Thomas Wüst

Versatile approach to access the low temperature thermodynamics of lattice polymers and proteins.

We show that Wang-Landau sampling, combined with suitable Monte Carlo trial moves, provides a powerful method for both the ground state search and the determination of the density of states for the hydrophobic-polar (HP) protein model and the interacting self-avoiding walk (ISAW) model for homopolymers. We obtain accurate estimates of thermodynamic quantities for HP sequences with >100 monomers and for ISAWs up to >500 monomers. Our procedure possesses an intrinsic simplicity and overcomes the limitations inherent in more tailored approaches making it interesting for a broad range of protein and polymer models.

The HP model of protein folding: A challenging testing ground for Wang–Landau sampling

Abstract The hydrophobic-polar (HP) lattice protein model has gained much attention as a standard in assessing the efficiency of computational methods for protein structure prediction as well as for exploring the statistical physics of protein folding. In this work we show that Wang–Landau sampling, in connection with a suitable move set (pull moves), provides a powerful route for both the search of global energy minimum conformations and the precise determination of the density of states for HP sequences with up to 100 monomers in two and three dimensions. The main advantage of our approach lies in its general applicability to a broad range of lattice protein models that go beyond the scope of the HP model.

Unraveling the Beautiful Complexity of Simple Lattice Model Polymers and Proteins Using Wang-Landau Sampling

We describe a class of “bare bones” models of homopolymers which undergo coil-globule collapse and proteins which fold into their native states in free space or into denatured states when captured by an attractive substrate as the temperature is lowered. We then show how, with the use of a properly chosen trial move set, Wang-Landau Monte Carlo sampling can be used to study the rough free energy landscape and ground (native) states of these intriguingly simple systems and thus elucidate their thermodynamic complexity.

Optimized Wang-Landau sampling of lattice polymers: Ground state search and folding thermodynamics of HP model proteins

Coarse-grained (lattice-) models have a long tradition in aiding efforts to decipher the physical or biological complexity of proteins. Despite the simplicity of these models, however, numerical simulations are often computationally very demanding and the quest for efficient algorithms is as old as the models themselves. Expanding on our previous work [T. Wüst and D. P. Landau, Phys. Rev. Lett. 102, 178101 (2009)], we present a complete picture of a Monte Carlo method based on Wang-Landau sampling in combination with efficient trial moves (pull, bond-rebridging, and pivot moves) which is particularly suited to the study of models such as the hydrophobic-polar (HP) lattice model of protein folding. With this generic and fully blind Monte Carlo procedure, all currently known putative ground states for the most difficult benchmark HP sequences could be found. For most sequences we could also determine the entire energy density of states and, together with suitably designed structural observables, explore the thermodynamics and intricate folding behavior in the virtually inaccessible low-temperature regime. We analyze the differences between random and protein-like heteropolymers for sequence lengths up to 500 residues. Our approach is powerful both in terms of robustness and speed, yet flexible and simple enough for the study of many related problems in protein folding.

A Wang–Landau study of the phase transitions in a flexible homopolymer

Abstract Using Wang–Landau sampling we study the characteristic behavior of a flexible homopolymer (off-lattice) for chain lengths up to N = 300 . The Hamiltonian consists of a Lennard-Jones potential between all monomers, and an additional FENE potential between bonded monomers. From the resultant density of states, we calculate thermodynamic properties for a wide range of temperatures, including low temperatures that are inaccessible to traditional Monte Carlo algorithms. Peaks in the specific heat and radius of gyration indicate the coil–globule and solid–liquid transitions. With a careful implementation of the algorithm, we find no evidence of a liquid–liquid transition.

Scalable replica-exchange framework for Wang-Landau sampling

We investigate a generic, parallel replica-exchange framework for Monte Carlo simulations based on the Wang-Landau method. To demonstrate its advantages and general applicability for massively parallel simulations of complex systems, we apply it to lattice spin models, the self-assembly process in amphiphilic solutions, and the adsorption of molecules on surfaces. While of general current interest, the latter phenomena are challenging to study computationally because of multiple structural transitions occurring over a broad temperature range. We show how the parallel framework facilitates simulations of such processes and, without any loss of accuracy or precision, gives a significant speedup and allows for the study of much larger systems and much wider temperature ranges than possible with single-walker methods.

Application of the Wang–Landau algorithm to the dimerization of glycophorin A

A two-step Monte Carlo procedure is developed to investigate the dimerization process of the homodimer glycophorin A. In the first step, the energy density of states of the system is estimated by the Wang-Landau algorithm. In the second step, a production run is performed during which various energetical and structural observables are sampled to provide insight into the thermodynamics of the system. All seven residues LIxxGVxxGVxxT constituting the contact interface play a dominating role in the dimerization, however at different stages of the process. The leucine motif and to some extent the GxxxG motif are involved at the very beginning of the dimerization when the two helices come into contact, ensuring an interface already similar to the native one. At a lower temperature, the threonine motif stabilizes by hydrogen bonding the dimer, which finally converges toward its native state at around 300 K. The power and flexibility of the procedure employed here makes it an interesting alternative to other Monte Carlo methods for the study of similar protein systems.

Generic folding and transition hierarchies for surface adsorption of hydrophobic-polar lattice model proteins.

The thermodynamic behavior and structural properties of hydrophobic-polar (HP) lattice proteins interacting with attractive surfaces are studied by means of Wang-Landau sampling. Three benchmark HP sequences (48mer, 67mer, and 103mer) are considered with different types of surfaces, each of which attract either all monomers, only hydrophobic (H) monomers, or only polar (P) monomers, respectively. The diversity of folding behavior in dependence of surface strength is discussed. Analyzing the combined patterns of various structural observables, such as, e.g., the derivatives of the numbers of surface contacts, together with the specific heat, we are able to identify generic categories of folding and transition hierarchies. We also infer a connection between these transition categories and the relative surface strengths, i.e., the ratio of the surface attractive strength to the interchain attraction among H monomers. The validity of our proposed classification scheme is reinforced by the analysis of additional benchmark sequences. We thus believe that the folding hierarchies and identification scheme are generic for HP proteins interacting with attractive surfaces, regardless of chain length, sequence, or surface attraction.

Numerical integration using Wang–Landau sampling

Abstract We report a new application of Wang–Landau sampling to numerical integration that is straightforward to implement. It is applicable to a wide variety of integrals without restrictions and is readily generalized to higher-dimensional problems. The feasibility of the method results from a reinterpretation of the density of states in statistical physics to an appropriate measure for numerical integration. The properties of this algorithm as a new kind of Monte Carlo integration scheme are investigated with some simple integrals, and a potential application of the method is illustrated by the evaluation of integrals arising in perturbation theory of quantum many-body systems.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.