Quantifying the roughness on the free energy landscape: entropic bottlenecks and protein folding rates

Modulating Coarse-Grained Dynamics by Perturbing Free Energy Landscapes

We introduce an approach to describe the long-time dynamics of multiatomic molecules by modulating the free energy landscape (FEL) to capture dominant features of the energy-barrier crossing dynamics of the all-atom (AA) system. Notably, we establish that the self-diffusion coefficient of coarse-grained (CG) systems can be accurately delineated by enhancing conservative force fields with high-frequency perturbations. Using theoretical arguments, we show that these perturbations do not alter the lower-order distribution functions, thereby preserving the structure of the AA system after coarse-graining. We demonstrate the utility of this approach using molecular dynamics simulations of simple molecules in bulk with distinct dynamical characteristics with and without time scale separations as well as for inhomogeneous systems where a fluid is confined in a slit-like nanochannel. Additionally, we also apply our approach to more powerful many-body potentials optimized by using machine learning (ML).

Novel Covalent Modifier-Induced Local Conformational Changes within the Intrinsically Disordered Region of the Androgen Receptor

Intrinsically disordered regions (IDRs) of transcription factors play an important biological role in liquid condensate formation and gene regulation. It is thus desirable to investigate the druggability of IDRs and how small-molecule binders can alter their conformational stability. For the androgen receptor (AR), certain covalent ligands induce important changes, such as the neutralization of the condensate. To understand the specificity of ligand-IDR interaction and potential implications for the mechanism of neutralizing liquid-liquid phase separation (LLPS), we modeled and performed computer simulations of ligand-bound peptide segments obtained from the human AR. We analyzed how different covalent ligands affect local secondary structure, protein contact map, and protein-ligand contacts for these protein systems. We find that effective neutralizers make specific interactions (such as those between cyanopyrazole and tryptophan) that alter the helical propensity of the peptide segments. These findings on the mechanism of action can be useful for designing molecules that influence IDR structure and condensate of the AR in the future.

Machine learning coarse-grained potentials of protein thermodynamics

A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.

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.

Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides a Fast but Still Accurate Treatment of Hydrodynamic Interactions in Brownian Dynamics Simulations of Biological Macromolecules

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HIs). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here, we explore the use of an alternative way to accelerate the calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA-RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA-RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast, approximate way of including HIs in BD simulations of intermediate-scale systems.

An Orientationally Averaged Version of the Rotne-Prager-Yamakawa Tensor Provides A Fast But Still Accurate Treatment Of Hydrodynamic Interactions In Brownian Dynamics Simulations Of Biological Macromolecules

The Brownian dynamics (BD) simulation technique is widely used to model the diffusive and conformational dynamics of complex systems comprising biological macromolecules. For the diffusive properties of macromolecules to be described correctly by BD simulations, it is necessary to include hydrodynamic interactions (HI). When modeled at the Rotne-Prager-Yamakawa (RPY) level of theory, for example, the translational and rotational diffusion coefficients of isolated macromolecules can be accurately reproduced; when HIs are neglected, however, diffusion coefficients can be underestimated by an order of magnitude or more. The principal drawback to the inclusion of HIs in BD simulations is their computational expense, and several previous studies have sought to accelerate their modeling by developing fast approximations for the calculation of the correlated random displacements. Here we explore the use of an alternative way to accelerate calculation of HIs, i.e., by replacing the full RPY tensor with an orientationally averaged (OA) version which retains the distance dependence of the HIs but averages out their orientational dependence. We seek here to determine whether such an approximation can be justified in application to the modeling of typical proteins and RNAs. We show that the use of an OA RPY tensor allows translational diffusion of macromolecules to be modeled with very high accuracy at the cost of rotational diffusion being underestimated by ∼25%. We show that this finding is independent of the type of macromolecule simulated and the level of structural resolution employed in the models. We also show, however, that these results are critically dependent on the inclusion of a non-zero term that describes the divergence of the diffusion tensor: when this term is omitted from simulations that use the OA RPY model, unfolded macromolecules undergo rapid collapse. Our results indicate that the orientationally averaged RPY tensor is likely to be a useful, fast approximate way of including HIs in BD simulations of intermediate-scale systems.

Probing the Energy Landscape of Spectrin R15 and R16 and the Effects of Non-native Interactions

Understanding the details of a protein folding mechanism can be a challenging and complex task. One system with an interesting folding behavior is the α-spectrin domain, where the R15 folds three-orders of magnitude faster than its homologues R16 and R17, despite having similar structures. The molecular origins that explain these folding rate differences remain unclear, but our previous work revealed that a combined effect produced by non-native interactions could be a reasonable cause for these differences. In this study, we explore further the folding process by identifying the molecular paths, metastable states, and the collective motions that lead these unfolded proteins to their native state conformation. Our results uncovered the differences between the folding pathways for the wild-type R15 and R16 and an R16 mutant. The metastable ensembles that speed down the folding were identified using an energy landscape visualization method (ELViM). These ensembles correspond to similar experimentally reported configurations. Our observations indicate that the non-native interactions are also associated with secondary structure misdocking. This computational methodology can be used as a fast, straightforward protocol for shedding light on systems with unclear folding or conformational traps.

Exploring the Folding Mechanism of Dimeric Superoxide Dismutase

The Cu/Zn Human Superoxide Dismutase (SOD1) is a dimeric metalloenzyme whose genetic mutations are directly related to amyotrophic lateral sclerosis (ALS), so understanding its folding mechanism is of fundamental importance. Currently, the SOD1 dimer formation is studied via molecular dynamics simulations using a simplified structure-based model and an all-atom model. Results from the simplified model reveal a mechanism dependent on distances between monomers, which are limited by constraints to mimic concentration dependence. The stability of intermediates (during the int state) is significantly affected by this distance, as well as by the presence of two folded monomers prior to dimer formation. The kinetics of interface formation are also highly dependent on the separation distance. The folding temperature of the dimer is about 4.2% higher than that of the monomer, a value not too different from experimental data. All-atom simulations on the apo dimer give binding free energy between monomers similar to experimental values. An intermediate state is evident for the apo form at a separation distance between monomers slightly larger than the native distance which has little formed interface between monomers. We have shown that this intermediate is stabilized by non-native intra- and intercontacts.

Engineering the kinetic stability of a β-trefoil protein by tuning its topological complexity

Kinetic stability, defined as the rate of protein unfolding, is central to determining the functional lifetime of proteins, both in nature and in wide-ranging medical and biotechnological applications. Further, high kinetic stability is generally correlated with high resistance against chemical and thermal denaturation, as well as proteolytic degradation. Despite its significance, specific mechanisms governing kinetic stability remain largely unknown, and few studies address the rational design of kinetic stability. Here, we describe a method for designing protein kinetic stability that uses protein long-range order, absolute contact order, and simulated free energy barriers of unfolding to quantitatively analyze and predict unfolding kinetics. We analyze two β-trefoil proteins: hisactophilin, a quasi-three-fold symmetric natural protein with moderate stability, and ThreeFoil, a designed three-fold symmetric protein with extremely high kinetic stability. The quantitative analysis identifies marked differences in long-range interactions across the protein hydrophobic cores that partially account for the differences in kinetic stability. Swapping the core interactions of ThreeFoil into hisactophilin increases kinetic stability with close agreement between predicted and experimentally measured unfolding rates. These results demonstrate the predictive power of readily applied measures of protein topology for altering kinetic stability and recommend core engineering as a tractable target for rationally designing kinetic stability that may be widely applicable.

Potential Self-Peptide Inhibitors of the SARS-CoV-2 Main Protease

The SARS-CoV-2 main protease (Mpro) plays an essential role in viral replication, cleaving viral polyproteins into functional proteins. This makes Mpro an important drug target. Mpro consists of an N-terminal catalytic domain and a C-terminal α-helical domain (MproC). Previous studies have shown that peptides derived from a given protein sequence (self-peptides) can affect the folding and, in turn, the function of that protein. Since the SARS-CoV-1 MproC is known to stabilize its Mpro and regulate its function, we hypothesized that SARS-CoV-2 MproC-derived self-peptides may modulate the folding and the function of SARS-CoV-2 Mpro. To test this, we studied the folding of MproC in the presence of various self-peptides using coarse-grained structure-based models and molecular dynamics simulations. In these simulations of MproC and one self-peptide, we found that two self-peptides, the α1-helix and the loop between α4 and α5 (loop4), could replace the equivalent native sequences in the MproC structure. Replacement of either sequence in full-length Mpro should, in principle, be able to perturb Mpro function albeit through different mechanisms. Some general principles for the rational design of self-peptide inhibitors emerge: The simulations show that prefolded self-peptides are more likely to replace native sequences than those which do not possess structure. Additionally, the α1-helix self-peptide is kinetically stable and once inserted rarely exchanges with the native α1-helix, while the loop4 self-peptide is easily replaced by the native loop4, making it less useful for modulating function. In summary, a prefolded α1-derived peptide should be able to inhibit SARS-CoV-2 Mpro function.

Biotinylation Eliminates the Intermediate State of Top7 Designed with an HIV-1 Epitope

Broadly neutralizing antibodies against HIV-1 are rare with the 2F5 antibody being one of the most protective. Insertion of an antibody epitope into a stable and small protein scaffold overcomes many of the obstacles found to produce antibodies. However, the design leads to grafting of epitopes that may cause protein aggregation. Here, I investigated the 2F5 epitope grafted into the Top7 as the scaffold in which the resulting immunoreactive protein precipitates along the storage time, as opposed to its completely soluble biotinylated version. Molecular dynamics showed that biotinylation eliminates the intermediate state of the scaffold-epitope Top7-2F5 by switching a noncooperative to a cooperative folding. The aggregation propensity of the Top7-designed proteins is examined in light of thermodynamic cooperativity and kinetic traps along the decreasing depth of the intermediate ensemble in the free energy landscape. This protocol may predict stable and soluble scaffold-epitopes with the purpose of composing novel therapeutic and diagnostic platforms.

A Method for Assessing the Robustness of Protein Structures by Randomizing Packing Interactions

Many single-domain proteins are not only stable and water-soluble, but they also populate few to no intermediates during folding. This reduces interactions between partially folded proteins, misfolding, and aggregation, and makes the proteins tractable in biotechnological applications. Natural proteins fold thus, not necessarily only because their structures are well-suited for folding, but because their sequences optimize packing and fit their structures well. In contrast, folding experiments on the de novo designed Top7 suggest that it populates several intermediates. Additionally, in de novo protein design, where sequences are designed for natural and new non-natural structures, tens of sequences still need to be tested before success is achieved. Both these issues may be caused by the specific scaffolds used in design, i.e., some protein scaffolds may be more tolerant to packing perturbations and varied sequences. Here, we report a computational method for assessing the response of protein structures to packing perturbations. We then benchmark this method using designed proteins and find that it can identify scaffolds whose folding gets disrupted upon perturbing packing, leading to the population of intermediates. The method can also isolate regions of both natural and designed scaffolds that are sensitive to such perturbations and identify contacts which when present can rescue folding. Overall, this method can be used to identify protein scaffolds that are more amenable to whole protein design as well as to identify protein regions which are sensitive to perturbations and where further mutations should be avoided during protein engineering.

Biotin-painted proteins have thermodynamic stability switched by kinetic folding routes

Biotin-labeled proteins are widely used as tools to study protein-protein interactions and proximity in living cells. Proteomic methods broadly employ proximity-labeling technologies based on protein biotinylation in order to investigate the transient encounters of biomolecules in subcellular compartments. Biotinylation is a post-translation modification in which the biotin molecule is attached to lysine or tyrosine residues. So far, biotin-based technologies proved to be effective instruments as affinity and proximity tags. However, the influence of biotinylation on aspects such as folding, binding, mobility, thermodynamic stability, and kinetics needs to be investigated. Here, we selected two proteins [biotin carboxyl carrier protein (BCCP) and FKBP3] to test the influence of biotinylation on thermodynamic and kinetic properties. Apo (without biotin) and holo (biotinylated) protein structures were used separately to generate all-atom structure-based model simulations in a wide range of temperatures. Holo BCCP contains one biotinylation site, and FKBP3 was modeled with up to 23 biotinylated lysines. The two proteins had their estimated thermodynamic stability changed by altering their energy landscape. In all cases, after comparison between the apo and holo simulations, differences were observed on the free-energy profiles and folding routes. Energetic barriers were altered with the density of states clearly showing changes in the transition state. This study suggests that analysis of large-scale datasets of biotinylation-based proximity experiments might consider possible alterations in thermostability and folding mechanisms imposed by the attached biotins.

Coarse-Grained Simulations of Protein Folding: Bridging Theory and Experiments

Computational coarse-grained models play a fundamental role as a research tool in protein folding, and they are important in bridging theory and experiments. Folding mechanisms are generally discussed using the energy landscape framework, which is well mapped within a class of simplified structure-based models. In this chapter, simplified computer models are discussed with special focus on structure-based ones.

Small Neutral Crowding Solute Effects on Protein Folding Thermodynamic Stability and Kinetics

Molecular crowding is a ubiquitous phenomenon in biological systems, with significant consequences on protein folding and stability. Small compounds, such as the osmolyte trimethylamine N-oxide (TMAO), can also present similar effects. To analyze the effects arising from these solute-like molecules, we performed a series of crowded coarse-grained folding simulations. Two well-known proteins were chosen, CI2 and SH3, modeled by the alpha-carbon-structure-based model. In the simulations, the crowding molecules were represented by low-sized neutral atom beads in different concentrations. The results show that a low level of the volume fraction occupied by neutral agents can change protein stability and folding kinetics for the two systems. However, the kinetics were shown to be unaffected in their respective folding temperatures. The faster kinetics correlates with changes in the folding route for systems at the same temperature, where non-native contacts were shown to be relevant. The transition states of the two systems with and without crowders are similar. In the case of SH3, there are differences in the structuring of two strands, which may be associated with the increase in its folding rate, in addition to the destabilization of the denatured ensemble. The present study also detected a crossover in the thermodynamic stability behavior, previously observed experimentally and theoretically. As the temperature increases, crowders change from destabilizing to stabilizing agents.

Topological principles of protein folding

What is the topology of a protein and what governs protein folding to a specific topology? This is a fundamental question in biology. The protein folding reaction is a critically important cellular process, which is failing in many prevalent diseases. Understanding protein folding is also key to the design of new proteins for applications. However, our ability to predict the folding of a protein chain is quite limited and much is still unknown about the topological principles of folding. Current predictors of folding kinetics, including the contact order and size, present a limited predictive power, suggesting that these models are fundamentally incomplete. Here, we use a newly developed mathematical framework to define and extract the topology of a native protein conformation beyond knot theory, and investigate the relationship between native topology and folding kinetics in experimentally characterized proteins. We show that not only the folding rate, but also the mechanistic insight into folding mechanisms can be inferred from topological parameters. We identify basic topological features that speed up or slow down the folding process. The approach enabled the decomposition of protein 3D conformation into topologically independent elementary folding units, called circuits. The number of circuits correlates significantly with the folding rate, offering not only an efficient kinetic predictor, but also a tool for a deeper understanding of theoretical folding models. This study contributes to recent work that reveals the critical relevance of topology to protein folding with a new, contact-based, mathematically rigorous perspective. We show that topology can predict folding kinetics when geometry-based predictors like contact order and size fail.

Protein self-entanglement modulates successful folding to the native state: A multi-scale modeling study

The computer-aided investigation of protein folding has greatly benefited from coarse-grained models, that is, simplified representations at a resolution level lower than atomistic, providing access to qualitative and quantitative details of the folding process that would be hardly attainable, via all-atom descriptions, for medium to long molecules. Nonetheless, the effectiveness of low-resolution models is itself hampered by the presence, in a small but significant number of proteins, of nontrivial topological self-entanglements. Features such as native state knots or slipknots introduce conformational bottlenecks, affecting the probability to fold into the correct conformation; this limitation is particularly severe in the context of coarse-grained models. In this work, we tackle the relationship between folding probability, protein folding pathway, and protein topology in a set of proteins with a nontrivial degree of topological complexity. To avoid or mitigate the risk of incurring in kinetic traps, we make use of the elastic folder model, a coarse-grained model based on angular potentials optimized toward successful folding via a genetic procedure. This light-weight representation allows us to estimate in silico folding probabilities, which we find to anti-correlate with a measure of topological complexity as well as to correlate remarkably well with experimental measurements of the folding rate. These results strengthen the hypothesis that the topological complexity of the native state decreases the folding probability and that the force-field optimization mimics the evolutionary process these proteins have undergone to avoid kinetic traps.

Unfolding of Dynamical Events in the Early Stage of Insulin Dimer Dissociation

The dissociation of an insulin dimer is an important biochemical event that could also serve as a prototype of dissociations in similar biomolecular assemblies. We use a recently developed multidimensional free energy landscape for insulin dimer dissociation to unearth the microscopic and mechanistic aspects of the initial stages of the process that could hold the key to understanding the stability and the rate. The following sequence of events occurs in the initial stages: (i) The backbone hydrogen bonds break partially at the antiparallel β-sheet junction, (ii) the two α-helices (chain B) move away from each other while several residues (chain A) move closer, and (iii) a flow of adjacent water molecules occurs into the junction region. Interestingly, the intermonomeric center-to-center distance does not increase, but the number of native contacts exhibits a sharp decrease. Subsequent steps involve further disengagement of hydrophobic groups. This process is slow because of an entropic bottleneck created by the existence of the large configuration space available in the native state (NS), which is inhabited by low-frequency conformational fluctuations. We carry out a density-of-states analyses in the dimer NS to unearth distinctive features not present in the monomers. These low-frequency modes are also responsible for a large entropic stabilization of the NS. Hydrophobic disengagement in the early stage leads to the formation of a twisted intermediate state which itself is a metastable minimum (IS-1). The subsequent progress leads to another dimeric complex (IS-2), which is on the dissociative pathway and characterized by a further decrease in the native contacts. The dissociation process provides insights into the workings of a biomolecular assembly.

Resolving Site-Specific Heterogeneity of the Unfolded State under Folding Conditions

Understanding the properties of the unfolded state under folding conditions is of fundamental importance for gaining mechanistic insight into folding as well as misfolding reactions. Toward achieving this objective, the folding reaction of a small protein, monellin, has been resolved structurally and temporally, with the use of the multisite time-resolved FRET methodology. The present study establishes that the initial polypeptide chain collapse is not only heterogeneous but also structurally asymmetric and nonuniform. The population-averaged size for the segments spanning parts of the β-sheet decreases much more than that for the α-helix. Multisite measurements enabled specific and nonspecific components of the initial chain collapse to be discerned. The expanded and compact intermediate subensembles have the properties of a nonspecifically collapsed (hence, random-coil-like) and specifically collapsed (hence, globular) polymer, respectively. During subsequent folding, both the subensembles underwent contraction to varying extents at the four monitored segments, which was close to gradual in nature. The expanded intermediate subensemble exhibited an additional very slow contraction, suggestive of the presence of non-native interactions that result in a higher effective viscosity slowing down intrachain motions under folding conditions.

Prediction of Protein-Protein Binding Interactions in Dimeric Coiled Coils by Information Contained in Folding Energy Landscapes

Coiled coils represent the simplest form of a complex formed between two interacting protein partners. Their extensive study has led to the development of various methods aimed towards the investigation and design of complex forming interactions. Despite the progress that has been made to predict the binding affinities for protein complexes, and specifically those tailored towards coiled coils, many challenges still remain. In this work, we explore whether the information contained in dimeric coiled coil folding energy landscapes can be used to predict binding interactions. Using the published SYNZIP dataset, we start from the amino acid sequence, to simultaneously fold and dock approximately 1000 coiled coil dimers. Assessment of the folding energy landscapes showed that a model based on the calculated number of clusters for the lowest energy structures displayed a signal that correlates with the experimentally determined protein interactions. Although the revealed correlation is weak, we show that such correlation exists; however, more work remains to establish whether further improvements can be made to the presented model.

The Molecular Mechanism of Domain Swapping of the C-Terminal Domain of the SARS-Coronavirus Main Protease

In three-dimensional domain swapping, two protein monomers exchange a part of their structures to form an intertwined homodimer, whose subunits resemble the monomer. Several viral proteins domain swap to increase their structural complexity or functional avidity. The main protease (M^pro) of the severe acute respiratory syndrome (SARS) coronavirus proteolyzes viral polyproteins and has been a target for anti-SARS drug design. Domain swapping in the α-helical C-terminal domain of M^pro (M^proC) locks M^pro into a hyperactive octameric form that is hypothesized to promote the early stages of viral replication. However, in the absence of a complete molecular understanding of the mechanism of domain swapping, investigations into the biological relevance of this octameric M^pro have stalled. Isolated M^proC can exist as a monomer or a domain-swapped dimer. Here, we investigate the mechanism of domain swapping of M^proC using coarse-grained structure-based models and molecular dynamics simulations. Our simulations recapitulate several experimental features of M^proC folding. Further, we find that a contact between a tryptophan in the M^proC domain-swapping hinge and an arginine elsewhere forms early during folding, modulates the folding route, and promotes domain swapping to the native structure. An examination of the sequence and the structure of the tryptophan containing hinge loop shows that it has a propensity to form multiple secondary structures and contacts, indicating that it could be stabilized into either the monomer- or dimer-promoting conformations by mutations or ligand binding. Finally, because all residues in the tryptophan loop are identical in SARS-CoV and SARS-CoV-2, mutations that modulate domain swapping may provide insights into the role of octameric M^pro in the early-stage viral replication of both viruses.

Slow Folding of a Helical Protein: Large Barriers, Strong Internal Friction, or a Shallow, Bumpy Landscape?

The rate at which a protein molecule folds is determined by opposing energetic and entropic contributions to the free energy that shape the folding landscape. Delineating the extent to which they impact the diffusional barrier-crossing events, including the magnitude of internal friction and barrier height, has largely been a challenging task. In this work, we extract the underlying thermodynamic and dynamic contributions to the folding rate of an unusually slow-folding helical DNA-binding domain, PurR, which shares the characteristics of ultrafast downhill-folding proteins but nonetheless appears to exhibit an apparent two-state equilibrium. We combine equilibrium spectroscopy, temperature-viscosity-dependent kinetics, statistical mechanical modeling, and coarse-grained simulations to show that the conformational behavior of PurR is highly heterogeneous characterized by a large spread in melting temperatures, marginal thermodynamic barriers, and populated partially structured states. PurR appears to be at the threshold of disorder arising from frustrated electrostatics and weak packing that in turn slows down folding due to a shallow, bumpy landscape and not due to large thermodynamic barriers or strong internal friction. Our work highlights how a strong temperature dependence on the pre-exponential could signal a shallow landscape and not necessarily a slow-folding diffusion coefficient, thus determining the folding timescales of even millisecond folding proteins and hints at possible structural origins for the shallow landscape.

Transient Unfolding and Long-Range Interactions in Viral BCL2 M11 Enable Binding to the BECN1 BH3 Domain

Viral BCL2 proteins (vBCL2s) help to sustain chronic infection of host proteins to inhibit apoptosis and autophagy. However, details of conformational changes in vBCL2s that enable binding to BH3Ds remain unknown. Using all-atom, multiple microsecond-long molecular dynamic simulations (totaling 17 μs) of the murine γ-herpesvirus 68 vBCL2 (M11), and statistical inference techniques, we show that regions of M11 transiently unfold and refold upon binding of the BH3D. Further, we show that this partial unfolding/refolding within M11 is mediated by a network of hydrophobic interactions, which includes residues that are 10 Å away from the BH3D binding cleft. We experimentally validate the role of these hydrophobic interactions by quantifying the impact of mutating these residues on binding to the Beclin1/BECN1 BH3D, demonstrating that these mutations adversely affect both protein stability and binding. To our knowledge, this is the first study detailing the binding-associated conformational changes and presence of long-range interactions within vBCL2s.

Analyses of the folding sites of irregular β-trefoil fold proteins through sequence-based techniques and Gō-model simulations

Background

The details of the folding mechanisms have not yet been fully understood for many proteins, and it is believed that the information on the folding mechanism of a protein is encoded in its amino acid sequence. β-trefoil proteins are known to have the same 3D scaffold, namely, a three-fold symmetric scaffold, despite the proteins’ low sequence identity among superfamilies. In this study, we extract an initial folding unit from the amino acid sequences of irregular β-trefoil proteins by constructing an average distance map (ADM) and utilizing inter-residue average distance statistics to determine the relative contact frequencies for residue pairs in terms of F values. We compare our sequence-based prediction results with the packing between hydrophobic residues in native 3D structures and a Gō-model simulation.

Results

The ADM and F-value analyses predict that the N-terminal and C-terminal regions are compact and that the hydrophobic residues at the central region can be regarded as an interaction center with other residues. These results correspond well to those of the Gō-model simulations. Moreover, our results indicate that the irregular parts in the β-trefoil proteins do not hinder the protein formation. Conserved hydrophobic residues on the β5 strand are always the interaction center of packing between the conserved hydrophobic residues in both regular and irregular β-trefoil proteins.

Conclusions

We revealed that the β5 strand plays an important role in β-trefoil protein structure construction. The sequence-based methods used in this study can extract the protein folding information from only amino acid sequence data, and well corresponded to 3D structure-based Gō-model simulation and available experimental results.

Effects of Topology and Sequence in Protein Folding Linked via Conformational Fluctuations

Experiments have compared the folding of proteins with different amino acid sequences but the same basic structure, or fold. Results indicate that folding is robust to sequence variations for proteins with some nonlocal folds, such as all-β, whereas the folding of more local, all-α proteins typically exhibits a stronger sequence dependence. Here, we use a coarse-grained model to systematically study how variations in sequence perturb the folding energy landscapes of three model sequences with 3α, 4β + α, and β-barrel folds, respectively. These three proteins exhibit folding features in line with experiments, including expected rank order in the cooperativity of the folding transition and stability-dependent shifts in the location of the free-energy barrier to folding. Using a generalized-ensemble simulation approach, we determine the thermodynamics of around 2000 sequence variants representing all possible hydrophobic or polar single- and double-point mutations. From an analysis of the subset of stability-neutral mutations, we find that folding is perturbed in a topology-dependent manner, with the β-barrel protein being the most robust. Our analysis shows, in particular, that the magnitude of mutational perturbations of the transition state is controlled in part by the size or "width" of the underlying conformational ensemble. This result suggests that the mutational robustness of the folding of the β-barrel protein is underpinned by its conformationally restricted transition state ensemble, revealing a link between sequence and topological effects in protein folding.

The Role of Electrostatics and Folding Kinetics on the Thermostability of Homologous Cold Shock Proteins

Understanding which aspects contribute to the thermostability of proteins is a challenge that has persisted for decades, and it is of great relevance for protein engineering. Several types of interactions can influence the thermostability of a protein. Among them, the electrostatic interactions have been a target of particular attention. Aiming to explore how this type of interaction can affect protein thermostability, this paper investigated four homologous cold shock proteins from psychrophilic, mesophilic, thermophilic, and hyperthermophilic organisms using a set of theoretical methodologies. It is well-known that electrostatics as well as hydrophobicity are key-elements for the stabilization of these proteins. Therefore, both interactions were initially analyzed in the native structure of each protein. Electrostatic interactions present in the native structures were calculated with the Tanford-Kirkwood model with solvent accessibility, and the amount of hydrophobic surface area buried upon folding was estimated by measuring both folded and extended structures. On the basis of Energy Landscape Theory, the local frustration and the simplified alpha-carbon structure-based model were modeled with a Debye-Hückel potential to take into account the electrostatics and the effects of an implicit solvent. Thermodynamic data for the structure-based model simulations were collected and analyzed using the Weighted Histogram Analysis and Stochastic Diffusion methods. Kinetic quantities including folding times, transition path times, folding routes, and Φ values were also obtained. As a result, we found that the methods are able to qualitatively infer that electrostatic interactions play an important role on the stabilization of the most stable thermophilic cold shock proteins, showing agreement with the experimental data.

pH and Charged Mutations Modulate Cold Shock Protein Folding and Stability: A Constant pH Monte Carlo Study

The folding and stability of proteins is a fundamental problem in several research fields. In the present paper, we have used different computational approaches to study the effects caused by changes in pH and for charged mutations in cold shock proteins from Bacillus subtilis (Bs-CspB). First, we have investigated the contribution of each ionizable residue for these proteins to their thermal stability using the TKSA-MC, a Web server for rational mutation via optimizing the protein charge interactions. Based on these results, we have proposed a new mutation in an already optimized Bs-CspB variant. We have evaluated the effects of this new mutation in the folding energy landscape using structure-based models in Monte Carlo simulation at constant pH, SBM-CpHMC. Our results using this approach have indicated that the charge rearrangements already in the unfolded state are critical to the thermal stability of Bs-CspB. Furthermore, the conjunction of these simplified methods was able not only to predict stabilizing mutations in different pHs but also to provide essential information about their effects in each stage of protein folding.

Successes and challenges in simulating the folding of large proteins

Computational simulations of protein folding can be used to interpret experimental folding results, to design new folding experiments, and to test the effects of mutations and small molecules on folding. However, whereas major experimental and computational progress has been made in understanding how small proteins fold, research on larger, multidomain proteins, which comprise the majority of proteins, is less advanced. Specifically, large proteins often fold via long-lived partially folded intermediates, whose structures, potentially toxic oligomerization, and interactions with cellular chaperones remain poorly understood. Molecular dynamics based folding simulations that rely on knowledge of the native structure can provide critical, detailed information on folding free energy landscapes, intermediates, and pathways. Further, increases in computational power and methodological advances have made folding simulations of large proteins practical and valuable. Here, using serpins that inhibit proteases as an example, we review native-centric methods for simulating the folding of large proteins. These synergistic approaches range from Gō and related structure-based models that can predict the effects of the native structure on folding to all-atom-based methods that include side-chain chemistry and can predict how disease-associated mutations may impact folding. The application of these computational approaches to serpins and other large proteins highlights the successes and limitations of current computational methods and underscores how computational results can be used to inform experiments. These powerful simulation approaches in combination with experiments can provide unique insights into how large proteins fold and misfold, expanding our ability to predict and manipulate protein folding.

Competitive binding of HIF-1α and CITED2 to the TAZ1 domain of CBP from molecular simulations

Many intrinsically disordered proteins (IDPs) are involved in complex signalling networks inside the cell.

Binding without folding - the biomolecular function of disordered polyelectrolyte complexes

Recent evidence shows that oppositely charged intrinsically disordered proteins (IDPs) can form high-affinity complexes that involve neither the formation of secondary or tertiary structure nor site-specific interactions between individual residues. Similar electrostatically dominated interactions have also been identified for positively charged IDPs binding to nucleic acids. These highly disordered polyelectrolyte complexes constitute an extreme case within the spectrum of biomolecular interactions involving disorder. Such interactions are likely to be widespread, since sequence analysis predicts proteins with highly charged disordered regions to be surprisingly numerous. Here, we summarize the insights that have emerged from the highly disordered polyelectrolyte complexes identified so far, and we highlight recent developments and future challenges in (i) establishing models for the underlying highly dynamic structural ensembles, (ii) understanding the novel binding mechanisms associated with them, and (iii) identifying the functional consequences.

Limits in accuracy and a strategy of RNA structure prediction using experimental information

RNA structural complexity and flexibility present a challenge for computational modeling efforts. Experimental information and bioinformatics data can be used as restraints to improve the accuracy of RNA tertiary structure prediction. Regarding utilization of restraints, the fundamental questions are: (i) What is the limit in prediction accuracy that one can achieve with arbitrary number of restraints? (ii) Is there a strategy for selection of the minimal number of restraints that would result in the best structural model? We address the first question by testing the limits in prediction accuracy using native contacts as restraints. To address the second question, we develop an algorithm based on the distance variation allowed by secondary structure (DVASS), which ranks restraints according to their importance to RNA tertiary structure prediction. We find that due to kinetic traps, the greatest improvement in the structure prediction accuracy is achieved when we utilize only 40-60% of the total number of native contacts as restraints. When the restraints are sorted by DVASS algorithm, using only the first 20% ranked restraints can greatly improve the prediction accuracy. Our findings suggest that only a limited number of strategically selected distance restraints can significantly assist in RNA structure modeling.

Ultrafast folding kinetics of WW domains reveal how the amino acid sequence determines the speed limit to protein folding

Protein (un)folding rates depend on the free-energy barrier separating the native and unfolded states and a prefactor term, which sets the timescale for crossing such barrier or folding speed limit. Because extricating these two factors is usually unfeasible, it has been common to assume a constant prefactor and assign all rate variability to the barrier. However, theory and simulations postulate a protein-specific prefactor that contains key mechanistic information. Here, we exploit the special properties of fast-folding proteins to experimentally resolve the folding rate prefactor and investigate how much it varies among structural homologs. We measure the ultrafast (un)folding kinetics of five natural WW domains using nanosecond laser-induced temperature jumps. All five WW domains fold in microseconds, but with a 10-fold difference between fastest and slowest. Interestingly, they all produce biphasic kinetics in which the slower phase corresponds to reequilibration over the small barrier (<3 RT) and the faster phase to the downhill relaxation of the minor population residing at the barrier top [transition state ensemble (TSE)]. The fast rate recapitulates the 10-fold range, demonstrating that the folding speed limit of even the simplest all-β fold strongly depends on the amino acid sequence. Given this fold's simplicity, the most plausible source for such prefactor differences is the presence of nonnative interactions that stabilize the TSE but need to break up before folding resumes. Our results confirm long-standing theoretical predictions and bring into focus the rate prefactor as an essential element for understanding the mechanisms of folding.

Rapid interpretation of small-angle X-ray scattering data

The fundamental aim of structural analyses in biophysics is to reveal a mutual relation between a molecule’s dynamic structure and its physiological function. Small-angle X-ray scattering (SAXS) is an experimental technique for structural characterization of macromolecules in solution and enables time-resolved analysis of conformational changes under physiological conditions. As such experiments measure spatially averaged low-resolution scattering intensities only, the sparse information obtained is not sufficient to uniquely reconstruct a three-dimensional atomistic model. Here, we integrate the information from SAXS into molecular dynamics simulations using computationally efficient native structure-based models. Dynamically fitting an initial structure towards a scattering intensity, such simulations produce atomistic models in agreement with the target data. In this way, SAXS data can be rapidly interpreted while retaining physico-chemical knowledge and sampling power of the underlying force field. We demonstrate our method’s performance using the example of three protein systems. Simulations are faster than full molecular dynamics approaches by more than two orders of magnitude and consistently achieve comparable accuracy. Computational demands are reduced sufficiently to run the simulations on commodity desktop computers instead of high-performance computing systems. These results underline that scattering-guided structure-based simulations provide a suitable framework for rapid early-stage refinement of structures towards SAXS data with particular focus on minimal computational resources and time.

Proteins are the molecular nanomachines in biological cells and thus vital to any known form of life. From the evolutionary perspective, viable protein structure emerges on the basis of a ‘form-follows-function’ principle. A protein’s designated function is inextricably linked to dynamic conformational changes, which can be observed by small-angle X-ray scattering. Intensities from SAXS contain low-resolution information on the protein’s shape at different steps of its functional cycle. We are interested in directly getting an atomistic model of this encoded structure. One powerful approach is to include the experimental data into computational simulations of the protein’s function-related physical motions. We combine scattering intensities with coarse-grained native structure-based models. These models are computationally highly efficient yet describe the system’s dynamics realistically. Here, we present our method for rapid interpretation of scattering intensities from SAXS to derive structural models, using minimal computational resources and time.

Nonnative contact effects in protein folding

The folding simulations of three ββα-motifs and β-barrel structured proteins (NTL9, NuG2b, and CspA) were performed to determine the important roles of native and nonnative contacts in protein folding.

The Effect of Electrostatic Interactions on the Folding Kinetics of a 3-α-Helical Bundle Protein Family

The trio of protein segment repeats called spectrins diverges by more than 2 orders of magnitude in their folding and unfolding rates, despite having very similar stabilities and almost coincidental topologies. Experimental studies revealed that the mutation of five particular residues dramatically alters the kinetic rates in the slow folders, making them similar to the rates of the fast folder. This is considered to be an exceptional behavior which seems in principle to challenge the current understanding of the protein folding process. In this work, we analyze this scenario, using a simplified computational model, combined with state-of-the-art kinetic analysis techniques. Our model faithfully separates the kinetics of the fast and slow folders and captures the effect of the five mutations. We show that the inclusion of electrostatics in the model is necessary to explain the experimental findings.

Simulations Reveal Multiple Intermediates in the Unzipping Mechanism of Neuronal SNARE Complex

The assembling of the soluble N-ethylmaleimide-sensitive factor attachment protein receptor protein complex is a fundamental step in neuronal exocytosis, and it has been extensively studied in the last two decades. Yet, many details of this process remain inaccessible with the current experimental space and time resolution. Here, we study the zipping mechanism of the soluble N-ethylmaleimide-sensitive factor attachment protein receptor complex computationally by using a coarse-grained model. We explore the different pathways available and analyze their dependence on the computational model employed. We reveal and characterize multiple intermediate states, in agreement with previous experimental findings. We use our model to analyze the influence of single-residue mutations on the thermodynamics of the folding process.

Elucidation of the structural stability and dynamics of heterogeneous intermediate ensembles in unfolding pathway of the N-terminal domain of TDP-43

The N-terminal domain of the RNA binding protein TDP-43 (NTD) is essential to both physiology and proteinopathy; however, elucidation of its folding/unfolding still remains a major quest. In this study, we have investigated the biophysical behavior of intermediate ensembles employing all-atom molecular dynamics simulations in 8 M urea accelerated with high temperatures to achieve unfolded states in a confined computation time. The cumulative results of the 2.75 μs simulations show that unfolding of the NTD at 350 K evolves through different stable and meta-stable intermediate states. The free-energy landscape reveals two meta-stable intermediates (IN and IU) stabilized by non-native interactions, which are largely hydrophilic and highly energetically frustrated. A single buried tryptophan residue, W80, undergoes solvent exposure to different extents during unfolding; this suggests a structurally heterogeneous population of intermediate ensembles. Furthermore, the structure properties of the IN state show a resemblance to the molten globule (MG) state with most of the secondary structures intact. The unfolding of the NTD is initiated by the loss of β-strands, and the unfolded (U) states exhibit a population of non-native α-helices. These non-native unfolded intermediate ensembles may mediate protein oligomerization, leading to the formation of pathological, irreversible aggregates, characteristics of disease pathogenesis.

On the folding of a structurally complex protein to its metastable active state

For successful protease inhibition, the reactive center loop (RCL) of the two-domain serine protease inhibitor, α1-antitrypsin (α1-AT), needs to remain exposed in a metastable active conformation. The α1-AT RCL is sequestered in a β-sheet in the stable latent conformation. Thus, to be functional, α1-AT must always fold to a metastable conformation while avoiding folding to a stable conformation. We explore the structural basis of this choice using folding simulations of coarse-grained structure-based models of the two α1-AT conformations. Our simulations capture the key features of folding experiments performed on both conformations. The simulations also show that the free energy barrier to fold to the latent conformation is much larger than the barrier to fold to the active conformation. An entropically stabilized on-pathway intermediate lowers the barrier for folding to the active conformation. In this intermediate, the RCL is in an exposed configuration, and only one of the two α1-AT domains is folded. In contrast, early conversion of the RCL into a β-strand increases the coupling between the two α1-AT domains in the transition state and creates a larger barrier for folding to the latent conformation. Thus, unlike what happens in several proteins, where separate regions promote folding and function, the structure of the RCL, formed early during folding, determines both the conformational and the functional fate of α1-AT. Further, the short 12-residue RCL modulates the free energy barrier and the folding cooperativity of the large 370-residue α1-AT. Finally, we suggest experiments to test the predicted folding mechanism for the latent state.

Structure of the human monomeric NEET protein MiNT and its role in regulating iron and reactive oxygen species in cancer cells

The NEET family is a relatively new class of three related [2Fe-2S] proteins (CISD1-3), important in human health and disease. While there has been growing interest in the homodimeric gene products of CISD1 (mitoNEET) and CISD2 (NAF-1), the importance of the inner mitochondrial CISD3 protein has only recently been recognized in cancer. The CISD3 gene encodes for a monomeric protein that contains two [2Fe-2S] CDGSH motifs, which we term mitochondrial inner NEET protein (MiNT). It folds with a pseudosymmetrical fold that provides a hydrophobic motif on one side and a relatively hydrophilic surface on the diametrically opposed surface. Interestingly, as shown by molecular dynamics simulation, the protein displays distinct asymmetrical backbone motions, unlike its homodimeric counterparts that face the cytosolic side of the outer mitochondrial membrane/endoplasmic reticulum (ER). However, like its counterparts, our biological studies indicate that knockdown of MiNT leads to increased accumulation of mitochondrial labile iron, as well as increased mitochondrial reactive oxygen production. Taken together, our study suggests that the MiNT protein functions in the same pathway as its homodimeric counterparts (mitoNEET and NAF-1), and could be a key player in this pathway within the mitochondria. As such, it represents a target for anticancer or antidiabetic drug development.

Conformational Entropy as Collective Variable for Proteins

Many enhanced sampling methods rely on the identification of appropriate collective variables. For proteins, even small ones, finding appropriate descriptors has proven challenging. Here we suggest that the NMR S² order parameter can be used to this effect. We trace the validity of this statement to the suggested relation between S² and conformational entropy. Using the S² order parameter and a surrogate for the protein enthalpy in conjunction with metadynamics or variationally enhanced sampling, we are able to reversibly fold and unfold a small protein and draw its free energy at a fraction of the time that is needed in unbiased simulations. We also use S² in combination with the free energy flooding method to compute the unfolding rate of this peptide. We repeat this calculation at different temperatures to obtain the unfolding activation energy.