Stable Structure-Approximating Inverse Protein Folding in 2D Hydrophobic-Polar-Cysteine (HPC) Model

Improving coarse-grained models of protein folding through weighting of polar-polar/hydrophobic-hydrophobic interactions into crowded spaces

Herein were tested 7 hydrophobic-polar sequences in two types of 2D-square space lattices, homogeneous and correlated, the latter simulating molecular crowding included as a geometric boundary restriction. Optimization of 2D structures was carried out using a variant of Dill's model, inspired by convex function, taking into account both hydrophobic (Dill's model) and polar interactions, including more structural information to reach better folding solutions. While using correlated networks, degrees of freedom in the folding of sequences were limited; as a result in all cases, more successful structural trials were found in comparison to a homogeneous lattice. The majority of employed sequences were designed by our workgroup, two of them were folded with other approaches, and another is a modified version of a previous sequence, initial forms of the other two have been employed but without taking into account polar-polar contributions. Three of them are newly proposed, intended to test the conjoint hydrophobic-hydrophobic and polar-polar contributions in crowded spaces. One sequence turned out to be the most difficult of the seven folded, this perhaps due to intrinsic (i) degrees of freedom and (ii) motifs of the expected 2D HP structure. Meanwhile two-sequence, although optimal folding was not achieved for neither of the two approaches, folding with correlated network approach not only produced better results than homogeneous space, but for them the best values found with crowding were very close to the expected optimal fitness. In general, five sequences were better folded with medium lattice units for correlated media; instead, another two sequences were better folded with a bit larger degree of lattice unit, revealing that depending on the degrees of freedom and particular folding, motifs in each sequence would require tuned crowding to achieve better folding. Therefore, the main goal herein was to obtain a modified 2D HP lattice model to mimic folding of proteins or secondary structures, like β-sheets, taking into account both hydrophobic-hydrophobic and polar-polar interactions, and fold them in a crowded environment. This simple but enough construction would be conducted to determine the needed information to fold sequences in a sort of a minimal but complete heuristic model. Finally, we claim that all folded sequences into crowded spaces achieve better results than homogeneous ones.

In silico minimalist approach to study 2D HP protein folding into an inhomogeneous space mimicking osmolyte effect: First trial in the search of foldameric backbones

We have employed our bioinformatics workbench, named Evolution, a Multi-Agent System based architecture with lattice-bead-models, evolutionary-algorithms, and correlated-networks as inhomogeneous spaces, with different correlation lengths, mimicking osmolyte effect (molecular crowding), to in silico survey protein folding. Resolution is with hydrophobic-polar (H-P) sequences in inhomogeneous 2D square lattices, since general biophysicochemical trends consider i) that the backbone is one of the major components responsible for protein folding and ii) osmolyte effect plays an important role to better folding kinetics and reach deeper optima. We have designed foldamers, as square n × n (n = 3, 4, 5, 6) arrays of hydrophobic cores stabilized by H⋯H contacts, attached through short PP (P₂) or long PPPP (P₄) loops, giving rise to 8 sequences (S₁ to S₈) with known optimal scores. Designed sequences were folded into different inhomogeneous spaces and indeed crowded media induced deeper optima, being crowding necessary to best fold, but the space should be enough constrained to induce folding without banning chain movement. The constrained space plays an important role to reach the optimal structure, depending on designed foldamer sequence size, for an optimal correlation length, implying that media affects the folding pathways as happens in real systems. Designed structures were found, moreover, they undergo to degenerated states, both folding states could survey considering i) backbone information and ii) osmolyte effect. In nature, the proteins fold in different structures aiming to reach a global minimum, but a local minimum could be enough to the protein to be functional or dysfunctional.

On Stable States in a Topologically Driven Protein Folding Model

Theoretical models of protein folding often make simplifying assumptions that allow analysis, yielding interesting theoretical results. In this article, we study models where folding dynamics is primarily driven by local topological features in an iterative manner. We illustrate the merit of the proposed approach through its ability to simulate realistic protein folding processes even when the sequence content information is reduced to just hydrophobic and polar. We then analyze our models and show that under our simple assumptions, certain structures are inherently unstable, and that determining whether structures can be stable is an [Formula: see text]-hard problem. Interestingly, we find that when our model has only two amino acids, the problem becomes solvable in polynomial time.

Simulating the folding of HP-sequences with a minimalist model in an inhomogeneous medium

The phenomenon of protein folding is a fundamental issue in the field of the computational molecular biology. The protein folding inside the cells is performed in a highly inhomogeneous, tortuous, and correlated environment. Therefore, it is important to include in the theoretical studies the medium where the protein folding is developed. In this work we present the combination of three models to mimic the protein folding inside of an inhomogeneous medium. The models used here are Hydrophobic-Polar (HP) in 2D square arrangement, Evolutionary Algorithms (EA), and the Dual Site Bond Model (DSBM). The DSBM model is used to simulate the environment where the HP beads are folded; in this case the medium is correlated and is fractal-like. The analysis of five benchmark HP sequences shows that the inhomogeneous space provided with a given correlation length and fractal dimension plays an important role for correct folding of these sequences, which does not occur in a homogeneous space.

Inverse protein folding in 3D hexagonal prism lattice under HPC model

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. Previously, tubular structures for a three-dimensional (3D) hexagonal prism lattice were introduced and their stability was formally proved for simple instances under the hydrophobic-polar (HP) model of Dill. In this article, we generalize the design of tubular structures to allow for much larger variety of designable structures by allowing branching of tubes. Our generalized design could be used to roughly approximate given 3D shapes in the considered lattice. Although the generalized tubular structures are not stable under the HP model, we can prove that a simple instance of generalized tubular structures is structurally stable (all native folds have the designed shape) under a refined version of the HP model, called the HPC model. We conjecture that there is a way to choose which hydrophobic monomers are cysteines in all generalized tubular structures such that the designed proteins are structurally stable under the HPC model.