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

Organism complexity anti-correlates with proteomic β-aggregation propensity

We introduce a novel approach to estimate differences in the β-aggregation potential of eukaryotic proteomes. The approach is based on a statistical analysis of the β-aggregation propensity of polypeptide segments, which is calculated by an equation derived from first principles using the physicochemical properties of the natural amino acids. Our analysis reveals a significant decreasing trend of the overall β-aggregation tendency with increasing organism complexity and longevity. A comparison with randomized proteomes shows that natural proteomes have a higher degree of polarization in both low and high β-aggregation prone sequences. The former originates from the requirement of intrinsically disordered proteins, whereas the latter originates from the necessity of proteins with a stable folded structure. Published by Cold Spring Harbor Laboratory Press. Copyright © 2005 The Protein Society

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

Random-Anisotropy-Axis Magnet With Infinite Anisotropy

We have studied the random-axis magnet with infinite anisotropy by three methods: Cayley-tree approximation, Migdal-Kadanoff renormalization group (MKRG), and Imry-Ma scaling. In the Cayley-tree approximation, by an examination of susceptibilities, it is shown that there exists a competition between the coordination number z and the number of components n of the spins which leads to either ferromagnetic or spin-glass order. Using the MKRG at very low temperature we map out approximately the regimes of the ferromagnetic, spin-glass, and disordered phases as a function of n and the spatial dimension, d. The Imry-Ma arguments are made as an additional method for obtaining information on the critical dimension. Comparisons of these results with the previous literature are made

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

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

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

Phase Transitions in Chemisorbed Systems

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