Since the first demonstration of optical tweezers approximately 30 years ago, they have become widespread both as a subject of research in their own right and as an enabling tool in fields as diverse as molecular biology, statistical physics, materials science and quantum physics. Currently the number of active research groups worldwide is in the hundreds – and counting. Furthermore, with the advent of commercially available optical tweezers and low-cost lab kits, optical tweezers experiments can now be found as a common instructional tool in advanced undergraduate and graduate laboratories. This broad interest gives rise to a pressing need for a reference textbook covering the principles and applications of optical tweezers. We began our journey of writing this book with the aim of filling this gap. Therefore we sought to write a textbook with a strong pedagogic approach to both the theory and practice of optical manipulation, supplemented by an overview of the current state of the art in optical manipulation research, and supported by exercises and problems. Eventually, this book saw the light of day.

This book comprises three parts. Part I covers the theory of optical tweezing, providing intuitive and rigorous explanations of the physics behind optical trapping and manipulation, an introduction to the numerical methods most commonly employed in the study of optical forces and torques, and a detailed explanation of the dynamics of optically trapped particles. Part II focuses on the experimental practice of optical manipulation, including both the implementation of a working optical tweezers set-up – complete with detailed step-by-step advice on its construction, on troubleshooting and on the acquisition and analysis of data – and instructions on how to develop more advanced optical manipulation techniques. Parts I and II both include numerous exercises to illustrate the concepts, ideas and techniques discussed, and each chapter ends with problems to solve as a starting point for further investigations. Finally, Part III provides an overview of some of the most exciting applications that optical tweezers have found in various fields, from the study of biological systems to the investigation of the quantum limit for trapped mesoscale objects. Furthermore, we have enhanced this book with an extensive supplementary material, available online for download from the book website at www.opticaltweezers.org. This includes, in particular, the comprehensive OTS - the Optical Tweezers Software toolbox, which we encourage readers to download, use and develop further.

The main form of the double helix, the B form, is stabilized by only weak hydrogen bonds and van der Waals interactions. If we also take into account the remarkable flexibility of the backbone of ssDNA, it is not surprising that depending on the solution conditions DNA can be found in various alternative forms. Conformational flexibility of DNA is needed for its functioning, since it facilitates speciflc DNA-DNA, DNA-RNA and DNA–protein interactions inside the cell. When we are changing solution conditions gradually, DNA can undergo transitions from one form to another. Studying these transitions has brought a lot of important information about DNA conformational flexibility and the stability of the various forms. This is why the conformational transitions have been a subject of biophysical investigation for decades. In this chapter we start from general theoretical analysis of the transitions, and then consider individual transitions: DNA melting or the helix–coil transition, B–A and B–Z transitions. We mainly consider only equilibrium properties of the transitions; the corresponding dynamic properties will be the subject of Chapter 4.

Theoretical analysis of conformational transitions in DNA

2.1.1 Preliminary remarks

A key concept of the theoretical description of conformational transitions that will be used in this chapter is a concept of a macrostate. It seems that Zimm and Bragg were the first to apply this approach to the analysis of the helix–coil transition in polypeptides (Zimm & Bragg 1959), although a few groups were moving in the same direction at that time. In this approach all microscopic states of a base pair (or nucleotides that can form the base pair) are divided into two groups, which correspond to the two DNA forms under consideration. The exact numbers of microstates in the macrostates and their corresponding energies are not specified in this approach. To apply it we only need to know the ratio of the statistical weights of the macrostates.

Chemical structure and conformational flexibility of single-stranded DNA

Single-stranded DNA (ssDNA) is the building base for the double helix and other DNA structures. All these structures are formed due to noncovalent interactions between the components of ssDNA. ssDNA consists of a backbone of repeating units and bases that are attached to each unit as side chains (Fig. 1.1).

An isolated part of the repeating unit that consists of a base and the sugar is called a nucleoside. If a phosphate group is added to the nucleoside, it becomes a 3′- or 5′- nucleotide, depending on where the phosphate group is bound. Each repeating unit of the backbone consists of sugar and phosphate and has six skeletal bonds. The backbone has clear directionality, and the method of numbering of carbon atoms of the sugar, shown in Fig. 1.1, identifies 3′–5′ or 5′–3′ directions. It is common to assume a 5′–3′ direction of the polynucleotide chain when presenting a sequence of bases.

There is an important degree of freedom in isolated nucleosides that is related to rotation around the bond connecting the sugar and a base, the β-glycosidic bond. The rotation angle, χ, is measured with reference to the orientation of O1′–C1′ and N9–C8 bonds for purines and to the orientation of O1′–C1′ and N1–C6 bonds for pyrimidines. Although many different values of χ are sterically allowed, two major rotational isomers, called anti and syn, are particularly important. For the anti conformation χ is close to 0°, and for syn χ is around 210°. The conformations are diagramed in Fig. 1.2.

The bond lengths and the angles between the adjacent bonds do not change notably. The remarkable conformational flexibility of ssDNA is due to six rotation angles in each repeating unit of the backbone. Of course, the rotation angles cannot accept just any values, since there are many potential steric clashes between chemical groups of the unit.