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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↗
PubMed2005

Dynamic model-based clustering for time-course gene expression data.

Microarray technology has produced a huge body of time-course gene expression data. Such gene expression data has proved useful in genomic disease diagnosis and genomic drug design. The challenge is how to uncover useful information in such data. Cluster analysis has played an important role in analyzing gene expression data. Many distance/correlation- and static model-based clustering techniques have been applied to time-course expression data. However, these techniques are unable to account for the dynamics of such data. It is the dynamics that characterize the data and that should be considered in cluster analysis so as to obtain high quality clustering. This paper proposes a dynamic model-based clustering method for time-course gene expression data. The proposed method regards a time-course gene expression dataset as a set of time series, generated by a number of stochastic processes. Each stochastic process defines a cluster and is described by an autoregressive model. A relocation-iteration algorithm is proposed to identity the model parameters and posterior probabilities are employed to assign each gene to an appropriate cluster. A bootstrapping method and an average adjusted Rand index (AARI) are employed to measure the quality of clustering. Computational experiments are performed on a synthetic and three real time-course gene expression datasets to investigate the proposed method. The results show that our method allows the better quality clustering than other clustering methods (e.g. k-means) for time-course gene expression data, and thus it is a useful and powerful tool for analyzing time-course gene expression data.

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↗