Biomedical subjects

Olaf Wolkenhauer

Publications and source records attributed to Olaf Wolkenhauer.

10 recordsLinked to original sources

PubMed2005

The dynamic systems approach to control and regulation of intracellular networks.

Systems theory and cell biology have enjoyed a long relationship that has received renewed interest in recent years in the context of systems biology. The term 'systems' in systems biology comes from systems theory or dynamic systems theory: systems biology is defined through the application of systems- and signal-oriented approaches for an understanding of inter- and intra-cellular dynamic processes. The aim of the present text is to review the systems and control perspective of dynamic systems. The biologist's conceptual framework for representing the variables of a biochemical reaction network, and for describing their relationships, are pathway maps. A principal goal of systems biology is to turn these static maps into dynamic models, which can provide insight into the temporal evolution of biochemical reaction networks. Towards this end, we review the case for differential equation models as a 'natural' representation of causal entailment in pathways. Block-diagrams, commonly used in the engineering sciences, are introduced and compared to pathway maps. The stimulus-response representation of a molecular system is a necessary condition for an understanding of dynamic interactions among the components that make up a pathway. Using simple examples, we show how biochemical reactions are modelled in the dynamic systems framework and visualized using block-diagrams.

Animals↗

PubMed2004

Advanced significance analysis of microarray data based on weighted resampling: a comparative study and application to gene deletions in Mycobacterium bovis.

MOTIVATION: When analyzing microarray data, non-biological variation introduces uncertainty in the analysis and interpretation. In this paper we focus on the validation of significant differences in gene expression levels, or normalized channel intensity levels with respect to different experimental conditions and with replicated measurements. A myriad of methods have been proposed to study differences in gene expression levels and to assign significance values as a measure of confidence. In this paper we compare several methods, including SAM, regularized t-test, mixture modeling, Wilk's lambda score and variance stabilization. From this comparison we developed a weighted resampling approach and applied it to gene deletions in Mycobacterium bovis. RESULTS: We discuss the assumptions, model structure, computational complexity and applicability to microarray data. The results of our study justified the theoretical basis of the weighted resampling approach, which clearly outperforms the others.

Algorithms↗

PubMed2004

Optimal sampling time selection for parameter estimation in dynamic pathway modeling.

Systems Biology is an emerging research area, which considers mathematical representations of inter- and intra-cellular dynamics. Among the many research problems that have been addressed, dynamic modeling of signal transduction pathways has received increasing attention. The usual approach to represent intra-cellular dynamics are nonlinear, usually ordinary, differential equations. The purpose of the models is to test and generate hypothesis of specific pathways and it is therefore required to estimate model parameters from experimental data. The experiments to generate data are complex and expensive, as a consequence of which the time series available are usually rather short, with few if any replicates. Almost certainly, not all variables one would like to include in a model can be measured. Parameter estimation is therefore an important research problem in Systems Biology and the focus of this paper. In particular, we are interested in optimizing the sampling time selection in order to minimize the variance of the parameter estimation error. With few sampling time points feasible, their selection is of practical importance in experimental design. Finally, the theoretical results are supported with an application.

Computer Simulation↗

PubMed2004

Modeling and simulation of intracellular dynamics: choosing an appropriate framework.

Systems biology is a reemerging paradigm which, among other things, focuses on mathematical modeling and simulation of biochemical reaction networks in intracellular processes. For most simulation tools and publications, they are usually characterized by either preferring stochastic simulation or rate equation models. The use of stochastic simulation is occasionally accompanied with arguments against rate equations. Motivated by these arguments, we discuss in this paper the relationship between these two forms of representation. Toward this end, we provide a novel compact derivation for the stochastic rate constant that forms the basis of the popular Gillespie algorithm. Comparing the mathematical basis of the two popular conceptual frameworks of generalized mass action models and the chemical master equation, we argue that some of the arguments that have been put forward are ignoring subtle differences and similarities that are important for answering the question in which conceptual framework one should investigate intracellular dynamics.

Algorithms↗

PubMed2004

Analysis of DNA microarray data.

Recent advances in DNA microarray technology have great impact on many areas of biomedical research and pharmacogenomics: discovering novel targets and genes, elucidating signatures of complex diseases, transcriptional profiling of models for diseases, and the development of individually optimized drugs based on differential gene expression patterns. Consequently, there is demand for robust methods for data analysis and the choice of adequate statistical tests. This review guides through all steps in the cDNA microarray data analysis pipeline and gives a basic understanding of the challenges in interpreting large microarray datasets.

Animals↗

PubMed2003

Investigations into the analysis and modeling of the TNF alpha-mediated NF-kappa B-signaling pathway.

In this study, we propose a system-theoretic approach to the analysis and quantitative modeling of the TNFalpha-mediated NF-kappaB-signaling pathway. Tumor necrosis factor alpha (TNFalpha) is a potent proinflammatory cytokine that plays an important role in immunity and inflammation, in the control of cell proliferation, differentiation, and apoptosis. To date, there have been numerous approaches to model cellular dynamics. The most prominent uses ordinary differential equations (ODEs) to describe biochemical reactions. This approach can provide us with mathematically well-founded and tractable interpretations regarding pathways, especially those best described by enzyme reactions. This work first introduces a graphical method to intuitively represent the TNFalpha-mediated NF-kappaB-signaling pathway and then utilizes ODEs to quantitatively model the pathway. The simulation study shows qualitative validation of the proposed model compared with experimental results for this pathway. The proposed system-theoretic approach is expected to be further applicable to predict the signaling behavior of NF-kappaB in a quantitative manner for any variation of the ligand, TNFalpha.

Computer Simulation↗

PubMed2003

The statistical distribution of the intensity of pixels within spots of DNA microarrays: what is the appropriate single-value representative?

This paper opens a discussion about an important issue in the analysis of data from spotted DNA microarrays: how to summarise into a single value the distribution for the intensity values of the pixels within a spot. Although the most popular statistic used is the median, there is no clear study demonstrating why it is more appropriate than other measures of central tendency such as the mean or the mode. Here, we argue that the median intensity is not the most appropriate measure for many common cases and discuss a frequently encountered case of a 'doughnut'-shaped spot for which the mode is closest to the 'expected' spot intensity. For an 'ideal' spot with a clear boundary and uniformly hybridised, the intensity of its pixels should approximately be normally distributed. In practical situations, these two requirements are often not met due to the physical properties of pins and the particularities of the printing and hybridisation processes. As a consequence, the distribution of the intensity of the pixels is usually negatively skewed. This asymmetry results in a larger displacement for the mean and median than for the mode from the ideal situation mentioned above.

Algorithms↗

PubMed2003

Microarray data clustering based on temporal variation: FCV with TSD preclustering.

The aim of this paper is to present a new clustering algorithm for short time-series gene expression data that is able to characterise temporal relations in the clustering environment (ie data-space), which is not achieved by other conventional clustering algorithms such as k -means or hierarchical clustering. The algorithm called fuzzy c -varieties clustering with transitional state discrimination preclustering (FCV-TSD) is a two-step approach which identifies groups of points ordered in a line configuration in particular locations and orientations of the data-space that correspond to similar expressions in the time domain. We present the validation of the algorithm with both artificial and real experimental datasets, where k -means and random clustering are used for comparison. The performance was evaluated with a measure for internal cluster correlation and the geometrical properties of the clusters, showing that the FCV-TSD algorithm had better performance than the k -means algorithm on both datasets.

Algorithms↗

PubMed2002

Information-theoretic analysis of protein sequences shows that amino acids self-cluster.

We analyse for each of 20 amino acids X the statistics of spacings between consecutive occurrences of X within the well-characterized Saccharomyces cerevisiae genome. The occurrences of amino acids may exhibit near random, clustered or smoothed out behaviour, like one-dimensional stochastic processes along the protein chain. If amino acids are distributed randomly within a sequence, then they follow a Poisson process, and a histogram of the number of observations of each gap size would asymptotically follow a negative exponential distribution. The novelty of the present approach lies in the use of differential geometric methods to quantify information on sequencing of amino acids and groups of amino acids, via the sequences of intervals between their occurrences. The differential geometry arises from an information-theoretic distance function on the two-dimensional space of stochastic processes subordinate to gamma distributions-which latter include the random process as a special case. We find that maximum-likelihood estimates of parametric statistics show that all 20 amino acids tend to cluster, some substantially. In other words, the frequencies of short gap lengths tend to be higher and the variance of the gap lengths is greater than expected by chance. This may be because localizing amino acids with the same properties may favour secondary structure formation or transmembrane domains. Gap sizes of 1 or 2 are generally disfavoured, 1 strongly so. The only exceptions to this are Gln and Ser, as a result of poly(Gln) or poly(Ser) sequences. There are preferences for gaps of 4 and 7 that can be attributed to alpha -helices. In particular, a favoured gap of 7 for Leu is found in coiled coils. Our method contributes to the characterization of whole sequences by extracting and quantifying stable stochastic features.

Amino Acids↗

PubMed2002

Mathematical modelling in the post-genome era: understanding genome expression and regulation--a system theoretic approach.

This paper introduces a mathematical framework for modelling genome expression and regulation. Starting with a philosophical foundation, causation is identified as the principle of explanation of change in the realm of matter. Causation is, therefore, a relationship, not between components, but between changes of states of a system. We subsequently view genome expression (formerly known as 'gene expression') as a dynamic process and model aspects of it as dynamic systems using methodologies developed within the areas of systems and control theory. We begin with the possibly most abstract but general formulation in the setting of category theory. The class of models realised are state-space models, input--output models, autoregressive models or automata. We find that a number of proposed 'gene network' models are, therefore, included in the framework presented here. The conceptual framework that integrates all of these models defines a dynamic system as a family of expression profiles. It becomes apparent that the concept of a 'gene' is less appropriate when considering mathematical models of genome expression and regulation. The main claim of this paper is that we should treat (model) the organisation and regulation of genetic pathways as what they are: dynamic systems. Microarray technology allows us to generate large sets of time series data and is, therefore, discussed with regard to its use in mathematical modelling of gene expression and regulation.

Gene Expression↗