Wang-Landau sampling in face-centered-cubic hydrophobic-hydrophilic lattice model proteins

Thermodynamics of hydrophobic-polar model proteins on the face-centered cubic lattice

The HP model, a coarse-grained protein representation with only hydrophobic (H) and polar (P) amino acids, has already been extensively studied on the simple cubic (SC) lattice. However, this geometry severely restricts possible bond angles, and a simple improvement is to instead use the face-centered cubic (fcc) lattice. In this paper, the density of states and ground state energies are calculated for several benchmark HP sequences on the fcc lattice using the replica-exchange Wang-Landau algorithm and a powerful set of Monte Carlo trial moves. Results from the fcc lattice proteins are directly compared with those obtained from a previous lattice protein folding study with a similar methodology on the SC lattice. A thermodynamic analysis shows comparable folding behavior between the two lattice geometries, but with a greater rate of hydrophobic-core formation persisting into lower temperatures on the fcc lattice.

An Adaptive Image Watermarking Method Combining SVD and Wang-Landau Sampling in DWT Domain

To keep a better trade-off between robustness and imperceptibility is difficult for traditional digital watermarks. Therefore, an adaptive image watermarking method combining singular value decomposition (SVD) and the Wang–Landau (WL) sampling method is proposed to solve the problem. In this method, the third-level approximate sub-band obtained by applying the three-level wavelet transform is decomposed by SVD to obtain the principal component, which is firstly selected as the embedded position. Then, the information is finally embedded into the host image by the scaling factor. The Wang–Landau sampling method is devoted to finding the best embedding coefficient through the proposed objective evaluation function, which is a global optimization algorithm. The embedding strength is adaptively adjusted by utilizing the historical experience, which overcomes the problem of falling into local optimization easily in many traditional optimization algorithms. To affirm the reliability of the proposed method, several image processing attacks are applied and the experimental results are given in detail. Compared with other existing related watermarking techniques based on both qualitative and quantitative evaluation parameters, such as peak signal to noise ratio (PSNR) and normalized cross-correlation (NC), this method has been proven to achieve a trade-off between robustness and invisibility.

Characterizing folding funnels with replica exchange Wang-Landau simulation of lattice proteins

We have studied the folding of ribonuclease A by mapping it onto coarse-grained lattice protein models. With replica exchange Wang-Landau sampling, we calculated the free energy vs end-to-end distance as a function of temperature. A mapping to the famous hydrophobic-polar (HP) model shows a relatively shallow folding funnel and flat free energy minimum, reflecting the high degeneracy of the ground state. In contrast, extending the HP model with an additional "neutral" monomer type (i.e., a mapping to the three-letter H0P model) has a well developed, rough free energy funnel with a low degeneracy ground state. In both cases, folding funnels are asymmetric with temperature dependent shape.

Thermodynamics and structure of macromolecules from flat-histogram Monte Carlo simulations

Over the last decade flat-histogram Monte Carlo simulations, especially multi-canonical and Wang-Landau simulations, have emerged as a strong tool to study the statistical mechanics of polymer chains. These investigations have focused on coarse-grained models of polymers on the lattice and in the continuum. Phase diagrams of chains in bulk as well as chains attached to surfaces were studied, for homopolymers as well as for protein-like models. Also, aggregation behavior in solution of these models has been investigated. We will present here the theoretical background for these simulations, explain the algorithms used and discuss their performance and give an overview over the systems studied with these methods in the literature, where we will limit ourselves to studies of coarse-grained model systems. Implementations of these algorithms on parallel computers will be also briefly described. In parallel to the development of these simulation methods, the power of a micro-canonical analysis of such simulations has been recognized, and we present the current state of the art in applying the micro-canonical analysis to phase transitions in nanoscopic polymer systems.