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PubMed2002

Multivariate Markov processes for stochastic systems with delays: application to the stochastic Gompertz model with delay.

Using the method of steps, we describe stochastic processes with delays in terms of Markov diffusion processes. Thus, multivariate Langevin equations and Fokker-Planck equations are derived for stochastic delay differential equations. Natural, periodic, and reflective boundary conditions are discussed. Both Ito and Stratonovich calculus are used. In particular, our Fokker-Planck approach recovers the generalized delay Fokker-Planck equation proposed by Guillouzic et al. The results obtained are applied to a model for population growth: the Gompertz model with delay and multiplicative white noise.

Biophysical Phenomena↗
PubMed1994

Modelling of vascular growth processes: a stochastic biophysical approach to embryonic angiogenesis.

In a computer simulation, growth of a capillary network is driven by a stochastic process on a planar hexagonal grid. Starting at a point source, the probabilities for the formation of new capillary elements depend on local biophysical knowledge. This knowledge is mainly derived from the flow theorem of Hagen-Poiseuille and the diameter exponent delta. The hexagonal grid is visualized as being supported by a cylinder or a sphere. An arterial tree results from the adaptive diameter augmentation, and is considered to have limited fractal properties. The dimension of its border, and the time course of growth and of blood pressure are compared with biological data from the chorioallantoic membrane (CAM) of incubated chicken eggs. The model is discussed in view of mechanosensitivity and cell-matrix interactions of endothelial cells, and CAM haemodynamics.

Allantois↗
PubMed1990

A biological and computational model of megakaryocyte development as a stochastic branching process.

The purpose of this paper is to describe a model of megakaryocytopoiesis as a branching process with stochastic processes regulating critical control points of differentiation along the stem cell megakaryocyte platelet axis. Progress of cells through these critical control points are regulated by transitional probabilities, which in turn are regulated by influences such as growth factors. The critical control points include transition of resting megakaryocytic stem cells (CFU-meg) into proliferating stem cells, the cessation of cytokinesis, and the cessation of DNA synthesis. A computerized computational method has been developed for directly fitting the stochastic branching model to colony growth data. The computational model has allowed transitional probabilities to be derived from colony size data. The model provides a unifying explanation for much of the heterogeneity of stages of maturation within populations of megakaryocytes and is fully compatible with historical data supporting the stochastic nature of hematopoietic stem cell regulation and with modern molecular concepts about control of the cell cycle.

Cell Differentiation↗
PubMed1986

Inactivation of macromolecules by ionizing radiation. Deterministic single-hit or stochastic multievent process?

A stochastic theory concerning the radiation inactivation of macromolecules such as enzymes or receptors is elaborated. In contrast with the single-hit theory, which assumes a complete inactivation of the target as the result of one hit, the stochastic theory postulates that the degree of inactivation by one hit is a random variable. This distinguishing feature has been considered in order to give a possible interpretation to the observed effect of temperature on the radiation-sensitivity of enzymes. As a consequence of the progressive inactivation during irradiation, the binding affinity of a ligand for the macromolecule is impaired by irradiation. Although this property might discriminate the stochastic theory from the classical single-hit theory on the basis of a statistical analysis of experimentally obtained data, it is shown that the commonly obtained degree of inaccuracy may render the statistical test non-conclusive.

Ligands↗
PubMed1999

Non-linear optimization of biotechnological processes by stochastic algorithms: application to the maximization of the production rate of ethanol, glycerol and carbohydrates by Saccharomyces cerevisiae.

A non-linear optimization, based on an stochastic multi-start search algorithm, has been applied to the maximization of the production rates of ethanol, glycerol and carbohydrates by Saccharomyces cerevisiae. This optimization is applied to two alternative (non-linear) model representations of the same system, namely the Michaelis-Menten and the generalized mass action forms. We find a complete agreement between the results obtained using both representations. This is, maximization of the ethanol production rate requires modulation of up to six enzymes, while modification of only one enzyme is sufficient to obtain a significant improvement in the production rate of glycerol and carbohydrates. When the results are compared with those previously obtained using an indirect linear optimization method (Torres, N.V., Voit, E.O., González-Alcón, C., Rodríguez, F. 1997. An integrated optimization method for biochemical systems. Description of method and application to ethanol, glycerol and carbohydrate production in S. cerevisiae. Biotechnol. Bioeng. 55(5), 758-772.), we find close agreement between both optimization techniques. Qualitatively, both optimization approaches render the same profile of enzymes to be modulated, while quantitatively, discrepancies arise when the objective function is the maximization of the ethanol production rate. Reasons for such discrepancies and an evaluation of the advantages of each method (linear vs non-linear) are given.

Algorithms↗
PubMedDate not supplied

A multi-nano-dot circuit and structure using thermal-noise-assisted tunneling for stochastic associative processing.

The single-electron circuit and nanostructure described in this paper are designed for stochastic associative processing, which is an expanded version of ordinary associative memory processing. In stochastic associative processing, the association probability of each stored pattern depends on the similarity between the stored pattern and the input pattern. Such unique processing is useful for sequential stochastic association and for clustering for vector quantization. Conventional single-electron circuits operate only at very low temperature for practical junction capacitance (i.e., 30 K for 0.1 aF) because the charging energy in these circuits is directly related to the tunnel junction capacitance. Our multi-nano-dot circuit and structure operate at room temperature with a junction capacitance around 0.1 aF through tunneling processes assisted by thermal noise. We analyze the operation of this circuit in detail and propose for it a stochastic associative processing operation, where the detection timing of the electron position controls the association probability distribution.

Computer Simulation↗
PubMed2001

STOCHSIM: modelling of stochastic biomolecular processes.

SUMMARY: STOCHSIM is a stochastic simulator for chemical reactions. Molecules are represented as individual software objects that react according to probabilities derived from concentrations and rate constants. Version 1.2 of STOCHSIM provides a novel cross-platform graphical interface written in Perl/Tk. A simple two-dimensional spatial structure has also been implemented, in which nearest-neighbour interactions of molecules in a 2-D lattice can be simulated.

Algorithms↗
PubMed1982

Stochastic information processing biological systems.

We propose a simple, biochemically-based model for stochastic information processing in brain, genetic, and, consequently, evolutionary modelling. The essential features of reaction-diffusion processes are realized by intrinsically stochastic probabilistic automata (Shannon and Weaver, 1948; see also Ashby, 1958, von Neumann, 1966; Burks, 1970; Paz, 1971) whose definition extends that of classical automata. (Classical automata are deterministic; earlier work on probabilistic automata focused on error correction and at least approximating deterministic behavior.) We call these probabilistic automata biochemical to emphasize the role of intrinsically stochastic process in biological information processing. Our model yields descriptions of gradualism (Conrad, 1974), learning, and apparent inefficiencies in the brain, and partially resolves the near impossibility of simultaneous point mutations (Conrad, 1972, 1978) in genetics. The genetic model implies an evolutionary dynamics of punctuated equilibria (Gould and Eldredge, 1977).

Animals↗
PubMed2000

Modeling and analysis of stochastic invasion processes.

In this paper we derive spatially explicit equations to describe a stochastic invasion process. Parents are assumed to produce a random number of offspring which then disperse according to a spatial redistribution kernel. Equations for population moments, such as expected density and covariance averaged over an ensemble of identical stochastic processes, take the form of deterministic integro-difference equations. These equations describe the spatial spread of population moments as the invasion progresses. We use the second order moments to analyse two basic properties of the invasion. The first property is 'permanence of form' in the correlation structure of the wave. Analysis of the asymptotic form of the invasion wave shows that either (i) the covariance in the leading edge of the wave of invasion asymptotically achieves a permanence of form with a characteristic structure described by an unchanging spatial correlation function, or (ii) the leading edge of the wave has no asymptotic permanence of form with the length scales of spatial correlations continually increasing over time. Which of these two outcomes pertains is governed by a single statistic, phi which depends upon the shape of the dispersal kernel and the net reproductive number. The second property of the invasion is its patchy structure. Patchiness, defined in terms of spatial correlations on separate short (within patch) and long (between patch) spatial scales, is linked to the dispersal kernel. Analysis shows how a leptokurtic dispersal kernel gives rise to patchiness in spread of a population.

Animals↗
PubMed1981

Some notes on the foundations and scope of intensive design.

IN THE application of single-case and intensive design to the study of psychopathology and interpersonal processes the primary focus is upon the data of the individual subject as distinct from that of a sample of subjects. Such models begin with the notion that personality processes are stochastic processes. That is, one's moods, affects, signs and symptoms, and interactions with others out of the past or from the present fluctuate over time and with respect to various contingencies in a probability space of a very high order of dimensionality. In practice--that is, in relation to application to a given study or set of studies--we are of course constrained to consider just a very small subspace of this huge hyperspace.

Ethics, Professional↗
PubMed1997

Stochastic threshold characterization of the intensity of active channel dynamical action potential generation.

Stochastic threshold characterization of the intensity of active channel dynamical action potential generation. J. Neurophysiol. 78: 2616-2630, 1997. This paper develops a stochastic intensity description for action potential generation formulated in terms of stochastic processes, which are direct analogues of the physiological processes of the pre- and postsynaptic complex of the cochlear nerve: 1) neurotransmitter release is modeled as an inhomogeneous Poisson counting process with release intensity mu t, 2) the excitatory postsynaptic conductance (EPSC) process is modeled as a marked, linearly filtered Poisson process resulting from the linear superposition of standard shaped postsynaptic conductances of size G, and 3) action potential generation is modeled as resulting from the EPSC exceeding a random threshold determined by active channel dynamics of the Hodgkin-Huxley type. The random threshold is defined to be the least upper bound in the size of a standard-shaped neurotransmitter release injected at time t given the previous action potential time and the number of releases occurring in a short preconditioning time increment. The action potential process is modeled as a self-exciting point process with stochastic intensity resulting from the probability that the random threshold process crosses the threshold in some small time increment that is a function of time since previous action potential, release intensity, and the probability that a single synaptic event exceeds the stochastic threshold. The stochastic intensity model is consistent with a direct simulation of the nonlinear Hodgkin-Huxley differential equations over a variety of parameters for the vesicle release intensity, vesicle size, vesicle duration, and temperatures. Results are presented showing that the regularity properties seen in the vestibular primary afferent in the lizard, Calotes versicolor, associated with a slow-to-activate potassium channel resulting in a long afterhyperpolarization can be accommodated directly by the stochastic intensity description. The stimulus dependence of the model is attributed to synaptic transmission and the probabilistic nature to the threshold conductance process, which is dependent upon the EPSC process. The stochastic intensity is seen to have a form consistent with the phenomenologically based Siebert-Gaumond model, a stimulus-related function of time multiplied by a refractory-related function of time since previous action potential.

Action Potentials↗