Extension of information geometry for modelling non-statistical systems

In this dissertation, an abstract formalism extending information geometry is introduced. This framework encompasses a broad range of modelling problems, including possible applications in machine learning and in the information theoretical foundations of quantum theory. Its purely geometrical foundations make no use of probability theory and very little assumptions about the data or the models are made. Starting only from a divergence function, a Riemannian geometrical structure consisting of a metric tensor and an affine connection is constructed and its properties are investigated. Also the relation to information geometry and in particular the geometry of exponential families of probability distributions is elucidated. It turns out this geometrical framework offers a straightforward way to determine whether or not a parametrised family of distributions can be written in exponential form. Apart from the main theoretical chapter, the dissertation also contains a chapter of examples illustrating the application of the formalism and its geometric properties, a brief introduction to differential geometry and a historical overview of the development of information geometry.Comment: PhD thesis, University of Antwerp, Advisors: Prof. dr. Jan Naudts and Prof. dr. Jacques Tempere, December 2014, 108 page

Computational genes: a tool for molecular diagnosis and therapy of aberrant mutational phenotype

<p>Abstract</p> <p>Background</p> <p>A finite state machine manipulating information-carrying DNA strands can be used to perform autonomous molecular-scale computations at the cellular level.</p> <p>Results</p> <p>We propose a new finite state machine able to detect and correct aberrant molecular phenotype given by mutated genetic transcripts. The aberrant mutations trigger a cascade reaction: specific molecular markers as input are released and induce a spontaneous self-assembly of a wild type protein or peptide, while the mutational disease phenotype is silenced. We experimentally demostrated in <it>in vitro </it>translation system that a viable protein can be autonomously assembled.</p> <p>Conclusion</p> <p>Our work demostrates the basic principles of computational genes and particularly, their potential to detect mutations, and as a response thereafter administer an output that suppresses the aberrant disease phenotype and/or restores the lost physiological function.</p

Modeling and identification of a gene regulatory network programming erythropoiesis (1)

The development of mature blood cells of distinct lineages from the hematopoietic stem cells (hematopoiesis) involves a progressive restriction of differentiation potential and the establishment of lineage-speci&#64257;c gene expression profiles. The establishment of these profiles relies on lineage-speci&#64257;c transcription factors to modulate the expression of their target genes. This work is embedded in a wider ErasmusMC/CWI collaboration that develops the informatics and mathematics to underpin studies on gene expression regulation by mapping and analyzing the regulatory pathways and networks of transcription factors that control cellular functions (so called 'Gene Regulatory Networks' or 'GRNs'). This project is concerned with the mathematical part and concentrates on a GRN central to erythropoiesis. Among the many housekeeping and tissue-speci&#64257;c genes involved in the differentiation and the commitment of hematopoietic stem cells to erythrocytes (erythropoiesis), we focus on a small pool of genes (Gata-1, Gata-2, Pu.1, EKLF, FOG-1, alpha/beta-globin) known to be critically involved in an intricate but well-less investigated regulatory circuit. Based on the regulatory interactions in the GRN we have developed models in the form of a system to account for the dynamics of gene expression and regulation involved in this process. Because of the lack of information about a signi&#64257;cant number of model parameters, our focus is on system identi&#64257;cation. In this first report some preliminary results are presented based on synthetic data. However, time series of the levels of all relevant mRNA’s are available from micro-array analysis of G1E cells, a murine cell line which recapitulates erythropoiesis. In the follow-up report a detailed account will be given of the parameter estimation and identifiability analysis with respect to these data. This will eventually allow for a thorough evaluation of the role of various characterized as well as hypothetical regulatory mechanisms. In depth characterization of the necessary expression patterns and gene regulatory interactions responsible for the the set of commitments all along the erythroid lineage is essential to gain fundamental insight into the behaviour of these complex networks and to design further experiments. Ultimately, this may lead to ways to rescue erythroid differentiation in several anemic diseases