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This book presents a comprehensive overview of the foundations of single-molecule studies, based on manipulation of the molecules and observation of these with fluorescent probes. It first discusses the forces present at the single-molecule scale, the methods to manipulate them, and their pros and cons. It goes on to present an introduction to single-molecule fluorescent studies based on a quantum description of absorption and emission of radiation due to Einstein. Various considerations in the study of single molecules are introduced (including signal to noise, non-radiative decay, triplet states, etc.) and some novel super-resolution methods are sketched. The elastic and dynamic properties of polymers, their relation to experiments on DNA and RNA, and the structural transitions observed in those molecules upon stretching, twisting, and unzipping are presented. The use of these single-molecule approaches for the investigation of DNA–protein interactions is highlighted via the study of DNA and RNA polymerases, helicases, and topoisomerases. Beyond the confirmation of expected mechanisms (e.g., the relaxation of DNA torsion by topoisomerases in quantized steps) and the discovery of unexpected ones (e.g., strand-switching by helicases, DNA scrunching by RNA polymerases, and chiral discrimination by bacterial topoII), these approaches have also fostered novel (third generation) sequencing technologies.

From one cell to another, from one individual to another, and from one species to another, the content of DNA molecules is often similar. The organization of these molecules, however, differs dramatically, and the mutations that affect this organization are known as genome rearrangements. Combinatorial methods are used to reconstruct putative rearrangement scenarios in order to explain the evolutionary history of a set of species, often formalizing the evolutionary events that can explain the multiple combinations of observed genomes as combinatorial optimization problems. This book offers a comprehensive survey of this rapidly expanding application of combinatorial optimization. It can be used as a reference for experienced researchers or as an introductory text for a broader audience. Genome rearrangement problems have proved so interesting from a combinatorial point of view that the field now belongs as much to mathematics as to biology. The book takes a mathematically oriented approach, but provides biological background when necessary. It presents a series of models, beginning with the simplest (which is progressively extended by dropping restrictions), each constructing a genome rearrangement problem. The book also discusses an important generalization of the basic problem known as the median problem, surveys attempts to reconstruct the relationships between genomes with phylogenetic trees, and offers a collection of summaries and appendixes with additional information.