Folding Funnel Research Articles

The energy landscape of Aβ42: a funnel to disorder for the monomer becomes a folding funnel for self-assembly.

The aggregation of amyloid-β (Aβ) peptides, particularly Aβ1-42, plays a key role in Alzheimer's disease pathogenesis. In this study, we investigate how dimerisation transforms the free energy surface (FES) of the Aβ1-42 monomer when it interacts with another Aβ1-42 peptide. We find that the monomer FES is a structurally inverted funnel with a disordered state at the global minimum. However, in the presence of a second Aβ1-42 peptide, the landscape becomes a folding funnel, leading to a β-hairpin state. Using first passage time analysis, we analyse the pathway for the transition from disordered to the β-hairpin state, which highlights the initial formation of a D23-K28 salt bridge as the driving force, together with hydrophobic contacts.

A new kid in the folding funnel: Molecular chaperone activities of the BRICHOS domain.

The BRICHOS protein superfamily is a diverse group of proteins associated with a wide variety of human diseases, including respiratory distress, COVID-19, dementia, and cancer. A key characteristic of these proteins-besides their BRICHOS domain present in the ER lumen/extracellular part-is that they harbor an aggregation-prone region, which the BRICHOS domain is proposed to chaperone during biosynthesis. All so far studied BRICHOS domains modulate the aggregation pathway of various amyloid-forming substrates, but not all of them can keep denaturing proteins in a folding-competent state, in a similar manner as small heat shock proteins. Current evidence suggests that the ability to interfere with the aggregation pathways of substrates with entirely different end-point structures is dictated by BRICHOS quaternary structure as well as specific surface motifs. This review aims to provide an overview of the BRICHOS protein family and a perspective of the diverse molecular chaperone-like functions of various BRICHOS domains in relation to their structure and conformational plasticity. Furthermore, we speculate about the physiological implication of the diverse molecular chaperone functions and discuss the possibility to use the BRICHOS domain as a blood-brain barrier permeable molecular chaperone treatment of protein aggregation disorders.

Rhodopsin is a dynamically active receptor in lipid membranes.

G-protein-coupled receptors transmit signals across cellular membranes and regulate multiple biological functions with rhodopsin as an important prototype. Here we investigated the distribution of substates in rhodopsin activation unavailable by X-ray crystallography due to use of cryogenic temperatures and absence of the membrane environment [1]. Our hypothesis was that activation involves dynamic allostery whereby an ensemble of states is affected by the membrane soft matter (lipids and water) as well as pH and temperature [1-3]. We investigated rhodopsin in native retinal disk membranes and POPC or DOPC lipids using FTIR and UV-visible spectroscopy. By observing the pH dependence of the activating transition for various spectroscopic bands, we determined the distributions of states upon photoactivation. Data reduction and analysis of pH titration curves revealed equilibrium constants and thermodynamic parameters for the transition from inactive Meta-I to the active Meta-II state. Furthermore, we calculated the distribution of pKa and alkaline end-point values at all wave numbers of FTIR spectra where intensities change upon activation. We discovered that temperature not only shifts the rhodopsin equilibrium to the active state, but also enables coexistence of multiple inactive and active states. Our data support the concept of a dynamically active receptor, where the equilibrium of substates facilitates the high reaction rate for the next vision step (transducin activation). The calculated enthalpy and entropy values suggest partial unfolding of the receptor when forming of the active Meta-II state. Our results are consistent with the idea of activated rhodopsin as a conformational ensemble of states representing different tiers of the energy landscape, which are partially determined by an enthalpy-entropy folding funnel.

The Non-native Disulfide-Bond-Containing Landscape Orthogonal to the Oxidative Protein-Folding Trajectory: A Necessary Evil?

Oxidative protein folding describes the process by which disulfide-bond-containing proteins mature from their ribosomal, fully reduced and unfolded, origins. Over the past 40 years, a number of exemplar proteins including bovine pancreatic ribonuclease A (RNaseA), bovine pancreatic trypsin inhibitor (BPTI), and hen egg-white lysozyme (HEWL), among others, have provided rich insight into the nature of the intermolecular interactions that drive the formation of the native, biologically active fold. In this Review Article, we revisit the oxidative folding process of RNaseA with a focus on reconciling the role of non-native disulfide-bond-containing species that populate the oxidative folding landscape. Toward gaining such an understanding, we project the regeneration pathway onto a Cartesian coordinate system. This helps not only to recognize the magnitude of the seemingly "fruitless", non-native disulfide-bond-containing species that lie orthogonal to the "native-protein-forming" reaction progress but also to reconcile a role for their existence in the regenerative trajectory. Finally, we superimpose the folding funnel onto the regeneration trajectory to draw parallels between oxidative folders and conformational folders (proteins that lack disulfide bonds). The overall objective is to provide the reader with a semi-quantitative description of oxidative protein folding and the barriers to successful regeneration while underscoring a role of seemingly fruitless intermediates.

Protein folding problem: enigma, paradox, solution.

The ability of protein chains to spontaneously form their three-dimensional structures is a long-standing mystery in molecular biology. The most conceptual aspect of this mystery is how the protein chain can find its native, "working" spatial structure (which, for not too big protein chains, corresponds to the global free energy minimum) in a biologically reasonable time, without exhaustive enumeration of all possible conformations, which would take billions of years. This is the so-called "Levinthal's paradox." In this review, we discuss the key ideas and discoveries leading to the current understanding of protein folding kinetics, including folding landscapes and funnels, free energy barriers at the folding/unfolding pathways, and the solution of Levinthal's paradox. A special role here is played by the "all-or-none" phase transition occurring at protein folding and unfolding and by the point of thermodynamic (and kinetic) equilibrium between the "native" and the "unfolded" phases of the protein chain (where the theory obtains the simplest form). The modern theory provides an understanding of key features of protein folding and, in good agreement with experiments, it (i) outlines the chain length-dependent range of protein folding times, (ii) predicts the observed maximal size of "foldable" proteins and domains. Besides, it predicts the maximal size of proteins and domains that fold under solely thermodynamic (rather than kinetic) control. Complementarily, a theoretical analysis of the number of possible protein folding patterns, performed at the level of formation and assembly of secondary structures, correctly outlines the upper limit of protein folding times.

Variational embedding of protein folding simulations using Gaussian mixture variational autoencoders.

Conformational sampling of biomolecules using molecular dynamics simulations often produces a large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here, we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE), that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscape of protein folding with highly separated clusters that correspond to the metastable states during folding. Since GMVAE uses a mixture of Gaussians as its prior, it can directly acknowledge the multi-basinnature of the protein folding free energy landscape. To make the model end-to-end differentiable, we use a Gumbel-softmaxdistribution. We test the model on three long-timescale protein folding trajectories and show that GMVAE embedding resembles the folding funnel with folded states down the funnel and unfolded states outside the funnel path. Additionally, we show that the latent space of GMVAE can be used for kinetic analysis and Markov state models built on this embedding produce folding and unfolding timescales that are in close agreement with other rigorous dynamical embeddings such as time independent component analysis.

Characterization of different intermediate states in myoglobin induced by polyethylene glycol: A process of spontaneous molecular self-organization foresees the energy landscape theory via in vitro and in silico approaches

Practically proteins perform their functions exposed to various molecules (macro/micro) of different shapes, sizes, and high concentrations. In such conditions, proteins fold through various intermediate states to execute their type of functions. There are various in vitro studies that showed that proteins yield intermediate states (either pre-molten globule, PMG or molten globules, MG) in changing environments (pH, temperature, and co-solute). Here, we investigate that myoglobin (Mb) yields two intermediate states in the presence of polyethylene glycol, PEG (4 kDa molecular weight) at two different concentrations. These intermediates were characterized by various spectroscopic techniques, further; we demonstrated that these changes in the structure of the protein were due to soft interactions which were confirmed by isothermal titration calorimetric and computational studies. Besides, in silico (molecular dynamic simulations) studies were exploited to know the atomic-level details of the protein which are useful to comprehend the functional characteristics of the bio-molecule with structural change and to study atomic motions and inter-atomic interactions in the bio-molecular systems. This is the first time that two intermediates (MG and PMG state) in the protein (Mb) at two different concentrations in the presence of solo size of PEG are yielded. This study shows folding of a protein does not follow a singular and specific pathway but occurs through routes down a folding funnel more like rain flowing down a funnel, hence foresees the energy landscape theory. Moreover, the study provides the significance of crowding concentrations in the cellular organism.

Folding Rate Optimization Promotes Frustrated Interactions in Entangled Protein Structures.

Many native structures of proteins accomodate complex topological motifs such as knots, lassos, and other geometrical entanglements. How proteins can fold quickly even in the presence of such topological obstacles is a debated question in structural biology. Recently, the hypothesis that energetic frustration might be a mechanism to avoid topological frustration has been put forward based on the empirical observation that loops involved in entanglements are stabilized by weak interactions between amino-acids at their extrema. To verify this idea, we use a toy lattice model for the folding of proteins into two almost identical structures, one entangled and one not. As expected, the folding time is longer when random sequences folds into the entangled structure. This holds also under an evolutionary pressure simulated by optimizing the folding time. It turns out that optmized protein sequences in the entangled structure are in fact characterized by frustrated interactions at the closures of entangled loops. This phenomenon is much less enhanced in the control case where the entanglement is not present. Our findings, which are in agreement with experimental observations, corroborate the idea that an evolutionary pressure shapes the folding funnel to avoid topological and kinetic traps.

Trajectory Taken by Dimeric Cu/Zn Superoxide Dismutase through the Protein Unfolding and Dissociation Landscape Is Modulated by Salt Bridge Formation.

Native mass spectrometry (MS) is a powerful means for studying macromolecular protein assemblies, including accessing activated states. However, much remains to be understood about what governs which regions of the protein (un)folding funnel, which can be explored by activation of protein ions in a vacuum. Here, we examine the trajectory that Cu/Zn superoxide dismutase (SOD1) dimers take over the unfolding and dissociation free energy landscape in a vacuum. We examined wild-type SOD1 and six disease-related point mutants by using tandem MS and ion-mobility MS as a function of collisional activation. For six of the seven SOD1 variants, increasing activation prompted dimers to transition through two unfolding events and dissociate symmetrically into monomers with (as near as possible) equal charges. The exception was G37R, which proceeded only through the first unfolding transition and displayed a much higher abundance of asymmetric products. Supported by the observation that ejected asymmetric G37R monomers were more compact than symmetric G37R ones, we localized this effect to the formation of a gas-phase salt bridge in the first activated conformation. To examine the data quantitatively, we applied Arrhenius-type analysis to estimate the barriers on the corresponding free energy landscape. This reveals a heightening of the barrier to unfolding in G37R by >5 kJ/mol-1 over the other variants, consistent with expectations for the strength of a salt bridge. Our work demonstrates weaknesses in the simple general framework for understanding protein complex dissociation in a vacuum and highlights the importance of individual residues, their local environment, and specific interactions in governing product formation.

Search optimization, funnel topography, and dynamical criticality on the string landscape

A striking feature of our universe is its near criticality. The cosmological constant and weak hierarchy problems, as well as the metastability of the electroweak vacuum, can all be understood as problems of criticality. This suggests a statistical physics approach, based on the landscape of string theory. In this paper we present a dynamical selection mechanism for hospitable vacua based on search optimization. Instead of focusing on late-time, stationary probability distributions for the different vacua, we are interested in the approach to equilibrium. This is particularly relevant if cosmological evolution on the multiverse has occurred for a finite time much shorter than the exponentially-long mixing time for the landscape. We argue this imposes a strong selection pressure among hospitable vacua, favoring those that lie in regions where the search algorithm is efficient. Specifically, we show that the mean first passage time is minimized for hospitable vacua lying at the bottom of funnel-like regions, akin to the smooth folding funnels of naturally-occurring proteins and the convex loss functions of well-trained deep neural networks. The optimality criterion is time-reparametrization invariant and defined by two competing requirements: search efficiency, which requires minimizing the mean first passage time, and sweeping exploration, which requires that random walks are recurrent. Optimal landscape regions reach a compromise by lying at the critical boundary between recurrence and transience, thereby achieving dynamical criticality. Remarkably, this implies that the optimal lifetime of vacua coincides with the de Sitter Page time, τcrit ∼ MPl2/H3. Our mechanism makes concrete phenomenological predictions: 1. The expected lifetime of our universe is 10130 years, which is ≳ 2σ from the Standard Model metastability estimate; 2. The supersymmetry breaking scale should be high, ≳ 1010 GeV. The present framework suggests a correspondence between the near-criticality of our universe and non-equilibrium critical phenomena on the landscape.

Folding Free Energy Landscape of Ordered and Intrinsically Disordered Proteins

Folding funnel is the essential concept of the free energy landscape for ordered proteins. How does this concept apply to intrinsically disordered proteins (IDPs)? Here, we address this fundamental question through the explicit characterization of the free energy landscapes of the representative α-helical (HP-35) and β-sheet (WW domain) proteins and of an IDP (pKID) that folds upon binding to its partner (KIX). We demonstrate that HP-35 and WW domain indeed exhibit the steep folding funnel: the landscape slope for these proteins is ca. −50 kcal/mol, meaning that the free energy decreases by ~5 kcal/mol upon the formation of 10% native contacts. On the other hand, the landscape of pKID is funneled but considerably shallower (slope of −24 kcal/mol), which explains why pKID is disordered in free environments. Upon binding to KIX, the landscape of pKID now becomes significantly steep (slope of −54 kcal/mol), which enables otherwise disordered pKID to fold. We also show that it is the pKID–KIX intermolecular interactions originating from hydrophobic residues that mainly confer the steep folding funnel. The present work not only provides the quantitative characterization of the protein folding free energy landscape, but also establishes the usefulness of the folding funnel concept to IDPs.

PourRNA-a time- and memory-efficient approach for the guided exploration of RNA energy landscapes.

The folding dynamics of ribonucleic acids (RNAs) are typically studied via coarse-grained models of the underlying energy landscape to face the exponential growths of the RNA secondary structure space. Still, studies of exact folding kinetics based on gradient basin abstractions are currently limited to short sequence lengths due to vast memory requirements. In order to compute exact transition rates between gradient basins, state-of-the-art approaches apply global flooding schemes that require to memorize the whole structure space at once. pourRNA tackles this problem via local flooding techniques where memorization is limited to the structure ensembles of individual gradient basins. Compared to the only available tool for exact gradient basin-based macro-state transition rates (namely barriers), pourRNA computes the same exact transition rates up to 10 times faster and requires two orders of magnitude less memory for sequences that are still computationally accessible for exhaustive enumeration. Parallelized computation as well as additional heuristics further speed up computations while still producing high-quality transition model approximations. The introduced heuristics enable a guided trade-off between model quality and required computational resources. We introduce and evaluate a macroscopic direct path heuristics to efficiently compute refolding energy barrier estimations for the co-transcriptionally trapped RNA sv11 of length 115 nt. Finally, we also show how pourRNA can be used to identify folding funnels and their respective energetically lowest minima. pourRNA is freely available at https://github.com/ViennaRNA/pourRNA. Supplementary data are available at Bioinformatics online.

On identifying low energy conformational excited states with differential ruggedness in human γS-crystallin promoting severe infantile cataracts

Transient excited states in proteins can be accurately probed from temperature dependence of amide proton (1HN) chemical shifts displaying significant curvatures. Characterizing these near-native alternative states is of high therapeutic relevance in conformational diseases wherein missense mutations promote structural instability that leads to conformational heterogeneity. Extending the structure-function paradigm from physiology to pathology, we recently reported the solution NMR structure and dynamics of a severe congenital cataract variant, G57W of human γS-crystallin (abbreviated as γS-G57W) which is resistant towards crystallization. In an endeavour to explore the functional consequences of this mutation, here we report for the first time, native state conformational ruggedness in human γS-G57W as compared to its wild-type counterpart from residue resolved nonlinear temperature dependence of backbone 1HN chemical shifts using solution NMR spectroscopy. Our calculations suggest that the simulated chemical shift curvatures are indicative of low energy excited states within 2–4 kcal mol−1 from the native state. Residues accessing alternative conformations populate the N-terminal domain of γS-G57W more than its C-terminal counterpart. Collectively, curvatures retaining native state ensemble on mild denaturation suggest that the free energy landscape in human γS-G57W at the bottom of the folding funnel is sufficiently robust and malleable against such perturbations. Overall, this critical study highlights the functional aspects of such structural malleability promoting infantile cataracts as a global health risk marker.

Recovery of Protein Folding Funnels from Single-Molecule Time Series by Delay Embeddings and Manifold Learning.

The stability and folding of proteins is governed by the underlying single-molecule free energy surface (smFES) mapping the free energy of the molecule as a function of configurational state. Ascertaining the smFES is of great value in understanding and engineering protein structure and function. By integrating tools from dynamical systems theory and nonlinear manifold learning, we describe an approach to reconstruct the multidimensional smFES for a protein from a time series in a single experimentally measurable observable. We employ Takens' delay embeddings to project the time series into a high-dimensional space in which the projected dynamics are C1-equivalent to the true system dynamics and employ diffusion maps to recover a low-dimensional reconstruction of the smFES that is equivalent to the true smFES up to a smooth and invertible transformation. We validate the approach in molecular dynamics simulations of Trp-cage, Villin, and BBA to demonstrate that landscapes recovered from univariate time series in the head-to-tail distance are topologically identical-they precisely preserve the metastable states and folding pathways-and topographically approximate-the free energy barrier heights and well depths are approximately preserved-to the true landscapes determined from complete knowledge of all atomic coordinates. We go on to show that the reconstructed landscapes reliably predict temperature denaturation and identify point mutations and groups of mutations critical to folding. These results demonstrate that protein folding funnels can be reconstructed from experimentally measurable time series and used to understand and engineer folding.

Elucidating thermal behavior, native contacts, and folding funnels of simple lattice proteins using replica exchange Wang-Landau sampling.

We studied the folding behavior of two coarse-grained, lattice models, the HP (hydrophobic-polar) model and the semi-flexible H0P model, whose 124 monomer long sequences were derived from the protein Ribonuclease A. Taking advantage of advanced parallel computing techniques, we applied replica exchange Wang-Landau sampling and calculated the density of states over the models entire energy ranges to high accuracy. We then determined both energetic and structural quantities in order to elucidate the folding behavior of each model completely. As a result of sufficiently long sequences and model complexity, yet computational accessibility, we were able to depict distinct free energy folding funnels for both models. In particular, we found that the HP model folds in a single-step process with a very highly degenerate native state and relatively flat low temperature folding funnel minimum. By contrast, the semi-flexible H0P model folds via a multi-step process and the native state is almost four orders of magnitude less degenerate than that for the HP model. In addition, for the H0P model, the bottom of the free energy folding funnel remains rough, even at low temperatures.

Predicting improved protein conformations with a temporal deep recurrent neural network.

Accurate protein structure prediction from amino acid sequence is still an unsolved problem. The most reliable methods centre on template based modelling. However, the accuracy of these models entirely depends on the availability of experimentally resolved homologous template structures. In order to generate more accurate models, extensive physics based molecular dynamics (MD) refinement simulations are performed to sample many different conformations to find improved conformational states. In this study, we propose a deep recurrent network model, called DeepTrajectory, that is able to identify these improved conformational states, with high precision, from a variety of different MD based sampling protocols. The proposed model learns the temporal patterns of features computed from MD trajectory data in order to classify whether each recorded simulation snapshot is an improved quality conformational state, decreased quality conformational state or whether there is no perceivable change in state with respect to the starting conformation. The model was trained and tested on 904 trajectories from 42 different protein systems with a cumulative number of more than 1.7 million snapshots. We show that our model outperforms other state of the art machine-learning algorithms that do not consider temporal dependencies. To our knowledge, DeepTrajectory is the first implementation of a time-dependent deep-learning protocol that is re-trainable and able to adapt to any new MD based sampling procedure, thereby demonstrating how a neural network can be used to learn the latter part of the protein folding funnel.

Tuning Free Energy by Backbone Conformational Entropy: A Strategy from Disordered Proteins

Tuning Free Energy by Backbone Conformational Entropy: A Strategy from Disordered Proteins

A non-equilibrium approach to allosteric communication.

While the theory of protein folding is well developed, including concepts such as rugged energy landscape, folding funnel, etc., the same degree of understanding has not been reached for the description of the dynamics of allosteric transitions in proteins. This is not only due to the small size of the structural change upon ligand binding to an allosteric site, but also due to challenges in designing experiments that directly observe such an allosteric transition. On the basis of recent pump-probe-type experiments (Buchli et al. 2013 Proc. Natl Acad. Sci. USA110, 11 725-11 730. (doi:10.1073/pnas.1306323110)) and non-equilibrium molecular dynamics simulations (Buchenberg et al. 2017 Proc. Natl Acad. Sci. USA114, E6804-E6811. (doi:10.1073/pnas.1707694114)) studying an photoswitchable PDZ2 domain as model for an allosteric transition, we outline in this perspective how such a description of allosteric communication might look. That is, calculating the dynamical content of both experiment and simulation (which agree remarkably well with each other), we find that allosteric communication shares some properties with downhill folding, except that it is an 'order-order' transition. Discussing the multiscale and hierarchical features of the dynamics, the validity of linear response theory as well as the meaning of 'allosteric pathways', we conclude that non-equilibrium experiments and simulations are a promising way to study dynamical aspects of allostery.This article is part of a discussion meeting issue 'Allostery and molecular machines'.

Multiple Pathways in the Self-Assembly Process of a Pd4L8 Coordination Tetrahedron.

The self-assembly of a Pd418 coordination tetrahedron (Tet) from a ditopic ligand, 1, and palladium(II) ions, [PdPy*4]2+ (Py* = 3-chloropyridine), was investigated by a 1H NMR-based quantitative approach (quantitative analysis of self-assembly process, QASAP), which allows one to monitor the average composition of the intermediates not observed by NMR spectroscopy. The self-assembly of Tet takes place mainly through three pathways and about half of the Tet structures were produced through the reaction of a kinetically produced Pd3L6 double-walled triangle (DWT) and 200-nm-sized large intermediates (IntL). In two of the three pathways, the leaving ligand (Py*), which is not a component of Tet, catalytically assisted the self-assembly. Such a multiplicity of the self-assembly process of Tet suggests that molecular self-assembly takes place on an energy landscape like a protein-folding funnel.

Folding Funnels (or Lack Thereof) in Amyloid Aggregation

Folding Funnels (or Lack Thereof) in Amyloid Aggregation