In this review, we give an overview of recent literature on the structure and stability of unimolecular G-rich quadruplex structures that are relevant to drug design and for in vivo function The unifying theme in this review is energetics The thermodynamic stability of quadruplexes has not been studied in the same detail as DNA and RNA duplexes, and there are important differences in the balance of forces between these classes of folded oligonucleotides We provide an overview of the principles of stability and where available the experimental data that report on these principles Significant gaps in the literature have been identified, that should be filled by a systematic study of well-defined quadruplexes not only to provide the basic understanding of stability both for design purposes, but also as it relates to in vivo occurrence of quadruplexes Techniques that are commonly applied to the determination of the structure, stability and folding are discussed in terms of information content and limitations Quadruplex structures fold and unfold comparatively slowly, and DNA unwinding events associated with transcription and replication may be operating far from equilibrium The kinetics of formation and resolution of quadruplexes, and methodologies are discussed in the context of stability and their possible biological occurrence

Stability and kinetics of G-quadruplex structures

Among the Various methods for characterizing macromolecules in solution, hydrodynamic techniques play a major role. Since the advent of the ultracentrifuge and the development of viscometric apparatus, sedimentation coefficients and intrinsic viscosities have been extensively used to learn about the size and shape of synthetic and biological polymers. More recently, refined techniques such as quasielastic light scattering, transient electric birefringence and fluorescence anisotropy decay have made it possible to obtain in a simple and rapid way quantitative information of high precision on the translational and rotational brownian dynamics of dissolved macromolecules.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0033583500002080

Hydrodynamic properties of complex, rigid, biological macromolecules: theory and applications.

Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.

Dynamic Light Scattering Measurement of Nanometer Particles in Liquids

Two theories relating the translational and rotational diffusion coefficients Dt and Dr of a rod‐like macromolecule to its length and diameter, proposed by Broersma [J. Chem. Phys. 74, 6989 (1981)], and Tirado and Garcia de la Torre [J. Chem. Phys. 71, 2581 (1979); 73, 1986 (1980)] are shown to predict different values of the coefficients for a particle of given dimensions. Next, we use the two theories to analyze existing experimental data of sedimentation coefficients s and translational and rotational diffusion coefficients of short DNA fragments, and obtain values of the hydrated diameter of DNA d which is treated as an adjustable parameter. The results are compared with the expected value, d≂26A. This comparison favors clearly the Tirado–Garcia de la Torre theory in the case of Dt and s. For Dr, and using a rise per base pair r=3.4 A, this theory gives best agreement for all the data examined, while when r=3.3 A, the agreement depends on the source of data.

Comparison of theories for the translational and rotational diffusion coefficients of rod‐like macromolecules. Application to short DNA fragments

The formalism for the calculation of translational friction coefficients of symmetric top macromolecules presented in a previous paper [M. M. Tirado and J. Garcia de la Torre, J. Chem. Phys. 71, 2585 (1979)] is here extended to the evaluation of rotational friction and diffusion coefficients. We show how the introduction of symmetry considerations leads to a great reduction of the computational requirements needed to solve the hydrodynamic interaction equations. We also obtain the translation–rotation coupling tensor from which the center of hydrodynamic stress can be obtained. For a rigid ring we have derived analytical solutions that reduce to those obtained by other authors when the unmodified interaction tensor is used. The general formalism is finally applied to the calculation of the rotational diffusion coefficients of circular cylinders modeled as stacks of rings and extrapolated to zero bead size. The resulting values are critically compared with those from earlier studies.

Rotational dynamics of rigid, symmetric top macromolecules. Application to circular cylinders

The hydrodynamic interaction equations and the interaction tensor that appear in the theoretical formalism for calculating translational friction coefficients of rigid particles modeled as assemblies of beads, are formulated in cylindrical coordinates For symmetric top particles, the cylindrical shielding tensors of symmetry‐equivalent beads are the same, and have only five nonzero components This effects a great simplification with respect to the Cartesian formalism Application is made to the end‐effect correction, for translational motion of right circular cylinders modeled as stacks of rings, extrapolated to zero bead size No appreciable changes in the translational friction coefficients are found when the hollow cylindrical models are capped at the ends with disc‐shaped plates For finite cylinders with axial ratio p≳2, our results, as well as those from other theoretical and experimental studies, are in remarkable disagreement with the previous calculations by Broersma

Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders

Methode basee sur la theorie de Kirkwood Riseman. Application a une chaine polymethylenique (differences tres faibles)

Monte Carlo study of hydrodynamic properties of flexible linear chains: analysis of several approximate methods

In this work we examine several approximate methods that can be used to calculate hydrodynamic properties of macromolecules in solution. We consider some well-known approximations such as the preaveraging approximation and the double-sum formula of Kirkwood for translation. We also consider newer methods such as the diagonal approximation and other double-sum formulas for rotation and viscosity. The obvious advantage of the approximate methods is that they require much less computational effort than the rigorous treatments. We first describe the nature of the approximations used in the various methods. Then we calculate translational and rotational coefficients and intrinsic viscosities of rigid rods and rings and other polygonal or polyhedral structures, using both the rigorous theory and the approximate methods. This enables us to determine the errors of the methods in terms of the geometry and size of the structures. The relative performance of the methods is discussed. A remarkable finding is the large effect from preaveraging the interaction tensor on the rotational coefficients and intrinsic viscosities. This effect is generally larger than that caused by the approximations used to derive the double-sum formulas.

Maria M. Tirado

Papers

Rotational dynamics of rigid, symmetric top macromolecules. Application to circular cylinders

Translational friction coefficients of rigid, symmetric top macromolecules. Application to circular cylinders

Monte Carlo study of hydrodynamic properties of flexible linear chains: analysis of several approximate methods

Approximate methods for calculating hydrodynamic properties of macromolecules in dilute solution. Theory and application to rigid structures