Biomedical subjects

John Goutsias

Publications and source records attributed to John Goutsias.

7 recordsLinked to original sources

PubMed2007

Classical versus stochastic kinetics modeling of biochemical reaction systems.

We study fundamental relationships between classical and stochastic chemical kinetics for general biochemical systems with elementary reactions. Analytical and numerical investigations show that intrinsic fluctuations may qualitatively and quantitatively affect both transient and stationary system behavior. Thus, we provide a theoretical understanding of the role that intrinsic fluctuations may play in inducing biochemical function. The mean concentration dynamics are governed by differential equations that are similar to the ones of classical chemical kinetics, expressed in terms of the stoichiometry matrix and time-dependent fluxes. However, each flux is decomposed into a macroscopic term, which accounts for the effect of mean reactant concentrations on the rate of product synthesis, and a mesoscopic term, which accounts for the effect of statistical correlations among interacting reactions. We demonstrate that the ability of a model to account for phenomena induced by intrinsic fluctuations may be seriously compromised if we do not include the mesoscopic fluxes. Unfortunately, computation of fluxes and mean concentration dynamics requires intensive Monte Carlo simulation. To circumvent the computational expense, we employ a moment closure scheme, which leads to differential equations that can be solved by standard numerical techniques to obtain more accurate approximations of fluxes and mean concentration dynamics than the ones obtained with the classical approach.

Biochemistry↗

PubMed2006

Stochastic transcriptional regulatory systems with time delays: a mean-field approximation.

Modeling transcriptional regulation with time delays is an important problem of computational cell biology. In this paper, we propose a computational tool for studying transcriptional regulation in single cells based on a mean-field approximation method. The main idea is to replace the occurrence probabilities of the underlying transcriptional events by their mean values and use appropriately chosen additive noise terms to model statistical variations not accounted by this approximation. The proposed methodology allows us to characterize the transient and steady-state behavior of transcriptional regulation. Moreover, it provides a rather simple and computationally attractive tool for rapid statistical characterization of the dynamic behavior of a nonlinear transcriptional regulatory system with time delays.

Computational Biology↗

PubMed2005

Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems.

We address the problem of eliminating fast reaction kinetics in stochastic biochemical systems by employing a quasiequilibrium approximation. We build on two previous methodologies developed by [Haseltine and Rawlings, J. Chem. Phys. 117, 6959 (2002)] and by [Rao and Arkin, J. Chem. Phys. 118, 4999 (2003)]. By following Haseltine and Rawlings, we use the numbers of occurrences of the underlying reactions to characterize the state of a biochemical system. We consider systems that can be effectively partitioned into two distinct subsystems, one that comprises "slow" reactions and one that comprises "fast" reactions. We show that when the probabilities of occurrence of the slow reactions depend at most linearly on the states of the fast reactions, we can effectively eliminate the fast reactions by modifying the probabilities of occurrence of the slow reactions. This modification requires computation of the mean states of the fast reactions, conditioned on the states of the slow reactions. By assuming that within consecutive occurrences of slow reactions, the fast reactions rapidly reach equilibrium, we show that the conditional state means of the fast reactions satisfy a system of at most quadratic equations, subject to linear inequality constraints. We present three examples which allow analytical calculations that clearly illustrate the mathematical steps underlying the proposed approximation and demonstrate the accuracy and effectiveness of our method.

Algorithms↗

PubMed2005

Object-based image analysis using multiscale connectivity.

This paper introduces a novel approach for image analysis based on the notion of multiscale connectivity. We use the proposed approach to design several novel tools for object-based image representation and analysis which exploit the connectivity structure of images in a multiscale fashion. More specifically, we propose a nonlinear pyramidal image representation scheme, which decomposes an image at different scales by means of multiscale grain filters. These filters gradually remove connected components from an image that fail to satisfy a given criterion. We also use the concept of multiscale connectivity to design a hierarchical data partitioning tool. We employ this tool to construct another image representation scheme, based on the concept of component trees, which organizes partitions of an image in a hierarchical multiscale fashion. In addition, we propose a geometrically-oriented hierarchical clustering algorithm which generalizes the classical single-linkage algorithm. Finally, we propose two object-based multiscale image summaries, reminiscent of the well-known (morphological) pattern spectrum, which can be useful in image analysis and image understanding applications.

Algorithms↗

PubMed2004

A nonlinear discrete dynamical model for transcriptional regulation: construction and properties.

Transcriptional regulation is a fundamental mechanism of living cells, which allows them to determine their actions and properties, by selectively choosing which proteins to express and by dynamically controlling the amounts of those proteins. In this article, we revisit the problem of mathematically modeling transcriptional regulation. First, we adopt a biologically motivated continuous model for gene transcription and mRNA translation, based on first-order rate equations, coupled with a set of nonlinear equations that model cis-regulation. Then, we view the processes of transcription and translation as being discrete, which, together with the need to use computational techniques for large-scale analysis and simulation, motivates us to model transcriptional regulation by means of a nonlinear discrete dynamical system. Classical arguments from chemical kinetics allow us to specify the nonlinearities underlying cis-regulation and to include both activators and repressors as well as the notion of regulatory modules in our formulation. We show that the steady-state behavior of the proposed discrete dynamical system is identical to that of the continuous model. We discuss several aspects of our model, related to homeostatic and epigenetic regulation as well as to Boolean networks, and elaborate on their significance. Simulations of transcriptional regulation of a hypothetical metabolic pathway illustrate several properties of our model, and demonstrate that a nonlinear discrete dynamical system may be effectively used to model transcriptional regulation in a biologically relevant way.

Algorithms↗

PubMed2004

Grayscale level connectivity: theory and applications.

A novel notion of connectivity for grayscale images is introduced, defined by means of a binary connectivity assigned at image-level sets. In this framework, a grayscale image is connected if all level sets below a prespecified threshold are connected. The proposed notion is referred to as grayscale level connectivity and includes, as special cases, other well-known notions of grayscale connectivity, such as fuzzy grayscale connectivity and grayscale blobs. In contrast to those approaches, the present framework does not require all image-level sets to be connected. Moreover, a connected grayscale object may contain more than one regional maximum. Grayscale level connectivity is studied in the rigorous framework of connectivity classes. The use of grayscale level connectivity in image analysis applications, such as object extraction, image segmentation, object-based filtering, and hierarchical image representation, is discussed and illustrated.

Algorithms↗

PubMedDate not supplied

A hidden Markov model for transcriptional regulation in single cells.

We discuss several issues pertaining to the use of stochastic biochemical systems for modeling transcriptional regulation in single cells. By appropriately choosing the system state, we can model transcriptional regulation by a hidden Markov model (HMM). This opens the possibility of using well-known techniques for the statistical analysis and stochastic control of HMMs to mathematically and computationally study transcriptional regulation in single cells. Unfortunately, in all but a few simple cases, analytical characterization of the statistical behavior of the proposed HMM is not possible. Moreover, analysis by Monte Carlo simulation is computationally cumbersome. We discuss several techniques for approximating the HMM by one that is more tractable. We employ simulations, based on a biologically relevant transcriptional regulatory system, to show the relative merits and limitations of various approximation techniques and provide general guidelines for their use.

Cell Physiological Phenomena↗