Extracting physical chemistry from mechanics: a new approach to investigate DNA interactions with drugs and proteins in single molecule experiments

In this review we focus on the idea of establishing connections between the mechanical properties of DNAligand complexes and the physical chemistry of DNA-ligand interactions. This type of connection is interesting because it opens the possibility of performing a robust characterization of such interactions by using only one experimental technique: single molecule stretching. Furthermore, it also opens new possibilities in comparing results obtained by very different approaches, in special when comparing single molecule techniques to ensemble-averaging techniques. We start the manuscript reviewing important concepts of the DNA mechanics, from the basic mechanical properties to the Worm-Like Chain model. Next we review the basic concepts of the physical chemistry of DNA-ligand interactions, revisiting the most important models used to analyze the binding data and discussing their binding isotherms. Then, we discuss the basic features of the single molecule techniques most used to stretch the DNA-ligand complexes and to obtain force x extension data, from which the mechanical properties of the complexes can be determined. We also discuss the characteristics of the main types of interactions that can occur between DNA and ligands, from covalent binding to simple electrostatic driven interactions. Finally, we present a historical survey on the attempts to connect mechanics to physical chemistry for DNA-ligand systems, emphasizing a recently developed fitting approach useful to connect the persistence length of the DNA-ligand complexes to the physicochemical properties of the interaction. Such approach in principle can be used for any type of ligand, from drugs to proteins, even if multiple binding modes are present

Transition on the entropic elasticity of DNA induced by intercalating molecules

We use optical tweezers to perform stretching experiments on DNA molecules when interacting with the drugs daunomycin and ethidium bromide, which intercalate the DNA molecule. These experiments are performed in the low-force regime from zero up to 2 pN. Our results show that the persistence length of the DNA-drug complexes increases strongly as the drug concentration increases up to some critical value. Above this critical value, the persistence length decreases abruptly and remains practically constant for larger drug concentrations. The contour length of the molecules increases monotonically and saturates as drugs concentration increases. Measured in- tercalants critical concentrations for the persistence length transition coincide with reported values for the helix-coil transition of DNA-drug complexes, obtained from sedimentation experiments.Comment: This experimental article shows and discuss a transition observed in the persistence length of DNA molecules when studied as a function of some intercalating drug concentrations, like daunomycin and ethidium bromide. It has 15 pages and 4 figures. The article presented here is in preprint forma

Eisenstein Series and String Thresholds

We investigate the relevance of Eisenstein series for representing certain $G(Z)$-invariant string theory amplitudes which receive corrections from BPS states only. $G(Z)$ may stand for any of the mapping class, T-duality and U-duality groups $Sl(d,Z)$, $SO(d,d,Z)$ or $E_{d+1(d+1)}(Z)$ respectively. Using $G(Z)$-invariant mass formulae, we construct invariant modular functions on the symmetric space $K\backslash G(R)$ of non-compact type, with $K$ the maximal compact subgroup of $G(R)$, that generalize the standard non-holomorphic Eisenstein series arising in harmonic analysis on the fundamental domain of the Poincar\'e upper half-plane. Comparing the asymptotics and eigenvalues of the Eisenstein series under second order differential operators with quantities arising in one- and $g$-loop string amplitudes, we obtain a manifestly T-duality invariant representation of the latter, conjecture their non-perturbative U-duality invariant extension, and analyze the resulting non-perturbative effects. This includes the $R^4$ and $R^4 H^{4g-4}$ couplings in toroidal compactifications of M-theory to any dimension $D\geq 4$ and $D\geq 6$ respectively.Comment: Latex2e, 60 pages; v2: Appendix A.4 extended, 2 refs added, thms renumbered, plus minor corrections; v3: relation (1.7) to math Eis series clarified, eq (3.3) and minor typos corrected, final version to appear in Comm. Math. Phys; v4: misprints and Eq C.13,C.24 corrected, see note adde

On the dimensional dependence of duality groups for massive p-forms

We study the soldering formalism in the context of abelian p-form theories. We develop further the fusion process of massless antisymmetric tensors of different ranks into a massive p-form and establish its duality properties. To illustrate the formalism we consider two situations. First the soldering mass generation mechanism is compared with the Higgs and Julia-Toulouse mechanisms for mass generation due to condensation of electric and magnetic topological defects. We show that the soldering mechanism interpolates between them for even dimensional spacetimes, in this way confirming the Higgs/Julia-Toulouse duality proposed by Quevedo and Trugenberger \cite{QT} a few years ago. Next, soldering is applied to the study of duality group classification of the massive forms. We show a dichotomy controlled by the parity of the operator defining the symplectic structure of the theory and find their explicit actions.Comment: Reference [8] has been properly place

DNA-psoralen: single-molecule experiments and first principles calculations

The authors measure the persistence and contour lengths of DNA-psoralen complexes, as a function of psoralen concentration, for intercalated and crosslinked complexes. In both cases, the persistence length monotonically increases until a certain critical concentration is reached, above which it abruptly decreases and remains approximately constant. The contour length of the complexes exhibits no such discontinuous behavior. By fitting the relative increase of the contour length to the neighbor exclusion model, we obtain the exclusion number and the intrinsic intercalating constant of the psoralen-DNA interaction. Ab initio calculations are employed in order to provide an atomistic picture of these experimental findings.Comment: 9 pages, 4 figures in re-print format 3 pages, 4 figures in the published versio

General CMB and Primordial Bispectrum Estimation I: Mode Expansion, Map-Making and Measures of f_NL

We present a detailed implementation of two bispectrum estimation methods which can be applied to general non-separable primordial and CMB bispectra. The method exploits bispectrum mode decompositions on the domain of allowed wavenumber or multipole values. Concrete mode examples constructed from symmetrised tetrahedral polynomials are given, demonstrating rapid convergence for known bispectra. We use these modes to generate simulated CMB maps of high resolution (l > 2000) given an arbitrary primordial power spectrum and bispectrum or an arbitrary late-time CMB angular power spectrum and bispectrum. By extracting coefficients for the same separable basis functions from an observational map, we are able to present an efficient and general f_NL estimator for a given theoretical model. The estimator has two versions comparing theoretical and observed coefficients at either primordial or late times, thus encompassing a wider range of models, including secondary anisotropies, lensing and cosmic strings. We provide examples and validation of both f_NL estimation methods by direct comparison with simulations in a WMAP-realistic context. In addition, we show how the full bispectrum can be extracted from observational maps using these mode expansions, irrespective of the theoretical model under study. We also propose a universal definition of the bispectrum parameter F_NL for more consistent comparison between theoretical models. We obtain WMAP5 estimates of f_NL for the equilateral model from both our primordial and late-time estimators which are consistent with each other, as well as with results already published in the literature. These general bispectrum estimation methods should prove useful for the analysis of nonGaussianity in the Planck satellite data, as well as in other contexts.Comment: 41 pages, 17 figure

Macroscopic Distinguishability Between Quantum States Defining Different Phases of Matter: Fidelity and the Uhlmann Geometric Phase

We study the fidelity approach to quantum phase transitions (QPTs) and apply it to general thermal phase transitions (PTs). We analyze two particular cases: the Stoner-Hubbard itinerant electron model of magnetism and the BCS theory of superconductivity. In both cases we show that the sudden drop of the mixed state fidelity marks the line of the phase transition. We conduct a detailed analysis of the general case of systems given by mutually commuting Hamiltonians, where the non-analyticity of the fidelity is directly related to the non-analyticity of the relevant response functions (susceptibility and heat capacity), for the case of symmetry-breaking transitions. Further, on the case of BCS theory of superconductivity, given by mutually non-commuting Hamiltonians, we analyze the structure of the system's eigenvectors in the vicinity of the line of the phase transition showing that their sudden change is quantified by the emergence of a generically non-trivial Uhlmann mixed state geometric phase.Comment: 18 pages, 8 figures. Version to be publishe