduction of the habitat area available, is known to greatly reduce resident species' expected time to extinction. This process is widely recognized, if not adequately understood or quantified except in very simple models. However, it is not well understood how the time to extinction will change if the remaining habitat is distributed across a set of smaller, isolated patches, instead of being left in one single, continuous tract. The effect of habitat fragmentation on population persistence under demographic stochasticity has not been resolved. Specifically, it is not known whether a single large population will persist longer than an aggregate set of several smaller populations (with the same total size). Analytical studies of birth-death processes typically report the mean time to extinction for a single population as a function of the maximum population size, but omit higher moments. To estimate the overall persistence time, or the probability of extinction as a function of time, for a set of small populations, the entire distribution of extinction times must be known for a single population of each size. Knowing all the moments of the distribution of extinction times is not adequate, unless one can reconstruct the distribution from them. Here I analyse stochastic birth-death processes with linear density dependence in per capita birth and death rates, and obtain analytical expressions and numerical solutions for the distribution of extinction times in both subdivided and continuous populations. This is a single-species model that deals with demographic stochasticity only, and assumes independence of extinction events in different patches. These assumptions are relaxed elsewhere. Habitat fragmentation, even without any loss of overall area, has a great and detrimental effect on the persistence time of populations across all temporal and spatial scales. The effect is similar across spatial scales, but shifted in time-larger populations take longer to go extinct but the extinction risk relative to that of a smaller or more fragmented population is the same across spatial scales for the available habitat. Copyright 1999 Academic Press.

Journal Article↗
PubMed1995

Parkinson's disease affects automatic and spares intentional verbal learning. A stochastic approach to explicit learning processes.

We studied word list and paired associates learning in patients with idiopathic Parkinson's disease and normal controls by means of a two-stage stochastic model, which allows independent measurements of encoding, storage and retrieval abilities. We preliminarily ascertained that the model components were both sufficient and necessary to account for the overall performance of the subjects, and then compared the learning abilities between the two groups. Parkinson's disease patients were selectively impaired in identifying well-known engrams, for which learning is superfluous, and in automatic retrieval, namely in abilities that do not need attentional effort. By contrast, they were unimpaired in encoding and intentional retrieval, which require a purposeful effort. The automatic-voluntary dissociation of Parkinson's disease patients' motor behaviour is, therefore, paralleled by some features of their memory performance.

Aged↗
PubMedDate not supplied

An improved hybrid HIV/AIDS model geared to specific public health data and decision making.

An improved version of a previously described compartmental dynamic model for the spread of the HIV virus and AIDS is presented in which the estimation of key parameters depends entirely on the use of good public health data. This means that practical applications to specific regions, using only local data, can be of great value to public health decision makers dealing with local problems. It is assumed that scientific support is available within an interdisciplinary operations research context. The improved model incorporates physicians' delays in reporting AIDS incidence, additional cases revealed by death certificate analysis, and a high-risk core group of HIV positives involving a limited residence time, followed by a low-risk group with extended residence, both groups leading to AIDS cases. The model is hybrid in character in the sense that the HIV infection process with large numbers is deterministic while the incubation process with small numbers initially is stochastic. Applications have been made to Switzerland. Key parameters estimated include, in particular, the actual sizes of the original core groups for gay men and intravenous drug users. Current numbers of circulating HIV positives are also obtained.

Acquired Immunodeficiency Syndrome↗
PubMed2003

Reproduction and survival in Mediterranean fruit flies: a "protein and energy" free radical model of aging.

We propose a "protein and energy" free radical model of aging that predicts patterns of survival and fertility curves for Mediterranean fruit flies. Mathematical and simulation models of individual physiological processes were constructed in terms of stochastic differential equations. The free radical theory of aging was used as a basis for construction of the model and was extended to describe the dynamics of the protein and energy balance in the functioning organism, including the concept of a maximum capacity for energy production. We fit the model to observed patterns of survival and fertility in flies given the basic diet schemes used in respective experiments. Age patterns of fertility and survival were predicted under various diet scenarios using the model, revealing that the predictions of the model are in good agreement with experimental data.

Aging↗
PubMed2005

Coupling of two motor proteins: a new motor can move faster.

We study the effect of a coupling between two motor domains in highly processive motor protein complexes. A simple stochastic discrete model, in which the two parts of the protein molecule interact through some energy potential, is presented. The exact analytical solutions for the dynamic properties of the combined motor species, such as the velocity and dispersion, are derived in terms of the properties of free individual motor domains and the interaction potential. It is shown that the coupling between the motor domains can create a more efficient motor protein that can move faster than individual particles. The results are applied to analyze the motion of RecBCD helicase molecules.

DNA↗
PubMed2006

Evolution of the human immunodeficiency virus envelope gene is dominated by purifying selection.

The evolution of the human immunodeficiency virus (HIV-1) during chronic infection involves the rapid, continuous turnover of genetic diversity. However, the role of natural selection, relative to random genetic drift, in governing this process is unclear. We tested a stochastic model of genetic drift using partial envelope sequences sampled longitudinally in 28 infected children. In each case the Bayesian posterior (empirical) distribution of coalescent genealogies was estimated using Markov chain Monte Carlo methods. Posterior predictive simulation was then used to generate a null distribution of genealogies assuming neutrality, with the null and empirical distributions compared using four genealogy-based summary statistics sensitive to nonneutral evolution. Because both null and empirical distributions were generated within a coalescent framework, we were able to explicitly account for the confounding influence of demography. From the distribution of corrected P-values across patients, we conclude that empirical genealogies are more asymmetric than expected if evolution is driven by mutation and genetic drift only, with an excess of low-frequency polymorphisms in the population. This indicates that although drift may still play an important role, natural selection has a strong influence on the evolution of HIV-1 envelope. A negative relationship between effective population size and substitution rate indicates that as the efficacy of selection increases, a smaller proportion of mutations approach fixation in the population. This suggests the presence of deleterious mutations. We therefore conclude that intrahost HIV-1 evolution in envelope is dominated by purifying selection against low-frequency deleterious mutations that do not reach fixation.

Base Sequence↗