Robustness of atomistic Gō models in predicting native-like folding intermediates

Simulations of a protein fold switch reveal crowding-induced population shifts driven by disordered regions

Macromolecular crowding effects on globular proteins, which usually adopt a single stable fold, have been widely studied. However, little is known about crowding effects on fold-switching proteins, which reversibly switch between distinct folds. Here we study the mutationally driven switch between the folds of GA and GB, the two 56-amino acid binding domains of protein G, using a structure-based dual-basin model. We show that, in the absence of crowders, the fold populations PA and PB can be controlled by the strengths of contacts in the two folds, κA and κB. A population balance, PA ≈ PB, is obtained for κB/κA = 0.92. The resulting model protein is subject to crowding at different packing fractions, ϕc. We find that crowding increases the GB population and reduces the GA population, reaching PB/PA ≈ 4 at ϕc = 0.44. We analyze the ϕc-dependence of the crowding-induced GA-to-GB switch using scaled particle theory, which provides a qualitative, but not quantitative, fit of our data, suggesting effects beyond a spherical description of the folds. We show that the terminal regions of the protein chain, which are intrinsically disordered only in GA, play a dominant role in the response of the fold switch to crowding effects.

Key aspects of the past 30 years of protein design

Proteins are the workhorse of life. They are the building infrastructure of living systems; they are the most efficient molecular machines known, and their enzymatic activity is still unmatched in versatility by any artificial system. Perhaps proteins' most remarkable feature is their modularity. The large amount of information required to specify each protein's function is analogically encoded with an alphabet of just ∼20 letters. The protein folding problem is how to encode all such information in a sequence of 20 letters. In this review, we go through the last 30 years of research to summarize the state of the art and highlight some applications related to fundamental problems of protein evolution.

Multi-eGO: An in silico lens to look into protein aggregation kinetics at atomic resolution

Protein aggregation into amyloid fibrils is the archetype of aberrant biomolecular self-assembly processes, with more than 50 associated diseases that are mostly uncurable. Understanding aggregation mechanisms is thus of fundamental importance and goes in parallel with the structural characterization of the transient oligomers formed during the process. Oligomers have been proven elusive to high-resolution structural techniques, while the large sizes and long time scales, typical of aggregation processes, have limited the use of computational methods to date. To surmount these limitations, we here present multi-eGO, an atomistic, hybrid structure-based model which, leveraging the knowledge of monomers conformational dynamics and of fibril structures, efficiently captures the essential structural and kinetics aspects of protein aggregation. Multi-eGO molecular dynamics simulations can describe the aggregation kinetics of thousands of monomers. The concentration dependence of the simulated kinetics, as well as the structural features of the resulting fibrils, are in qualitative agreement with in vitro experiments carried out on an amyloidogenic peptide from Transthyretin, a protein responsible for one of the most common cardiac amyloidoses. Multi-eGO simulations allow the formation of primary nuclei in a sea of transient lower-order oligomers to be observed over time and at atomic resolution, following their growth and the subsequent secondary nucleation events, until the maturation of multiple fibrils is achieved. Multi-eGO, combined with the many experimental techniques deployed to study protein aggregation, can provide the structural basis needed to advance the design of molecules targeting amyloidogenic diseases.

The folding space of proteinβ2-microglobulin is modulated by a single disulfide bridge

Protein beta-2-microglobulin (β2m) is classically considered the causative agent of dialysis related amyloidosis, a conformational disorder that affects patients undergoing long-term hemodialysis. The wild type (WT) form, the ΔN6 structural variant, and the D76N mutant have been extensively used as model systems ofβ2m aggregation. In all of them, the native structure is stabilized by a disulfide bridge between the sulphur atoms of the cysteine residues 25 (at B strand) and 80 (at F strand), which has been considered fundamental inβ2m fibrillogenesis. Here, we use extensive discrete molecular dynamics simulations of a full atomistic structure-based model to explore the role of this disulfide bridge as a modulator of the folding space ofβ2m. In particular, by considering different models for the disulfide bridge, we explore the thermodynamics of the folding transition, and the formation of intermediate states that may have the potential to trigger the aggregation cascade. Our results show that the dissulfide bridge affects folding transition and folding thermodynamics of the considered model systems, although to different extents. In particular, when the interaction between the sulphur atoms is stabilized relative to the other intramolecular interactions, or even locked (i.e. permanently established), the WT form populates an intermediate state featuring a well preserved core and two unstructured termini, which was previously detected only for the D76N mutant. The formation of this intermediate state may have important implications in our understanding ofβ2m fibrillogenesis.

Behavior of Proteins under Pressure from Experimental Pressure-Dependent Structures

Structure-based models are coarse-grained representations of the interactions responsible for the protein folding process. In their simplest form, they use only the native contact map of a given protein to predict the main features of its folding process by computer simulation. Given their limitations, these models are frequently complemented with sequence-dependent contributions or additional information. Specifically, to analyze the effect of pressure on the folding/unfolding transition, special forms of these interaction potentials are employed, which may a priori determine the outcome of the simulations. In this work, we have tried to keep the original simplicity of structure-based models. Therefore, we have used folded structures that have been experimentally determined at different pressures to define native contact maps and thus interactions dependent on pressure. Despite the apparently tiny structural differences induced by pressure, our simulation results provide different thermodynamic and kinetic behaviors, which roughly correspond to experimental observations (when there is a possible comparison) of two proteins used as benchmarks, hen egg-white lysozyme and dihydrofolate reductase. Therefore, this work shows the feasibility of using experimental native structures at different pressures to analyze the global effects of this physical property on the protein folding process.

Native-Based Dissipative Particle Dynamics Approach for α-Helical Folding

We developed a dissipative particle dynamics (DPD) approach that captures polyalanine folding into a stable helical conformation. Within the proposed native-based approach, the DPD parameters are derived based on the contact map constructed from the molecular dynamics (MD) simulations. We show that the proposed approach reproduces the folding of polypeptides of various lengths, including bundle formation for sufficiently long polypeptides. The proposed approach also allows one to capture the folding of the helical segments of the lysozyme. With further development of computationally efficient native-based DPD approaches for folding, modeling of a range of biomaterials incorporating α-helical segments could be extended to time and length scales far beyond those accessible in molecular dynamics simulations.

The Early Phase of β2-Microglobulin Aggregation: Perspectives From Molecular Simulations

Protein β2-microglobulin is the causing agent of two amyloidosis, dialysis related amyloidosis (DRA), affecting the bones and cartilages of individuals with chronic renal failure undergoing long-term hemodialysis, and a systemic amyloidosis, found in one French family, which impairs visceral organs. The protein’s small size and its biomedical significance attracted the attention of theoretical scientists, and there are now several studies addressing its aggregation mechanism in the context of molecular simulations. Here, we review the early phase of β2-microglobulin aggregation, by focusing on the identification and structural characterization of monomers with the ability to trigger aggregation, and initial small oligomers (dimers, tetramers, hexamers etc.) formed in the so-called nucleation phase. We focus our analysis on results from molecular simulations and integrate our views with those coming from in vitro experiments to provide a broader perspective of this interesting field of research. We also outline directions for future computer simulation studies.

The Early Phase of β2m Aggregation: An Integrative Computational Study Framed on the D76N Mutant and the ΔN6 Variant

Human β2-microglobulin (b2m) protein is classically associated with dialysis-related amyloidosis (DRA). Recently, the single point mutant D76N was identified as the causative agent of a hereditary systemic amyloidosis affecting visceral organs. To get insight into the early stage of the β2m aggregation mechanism, we used molecular simulations to perform an in depth comparative analysis of the dimerization phase of the D76N mutant and the ΔN6 variant, a cleaved form lacking the first six N-terminal residues, which is a major component of ex vivo amyloid plaques from DRA patients. We also provide first glimpses into the tetramerization phase of D76N at physiological pH. Results from extensive protein–protein docking simulations predict an essential role of the C- and N-terminal regions (both variants), as well as of the BC-loop (ΔN6 variant), DE-loop (both variants) and EF-loop (D76N mutant) in dimerization. The terminal regions are more relevant under acidic conditions while the BC-, DE- and EF-loops gain importance at physiological pH. Our results recapitulate experimental evidence according to which Tyr10 (A-strand), Phe30 and His31 (BC-loop), Trp60 and Phe62 (DE-loop) and Arg97 (C-terminus) act as dimerization hot-spots, and further predict the occurrence of novel residues with the ability to nucleate dimerization, namely Lys-75 (EF-loop) and Trp-95 (C-terminus). We propose that D76N tetramerization is mainly driven by the self-association of dimers via the N-terminus and DE-loop, and identify Arg3 (N-terminus), Tyr10, Phe56 (D-strand) and Trp60 as potential tetramerization hot-spots.

Steric confinement and enhanced local flexibility assist knotting in simple models of protein folding

The chaperonin complex GroEL-GroES is able to accelerate the folding process of knotted proteins considerably. However, the folding mechanism inside the chaperonin cage is elusive. Here we use a combination of lattice and off-lattice Monte Carlo simulations of simple Gō models to study the effect of physical confinement and local flexibility on the folding process of protein model systems embedding a trefoil knot in their native structure. This study predicts that steric confinement plays a specific role in the folding of knotted proteins by increasing the knotting probability for very high degrees of confinement. This effect is observed for protein MJ0366 even above the melting temperature for confinement sizes compatible with the size of the GroEL/GroES chaperonin cage. An enhanced local flexibility produces the same qualitative effects on the folding process. In particular, we observe that knotting probability increases up to 40% in the transition state of protein MJ0366 when flexibility is enhanced. This is underlined by a structural change in the transition state, which becomes devoid of helical content. No relation between the knotting mechanism and flexibility was found in the context of the off-lattice model adopted in this work.

A random version of principal component analysis in data clustering

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance/correlation matrix of the analyzed data. However, to properly work with high-dimensional data sets, PCA poses severe mathematical constraints on the minimum number of different replicates, or samples, that must be included in the analysis. Generally, improper sampling is due to a small number of data respect to the number of the degrees of freedom that characterize the ensemble. In the field of life sciences it is often important to have an algorithm that can accept poorly dimensioned data sets, including degenerated ones. Here a new random projection algorithm is proposed, in which a random symmetric matrix surrogates the covariance/correlation matrix of PCA, while maintaining the data clustering capacity. We demonstrate that what is important for clustering efficiency of PCA is not the exact form of the covariance/correlation matrix, but simply its symmetry.

Pierced Lasso Topology Controls Function in Leptin

Protein engineering is a powerful tool in drug design and therapeutics, where disulphide bridges are commonly introduced to stabilize proteins. However, these bonds also introduce covalent loops, which are often neglected. These loops may entrap the protein backbone on opposite sides, leading to a "knotted" topology, forming a so-called Pierced Lasso (PL). In this elegant system, the "knot" is held together with a single disulphide bridge where part of the polypeptide chain is threaded through. The size and position of these covalent loops can be manipulated through protein design in vitro, whereas nature uses polymorphism to switch the PL topology. The PL protein leptin shows genetic modification of an N-terminal residue, adding a third cysteine to the same sequence. In an effort to understand the mechanism of threading of these diverse topologies, we designed three loop variants to mimic the polymorphic sequence. This adds elegance to the system under study, as it allows the generation of three possible covalent loops; they are the original wild-type C-terminal loop protein, the fully circularized unthreaded protein, and the N-terminal loop protein, responsible for different lasso topologies. The size of the loop changes the threading mechanism from a slipknotting to a plugging mechanism, with increasing loop size. Interestingly, the ground state of the native protein structure is largely unaffected, but biological assays show that the activity is maximized by properly controlled dynamics in the threaded state. A threaded topology with proper conformational dynamics is important for receptor interaction and activation of the signaling pathways in vivo.

Recapturing the Correlated Motions of Protein Using Coarse- Grained Models

Long-range interactions and allostery are important for many biological processes. Increasing numbers of studies, both experimental and computational, show that internal dynamics may play an important role in such behaviors. Investigating the dynamical effects of proteins, how- ever, is a challenging problem using all-atom molecular dynamics because of the length-scales and timescales involved. As a result, coarse-grained models are often implemented. Herein, we use three well-defined coarse-grained models: Go, Martini and Cafemol, and a small model protein Eglin C, which is readily studied via all-atom molecular dynamics, to examine if these coarse grained models can explore the dynamics of Eglin C accurately as well as to see how these models respond to mutations. We found that all three models can recapture the dynamics of Eglin C to a significant extent - where we focus on root-mean square fluctuations and correlated motions as dynamical measures - but that the Cafemol and Go models are superior. The best agreement with all-atom simulations is for structured regions of Eglin C.

A dynamical coarse-grained model to disclose allosteric control of misfolding β2-microglobulin

Development of a novel Coarse-Grained (CG) model to study β₂-microglobulin dynamical features related to fibrillation: our one CG bead model is able to indicate propensities in the deformation behavior of the protein via investigation of the protein motion correlations.

Thermal unfolding simulations of NBD1 domain variants reveal structural motifs associated with the impaired folding of F508del-CFTR

The deletion of phenylalanine 508 reshapes the conformational space of the NBD1 domain that populates unique intermediate states that provide insights into the molecular events that underlie the impaired folding of F508del-NBD1.

Knotted proteins: A tangled tale of Structural Biology

Knotted proteins have their native structures arranged in the form of an open knot. In the last ten years researchers have been making significant efforts to reveal their folding mechanism and understand which functional advantage(s) knots convey to their carriers. Molecular simulations have been playing a fundamental role in this endeavor, and early computational predictions about the knotting mechanism have just been confirmed in wet lab experiments. Here we review a collection of simulation results that allow outlining the current status of the field of knotted proteins, and discuss directions for future research.

How determinant is N-terminal to C-terminal coupling for protein folding?

The existence of native interactions between the protein termini is a major determinant of the free energy barrier in a two-state folding transition being therefore a critical modulator of protein folding cooperativity.

Calcium binding to gatekeeper residues flanking aggregation-prone segments underlies non-fibrillar amyloid traits in superoxide dismutase 1 (SOD1)

Calcium deregulation is a central feature among neurodegenerative diseases, including amyotrophic lateral sclerosis (ALS). Calcium accumulates in the spinal and brain stem motor neurons of ALS patients triggering multiple pathophysiological processes which have been recently shown to include direct effects on the aggregation cascade of superoxide dismutase 1 (SOD1). SOD1 is a Cu/Zn enzyme whose demetallated form is implicated in ALS protein deposits, contributing to toxic gain of function phenotypes. Here we undertake a combined experimental and computational study aimed at establishing the molecular details underlying the regulatory effects of Ca(2+) over SOD1 aggregation potential. Isothermal titration calorimetry indicates entropy driven low affinity association of Ca(2+) ions to apo SOD1, at pH7.5 and 37°C. Molecular dynamics simulations denote a noticeable loss of native structure upon Ca(2+) association that is especially prominent at the zinc-binding and electrostatic loops, whose decoupling is known to expose the central SOD1 β-barrel triggering aggregation. Structural mapping of the preferential apo SOD1 Ca(2+) binding locations reveals that among the most frequent ligands for Ca(2+) are negatively-charged gatekeeper residues located in boundary positions with respect to segments highly prone to edge-to-edge aggregation. Calcium interactions thus diminish gatekeeping roles of these residues, by shielding repulsive interactions via stacking between aggregating β-sheets, partly blocking fibril formation and promoting amyloidogenic oligomers such as those found in ALS inclusions. Interestingly, many fALS mutations occur at these positions, disclosing how Ca(2+) interactions recreate effects similar to those of genetic defects, a finding with relevance to understand sporadic ALS pathomechanisms.

A simulated intermediate state for folding and aggregation provides insights into ΔN6 β2-microglobulin amyloidogenic behavior

A major component of ex vivo amyloid plaques of patients with dialysis-related amyloidosis (DRA) is a cleaved variant of β₂-microglobulin (ΔN6) lacking the first six N-terminal residues. Here we perform a computational study on ΔN6, which provides clues to understand the amyloidogenicity of the full-length β₂-microglobulin. Contrary to the wild-type form, ΔN6 is able to efficiently nucleate fibrillogenesis in vitro at physiological pH. This behavior is enhanced by a mild acidification of the medium such as that occurring in the synovial fluid of DRA patients. Results reported in this work, based on molecular simulations, indicate that deletion of the N-terminal hexapeptide triggers the formation of an intermediate state for folding and aggregation with an unstructured strand A and a native-like core. Strand A plays a pivotal role in aggregation by acting as a sticky hook in dimer assembly. This study further predicts that the detachment of strand A from the core is maximized at pH 6.2 resulting into higher aggregation efficiency. The structural mapping of the dimerization interface suggests that Tyr10, His13, Phe30 and His84 are hot-spot residues in ΔN6 amyloidogenesis.

Dialysis-related amyloidosis (DRA) is a conformational disease that affects individuals undergoing long-term haemodialysis. In DRA the progressive accumulation of protein human β₂-microglobulin (Hβ₂m) in the osteoarticular system, followed by its assembly into amyloid fibrils, eventually leads to tissue erosion and destruction. Disclosing the aggregation mechanism of Hβ₂m under physiologically relevant conditions represents a major challenge due to the inability of the protein to efficiently nucleate fibrillogenesis in vitro at physiological pH. On the other hand, ΔN6, a truncated variant of Hβ₂m, which is also a major component of ex vivo amyloid deposits extracted from DRA patients, is able to efficiently form amyloid fibrils de novo in physiological conditions. This amyloidogenic behavior is dramatically enhanced in a slightly more acidic pH (6.2) compatible with the mild acidification that occurs in the synovial fluid of DRA patients. In this work, an innovative three-stage methodological approach, relying on an array of molecular simulations, spanning different levels of resolution is used to investigate the initial stage of the de novo aggregation mechanism of ΔN6 in a physiologically relevant pH range. We identify an intermediate state for folding and aggregation, whose potential to dimerize is enhanced at pH 6.2. Our results provide rationalizations for previous experimental observations and new insights into the molecular basis of DRA.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Assessing the effect of loop mutations in the folding space of β2-microglobulin with molecular dynamics simulations

We use molecular dynamics simulations of a full atomistic Gō model to explore the impact of selected DE-loop mutations (D59P and W60C) on the folding space of protein human β₂-microglobulin (Hβ₂m), the causing agent of dialysis-related amyloidosis, a conformational disorder characterized by the deposition of insoluble amyloid fibrils in the osteoarticular system. Our simulations replicate the effect of mutations on the thermal stability that is observed in experiments in vitro. Furthermore, they predict the population of a partially folded state, with 60% of native internal free energy, which is akin to a molten globule. In the intermediate state, the solvent accessible surface area increases up to 40 times relative to the native state in 38% of the hydrophobic core residues, indicating that the identified species has aggregation potential. The intermediate state preserves the disulfide bond established between residue Cys25 and residue Cys80, which helps maintain the integrity of the core region, and is characterized by having two unstructured termini. The movements of the termini dominate the essential modes of the intermediate state, and exhibit the largest displacements in the D59P mutant, which is the most aggregation prone variant. PROPKA predictions of pK_a suggest that the population of the intermediate state may be enhanced at acidic pH explaining the larger amyloidogenic potential observed in vitro at low pH for the WT protein and mutant forms.

Thermodynamics of ideal proteinogenic homopolymer chains as a function of the energy spectrum E, helical propensity ω and enthalpic energy barrier

A reformulation and generalization of the Zwanzig model (ZW model) for ideal homopolymer chains poly-X, where X represents any of the twenty naturally occurring proteinogenic amino acid residues is presented. This reformulation and generalization provides a direct connection between coarse-grained parameters originally proposed in the ZW model with variables from the Lifson-Roig (LR) theory, such as the helical propensity per residue ω, and new variables introduced here, such as the energy gap Δ between unfolded and folded structures, as well as the ratio f of the energy scales involved. This enables us to discover the relevance of the energy spectrum E to the onset of configurational phase transitions. From the configurational partition function Q, thermodynamic properties such as the configurational entropy S, specific heat v and average energy <E> are calculated in terms of the number of residues K, temperature T, helical propensity ω and energy barrier ΔH for different poly-X chains in vacuo. Results obtained here provide substantial evidence that configurational phase transitions for ideal poly-X chains correspond to first-order phase transitions. An anomalous behavior of the thermodynamic functions <E>, Cv, S with respect to the number K of residues is also highlighted. On-going methods of solution are outlined.