Enhancing protein aggregation prediction: a unified analysis leveraging graph convolutional networks and active learning

Protein aggregation (PA) is a critical phenomenon associated with Alzheimer's and Parkinson's disease. Recent studies have suggested that factors like aggregation-prone regions (APRs) and β-strand interactions are crucial in understanding such behavior. While experimental methods have provided valuable insights, there has been a shift towards computational strategies, particularly machine learning, for their efficacy and speed. The challenge, however, lies in effectively incorporating structural information into these models. This study constructs a Graph Convolutional Network (GCN) to predict PA scores with the expanded and refined Protein Data Bank (PDB) and AlphaFold2.0 dataset. We employed AGGRESCAN3D 2.0 to calculate PA propensity and to enhance the dataset, we systematically separated multi polypeptide chains within PDB data into single polypeptide chains, removing redundancy. This effort resulted in a dataset comprising 302 032 unique PDB entries. Subsequently, we compared sequence similarity and obtained 22 774 Homo sapiens data from AlphaFold2.0. Using this expanded and refined dataset, the trained GCN model for PA prediction achieves a remarkable coefficient of determination (R 2) score of 0.9849 and a low mean absolute error (MAE) of 0.0381. Furthermore, the efficacy of the active learning process was demonstrated through its rapid identification of proteins with high PA propensity. Consequently, the active learning approach achieved an MAE of 0.0291 in expected improvement, surpassing other methods. It identified 99% of the target proteins by exploring merely 29% of the entire search space. This improved GCN model demonstrates promise in selecting proteins susceptible to PA, advancing protein science. This work contributes to the development of efficient computational tools for PA prediction, with potential applications in disease diagnosis and therapy.

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.

Contributions of topological polar-polar contacts to achieve better folding stability of 2D/3D HP lattice proteins: An in silico approach

<abstract> <p>Many of the simplistic hydrophobic-polar lattice models, such as Dill's model (called <bold>Model 1</bold> herein), are aimed to fold structures through hydrophobic-hydrophobic interactions mimicking the well-known hydrophobic collapse present in protein structures. In this work, we studied 11 designed hydrophobic-polar sequences, S₁-S₈ folded in 2D-square lattice, and S₉-S₁₁ folded in 3D-cubic lattice. And to better fold these structures we have developed <bold>Model 2</bold> as an approximation to convex function aimed to weight hydrophobic-hydrophobic but also polar-polar contacts as an augmented version of <bold>Model 1</bold>. In this partitioned approach hydrophobic-hydrophobic ponderation was tuned as <italic>α</italic>-1 and polar-polar ponderation as <italic>α</italic>. This model is centered in preserving required hydrophobic substructure, and at the same time including polar-polar interactions, otherwise absent, to reach a better folding score now also acquiring the polar-polar substructure. In all tested cases the folding trials were better achieved with <bold>Model 2</bold>, using <italic>α</italic> values of 0.05, 0.1, 0.2 and 0.3 depending of sequence size, even finding optimal scores not reached with <bold>Model 1</bold>. An important result is that the better folding score, required the lower <italic>α</italic> weighting. And when <italic>α</italic> values above 0.3 are employed, no matter the nature of the hydrophobic-polar sequence, banning of hydrophobic-hydrophobic contacts started, thus yielding misfolding of sequences. Therefore, the value of <italic>α</italic> to correctly fold structures is the result of a careful weighting among hydrophobic-hydrophobic and polar-polar contacts.</p> </abstract>

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.

The role of directional interactions in the designability of generalized heteropolymers

Heteropolymers are important examples of self-assembling systems. However, in the design of artificial heteropolymers the control over the single chain self-assembling properties does not reach that of the natural bio-polymers, and in particular proteins. Here, we introduce a sufficiency criterion to identify polymers that can be designed to adopt a predetermined structure and show that it is fulfilled by polymers made of monomers interacting through directional (anisotropic) interactions. The criterion is based on the appearance of a particular peak in the radial distribution function, that we show being a universal feature of all designable heteropolymers, as it is present also in natural proteins. Our criterion can be used to engineer new self-assembling modular polymers that will open new avenues for applications in materials science.

Accounting for protein-solvent contacts facilitates design of nonaggregating lattice proteins

The folding specificity of proteins can be simulated using simplified structural models and knowledge-based pair-potentials. However, when the same models are used to simulate systems that contain many proteins, large aggregates tend to form. In other words, these models cannot account for the fact that folded, globular proteins are soluble. Here we show that knowledge-based pair-potentials, which include explicitly calculated energy terms between the solvent and each amino acid, enable the simulation of proteins that are much less aggregation-prone in the folded state. Our analysis clarifies why including a solvent term improves the foldability. The aggregation for potentials without water is due to the unrealistically attractive interactions between polar residues, causing artificial clustering. When a water-based potential is used instead, polar residues prefer to interact with water; this leads to designed protein surfaces rich in polar residues and well-defined hydrophobic cores, as observed in real protein structures. We developed a simple knowledge-based method to calculate interactions between the solvent and amino acids. The method provides a starting point for modeling the folding and aggregation of soluble proteins. Analysis of our simple model suggests that inclusion of these solvent terms may also improve off-lattice potentials for protein simulation, design, and structure prediction.

In silico protein fragmentation reveals the importance of critical nuclei on domain reassembly

Protein complementation assays (PCAs) based on split protein fragments have become powerful tools that facilitate the study and engineering of intracellular protein-protein interactions. These assays are based on the observation that a given protein can be split into two inactive fragments and these fragments can reassemble into the original properly folded and functional structure. However, one experimentally observed limitation of PCA systems is that the folding of a protein from its fragments is dramatically slower relative to that of the unsplit parent protein. This is due in part to a poor understanding of how PCA design parameters such as split site position in the primary sequence and size of the resulting fragments contribute to the efficiency of protein reassembly. We used a minimalist on-lattice model to analyze how the dynamics of the reassembly process for two model proteins was affected by the location of the split site. Our results demonstrate that the balanced distribution of the "folding nucleus," a subset of residues that are critical to the formation of the transition state leading to productive folding, between protein fragments is key to their reassembly.

Folding kinetics of a lattice protein via a forward flux sampling approach

We implement a forward flux sampling approach [R. J. Allen et al., J. Chem. Phys. 124, 194111 (2006)] for calculating transition rate constants and for sampling paths of protein folding events. The algorithm generates trajectories for the transition between the unfolded and folded states as chains of partially connected paths, which can be used to obtain the transition-state ensemble and the properties that characterize these intermediates. We apply this approach to Monte Carlo simulations of a model lattice protein in open space and in confined spaces of varying dimensions. We study the effect of confinement on both protein thermodynamic stability and folding kinetics; the former by mapping free-energy landscapes and the latter by the determination of rate constants and mechanistic details of the folding pathway. Our results show that, for the range of temperatures where the native state is stable, confinement of a protein destabilizes the unfolded state by reducing its entropy, resulting in increased thermodynamic stability of the folded state. Relative to the folding in open space, we find that the kinetics can be accelerated at temperatures above the temperature at which the unconfined protein folds fastest and that the rate constant increases with the number of constrained dimensions. By examining the statistical properties of the transition-state ensemble, we detect signs of a classical nucleation folding mechanism for a core of native contacts formed at an early stage of the process. This nucleus acts as folding foci and is composed of those residues that have higher probability to form native contacts in the transition-state intermediates, which can vary depending on the confinement conditions of the system.

A lattice protein with an amyloidogenic latent state: stability and folding kinetics

We have designed a model lattice protein that has two stable folded states, the lower free energy native state and a latent state of somewhat higher energy. The two states have a sizable part of their structures in common (two "alpha-helices") and differ in the content of "alpha-helices" and "beta-strands" in the rest of their structures; i.e. for the native state, this part is alpha-helical, and for the latent state it is composed of beta-strands. Thus, the lattice protein free energy surface mimics that of amyloidogenic proteins that form well organized fibrils under appropriate conditions. A Go-like potential was used and the folding process was simulated with a Monte Carlo method. To gain insight into the equilibrium free energy surface and the folding kinetics, we have combined standard approaches (reduced free energy surfaces, contact maps, time-dependent populations of the characteristic states, and folding time distributions) with a new approach. The latter is based on a principal coordinate analysis of the entire set of contacts, which makes possible the introduction of unbiased reaction coordinates and the construction of a kinetic network for the folding process. The system is found to have four characteristic basins, namely a semicompact globule, an on-pathway intermediate (the bifurcation basin), and the native and latent states. The bifurcation basin is shallow and consists of the structure common to the native and latent states, with the rest disorganized. On the basis of the simulation results, a simple kinetic model describing the transitions between the characteristic states was developed, and the rate constants for the essential transitions were estimated. During the folding process the system dwells in the bifurcation basin for a relatively short time before it proceeds to the native or latent state. We suggest that such a bifurcation may occur generally for proteins in which native and latent states have a sizable part of their structures in common. Moreover, there is the possibility of introducing changes in the system (e.g., mutations), which guide the system toward the native or misfolded state.

Thermodynamics of folding and association of lattice-model proteins

Closely related to the "protein folding problem" is the issue of protein misfolding and aggregation. Protein aggregation has been associated with the pathologies of nearly 20 human diseases and presents serious difficulties during the manufacture of pharmaceutical proteins. Computational studies of multiprotein systems have recently emerged as a powerful complement to experimental efforts aimed at understanding the mechanisms of protein aggregation. We describe the thermodynamics of systems containing two lattice-model 64-mers. A parallel tempering algorithm abates problems associated with glassy systems and the weighted histogram analysis method improves statistical quality. The presence of a second chain has a substantial effect on single-chain conformational preferences. The melting temperature is substantially reduced, and the increase in the population of unfolded states is correlated with an increase in interactions between chains. The transition from two native chains to a non-native aggregate is entropically favorable. Non-native aggregates receive approximately 25% of their stabilizing energy from intraprotein contacts not found in the lowest-energy structure. Contact maps show that for non-native dimers, nearly 50% of the most probable interprotein contacts involve pairs of residues that form native contacts, suggesting that a domain-swapping mechanism is involved in self-association.

Effect of single-point sequence alterations on the aggregation propensity of a model protein

Sequences of contemporary proteins are believed to have evolved through a process that optimized their overall fitness, including their resistance to deleterious aggregation. Biotechnological processing may expose therapeutic proteins to conditions that are much more conducive to aggregation than those encountered in a cellular environment. An important task of protein engineering is to identify alternative sequences that would protect proteins when processed at high concentrations without altering their native structure associated with specific biological function. Our computational studies exploit parallel tempering simulations of coarse-grained model proteins to demonstrate that isolated amino acid residue substitutions can result in significant changes in the aggregation resistance of the protein in a crowded environment while retaining protein structure in isolation. A thermodynamic analysis of protein clusters subject to competing processes of folding and association shows that moderate mutations can produce effects similar to those caused by changes in system conditions, including temperature, concentration, and solvent composition, that affect the aggregation propensity. The range of conditions where a protein can resist aggregation can therefore be tuned by sequence alterations, although the protein generally may retain its generic ability for aggregation.

Three-dimensional lattice Monte Carlo simulations of model proteins. IV. Proteins at an oil-water interface

Lattice Monte Carlo simulations describe the adsorption of protein-like heteropolymer chains at an oil/water interface. The heteropolymers are designed sequences of 27 and 64 amino acid-type lattice sites taken from a 20-letter alphabet. We use our recently suggested energy scale to model oil and water. We investigate the effect of the oil parameters on adsorption properties of a single chain and on the aggregation of adsorbed chains while keeping the water parameters fixed to their optimum values found previously. By varying the oil parameters, we can cause a large range of adsorption behavior: from no adsorption to reversible adsorption to irreversible adsorption. We compare adsorption at a liquid/solid interface to that at a liquid/liquid interface. A liquid interface leads to stronger adsorption and denaturation than a solid interface with the same water and oil interaction parameters. We propose "optimal" oil parameters and use them to study multichain adsorption at a liquid interface.

Adsorption of comb copolymers on weakly attractive solid surfaces

In this work continuum and lattice Monte Carlo simulation methods are used to study the adsorption of linear and comb polymers on flat surfaces. Selected polymer segments, located at the tips of the side chains in comb polymers or equally spaced along the linear polymers, are attracted to each other and to the surface via square-well potentials. The rest of the polymer segments are modeled as tangent hard spheres in the continuum model and as self-avoiding random walks in the lattice model. Results are presented in terms of segment-density profiles, distribution functions, and radii of gyration of the adsorbed polymers. At infinite dilution the presence of short side chains promotes the adsorption of polymers favoring both a decrease in the depletion-layer thickness and a spreading of the polymer molecule on the surface. The presence of long side chains favors the adsorption of polymers on the surface, but does not permit the spreading of the polymers. At finite concentration linear polymers and comb polymers with long side chains readily adsorb on the solid surface, while comb polymers with short side chains are unlikely to adsorb. The simple models of comb copolymers with short side chains used here show properties similar to those of associating polymers and of globular proteins in aqueous solutions, and can be used as a first approximation to investigate the mechanism of adsorption of proteins onto hydrophobic surfaces.

Protein-folding landscapes in multichain systems

Computational studies of proteins have significantly improved our understanding of protein folding. These studies are normally carried out by using chains in isolation. However, in many systems of practical interest, proteins fold in the presence of other molecules. To obtain insight into folding in such situations, we compare the thermodynamics of folding for a Miyazawa-Jernigan model 64-mer in isolation to results obtained in the presence of additional chains. The melting temperature falls as the chain concentration increases. In multichain systems, free-energy landscapes for folding show an increased preference for misfolded states. Misfolding is accompanied by an increase in interprotein interactions; however, near the folding temperature, the transition from folded chains to misfolded and associated chains is entropically driven. A majority of the most probable interprotein contacts are also native contacts, suggesting that native topology plays a role in early stages of aggregation.

The competition between protein folding and aggregation: off-lattice minimalist model studies

Protein aggregation has been associated with a number of human diseases, and is a serious problem in the manufacture of recombinant proteins. Of particular interest to the biotechnology industry is deleterious aggregation that occurs during the refolding of proteins from inclusion bodies. As a complement to experimental efforts, computer simulations of multi-chain systems have emerged as a powerful tool to investigate the competition between folding and aggregation. Here we report results from Langevin dynamics simulations of minimalist model proteins. Order parameters are developed to follow both folding and aggregation. By mapping natural units to real units, the simulations are shown to be carried out under experimentally relevant conditions. Data pertaining to the contacts formed during the association process show that multiple mechanisms for aggregation exist, but certain pathways are statistically preferred. Kinetic data show that there are multiple time scales for aggregation, although most association events take place at times much shorter than those required for folding. Last, we discuss results presented here as a basis for future work aimed at rational design of mutations to reduce aggregation propensity, as well as for development of small-molecular weight refolding enhancers.

Computer simulation of polypeptide adsorption on model biomaterials

When biomaterials are inserted in a biological environment, for instance in a body implant, proteins do quickly adsorb on the exposed surface. Such process is of fundamental importance, since it directs the subsequent cell adhesion. Here we review recent advances in this field obtained with molecular simulations. While coarse-grained models can provide important general results, as it has long been recognized in polymer science, the hierarchical structure of a very complex copolymer such as a protein, together with the nature of the biomaterial surface suggest that atomistic models are better suited to investigate these phenomena. Thus, after briefly mentioning some common features of coarse-grained and atomistic force fields, we first discuss early theoretical and coarse-grained simulation results about protein adsorption, and then we highlight the main results recently obtained by us with atomistic models. In particular, we discuss some conformational and energetic aspects of the adsorption of protein fragments with different secondary structure on surfaces of different wettability, including hydrophobic graphite and hydrophilic poly(vinylalcohol). We also consider other features, such as the simulation of the materials wettability, the hydration of the adsorbed fragments, their kinetics of spreading, and the sequential adsorption of two protein fragments on top of each other, highlighting the results of general interest.

Lattice models of peptide aggregation: Evaluation of conformational search algorithms

We present a series of conformational search calculations on the aggregation of short peptide fragments that form fibrils similar to those seen in many protein mis-folding diseases. The proteins were represented by a face-centered cubic lattice model with the conformational energies calculated using the Miyazawa-Jernigan potential. The searches were performed using algorithms based on the Metropolis Monte Carlo method, including simulated annealing and replica exchange. We also present the results of searches using the tabu search method, an algorithm that has been used for many optimization problems, but has rarely been used in protein conformational searches. The replica exchange algorithm consistently found more stable structures then the other algorithms, and was particularly effective for the octamers and larger systems.