Computer simulation of expansions of DNA triplet repeats in the fragile X syndrome and Huntington's disease

WHY MATHEMATICS IS NEEDED TO UNDERSTAND COMPLEX GENETICS DISEASES

We discuss mathematical approaches to population genetics and evolutionary theory in the context of complex genetic disease. Mechanisms, which we discuss, include gene-environment interaction in lung cancer as well as classical mechanisms of stabilization of genetic disease such as overdominance, antagonistic pleiotropy and recurring mutations. Specific modeling approaches discussed include: (1) Mathematical model of the evolution of disease chromosome applied to mapping of a disease gene. (2) Iterated Galton–Watson branching process applied to modeling of trinucleotide expansion in triplet-repeat diseases. (3) Application of Ewens' sampling formula to analysis of Single Nucleotide Polymorphism haplotypes at disease-related genes. The aim of this paper is not to present an exhaustive review, but rather to advocate mathematical modeling approaches in a field of current interest.

Introduction: reminiscing on models and modeling

This chapter answers three basic questions, which are: (1) Why build models, (2) why build models of fragile X syndrome, and (3) what has been learned from the models of fragile X syndrome that have been made? The first question is used to frame the other two questions, providing the appropriate context by which the rest of the book should be examined. Of necessity the last two questions are only addressed briefly, and from one man's point of view, as they contain the subject matter of the entirety of the book. Thus, the reader is introduced to the various topics under review and urged to read for him/herself their contents, drawing such conclusions as he/she thinks are warranted.

Identification of a unique library of complex, but ordered, arrays of repetitive elements in the human genome and implication of their potential involvement in pathobiology

Approximately 2% of the human genome is reported to be occupied by genes. Various forms of repetitive elements (REs), both characterized and uncharacterized, are presumed to make up the vast majority of the rest of the genomes of human and other species. In conjunction with a comprehensive annotation of genes, information regarding components of genome biology, such as gene polymorphisms, non-coding RNAs, and certain REs, is found in human genome databases. However, the genome-wide profile of unique RE arrangements formed by different groups of REs has not been fully characterized yet. In this study, the entire human genome was subjected to an unbiased RE survey to establish a whole-genome profile of REs and their arrangements. Due to the limitation in query size within the bl2seq alignment program (National Center for Biotechnology Information [NCBI]) utilized for the RE survey, the entire NCBI reference human genome was fragmented into 6206 units of 0.5M nucleotides. A number of RE arrangements with varying complexities and patterns were identified throughout the genome. Each chromosome had unique profiles of RE arrangements and density, and high levels of RE density were measured near the centromere regions. Subsequently, 175 complex RE arrangements, which were selected throughout the genome, were subjected to a comparison analysis using five different human genome sequences. Interestingly, three of the five human genome databases shared the exactly same arrangement patterns and sequences for all 175 RE arrangement regions (a total of 12,765,625 nucleotides). The findings from this study demonstrate that a substantial fraction of REs in the human genome are clustered into various forms of ordered structures. Further investigations are needed to examine whether some of these ordered RE arrangements contribute to the human pathobiology as a functional genome unit.

The FMR1 gene and fragile X-associated tremor/ataxia syndrome

The CGG-repeat present in the 5'UTR of the FMR1 gene is unstable upon transmission to the next generation. The repeat is up to 55 CGGs long in the normal population. In fragile X patients, a repeat length exceeding 200 CGGs (full mutation: FM) generally leads to methylation of the repeat and the promoter region, which is accompanied by silencing of the FMR1 gene. The gene product FMRP is involved in regulation of transport and translation of certain mRNA in the dendrite, thereby affecting synaptic plasticity. This is central to learning and memory processes. The absence of FMRP seen in FM is the cause of the mental retardation seen in fragile X patients. The premutation (PM) is defined as 55-200 CGGs. Female PM carriers are at risk of developing primary ovarian insufficiency. Recently it was discovered that elderly PM carriers might develop a progressive neurodegenerative disorder called fragile X-associated tremor/ataxia syndrome. Although arising from the mutations in the same gene, distinct mechanisms lead to fragile X syndrome (absence of FMRP) and FXTAS (toxic RNA gain of function). The pathogenic mechanisms thought to underlie these disorders are discussed, with a specific emphasis on FXTAS. This review gives insight on the implications of all possible repeat length categories seen in fragile X families.