Statistical mechanics of the extensible and shearable elastic rod and of DNA

Recent Advances in Organic Piezoelectric Biomaterials for Energy and Biomedical Applications

The past decade has witnessed significant advances in medically implantable and wearable devices technologies as a promising personal healthcare platform. Organic piezoelectric biomaterials have attracted widespread attention as the functional materials in the biomedical devices due to their advantages of excellent biocompatibility and environmental friendliness. Biomedical devices featuring the biocompatible piezoelectric materials involve energy harvesting devices, sensors, and scaffolds for cell and tissue engineering. This paper offers a comprehensive review of the principles, properties, and applications of organic piezoelectric biomaterials. How to tackle issues relating to the better integration of the organic piezoelectric biomaterials into the biomedical devices is discussed. Further developments in biocompatible piezoelectric materials can spark a new age in the field of biomedical technologies.

Characterization of Structural and Configurational Properties of DNA by Atomic Force Microscopy

We describe a method to extract quantitative information on DNA structural and configurational properties from high-resolution topographic maps recorded by atomic force microscopy (AFM). DNA molecules are deposited on mica surfaces from an aqueous solution, carefully dehydrated, and imaged in air in Tapping Mode. Upon extraction of the spatial coordinates of the DNA backbones from AFM images, several parameters characterizing DNA structure and configuration can be calculated. Here, we explain how to obtain the distribution of contour lengths, end-to-end distances, and gyration radii. This modular protocol can be also used to characterize other statistical parameters from AFM topographies.

Group theory and biomolecular conformation: I. Mathematical and computational models

Biological macromolecules, and the complexes that they form, can be described in a variety of ways ranging from quantum mechanical and atomic chemical models, to coarser grained models of secondary structure and domains, to continuum models. At each of these levels, group theory can be used to describe both geometric symmetries and conformational motion. In this survey, a detailed account is provided of how group theory has been applied across computational structural biology to analyze the conformational shape and motion of macromolecules and complexes.

DNA deformations near charged surfaces: electron and atomic force microscopy views

DNA is a very important cell structural element, which determines the level of expression of genes by virtue of its interaction with regulatory proteins. We use electron (EM) and atomic force microscopy (AFM) to characterize the flexibility of double-stranded DNA ( approximately 150-950 nm long) close to a charged surface. Automated procedures for the extraction of DNA contours ( approximately 10-120 nm for EM data and approximately 10-300 nm for AFM data) combined with new statistical chain descriptors indicate a uniquely two-dimensional equilibration of the molecules on the substrate surface regardless of the procedure of molecule mounting. However, in contrast to AFM, the EM mounting leads to a noticeable decrease in DNA persistence length together with decreased kurtosis. Analysis of local bending on short length scales (down to 6 nm in the EM study) shows that DNA flexibility behaves as predicted by the wormlike chain model. We therefore argue that adhesion of DNA to a charged surface may lead to additional static bending (kinking) of approximately 5 degrees per dinucleotide step without impairing the dynamic behavior of the DNA backbone. Implications of this finding are discussed.

The persistence length of double stranded DNA determined using dark field tethered particle motion

The wormlike chain model describes the micromechanics of semiflexible polymers by introducing the persistence length. We propose a method of measuring the persistence length of DNA in a controllable near-native environment. Using a dark field microscope, the projected positions of a gold nanoparticle undergoing constrained Brownian motion are captured. The nanoparticle is tethered to a substrate using a single double stranded DNA (dsDNA) molecule and immersed in buffer. No force is exerted on the DNA. We carried out Monte Carlo simulations of the experiment, which give insight into the micromechanics of the DNA and can be used to interpret the motion of the nanoparticle. Our simulations and experiments demonstrate that, unlike other similar experiments, the use of nanometer instead of micrometer sized particles causes particle-substrate and particle-DNA interactions to be of negligible effect on the position distribution of the particle. We also show that the persistence length of the tethering DNA can be estimated with a statistical error of 2 nm, by comparing the statistics of the projected position distribution of the nanoparticle to the Monte Carlo simulations. The persistence lengths of 45 single molecules of four different lengths of dsDNA were measured under the same environmental conditions at high salt concentration. The persistence lengths we found had a mean value of 35 nm (standard error of 2.8 nm), which compares well to previously found values using similar salt concentrations. Our method can be used to directly study the effect of the environmental conditions (e.g., buffer and temperature) on the persistence length.

Coupling between denaturation and chain conformations in DNA: stretching, bending, torsion and finite size effects

We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri et al 2007 Phys. Rev. Lett. 99 088103). Our discrete helical wormlike chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in dsDNA and ssDNA, these effects are important. Moreover, we explore in this context the role of an additional loop entropy and analyze finite size effects in an experimental context, where polydA-polydT is clamped by two G-C strands, as well as for free polymers.

The Stochastic Elastica and Excluded-Volume Perturbations of DNA Conformational Ensembles

A coordinate-free Lie-group formulation for generating ensembles of DNA conformations in solution is presented. In this formulation, stochastic differential equations define sample paths on the Euclidean motion group. The ensemble of these paths exhibits the same behavior as solutions of the Fokker-Planck equation for the stochastically forced elastica. Longer chains for which the effects of excluded volume become important are handled by piecing together shorter chains and modeling their interactions. It is assumed that the final chain lengths of interest are long enough for excluded volume effects to become important, but not so long that the semi-flexible nature of the chain is lost. The effect of excluded volume is then taken into account by grouping short self-avoiding conformations into 'bundles' with common end constraints and computing average interaction effects between bundles. The accuracy of this approximation is shown to be good when using a numerically generated ensemble of self-avoiding sample paths as the baseline for comparison.

Conformational Analysis of Stiff Chiral Polymers with End-Constraints

We present a Lie-group-theoretic method for the kinematic and dynamic analysis of chiral semi-flexible polymers with end constraints. The first is to determine the minimum energy conformations of semi-flexible polymers with end constraints, and the second is to perform normal mode analysis based on the determined minimum energy conformations. In this paper, we use concepts from the theory of Lie groups and principles of variational calculus to model such polymers as inextensible or extensible chiral elastic rods with coupling between twisting and bending stiffnesses, and/or between twisting and extension stiffnesses. This method is general enough to include any stiffness and chirality parameters in the context of elastic filament models with the quadratic elastic potential energy function. As an application of this formulation, the analysis of DNA conformations is discussed. We demonstrate our method with examples of DNA conformations in which topological properties such as writhe, twist, and linking number are calculated from the results of the proposed method. Given these minimum energy conformations, we describe how to perform the normal mode analysis. The results presented here build both on recent experimental work in which DNA mechanical properties have been measured, and theoretical work in which the mechanics of non-chiral elastic rods has been studied.

Conformational statistics of stiff macromolecules as solutions to partial differential equations on the rotation and motion groups

Partial differential equations (PDE's) for the probability density function (PDF) of the position and orientation of the distal end of a stiff macromolecule relative to its proximal end are derived and solved. The Kratky-Porod wormlike chain, the Yamakawa helical wormlike chain, and the original and revised Marko-Siggia models are examples of stiffness models to which the present formulation is applied. The solution technique uses harmonic analysis on the rotation and motion groups to convert PDE's governing the PDF's of interest into linear algebraic equations which have mathematically elegant solutions.