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

Two-state folding, folding through intermediates, and metastability in a minimalistic hydrophobic-polar model for proteins

Within the frame of an effective, coarse-grained hydrophobic-polar protein model, we employ multicanonical Monte Carlo simulations to investigate free-energy landscapes and folding channels of exemplified heteropolymer sequences, which are permutations of each other. Despite the simplicity of the model, the knowledge of the free-energy landscape in dependence of a suitable system order parameter enables us to reveal complex folding characteristics known from real bioproteins and synthetic peptides, such as two-state folding, folding through weakly stable intermediates, and glassy metastability.

Microcanonical analyses of peptide aggregation processes

We propose the use of microcanonical analyses for numerical studies of peptide aggregation transitions. Performing multicanonical Monte Carlo simulations of a simple hydrophobic-polar continuum model for interacting heteropolymers of finite length, we find that the microcanonical entropy behaves convex in the transition region, leading to a negative microcanonical specific heat. As this effect is also seen in first-order-like transitions of other finite systems, our results provide clear evidence for recent hints that the characterization of phase separation in first-order-like transitions of finite systems profits from this microcanonical view.

Structural properties of small semiconductor-binding synthetic peptides

We have performed exhaustive multicanonical Monte Carlo simulations of three 12-residue synthetic peptides in order to investigate the thermodynamic and structural properties as well as the characteristic helix-coil transitions. In these studies, we employ a realistic model where the interactions between all atoms are taken into account. Effects of solvation are also simulated by using an implicit-solvent model.

Energy optimization for off-lattice protein folding

Two three-dimensional AB off-lattice protein models consisting of hydrophobic and hydrophilic monomers are studied in this paper. By incorporating an extra energy contribution into the original energy function, the protein folding is converted from a constraint optimization problem into an unconstrained one which can be solved by the well-known gradient method. From the initial configurations randomly generated by the heuristic strategy proposed in this paper, our algorithm can find better results than those by nPERM for the four Fibonacci sequences. Based on the initial configurations obtained by energy landscape paving (ELP) routine, some of our results for the lowest energies are better than the best values reported in the literature.

Statistical-temperature Monte Carlo and molecular dynamics algorithms

A simulation method is presented that achieves a flat energy distribution by updating the statistical temperature instead of the density of states in Wang-Landau sampling. A novel molecular dynamics algorithm (STMD) applicable to complex systems and a Monte Carlo algorithm are developed from this point of view. Accelerated convergence for large energy bins, essential for large systems, is demonstrated in tests on the Ising model, the Lennard-Jones fluid, and bead models of proteins. STMD shows a superior ability to find local minima in proteins and new global minima are found for the 55 bead AB model in two and three dimensions. Calculations of the occupation probabilities of individual protein inherent structures provide new insights into folding and misfolding.

Structure optimization in a three-dimensional off-lattice protein model

We studied a three-dimensional off-lattice AB model with two species of monomers, hydrophobic (A) and hydrophilic (B), and present two optimization algorithms: face-centered-cubic (FCC)-lattice pruned-enriched-Rosenbluth method (PERM) and subsequent conjugate gradient (PERM++) minimization and heuristic conjugate gradient (HCG) simulation based on "off-trap" strategy. In PERM++, we apply the PERM to the FCC-lattice to produce the initial conformation, and conjugate gradient minimization is then used to reach the minimum energy state. Both algorithms have been tested in the three-dimensional AB model for all sequences with lengths 13 < or = n < or = 55. The numerical results show that the proposed methods are very promising for finding the ground states of proteins. In several cases, we renew the putative ground states energy values.

Deconstructing the energy landscape: constraint-based algorithms for folding heteropolymers

We apply the computational methodology of phase retrieval to the problem of folding heteropolymers. The ground state fold of the polymer is defined by the intersection of two sets in the configuration space of its constituent monomers: a geometrical chain constraint and a threshold constraint on the contact energy. A dynamical system is then defined in terms of the projections to these constraint sets, such that its fixed points solve the set intersection problem. We present results for two off-lattice hydrophobic-polar models: one with only rotameric degrees of freedom, and one proposed by Stillinger [Phys. Rev. E 48, 1469 (1993)] with flexible bond angles. Our phase retrieval inspired algorithm is competitive with more established algorithms and even finds lower-energy folds for one of the longer polymer chains.

Heuristic algorithm for off-lattice protein folding problem

Enlightened by the law of interactions among objects in the physical world, we propose a heuristic algorithm for solving the three-dimensional (3D) off-lattice protein folding problem. Based on a physical model, the problem is converted from a nonlinear constraint-satisfied problem to an unconstrained optimization problem which can be solved by the well-known gradient method. To improve the efficiency of our algorithm, a strategy was introduced to generate initial configuration. Computational results showed that this algorithm could find states with lower energy than previously proposed ground states obtained by nPERM algorithm for all chains with length ranging from 13 to 55.

A quasi-physical algorithm for the structure optimization in an off-lattice protein model

In this paper, we study an off-lattice protein AB model with two species of monomers, hydrophobic and hydrophilic, and present a heuristic quasi-physical algorithm. First, by elaborately simulating the movement of the smooth solids in the physical world, we find low-energy conformations for a given monomer chain. A subsequent off-trap strategy is then proposed to trigger a jump for a stuck situation in order to get out of the local minima. The algorithm has been tested in the three-dimensional AB model for all sequences with lengths of 13-55 monomers. In several cases, we renew the putative ground state energy values. The numerical results show that the proposed methods are very promising for finding the ground states of proteins.

Structure optimization by conformational space annealing in an off-lattice protein model

The optimization results by conformational space annealing are presented for an off-lattice protein model consisting of hydrophobic and hydrophilic residues in Fibonacci sequences. The ground-state energies found are lower than those reported in the literature. In addition, the ground-state conformations in three dimensions exhibit the important aspect of forming a single hydrophobic core in real proteins. The energy landscape for the population of local minima is also investigated.