Narrow Results

We discuss the results of a computer simulation of the biopolymer crystal growth and aggregation based on the 2D lattice Monte Carlo technique and the HP approximation of the biopolymers. As a modeled molecule (growth unit) we comparatively consider the previously studied non-mutant lysozyme protein, Protein Data Bank (PDB) ID: 193L, which forms, under a certain set of thermodynamic-kinetic conditions, the tetragonal crystals, and an amyloidogenic variant of the lysozyme, PDB ID: 1LYY, which is known as fibril-yielding and prone-to-aggregation agent. In our model, the site-dependent attachment, detachment and migration processes are involved. The probability of growth unit motion, attachment and detachment to/from the crystal surface are assumed to be proportional to the orientational factor representing the anisotropy of the molecule. Working within a two-dimensional representation of the truly three-dimensional process, we also argue that the crystal grows in a spiral way, whereby one or more screw dislocations on the crystal surface give rise to a terrace. We interpret the obtained results in terms of known models of crystal growth and aggregation such as B-C-F (Burton-Cabrera-Frank) dislocation driven growth and M-S (Mullins-Sekerka) instability concept, with stochastic aspects supplementing the latter. We discuss the conditions under which crystals vs non-crystalline protein aggregates appear, and how the process depends upon difference in chemical structure of the protein molecule seen as the main building block of the elementary crystal cell.

The hydrophobic-polar (HP) model has emerged as one of the standard approaches for simulating protein folding. In this work, we used this model together with Wang–Landau (WL) sampling and appropriate Monte Carlo trial moves to determine the density of states and thermodynamics for two cases: Protein adsorption and protein confinement, in the vicinity of attractive surfaces. The influence on the adsorption behavior of surface attractive strength in the adsorption case and volumetric spaces in the confinement case will be discussed.

Based on two-dimensional square lattice models of proteins, the relation between folding time and temperature is studied by Monte Carlo simulation. The results can be represented by a kinetic model with three states — random coil, molten globule, and native state. The folding process is composed of nonspecific collapse and final searching for the native state. At high temperature, it is easy to escape from local traps in the folding process. With decreasing temperature, because of the trapping in local traps, the final searching speed decreases. Then the folding shows chevron rollover. Through the analysis of the fitted parameters of the kinetic model, it is found that the main difference between the energy landscapes of the HP model and the Go model is that the number of local minima of the Go model is less than that of the HP model.

Prediction of least energy conformation of a protein from its primary structure (chain of amino acids) is an optimization problem associated with a large complex energy landscape. In this study, a simple 2D hydrophobic–hydrophilic model was used to model the protein sequence, which allows the fast and efficient design of genetic algorithm-based protein structure prediction approach. The neighborhood search strategy is integrated into the genetic operator. The neighborhood search guides the genetic operator to regions in the computational space with good solutions. To prevent convergence to local optima, the proposed method employs crowding-based parent replacement strategy, which improves the performance of the algorithm and the ability to deal with multiple numbers of solutions. The proposed algorithm was tested with a standard benchmark of HP sequences and comparative results demonstrate that the proposed system beats most of the evolutionary algorithms for seven sequences. It finds the best energy for a sequence of length $50(E=-22)$, $64(E=-42)$, $85(E=-54)$, $100(E=-71)$, $102(E=-75)$, $123(E=-91)$ and $136(E=-105)$.

In this paper, we introduce the 2D hexagonal lattice as a biologically meaningful alternative to the standard square lattice for the study of protein folding in the HP model. We show that the hexagonal lattice alleviates the "sharp turn" problem and models certain aspects of the protein secondary structure more realistically. We present a ⅙-approximation and a clustering heuristic for protein folding on the hexagonal lattice. In addition to these two algorithms, we also implement a Monte Carlo Metropolis algorithm and a branch-and-bound partial enumeration algorithm, and conduct experiments to compare their effectiveness.

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e.p(r) = p₁(r) +p₂(r), where p₁(r) and p₂(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N^-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of ε_HH, ε_HP and ε_PP. Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.

The inverse protein folding problem is that of designing an amino acid sequence which has a prescribed native protein fold. This problem arises in drug design where a particular structure is necessary to ensure proper protein-protein interactions. The input to the inverse protein folding problem is a shape and the goal is to design a protein sequence with a unique native fold that closely approximates the input shape. Gupta et al.¹ introduced a design in the 2D HP model of Dill that can be used to approximate any given (2D) shape. They conjectured that the protein sequences of their design are stable but only proved the stability for an infinite class of very basic structures. The HP model divides amino acids to two groups: hydrophobic (H) and polar (P), and considers only hydrophobic interactions between neighboring H amino in the energy formula. Another significant force acting during the protein folding are sulfide (SS) bridges between two cysteine amino acids. In this paper, we will enrich the HP model by adding cysteines as the third group of amino acids. A cysteine monomer acts as an H amino acid, but in addition two neighboring cysteines can form a bridge to further reduce the energy of the fold. We call our model the HPC model. We consider a subclass of linear structures designed in Gupta et al.¹ which is rich enough to approximate (although more coarsely) any given structure. We refine the structures for the HPC model by setting approximately a half of H amino acids to cysteine ones. We conjecture that these structures are stable under the HPC model and prove it under an additional assumption that non-cysteine amino acids act as cysteine ones, i.e., they tend to form their own bridges to reduce the energy. In the proof we will make an efficient use of a computational tool 2DHPSolver which significantly speeds up the progress in the technical part of the proof. This is a preliminary work, and we believe that the same techniques can be used to prove this result without the artificial assumption about non-cysteine H monomers.