Folding Free Energy Landscape Research Articles

Revolutionizing Synthetic Antibody Design: Harnessing Artificial Intelligence and Deep Sequencing Big Data for Unprecedented Advances.

Synthetic antibodies (Abs) represent a category of engineered proteins meticulously crafted to replicate the functions of their natural counterparts. Such Abs are generated in vitro, enabling advanced molecular alterations associated with antigen recognition, paratope site engineering, and biochemical refinements. In a parallel realm, deep sequencing has brought about a paradigm shift in molecular biology. It facilitates the prompt and cost-effective high-throughput sequencing of DNA and RNA molecules, enabling the comprehensive big data analysis of Ab transcriptomes, including specific regions of interest. Significantly, the integration of artificial intelligence (AI), based on machine- and deep- learning approaches, has fundamentally transformed our capacity to discern patterns hidden within deep sequencing big data,including distinctive Ab features and protein folding free energy landscapes. Ultimately, current AI advances can generate approximations of the most stable Ab structural configurations, enabling the prediction of de novo synthetic Abs. As a result, this manuscript comprehensively examines the latest and relevant literature concerning the intersection of deep sequencing big data and AI methodologies for the design and development of synthetic Abs. Together, these advancements have accelerated the exploration of antibody repertoires, contributing to the refinement of synthetic Ab engineering and optimizations, and facilitating advancements in the lead identification process.

Ligand-dependent folding and unfolding dynamics and free energy landscapes of acylphosphatase.

Acylphosphatase (AcP) is an enzyme which catalyses the hydrolysis of acylphosphate. The binding with the phosphate ion (Pi) assumes significance in preserving both the stability and enzymatic activity of AcP. While previous studies using single molecule force spectroscopy explored the mechanical properties of AcP, the influence of Pi on its folding and unfolding dynamic behaviors remains unexplored. In this work, using stable magnetic tweezers, we measured and compared the force-dependent folding and unfolding rates of AcP in the Tris buffer and phosphate buffer within a force range from 2 pN to 40 pN. We found that Pi exerts no discernible effect on the folding dynamics but consistently decreases the force-dependent unfolding rate of AcP by a constant ratio across the entire force spectrum. The free energy landscapes of AcP in the absence and presence of Pi are constructed. Our results reveal that Pi selectively binds to the native state of AcP, stabilizing it and suggesting the general properties of specific ligand-receptor interactions.

Exploring the folding landscape of leptin: Insights into threading pathways

The discovery of new protein topologies with entanglements and loop-crossings have shown the impact of local amino acid arrangement and global three-dimensional structures. This phenomenon plays a crucial role in understanding how protein structure relates to folding and function, affecting the global stability, and biological activity. Protein entanglements encompassing knots and non-trivial topologies add complexity to their folding free energy landscapes. However, the initial native contacts driving the threading event for entangled proteins remains elusive. The Pierced Lasso Topology (PLT) represents an entangled topology where a covalent linker creates a loop in which the polypeptide backbone is threaded through. Compared to true knotted topologies, PLTs are simpler topologies where the covalent-loop persists in all conformations. In this work, the PLT protein leptin, is used to visualize and differentiate the preference for slipknotting over plugging transition pathways along the folding route. We utilize the Energy Landscape Visualization Method (ELViM), a multidimensional projection technique, to visualize and distinguish early threaded conformations that cannot be observed in an in vitro experiment. Critical contacts for the leptin threading mechanisms were identified where the competing pathways are determined by the formation of a hairpin loop in the unfolded basin. Thus, prohibiting the dominant slipknotting pathway. Furthermore, ELViM offers insights into distinct folding pathways associated with slipknotting and plugging providing a novel tool for de novo design and in vitro experiments with residue specific information of threading events in silico.

Inferring Pathways of Oxidative Folding from Prefolding Free Energy Landscapes of Disulfide-Rich Toxins.

Short, cysteine-rich peptides can exist in stable or metastable structural ensembles due to the number of possible patterns of formation of their disulfide bonds. One interesting subset of this peptide group is the conotoxins, which are produced by aquatic snails in the family Conidae. The μ conotoxins, which are antagonists and blockers of the voltage-gated sodium channel, exist in a folding spectrum: on one end of the spectrum are more hirudin-like folders, which form disulfide bonds and then reshuffle them, leading to an ensemble of kinetically trapped isomers, and on the other end are more BPTI-like folders, which form the native disulfide bonds one by one in a particular order, leading to a preponderance of conformations existing in a single stable state. In this Article, we employ the composite diffusion map approach to study the unified free energy surface of prefolding μ-conotoxin equilibrium. We identify the two most important nonlinear collective modes of the unified folding landscape and demonstrate that in the absence of their disulfides, the conotoxins can be thought of as largely disordered polymers. A small increase in the number of hydrophobic residues in the protein shifts the free energy landscape toward hydrophobically collapsed coil conformations responsible for cysteine proximity in hirudin-like folders, compared to semiextended coil conformations with more distal cysteines in BPTI-like folders. Overall, this work sheds important light on the folding processes and free energy landscapes of cysteine-rich peptides and demonstrates the extent to which sequence and length contribute to these landscapes.

Folding and threading of leptin as a model for pierced lasso topologies.

The introduction of entanglements in proteins remains elusive, where the mechanism of formation is unclear. We have for the first time characterized the folding and threading mechanism of a “knot-like” protein. The recently discovered Pierced Lasso Topology (PLT) is a class of proteins in which a disulfide formed covalent loop is threaded by the protein backbone of a free terminus. Within the last decade PLTs have been identified in over 600 known protein structures across all kingdoms of life. These proteins vary in function from oxidoreductases to hydrolases and small hormones. Their presence in different cellular compartments is highly influenced by the redox potential of the environment acting as a potential molecular switch. A combination of experimental phi-value analysis and structure-based models were used to identify key residues within the folding pathway for the model human hormone leptin. Previous computational work uncovered that the threading event occurs within the early stage of the folding free energy landscape. Incorporation of a threading event adds ruggedness to the folding landscape, slowing the process. Our investigation of leptin's in vitro threading event utilized a variant designed to lock the structure in a pre-threaded conformation inhibiting unthreading of the chain in the denatured state. The designed variant folds 100 times faster than the wild type, demonstrating that leptin spontaneously threads/unthreads in oxidizing environments; with the covalent loop intact.

Synergism in the Molecular Crowding of Ligand-Induced Riboswitch Folding: Kinetic/Thermodynamic Insights from Single-Molecule Spectroscopy.

Conformational dynamics in riboswitches involves ligand binding and folding of RNA, each of which can be influenced by excluded volume effects under "crowded" in vivo cellular conditions and thus incompletely characterized by in vitro studies under dilute buffer conditions. In this work, temperature-dependent single-molecule fluorescence resonance energy transfer (FRET) spectroscopy is used to characterize the thermodynamics of (i) cognate ligand and (ii) molecular crowders (PEG, polyethylene glycol) on folding of the B. subtilis LysC lysine riboswitch. With the help of detailed kinetic analysis, we isolate and study the effects of PEG on lysine binding and riboswitch folding steps individually, from which we find that PEG crowding facilitates riboswitch folding primarily via a surprising increase in affinity for the cognate ligand. This is furthermore confirmed by temperature-dependent studies, which reveal that PEG crowding is not purely entropic and instead significantly impacts both enthalpic and entropic contributions to the free energy landscape for folding. The results indicate that PEG molecular crowding/stabilization of the lysine riboswitch is more mechanistically complex and requires extension beyond the conventional picture of purely repulsive solvent-solute steric interactions arising from excluded volume and entropy. Instead, the current experimental FRET data support an alternative multistep mechanism, whereby PEG first entropically crowds the unfolded riboswitch into a "pre-folded" conformation, which in turn greatly increases the ligand binding affinity and thereby enhances the overall equilibrium for riboswitch folding.

In silico folding of hydrophobic peptides that form β-hairpin structures in solution.

Peptides designed with residues that have a high propensity to occur in β-turns form β-hairpin structures in apolar as well as in polar organic solvents such as dimethyl sulfoxide (DMSO). Due to limited solubility, their conformations have not been investigated experimentally in water. We have examined the conformations of four of such designed peptides that fold into well-defined β-hairpin structures facilitated by β-turns, in the crystalline state and in solution, by molecular dynamics simulations (MDS). The peptides folded into β-hairpin structures in water, starting from the fully extended conformation. However, in DMSO, neither folding nor unfolding was observed during MDS, when the starting structures were unfolded and folded, respectively. The lack of folding in DMSO was investigated by constructing folding free energy landscapes by umbrella sampling. The folding free energy landscape is smooth in water, whereas in DMSO, folded and unfolded structures are separated by high-energy barriers. The folding free energy is less in DMSO compared with water due to a more stable unfolded structure in DMSO compared with water, which in turn is due to stabilisation of the unfolded state by hydrophobic interactions in DMSO. This finding will be helpful to researchers to accurately model and/or design small peptide structures in water and organic solvents.

Molecular Insight into the Extracellular Chaperone Serum Albumin in Modifying the Folding Free Energy Landscape of Client Proteins.

Serum albumin (SA) is the most abundant extracellular chaperone protein presenting in various bodily fluids. Recently, several studies have revealed molecular mechanisms of SA in preventing the amyloid formation of amyloidogenic proteins. However, our insight into the mechanism SA employed to sense and regulate the folding states of full-length native proteins is still limited. Addressing this question is technically challenging due to the intrinsic dynamic nature of both chaperones and clients. Here using nuclear magnetic resonance spectroscopy, we show SA modifies the folding free energy landscape of clients and subsequently alters the equilibria between different compact conformations of its clients, resulting in the increased populations of excited states of client proteins. This modulation of client protein conformation by SA can change the client protein activity in a way that cannot be interpreted on the basis of its ground state structure; therefore, our work provides an alternative insight of SA in retaining a balanced functional proteome.

Frustration in the coupled folding-binding process of colicin E3 rRNase with immunity protein Im3

The folding free energy landscapes of many small protein domains are rugged funnel shaped. While there is a strong energetic bias toward the native folded state, non-native interactions may be formed during the folding process. The residual local frustration could contribute to regulate the dynamics and function of a protein. In principle, similar frustration could be present in the coupled folding-binding process of intrinsically disordered proteins. Indeed, a recent bioinformatic analysis showed that disordered protein complexes exhibit a high degree of local frustration at the binding interface.

A Computational Study of RNA Tetraloop Thermodynamics, Including Misfolded States.

An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. We isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.

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.

Non-Markovian modeling of protein folding

We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide [Formula: see text] for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote-Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.

Extension-Dependent Drift Velocity and Diffusion (DrDiff) Directly Reconstructs the Folding Free Energy Landscape of Atomic Force Microscopy Experiments.

Two equilibrium force microscopy trajectories [q(t)] of high-precision single-molecule spectroscopy assays were analyzed: the pulling of an HIV RNA hairpin and of a 3-aa sequence of the bacteriorhodopsin membrane protein. Both present hundreds of two-state folding transitions, and their free-energy [F(q)] landscapes were previously obtained by deconvolving time signals with the inverse Boltzmann and pfold methods. In this letter, the two F profiles were reconstructed directly from the measured time-series by the drift-diffusion (DrDiff) framework that characterized the effective conformational drift-velocity [v(q)] and diffusion [D(q)] coefficients. The two thermodynamic F profiles reconstructed with DrDiff directly from q(t) were in good agreement with those previously obtained from the deconvolved time signals. q(t) trajectories simulated with a two-dimensional framework in which the diffusion coefficient of the pulling setup (q coordinate) differed from the molecule (x coordinate) were also analyzed by DrDiff. The performance in reconstructing F was investigated in different conditions of diffusion anisotropy in the simulated time-series using Brownian dynamics. In addition, recently developed theories were used in order to evaluate the quality of the analysis performed in the experimental time series: the memory effects and the intrinsic biomolecular dynamic properties after connecting the probe to the molecule. With the 2-dimensional diffusive models and the additional analyses, it is proposed that the different physical regimes imposed by the stiffer probes of the two biomolecules will have an impact in the measured extension-dependent D and, thus, in the reconstruction of F by DrDiff. Stiffer AFM probes may reflect the molecular behavior more faithfully and reconstruction of F might be more successful. The reported quantities extracted directly from q(t) highlights the current state of the biomolecule characterization by force spectroscopy experiments: it is still challenging despite the recent advances, yet it is very promising.

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.

The Coupled Folding-Binding Mechanisms of Intrinsically Disordered Proteins with Different Folded Structures

Many cellular functions, including signal transduction and gene regulation, are carried out by interactions between intrinsically disordered proteins (IDPs) and their biological targets. Although the coupled folding-binding processes of IDPs have been extensively studied, previous works mainly focused on IDPs folding into simple alpha-helical structures, it is not clear how folding of beta-strands and more complex structures are coupled with target binding. In this work, we studied the coupled folding-binding process of three IDPs with different folded structures, i.e., c-Myb, AF9, and E3 rRNase Y507A mutant using topology-based coarse-grained molecular dynamics simulations. Although the three IDPs initiated the binding process via unfolded conformations, the coupling mechanism between folding and binding was different. C-Myb folded into an alpha-helix upon binding with KIX and the folding free energy landscape was downhill. When the binding free energy barrier was crossed, folding of c-Myb processed synchronously with binding. AF9 folded into an alpha-beta structure upon binding with AF4. However, AF9 remained largely unfolded even when 70% of intermolecular contacts were formed. Further binding induced folding and packing of the N- and C-terminal helices of AF9. In contrast to AF9, E3 rRNase folded into native-like all-beta conformations upon encountering Im3 and further binding proceeded subsequently. Our results suggest that the coupled folding-binding mechanisms of IDPs may vary significantly depending on their folded structures and intermolecular interactions.

The influence of intrinsic folding mechanism of an unfolded protein on the coupled folding-binding process during target recognition.

Intrinsically disordered proteins (IDPs) are extensively involved in dynamic signaling processes which require a high association rate and a high dissociation rate for rapid binding/unbinding events and at the same time a sufficient high affinity for specific recognition. Although the coupled folding-binding processes of IDPs have been extensively studied, it is still impossible to predict whether an unfolded protein is suitable for molecular signaling via coupled folding-binding. In this work, we studied the interplay between intrinsic folding mechanisms and coupled folding-binding process for unfolded proteins through molecular dynamics simulations. We first studied the folding process of three representative IDPs with different folded structures, that is, c-Myb, AF9, and E3 rRNase. We found the folding free energy landscapes of IDPs are downhill or show low barriers. To further study the influence of intrinsic folding mechanism on the binding process, we modulated the folding mechanism of barnase via circular permutation and simulated the coupled folding-binding process between unfolded barnase permutant and folded barstar. Although folding of barnase was coupled to target binding, the binding kinetics was significantly affected by the intrinsic folding free energy barrier, where reducing the folding free energy barrier enhances binding rate up to two orders of magnitude. This accelerating effect is different from previous results which reflect the effect of structure flexibility on binding kinetics. Our results suggest that coupling the folding of an unfolded protein with no/low folding free energy barrier with its target binding may provide a way to achieve high specificity and rapid binding/unbinding kinetics simultaneously.

A topological order parameter for describing folding free energy landscapes of proteins.

We studied the refolding free energy landscape of 26 proteins using the Go-like model. The distance between the denaturated state and the transition state, X F, was calculated using the Bell theory and the nonlinear Dudko-Hummer-Szabo theory, and its relation to the geometrical properties of the native state was considered in detail. We showed that none of the structural parameters, such as the contact order, protein length, and radius of cross section, correlate with X F for all classes of proteins. To overcome this problem, we have introduced the nematic order parameter P 02, which describes the ordering of the structured elements of the native state. Due to its topologically global nature, P 02 is better than other structural parameters in describing the folding free energy landscape. In particular, P 02 displays a good correlation with X F extracted from the nonlinear theory for all three classes of proteins. Therefore, this parameter can be used to predict X F for any protein, if its native structure is known.

High-Precision Single-Molecule Characterization of the Folding of an HIV RNA Hairpin by Atomic Force Microscopy.

The folding of RNA into a wide range of structures is essential for its diverse biological functions from enzymatic catalysis to ligand binding and gene regulation. The unfolding and refolding of individual RNA molecules can be probed by single-molecule force spectroscopy (SMFS), enabling detailed characterization of the conformational dynamics of the molecule as well as the free-energy landscape underlying folding. Historically, high-precision SMFS studies of RNA have been limited to custom-built optical traps. Although commercial atomic force microscopes (AFMs) are widely deployed and offer significant advantages in ease-of-use over custom-built optical traps, traditional AFM-based SMFS lacks the sensitivity and stability to characterize individual RNA molecules precisely. Here, we developed a high-precision SMFS assay to study RNA folding using a commercial AFM and applied it to characterize a small RNA hairpin from HIV that plays a key role in stimulating programmed ribosomal frameshifting. We achieved rapid data acquisition in a dynamic assay, unfolding and then refolding the same individual hairpin more than 1,100 times in 15 min. In comparison to measurements using optical traps, our AFM-based assay featured a stiffer force probe and a less compliant construct, providing a complementary measurement regime that dramatically accelerated equilibrium folding dynamics. Not only did kinetic analysis of equilibrium trajectories of the HIV RNA hairpin yield the traditional parameters used to characterize folding by SMFS (zero-force rate constants and distances to the transition state), but we also reconstructed the full 1D projection of the folding free-energy landscape comparable to state-of-the-art studies using dual-beam optical traps, a first for this RNA hairpin and AFM studies of nucleic acids in general. Looking forward, we anticipate that the ease-of-use of our high-precision assay implemented on a commercial AFM will accelerate studying folding of diverse nucleic acid structures.

Monte Carlo Sampling of Protein Folding by Combining an All-Atom Physics-Based Model with a Native State Bias.

Energy landscape theory suggests that native interactions are a major determinant of the folding mechanism of a protein. Thus, structure-based (Go̅) models have, aided by coarse-graining techniques, shown great success in capturing the mechanisms of protein folding and conformational changes. In certain cases, however, non-native interactions and atomic details are also essential to describe the protein dynamics, prompting the development of a variety of structure-based models that include non-native interactions, and differentiate between different types of attractive potentials. Here, we describe an all-protein-atom hybrid model, termed ProfasiGo, that integrates an implicit solvent all-atom physics-based model (called Profasi) and a structure-based Go̅ potential and its implementation in two software packages (PHAISTOS and ProFASi) that are developed for Monte Carlo sampling of protein molecules. We apply the ProfasiGo model to study the folding free energy landscapes of four topologically similar proteins, one of which can be folded by the simplified potential Profasi and two that have been folded by explicit solvent, all-atom molecular dynamics simulations with the CHARMM22* force field. Our results reveal that the hybrid ProfasiGo model is able to capture many of the details present in the physics-based potentials while retaining the advantages of Go̅ models for sampling and guiding to the native state. We expect that the model will be widely applicable to the study of the folding of more complex proteins or to the study of conformational dynamics and integration with experimental data.

Instrumental Effects in the Dynamics of an Ultrafast Folding Protein under Mechanical Force.

The analysis and interpretation of single molecule force spectroscopy (smFS) experiments is often complicated by hidden effects from the measuring device. Here we investigate these effects in our recent smFS experiments on the ultrafast folding protein gpW, which has been previously shown to fold without crossing a free energy barrier in the absence of force (i.e., downhill folding). Using atomic force microscopy (AFM) smFS experiments, we found that a very small force of ∼5 pN brings gpW near its unfolding midpoint and results in two-state (un)folding patterns that indicate the emergence of a force-induced free energy barrier. The change in the folding regime is concomitant with a 30,000-fold slowdown of the folding and unfolding times, from a few microseconds that it takes gpW to (un)fold at the midpoint temperature to seconds in the AFM. These results are puzzling because the barrier induced by force in the folding free energy landscape of gpW is far too small to account for such a difference in time scales. Here we use recently developed theoretical methods to resolve the origin of the strikingly slow dynamics of gpW under mechanical force. We find that, while the AFM experiments correctly capture the equilibrium distance distribution, the measured dynamics are entirely controlled by the response of the cantilever and polyprotein linker, which is much slower than the protein conformational dynamics. This interpretation is likely applicable to the folding of other small biomolecules in smFS experiments, and becomes particularly important in the case of systems with fast folding dynamics and small free energy barriers, and for instruments with slow response times.