Helix formation and folding in an artificial peptide

Be positive: optimizing pramlintide from microcanonical analysis of amylin isoforms

Amylin, or human islet amyloid polypeptide (hIAPP), is a 37-residue hormone synergistic to insulin and co-secreted with it by β-cells in the pancreas. The deposition of its cytotoxic amyloid fibrils is strongly related to the progression of Type II diabetes (T2D) and islet graft failures. Notably, isoforms from some mammalian species, such as rats (rIAPP) and porcine (pIAPP), present a few key mutations preventing aggregation. This has lead to biotechnological development of drugs for adjunct therapies of T2D, such as pramlintide, a variant of hIAPP inspired by rIAPP whose proline substitutions have β-strand fibril-breaking properties. Ideally, such a drug should be formulated with insulin and co-administered, but this has been prevented by a poor solubility profile at the appropriate pH. Hopefully, this could be improved with appropriate point mutations, increasing the molecular net charge. Despite experimental progress, preliminary screening during rational drug design can greatly benefit from thermodynamic insight derived from molecular simulations. So we introduce microcanonical thermostatistics analysis of multicanonical (MUCA) simulations of wild-type amylin isoforms as a systematic assessment of protein thermostability. As a consequence of this comprehensive investigation, the most suitable single-point mutations able to optimize pramlintide are located among the wild-type amylin isoforms. In particular, we find that aggregation inhibition and increased solubility are inherited by pramlintide through further S20R substitution typical of pIAPP. Thus, we provide a consistent thermostatistical methodology to aid the design of improved adjunct therapies for T2D according to current clinical knowledge.

Partition function zeros of the square-lattice Ising model with nearest- and next-nearest-neighbor interactions

The distributions of the partition function zeros in the complex a=e2betaJ1 plane of the square-lattice Ising model with nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions are investigated as a function of R=J2/J1. Starting from the well-known two-circle distribution of the zeros a=+/-1+sqrt[2]eitheta for R=0 , finally the partition function zeros lie on the unit circle a=eitheta for R=infinity . Between these two ends, the changes in the zero distributions are described. Using the partition function zeros, the critical point ac(R) and the thermal scaling exponent yt(R) are estimated for the Ising ferromagnet (equivalently, antiferromagnet) and superantiferromagnet. For the special case of R=1/2 , the possible implications of the zero distributions are also discussed.

Adsorption of a hydrophobic-polar-model heteropolymer in an attractive nanotube

The adsorption of an off-lattice hydrophobic-polar-model heteropolymer in an attractive hydrophobic nanotube is presented by means of a multicanonical Monte Carlo simulation. In the model, the Lennard-Jones potential is assumed as an interaction potential between the effective monomers and the nanotube wall. The global minimum-energy configurations and the values of radius of gyration and end-to-end distance of these configurations are compared for both pure hydrophobic and polar heteropolymer models and with interaction term included model. The low-energy conformations for heteropolymers are extended when they interact with the nanotube which the conformational extensions are detected with some structural parameters.

Ring polymer simulations with global radius of curvature

We simulate three-dimensional flexible off-lattice ring polymers of length L up to L=4000 for various values of the global radius of curvature Rgrc=0.25 , 0.48, and 1.0 and Rgrc=2.0 . We utilize two different ensembles: one with a delta -function constraint on the radius, and the other with a theta -function. For both cases the global radius of curvature provides a valid regularization of polymers with thickness D=2Rgrc . The Flory-type critical exponent nu SAW of self-avoiding rings at D=2 is found to be nu SAW=0.5869(5) from the radii of gyration chain length scaling, while other D values produce consistent results. For our current implementation, the numerical effort of chain thickness calculations is bounded by a number O(LlnL) per single update. We also study low-temperature configurations of spatially dense Lennard-Jones homopolymers on a ring and identify some conformational building blocks.

Generalized-ensemble simulations of the human parathyroid hormone fragment PTH(1-34)

A generalized-ensemble technique, multicanonical sampling, is used to study the folding of a 34-residue human parathyroid hormone fragment. An all-atom model of the peptide is employed and the protein-solvent interactions are approximated by an implicit solvent. Our results demonstrate that generalized-ensemble simulations are well suited to sample low-energy structures of such large polypeptides. Configurations with a root-mean-square deviation to the crystal structure of less than 1 A are found. Finally, we discuss limitations of our implicit solvent model.

Multicanonical study of coarse-grained off-lattice models for folding heteropolymers

We have performed multicanonical simulations of hydrophobic-hydrophilic heteropolymers with two simple effective, coarse-grained off-lattice models to study the influence of specific interactions in the models on conformational transitions of selected sequences with 20 monomers. Another aspect of the investigation was the comparison with the purely hydrophobic homopolymer and the study of general conformational properties induced by the "disorder" in the sequence of a heteropolymer. Furthermore, we applied an optimization algorithm to sequences with up to 55 monomers and compared the global-energy minimum found with lowest-energy states identified within the multicanonical simulation. This was used to find out how reliable the multicanonical method samples the free-energy landscape, in particular for low temperatures.

Towards protein folding with evolutionary techniques

We present design details and first tests of a new evolutionary algorithm approach to ab initio protein folding. It does not focus on dihedral angles exclusively, but mainly operates on introduction, extension, break-up, and destruction of secondary structure elements, given as correlated dihedral angle values. In first test applications to polyalanines (up to 60 residues) and random primary sequences (up to 40 residues), we demonstrate that this use of prior knowledge is well balanced: On the one hand, it ensures quick introduction of secondary structure elements if they are favorable for a given primary sequence, but still allows for efficient location of pure random coil solutions without enforcing any secondary structure elements, if folds of this type are preferred by the given primary sequence. Furthermore, the algorithm is clearly able to pack several secondary structure elements into favorable tertiary structure arrangements, although no part of the algorithm is explicitly designed to do this. In first test examples on real-life peptides between 21 and 44 residues from the Protein Data Bank, the quality of the results depends on the force field used (as expected); nevertheless, we can show that the algorithm is able to find structures in good agreement with the targets easily and consistently, if the force field allows for that.

All-atom generalized-ensemble simulations of small proteins

We give an overview of some generalized-ensemble techniques that have proven successful in all-atom simulations of proteins. We show that these techniques enable efficient investigations of secondary structure formation and folding in peptides and small proteins. Results are presented for various alanine-based artificial peptides and a small protein, the 36-residued villin headpiece subdomain (HP-36). Our results indicate that all-atom simulations of proteins may be more restricted by the accuracy of the present energy functions than by the efficiency of the search algorithms.

Stochastic formulation of sampling dynamics in generalized ensemble methods

The fundamental relations of the sampling process in the multicanonical ensemble and simulated tempering have been studied in the expanded ensembles formalism. The simulated tempering is identified as the multicanonical sampling with the generalized weight determined by a Laplace transform of the temperature weight. The characteristic dynamics of both sampling methods has been verified in the stochastic formulation of the sampling process. Our study gives a necessary and sufficient condition for the weights to realize a uniform sampling in the energy and temperature spaces. Based on the stochastic model, robust force biased iteration schemes have been proposed to allow automatic determinations of uniform sampling weights.

Helix versus sheet formation in a small peptide

Segments with the amino acid sequence EKAYLRT (glutamine-lysine-alanine-tyrosine-leucine-arginine-threonine) appear in naturally occurring proteins both in alpha-helices and beta-sheets. For this reason, we have used this peptide to study how secondary structure formation in proteins depends on the local environment. Our data rely on multicanonical Monte Carlo simulations where the interactions among all atoms are taken into account. Results in gas phase are compared with that in an implicit solvent. We find that both the solvated molecule and EKAYLRT in gas phase form an alpha-helix when not interacting with other molecules. However, in the vicinity of a beta-strand, the peptide forms a beta-strand. Because of this change in secondary structure our peptide may provide a simple model for the alpha-->beta transition that is supposedly related to the outbreak of prion diseases and similar illnesses.

Determination of multicanonical weight based on a stochastic model of sampling dynamics

Based on the stochastic interpretation of the sampling process modeled by a Langevin equation, we present an effective iteration scheme to determine the weight in multicanonical molecular dynamics. Our method enables an automatic determination of the weight producing a uniform energy sampling via an iterative cancellation of the deterministic force in a Langevin equation. The deterministic force has been calculated from the energy trajectory by identifying the moments of the transition probability of a Fokker-Planck equation associated with a Langevin equation. The intimate relationship between the sampling process and the stochastic dynamics has been verified by applying the iteration scheme to a helix-coil transition of the 8-polyalanine system in a gas phase.