We give a theoretical analysis of bead motion in tethered-particle experiments, a single-molecule technique that has been used to explore the dynamics of a variety of macromolecules of biological interest. Our analysis reveals that the proximity of the tethered bead to a nearby surface gives rise to a volumeexclusion effect, resulting in an entropic stretching-force on the molecule that changes its statistical properties. In addition, volume exclusion brings about intriguing scaling relations between key observables (statistical moments of the bead) and parameters such as bead size and contour length of the molecule. We present analytic and numerical results for these effects in both flexible and semiflexible tethers. Finally, our results give a precise, experimentally testable prediction for the probability distribution of the bead center measured from the polymer attachment point. DOI: 10.1103/PhysRevLett.96.088306 PACS numbers: 82.37.Rs, 36.20.Ey, 82.35.Pq, 87.14.Gg Single-molecule biophysics has rapidly become an experimental centerpiece in the dissection of cellular machinery. This part of the biophysics repertoire often relies, in turn, on the use of micron-scale beads as a reporter of underlying molecular motions in these single-molecule systems. Thus, a key part of the theoretical infrastructure of this field is a clear understanding of the role that these beads play in altering the statistical properties of the macromolecules which are the real target of interest in such experiments. Beyond interest in the in vitro consequences of tethered-particle motions, many processes within the cell themselves involve tethering. The statisticalmechanical analysis performed here may prove useful for understanding in vivo processes, in addition to the in vitro consequences that form the main motivation for the work.Figure 1 sketches the tethered-particle method (TPM). The main idea is that a macromolecule (for example DNA or some protein that translocates DNA or RNA) is anchored at one end to a surface, while the other end of the molecular complex is attached to an otherwise free microsphere (''bead''). In contrast to classic DNA-stretching experiments, no external stretching force is applied to the bead; instead its motion is passively observed, for example, using single-particle tracking. Thus, the observed motion of the bead serves as a reporter of the underlying, invisible, macromolecular motion. This technique has been used in a variety of settings, e.g., the examination of nanometerscale motions of motors like kinesin [1] or RNA polymerase [2,3], protein synthesis by ribosomes [4], exonuclease translocation on DNA [5,6], protein mediated deformation [7] and loop formation [8] in DNA, DNA hybridization [9], and DNA motion [10,11]. The main goal of this Letter is to show how the proximity of the reporter bead to the surface affects the interpretation of the reported data and can even alter the conformation of the macromolecule of interest. A theoretical understanding of these effects will improve the ability ...

We explore the apparent discrepancy between experimental data and theoretical calculations of the lattice resistance of bcc tantalum. We present an empirical potential calculation for the temperature dependence of the Peierls stress in this system and an ab initio calculation of the zero-temperature Peierls stress, which employs periodic boundary conditions, those best suited to the study of metallic systems at the electronic-structure level. Our ab initio value for the Peierls stress is over five times larger than current extrapolations of experimental lattice resistance to zero temperature. Although we find that the common techniques for such extrapolation indeed tend to underestimate the zero-temperature limit, the amount of the underestimation we observe is only 10%-20%, leaving open the possibility that mechanisms other than the lattice resistance to motion of an isolated, straight dislocation are important in controlling the process of low-temperature slip.

We initiate the development of a theory of the elasticity of nanoscale objects based upon new physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in terms of local group contributions and gives insight into the breakdown of standard continuum relations. We also give two applications. In the first, we show how to use the theory to derive a new relation between the bending and stretching properties of nanomechanical resonators and to prove that it is much more accurate than the continuum-based relations currently employed in present experimental analyses. In the second, we use the new approach to link features of the underlining electronic structure to the elastic response of a silicon nanoresonator. I INTRODUCTIONThe recent development of artificial free-standing structures of nanometer dimensions has led to great interest in their mechanical properties. A wealth of experimental information is now available for nanowires 1-4 and nanotubes, 1, 5, 6 and a computational literature is developing on the subject.7-13 Many of these works make use of results from the continuum theory of elasticity to analyze the behavior of nanometer structures. However, the applicability of continuum theories to nanoscale objects, where atomic-level inhomogeneities come to the fore, has yet to be explored in depth.Rigorous understanding of the elastic properties of nanoscale systems is crucial in understanding their mechanical behavior and presents an intriguing theoretical challenge lying at the cross-over between the atomic level and the continuum. In the absence of an appropriate theoretical description at this cross-over, critical questions remain to be answered including the extent to which continuum theories can be pushed into the nanoregime, how to provide systematic corrections to continuum theory, what effects do different bonding arrangements have on elastic response, and what signatures in the electronic structure correlate with the mechanical properties of the overall structure?Recently, there have been a number of theoretical explorations of the impact of nanoscale structure on mechanical properties.13-18 These studies fall under two broad approaches, either the addition of surface and edge corrections to bulk continuum theories 13, 14 or the extraction of overall mechanical response from atomic scale interactions.15-18 The latter approach has the distinct advantage of allowing first principles understanding of how different chemical groups and bonding arrangements contribute to overall elastic response, thus opening the potential for the rational design of nanostructures with specific properties.In coarse graining from interatomic interactions to mechanical response, some works rely upon the problematic decomposition of the total system energy into a direct sum of atomic energies, 15, 16 which is always arbitrary and particularly inconvenient for connection with ab initio electronic structure calculations. The remaining works which atte...

No abstract

Through the use of perturbation theory, in this work we develop a method which allows for a substantial reduction in the size of the plane-wave basis used in density-functional calculations. This method may be used for both pseudopotentials and all-electron calculations and is particularly beneficial in the latter case. In all cases, the approach has the advantage of allowing accurate predictions of transferability errors for any environment. Finally, this method can be easily implemented into conjugate gradient techniques and it is therefore computationally efficient. In this work, we apply this method to study high pressure phases of boron. We find that boron undergoes a phase transition from the α12-B structure to the αga-B structure, both of which are semiconducting. The αga-B structure has lower energy than traditional mono-atomic structures, which supports the assertion that the metallic, and hence superconducting phase, for boron is much more complicated than a simple mono-atomic crystal.

No abstract

We present a comparative study of the influence of atomic-scale surface steps on dislocation nucleation at crystal surfaces based on an all atom method and a hierarchal multiscale approach. The multiscale approach is based on the variational boundary integral formulation of the Peiersl-Nabarro dislocation model in which interatomic layer potentials derived from atomic calculations of generalized stacking fault energy surfaces are incorporated. We have studied nucleation of screw dislocations in two bcc material systems, molybdenum and tantalum, subjected to simple shear stress. Compared to dislocation nucleation from perfectly flat surfaces, the presence of atomic scale surface steps rapidly reduces the critical stress for dislocation nucleation by almost an order of magnitude as the step height increases. In addition, they may influence the slip planes on which dislocation nucleation occurs. The results of the all atom method and the multiscale approach are in good agreement, even for steps with height of only a single atomic layer. Such corroboration supports the further use of the multiscale approach to study dislocation nucleation phenomena in more realistic geometries of technological importance, which are beyond the reach of all current atom simulations.

The variational boundary integral formulation of the Peierls-Nabarro dislocation model has recently become one of the most effective multiscale approaches for the analysis of dislocation nucleation problems. By representing the structure of a dislocation as the relative displacement between two adjacent atomic layers along the slip plane, the model allows for the convenient incorporation of atomic information to treat the deformation of the dislocation core as continuous deformation, therefore eliminating the uncertain core cutoff parameter associated with the singularity of continuum elastic dislocation theory. By reducing many atomic degrees of freedom to fewer, yet more physically intuitive, degrees of freedom in this multiscale approach, one may gain a greater understanding of relevant physical processes in larger systems with more realistic geometries. Application of this approach requires the understanding of the reliability of this approach, or at least, it correlation to that of all atom calculations. Using nucleation of a 111 screw dislocation at a step from a {112} surface of tantalum as an example, this paper provides an atomistic corroborative study of this multiscale approach. The results show the critical stresses for dislocation nucleation in this configuration obtained by the multiscale approach are in good agreement with all atom calculations.