Editorial overview: Folding and binding: In silico, in vitro and in cellula

The essence of any biological processes relies on the conformational states of macromolecules and their interactions. It comes therefore with no surprises that the study of folding and binding has been centre stage since the birth of structural biology. In this context, the collaborative efforts of experimen- talists and theoreticians have tremendously increased our current knowl- edge on macromolecular structure and recognition. Nevertheless, several challenges and open questions are still present and a multidisciplinary approach would appear the most appropriate means to shed light onto the mechanisms of folding and binding to the highest level of detail. This thematic issue brings together a collection of reviews describing our current understanding of folding and binding, looking at these fundamental pro- blems from a wide perspective ranging from the single molecule to the complexity of the living cell, drawing on approaches that span from compu- tational (in silico), to the test tube (in vitro) and cell cultures (in cellula)

Estimation of protein folding probability from equilibrium simulations

The assumption that similar structures have similar folding probabilities ($p_{fold}$) leads naturally to a procedure to evaluate $p_{fold}$ for every snapshot saved along an equilibrium folding-unfolding trajectory of a structured peptide or protein. The procedure utilizes a structurally homogeneous clustering and does not require any additional simulation. It can be used to detect multiple folding pathways as shown for a three-stranded antiparallel $\beta$-sheet peptide investigated by implicit solvent molecular dynamics simulations.Comment: 7 pages, 4 figures, supplemetary material

Optimal randomized multilevel algorithms for infinite-dimensional integration on function spaces with ANOVA-type decomposition

In this paper, we consider the infinite-dimensional integration problem on weighted reproducing kernel Hilbert spaces with norms induced by an underlying function space decomposition of ANOVA-type. The weights model the relative importance of different groups of variables. We present new randomized multilevel algorithms to tackle this integration problem and prove upper bounds for their randomized error. Furthermore, we provide in this setting the first non-trivial lower error bounds for general randomized algorithms, which, in particular, may be adaptive or non-linear. These lower bounds show that our multilevel algorithms are optimal. Our analysis refines and extends the analysis provided in [F. J. Hickernell, T. M\"uller-Gronbach, B. Niu, K. Ritter, J. Complexity 26 (2010), 229-254], and our error bounds improve substantially on the error bounds presented there. As an illustrative example, we discuss the unanchored Sobolev space and employ randomized quasi-Monte Carlo multilevel algorithms based on scrambled polynomial lattice rules.Comment: 31 pages, 0 figure

Level Set Approach to Reversible Epitaxial Growth

We generalize the level set approach to model epitaxial growth to include thermal detachment of atoms from island edges. This means that islands do not always grow and island dissociation can occur. We make no assumptions about a critical nucleus. Excellent quantitative agreement is obtained with kinetic Monte Carlo simulations for island densities and island size distributions in the submonolayer regime.Comment: 7 pages, 9 figure

Pricing and Hedging Asian Basket Options with Quasi-Monte Carlo Simulations

In this article we consider the problem of pricing and hedging high-dimensional Asian basket options by Quasi-Monte Carlo simulation. We assume a Black-Scholes market with time-dependent volatilities and show how to compute the deltas by the aid of the Malliavin Calculus, extending the procedure employed by Montero and Kohatsu-Higa (2003). Efficient path-generation algorithms, such as Linear Transformation and Principal Component Analysis, exhibit a high computational cost in a market with time-dependent volatilities. We present a new and fast Cholesky algorithm for block matrices that makes the Linear Transformation even more convenient. Moreover, we propose a new-path generation technique based on a Kronecker Product Approximation. This construction returns the same accuracy of the Linear Transformation used for the computation of the deltas and the prices in the case of correlated asset returns while requiring a lower computational time. All these techniques can be easily employed for stochastic volatility models based on the mixture of multi-dimensional dynamics introduced by Brigo et al. (2004).Comment: 16 page

On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

The paper concerns $L^1$- convergence to equilibrium for weak solutions of the spatially homogeneous Boltzmann Equation for soft potentials (-4\le \gm<0), with and without angular cutoff. We prove the time-averaged $L^1$-convergence to equilibrium for all weak solutions whose initial data have finite entropy and finite moments up to order greater than 2+|\gm|. For the usual $L^1$-convergence we prove that the convergence rate can be controlled from below by the initial energy tails, and hence, for initial data with long energy tails, the convergence can be arbitrarily slow. We also show that under the integrable angular cutoff on the collision kernel with -1\le \gm<0, there are algebraic upper and lower bounds on the rate of $L^1$-convergence to equilibrium. Our methods of proof are based on entropy inequalities and moment estimates.Comment: This version contains a strengthened theorem 3, on rate of convergence, considerably relaxing the hypotheses on the initial data, and introducing a new method for avoiding use of poitwise lower bounds in applications of entropy production to convergence problem

Scaling dependence on the fluid viscosity ratio in the selective withdrawal transition

In the selective withdrawal experiment fluid is withdrawn through a tube with its tip suspended a distance S above a two-fluid interface. At sufficiently low withdrawal rates, Q, the interface forms a steady state hump and only the upper fluid is withdrawn. When Q is increased (or S decreased), the interface undergoes a transition so that the lower fluid is entrained with the upper one, forming a thin steady-state spout. Near this transition the hump curvature becomes very large and displays power-law scaling behavior. This scaling allows for steady-state hump profiles at different flow rates and tube heights to be scaled onto a single similarity profile. I show that the scaling behavior is independent of the viscosity ratio.Comment: 33 Pages, 61 figures, 1 tabl

Phase Transitions in Chemisorbed Systems

Contains report on five research projects.Joint Services Electronics Program (Contract DAAG29-83-K-0003

2D-IR Study of a Photoswitchable Isotope-Labeled α-Helix

A series of photoswitchable, α-helical peptides were studied using two-dimensional infrared spectroscopy (2D-IR). Single-isotope labeling with 13C18O at various positions in the sequence was employed to spectrally isolate particular backbone positions. We show that a single 13C18O label can give rise to two bands along the diagonal of the 2D-IR spectrum, one of which is from an amide group that is hydrogen-bonded internally, or to a solvent molecule, and the other from a non-hydrogen-bonded amide group. The photoswitch enabled examination of both the folded and unfolded state of the helix. For most sites, unfolding of the peptide caused a shift of intensity from the hydrogen-bonded peak to the non-hydrogen-bonded peak. The relative intensity of the two diagonal peaks gives an indication of the fraction of molecules hydrogen-bonded at a certain location along the sequence. As this fraction varies quite substantially along the helix, we conclude that the helix is not uniformly folded. Furthermore, the shift in hydrogen bonding is much smaller than the change of helicity measured by CD spectroscopy, indicating that non-native hydrogen-bonded or mis-folded loops are formed in the unfolded ensemble

Motion of a vortex sheet on a sphere with pole vortices

We cons i der the motion of a vortex sheet on the surface of a unit sphere in the presence of point vortices xed on north and south poles.Analytic and numerical research revealed that a vortex sheet in two-dimensional space has the following three properties.First,the vortex sheet is linearly unstable due to Kelvin-Helmholtz instability.Second,the curvature of the vortex sheet diverges in nite time.Last,the vortex sheet evolves into a rolling-up doubly branched spiral,when the equation of motion is regularized by the vortex method.The purpose of this article is to investigate how the curvature of the sphere and the presence of the pole vortices