Bayesian field theoretic reconstruction of bond potential and bond mobility in single molecule force spectroscopy

Quantifying the forces between and within macromolecules is a necessary first step in understanding the mechanics of molecular structure, protein folding, and enzyme function and performance. In such macromolecular settings, dynamic single-molecule force spectroscopy (DFS) has been used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, have been used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complex-shaped bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule, thereby presenting an incomplete picture of the overall bond dynamics. To solve these challenges, we have developed a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experiemental and statistical parameters in our method are estimated empirically directly from the data. Upon testing our method on simulated data, our regularized approach requires fewer data and allows simultaneous inference of both complex bond potentials and diffusivity profiles.Comment: In review - Python source code available on github. Abridged abstract on arXi

Unification of step bunching phenomena on vicinal surfaces

We unify step bunching (SB) instabilities occurring under various conditions on crystal surfaces below roughening. We show that when attachment-detachment of atoms at step edges is the rate-limiting process, the SB of interacting, concentric circular steps is equivalent to the commonly observed SB of interacting straight steps under deposition, desorption, or drift. We derive a continuum Lagrangian partial differential equation, which is used to study the onset of instabilities for circular steps. These findings place on a common ground SB instabilities from numerical simulations for circular steps and experimental observations of straight steps

Simulation of axisymmetric stepped surfaces with a facet

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.Includes bibliographical references (p. 255-266).A crystal lattice with a small miscut from the plane of symmetry has a surface which consists of a series of atomic height steps separated by terraces. If the surface of this crystal is not in equilibrium with the surrounding medium, then its evolution is strongly mediated by the presence of these steps, which act as sites for attachment and detachment of diffusing adsorbed atoms ('adatoms'). In the absence of material deposition and evaporation, steps move in response to two main physical effects: line tension, which is caused by curvature of the step edge, and step-step interactions which can arise because of thermal step fluctuations, or elastic effects. This thesis focuses on axisymmetric crystals, with the result that the position of a step is uniquely described by a single scalar variable, and the step positions obey a coupled system of "step-flow" Ordinary Differential Equations (step flow ODEs). Chapter 2 of this thesis concentrates on the derivation and numerical solution of these equations, and their properties in the limits of slow adatom terrace diffusion and slow adatom attachment-detachment. Chapter 3 focuses on the analysis carried out by Margetis, Aziz and Stone ('MAS') [78] on a Partial Differential Equation (PDE) description of surface evolution.(cont.) Here, the crystal is also axisymmetric and has a single macroscopically flat region, a facet. It is discovered that the boundary condition of Step Chemical Potential Continuity, first suggested by Spohn [109] yields results that are inconsistent with the scalings predicted by the MAS analysis and with results from the step flow ODEs. The 'step drop' condition suggested by Israeli and Kandel [50] is implemented instead, and is shown to give good agreement with the results from the step flow ODEs. Chapters 4 and 5 explore the evolution of algebraic profiles: instead of starting with steps that are equally spaced, the step radii are initialized as a more general algebraic function of the height. In these two chapters, results are presented which involve approximate self-similarity of the profiles, a stability analysis of small perturbations, and quantification of decay rates. Chapter 6 of this thesis details the numerical procedure used to integrate the step flow equations. A 'multi-adaptive' time integrator is used where different time steps are taken for different components of the solution. This procedure has benefits over a standard integrator, because when a few steps cluster tightly together, these steps (and these steps only) become very stiff to integrate.(cont.) Whereas the inner most steps in the structure undergo a rapid motion, the majority of steps which are sufficiently far away from the facet, move relatively slowly and exhibit smooth behaviour in time. Using the same time step for all components in the solution is therefore quite inefficient. This chapter discusses the concept of "local stiffness", and how the motion of the inner most steps is handled.by Pak-Wing Fok.Ph.D

Continuum Theory of Nanostructure Decay Via a Microscale Condition

The morphological relaxation of faceted crystal surfaces is studied via a continuum approach. Our formulation includes (i) an evolution equation for the surface slope that describes step line tension, g1, and step repulsion energy, g3; and (ii) a condition at the facet edge (a free boundary) that accounts for discrete effects via the collapse times, tn, of top steps. For initial cones and tn[approximate]t-tilde n4, we use t-tilde(g) from step simulations and predict self-similar slopes in agreement with simulations for any g=g3/g1>0. We show that for g>>1, (i) the theory simplifies to an equilibrium-thermodynamics model; (ii) the slope profiles reduce to a universal curve; and (iii) the facet radius scales as g-3/4.Engineering and Applied Science

Facet evolution on supported nanostructures: Effect of finite height

The surface of a nanostructure relaxing on a substrate consists of a finite number of interacting steps and often involves the expansion of facets. Prior theoretical studies of facet evolution have focused on models with an infinite number of steps, which neglect edge effects caused by the presence of the substrate. By considering diffusion of adsorbed atoms (adatoms) on terraces and attachment-detachment of atoms at steps, we show that these edge or finite height effects play an important role in the structure's macroscopic evolution. We assume diffusion-limited kinetics for adatoms and a homoepitaxial substrate. Specifically, using data from step simulations and a continuum theory, we demonstrate a switch in the time behavior of geometric quantities associated with facets: the facet edge position in a straight-step system and the facet radius of an axisymmetric structure. Our analysis and numerical simulations focus on two corresponding model systems where steps repel each other through entropic and elastic dipolar interactions. The first model is a vicinal surface consisting of a finite number of straight steps; for an initially uniform step train, the slope of the surface evolves symmetrically about the centerline, i.e., the middle step when the number of steps is odd. The second model is an axisymmetric structure consisting of a finite number of circular steps; in this case, we include curvature effects which cause steps to collapse under the effect of line tension. In the first case, we show that the position of the facet edge, measured from the centerline, switches from O(t^1/4) behavior to O(t^1/5) (where t is time). In the second case, the facet radius switches from O(t^1/4) to O(t). For the axisymmetric case, we also predict analytically through a continuum shock wave theory how the individual collapse times are modified by the effects of finite height under the assumption that step interactions are weak compared to the step line tension

Charge transport-mediated recruitment of DNA repair enzymes

Damaged or mismatched bases in DNA can be repaired by Base Excision Repair (BER) enzymes that replace the defective base. Although the detailed molecular structures of many BER enzymes are known, how they colocalize to lesions remains unclear. One hypothesis involves charge transport (CT) along DNA [Yavin, {\it et al.}, PNAS, {\bf 102}, 3546, (2005)]. In this CT mechanism, electrons are released by recently adsorbed BER enzymes and travel along the DNA. The electrons can scatter (by heterogeneities along the DNA) back to the enzyme, destabilizing and knocking it off the DNA, or, they can be absorbed by nearby lesions and guanine radicals. We develop a stochastic model to describe the electron dynamics, and compute probabilities of electron capture by guanine radicals and repair enzymes. We also calculate first passage times of electron return, and ensemble-average these results over guanine radical distributions. Our statistical results provide the rules that enable us to perform implicit-electron Monte-Carlo simulations of repair enzyme binding and redistribution near lesions. When lesions are electron absorbing, we show that the CT mechanism suppresses wasteful buildup of enzymes along intact portions of the DNA, maximizing enzyme concentration near lesions.Comment: 9 Figures, Accepted to J. Chem. Phy