Swollen-Collapsed Transition in Random Hetero-Polymers

A lattice model of a hetero-polymer with random hydrophilic-hydrophobic charges interacting with the solvent is introduced, whose continnuum counterpart has been proposed by T. Garel, L. Leibler and H. Orland {J. Phys. II France 4, 2139 (1994)]. The transfer matrix technique is used to study various constrained annealed systems which approximate at various degrees of accuracy the original quenched model. For highly hydrophobic chains an ordinary $\theta$-point transition is found from a high temperature swollen phase to a low temperature compact phase. Depending on the type of constrained averages, at very low temperatures a swollen phase or a coexistence between compact and swollen phases are found. The results are carefully compared with the corresponding ones obtained in the continuum limit, and various improvements in the original calculations are discussed.Comment: 13 pages, 8 figures; revised version with minor changes, accepted for publication in European Physical Journal

Cluster Derivation of the Parisi Scheme for Disordered Systems

We propose a general quantitative scheme in which systems are given the freedom to sacrifice energy equi-partitioning on the relevant time-scales of observation, and have phase transitions by separating autonomously into ergodic sub-systems (clusters) with different characteristic time-scales and temperatures. The details of the break-up follow uniquely from the requirement of zero entropy for the slower cluster. Complex systems, such as the Sherrington-Kirkpatrick model, are found to minimise their free energy by spontaneously decomposing into a hierarchy of ergodically equilibrating degrees of freedom at different (effective) temperatures. This leads exactly and uniquely to Parisi's replica symmetry breaking scheme. Our approach, which is somewhat akin to an earlier one by Sompolinsky, gives new insight into the physical interpretation of the Parisi scheme and its relations with other approaches, numerical experiments, and short range models. Furthermore, our approach shows that the Parisi scheme can be derived quantitatively and uniquely from plausible physical principles.Comment: 6 pages, 3 figures, proceedings of international conference on "Disordered And Complex Systems", 10-14 July 2000 King's College Londo

Solvable Lattice Gas Models of Random Heteropolymers at Finite Density: II. Dynamics and Transitions to Compact States

In this paper we analyse both the dynamics and the high density physics of the infinite dimensional lattice gas model for random heteropolymers recently introduced in \cite{jort}. Restricting ourselves to site-disordered heteropolymers, we derive exact closed deterministic evolution equations for a suitable set of dynamic order parameters (in the thermodynamic limit), and use these to study the dynamics of the system for different choices of the monomer polarity parameters. We also study the equilibrium properties of the system in the high density limit, which leads to a phase diagram exhibiting transitions between swollen states, compact states, and regions with partial compactification. Our results find excellent verification in numerical simulations, and have a natural and appealing interpretation in terms of real heteropolymers.Comment: 12 pages, 8 eps figures, revised version (to be published in EPJ

Magnetization enumerator of real-valued symmetric channels in Gallager error-correcting codes

Using the magnetization enumerator method, we evaluate the practical and theoretical limitations of symmetric channels with real outputs. Results are presented for several regular Gallager code constructions.Comment: 5 pages, 1 figure, to appear as Brief Report in Physical Review

Ultrafast electron diffraction using an ultracold source

We present diffraction patterns from micron-sized areas of mono-crystalline graphite obtained with an ultracold and ultrafast electron source. We show that high spatial coherence is manifest in the visibility of the patterns even for picosecond bunches of appreciable charge, enabled by the extremely low source temperature (~ 10 K). For a larger, ~ 100 um spot size on the sample, spatial coherence lengths > 10 nm result, sufficient to resolve diffraction patterns of complex protein crystals. This makes the source ideal for ultrafast electron diffraction of complex macromolecular structures such as membrane proteins, in a regime unattainable by conventional photocathode sources. By further reducing the source size, sub-um spot sizes on the sample become possible with spatial coherence lengths exceeding 1 nm, enabling ultrafast nano-diffraction for material science.Comment: 5 pages, 4 figure

Determination of Interaction Potentials of Amino Acids from Native Protein Structures: Test on Simple Lattice Models

We propose a novel method for the determination of the effective interaction potential between the amino acids of a protein. The strategy is based on the combination of a new optimization procedure and a geometrical argument, which also uncovers the shortcomings of any optimization procedure. The strategy can be applied on any data set of native structures such as those available from the Protein Data Bank (PDB). In this work, however, we explain and test our approach on simple lattice models, where the true interactions are known a priori. Excellent agreement is obtained between the extracted and the true potentials even for modest numbers of protein structures in the PDB. Comparisons with other methods are also discussed.Comment: 24 pages, 4 figure

Halogen-bonded guanine base pairs, quartets and ribbons

Halogen bonding is studied in different structures consisting of halogenated guanine DNA bases, including the Hoogsteen guanine–guanine base pair, two different types of guanine ribbons (R-I and R-II) consisting of two or three monomers, and guanine quartets. In the halogenated base pairs (except the Cl-base pair, which has a very non-planar structure with no halogen bonds) and R-I ribbons (except the At trimer), the potential N-X•••O interaction is sacrificed to optimise the N-X•••N halogen bond. In the At trimer, the astatines originally bonded to N1 in the halogen bond donating guanines have moved to the adjacent O6 atom, enabling O-At•••N, N-At•••O, and N-At•••At halogen bonds. The brominated and chlorinated R-II trimers contain two N-X•••N and two N-X•••O halogen bonds, whereas in the iodinated and astatinated trimers, one of the N-X•••N halogen bonds is lost. The corresponding R-II dimers keep the same halogen bond patterns. The G-quartets display a rich diversity of symmetries and halogen bond patterns, including N-X•••N, N-X•••O, N-X•••X, O-X•••X, and O-X•••O halogen bonds (the latter two facilitated by the transfer of halogens from N1 to O6). In general, halogenation decreases the stability of the structures. However, the stability increases with the increasing atomic number of the halogen, and the At-doped R-I trimer and the three most stable At-doped quartets are more stable than their hydrogenated counterparts. Significant deviations from linearity are found for some of the halogen bonds (with halogen bond angles around 150°).Publisher PDFPeer reviewe

Stacking with the unnatural DNA base 6-ethynylpyridone

The authors are grateful to EaStCHEM for computational support via the EaStCHEM Research Computing Facility.It was previously reported that the incorporation of 6-ethynylpyridone (E) into a DNA duplex (replacing T in a T:A base pair) leads to DNA duplexes that are more stable than the T:A-containing duplexes. DFT calculations at the M06-2X/6-31+G(d) and BLYP-D3/6-31+G(d) levels on various base pairs, stacked bases and stacked base pairs in continuum solvation water suggest that the observed increased stability of E:A-containing duplexes is due to the combined effects of stronger base pairing and enhanced stacking of the E:A base pair.PostprintPostprintPeer reviewe