Separating the effects of internal friction and transition state energy to explain the slow, frustrated folding of spectrin domains

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.

Temperature Dependence of Internal Friction of Peptides

Internal friction is a valuable concept to describe the kinetics of proteins. As is well known, internal friction can be modulated by solvent features (such as viscosity). How can internal friction be affected by environmental temperature? The answer to this question is not evident. In the present work, we approach this problem with simulations on two model peptides. The thermodynamics and relaxation kinetics are characterized through long molecular dynamics simulations, with the viscosity modulated by varying the mass of solvent molecules. Based on the extrapolation to zero viscosity together with scaling of the relaxation time scales, we discover that internal friction is almost invariant at various temperatures. Controlled simulations further support the idea that internal friction is independent of environmental temperature. Comparisons between the two model peptides help us to understand the diverse phenomena in experiments.

Cotranslational folding cooperativity of contiguous domains of α-spectrin

Proteins synthesized in the cell can begin to fold during translation before the entire polypeptide has been produced, which may be particularly relevant to the folding of multidomain proteins. Here, we study the cotranslational folding of adjacent domains from the cytoskeletal protein α-spectrin using force profile analysis (FPA). Specifically, we investigate how the cotranslational folding behavior of the R15 and R16 domains are affected by their neighboring R14 and R16, and R15 and R17 domains, respectively. Our results show that the domains impact each other's folding in distinct ways that may be important for the efficient assembly of α-spectrin, and may reduce its dependence on chaperones. Furthermore, we directly relate the experimentally observed yield of full-length protein in the FPA assay to the force exerted by the folding protein in piconewtons. By combining pulse-chase experiments to measure the rate at which the arrested protein is converted into full-length protein with a Bell model of force-induced rupture, we estimate that the R16 domain exerts a maximal force on the nascent chain of ∼15 pN during cotranslational folding.

Friction-Limited Folding of Disulfide-Reduced Monomeric SOD1

The folding reaction of a stable monomeric variant of Cu/Zn superoxide dismutase (mSOD1), an enzyme responsible for the conversion of superoxide free radicals into hydrogen peroxide and oxygen, is known to be among the slowest folding processes that adhere to two-state behavior. The long lifetime, ∼10 s, of the unfolded state presents ample opportunities for the polypeptide chain to transiently sample nonnative structures before the formation of the productive folding transition state. We recently observed the formation of a nonnative structure in a peptide model of the C-terminus of SOD1, a sequence that might serve as a potential source of internal chain friction-limited folding. To test for friction-limited folding, we performed a comprehensive thermodynamic and kinetic analysis of the folding mechanism of mSOD1 in the presence of the viscogens glycerol and glucose. Using a, to our knowledge, novel analysis of the folding reactions, we found the disulfide-reduced form of the protein that exposes the C-terminal sequence, but not its disulfide-oxidized counterpart that protects it, experiences internal chain friction during folding. The sensitivity of the internal friction to the disulfide bond status suggests that one or both of the cross-linked regions play a critical role in driving the friction-limited folding. We speculate that the molecular mechanisms giving rise to the internal friction of disulfide-reduced mSOD1 might play a role in the amyotrophic lateral sclerosis-linked aggregation of SOD1.

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.

Size and topology modulate the effects of frustration in protein folding

The presence of conflicting interactions, or frustration, determines how fast biomolecules can explore their configurational landscapes. Recent experiments have provided cases of systems with slow reconfiguration dynamics, perhaps arising from frustration. While it is well known that protein folding speed and mechanism are strongly affected by the protein native structure, it is still unknown how the response to frustration is modulated by the protein topology. We explore the effects of nonnative interactions in the reconfigurational and folding dynamics of proteins with different sizes and topologies. We find that structural correlations related to the folded state size and topology play an important role in determining the folding kinetics of proteins that otherwise have the same amount of nonnative interactions. In particular, we find that the reconfiguration dynamics of α-helical proteins are more susceptible to frustration than β-sheet proteins of the same size. Our results may explain recent experimental findings and suggest that attempts to measure the degree of frustration due to nonnative interactions might be more successful with α-helical proteins.

Comparative mechanical unfolding studies of spectrin domains R15, R16 and R17

Spectrins belong to repetitive three-helix bundle proteins that have vital functions in multicellular organisms and are of potential value in nanotechnology. To reveal the unique physical features of repeat proteins we have studied the structural and mechanical properties of three repeats of chicken brain α-spectrin (R15, R16 and R17) at the atomic level under stretching at constant velocities (0.01, 0.05 and 0.1 Å·ps^-1) and constant forces (700 and 900 pN) using molecular dynamics (MD) simulations at T = 300 K. 114 independent MD simulations were performed and their analysis has been done. Despite structural similarity of these domains we have found that R15 is less mechanically stable than R16, which is less stable than R17. This result is in agreement with the thermal unfolding rates. Moreover, we have observed the relationship between mechanical stability, flexibility of the domains and the number of aromatic residues involved in aromatic clusters.

Kinetic and thermodynamic studies reveal chemokine homologues CC11 and CC24 with an almost identical tertiary structure have different folding pathways

BACKGROUND

Proteins with low sequence identity but almost identical tertiary structure and function have been valuable to uncover the relationship between sequence, tertiary structure, folding mechanism and functions. Two homologous chemokines, CCL11 and CCL24, with low sequence identity but similar tertiary structure and function, provide an excellent model system for respective studies.

RESULTS

The kinetics and thermodynamics of the two homologous chemokines were systematically characterized. Despite their similar tertiary structures, CCL11 and CCL24 show different thermodynamic stability in guanidine hydrochloride titration, with D_50% = 2.20 M and 4.96 M, respectively. The kinetics curves clearly show two phases in the folding/unfolding processes of both CCL11 and CCL24, which suggests the existence of an intermediate state in their folding/unfolding processes. The folding pathway of both CCL11 and CCL24 could be well described using a folding model with an on-pathway folding intermediate. However, the folding kinetics and stability of the intermediate state of CCL11 and CCL24 are obviously different.

CONCLUSION

Our results suggest homologous proteins with low sequence identity can display almost identical tertiary structure, but very different folding mechanisms, which applies to homologues in the chemokine protein family, extending the general applicability of the above observation.

Transition Path Times Measured by Single-Molecule Spectroscopy

The transition path is a tiny fraction of a molecular trajectory during which the free-energy barrier is crossed. It is a single-molecule property and contains all mechanistic information of folding processes of biomolecules such as proteins and nucleic acids. However, the transition path has been difficult to probe because it is short and rarely visited when transitions actually occur. Recent technical advances in single-molecule spectroscopy have made it possible to directly probe transition paths, which has opened up new theoretical and experimental approaches to investigating folding mechanisms. This article reviews recent single-molecule fluorescence and force spectroscopic measurements of transition path times and their connection to both theory and simulations.

Counteraction of Trehalose on N, N-Dimethylformamide-Induced Candida rugosa Lipase Denaturation: Spectroscopic Insight and Molecular Dynamic Simulation

Candida rugosa lipase (CRL) has been widely used as a biocatalyst for non-aqueous synthesis in biotechnological applications, which, however, often suffers significant loss of activity in organic solvent. Experimental results show that trehalose could actively counteract the organic-solvent-induced protein denaturation, while the molecular mechanisms still don’t unclear. Herein, CRL was used as a model enzyme to explore the effects of trehalose on the retention of enzymatic activity upon incubation in N,N-dimethylformamide (DMF). Results showed that both catalytic activity and conformation changes of CRL influenced by DMF solvent were inhibited by trehalose in a dose-dependent fashion. The simulations further indicated that the CRL protein unfolded in binary DMF solution, but retained the native state in the ternary DMF/trehalose system. Trehalose as the second osmolyte added into binary DMF solution decreased DMF-CRL hydrogen bonds efficiently, whereas increased the intermolecular hydrogen bondings between DMF and trehalose. Thus, the origin of its denaturing effects of DMF on protein is thought to be due to the preferential exclusion of trehalose as well as the intermolecular hydrogen bondings between trehalose and DMF. These findings suggest that trehalose protect the CRL protein from DMF-induced unfolding via both indirect and direct interactions.

Modulation of Folding Internal Friction by Local and Global Barrier Heights

Recent experiments have revealed an unexpected deviation from a first power dependence of protein relaxation times on solvent viscosity, an effect that has been attributed to "internal friction". One clear source of internal friction in protein dynamics is the isomerization of dihedral angles. A key outstanding question is whether the global folding barrier height influences the measured internal friction, based on the observation that the folding rates of fast-folding proteins, with smaller folding free energy barriers, tend to exhibit larger internal friction. Here, by studying two alanine-based peptides, we find that systematic variation of global folding barrier heights has little effect on the internal friction for folding rates. On the other hand, increasing local torsion angle barriers leads to increased internal friction, which is consistent with solvent memory effects being the origin of the viscosity dependence. Thus, it appears that local torsion transitions determine the viscosity dependence of the diffusion coefficient on the global coordinate and, in turn, internal friction effects on the folding rate.

Structural origin of slow diffusion in protein folding

Experimental, theoretical, and computational studies of small proteins suggest that interresidue contacts not present in the folded structure play little or no role in the self-assembly mechanism. Non-native contacts can, however, influence folding kinetics by introducing additional local minima that slow diffusion over the global free-energy barrier between folded and unfolded states. Here, we combine single-molecule fluorescence with all-atom molecular dynamics simulations to discover the structural origin for the slow diffusion that markedly decreases the folding rate for a designed α-helical protein. Our experimental determination of transition path times and our analysis of the simulations point to non-native salt bridges between helices as the source, which provides a quantitative glimpse of how specific intramolecular interactions influence protein folding rates by altering dynamics and not activation free energies.

Mechanistic studies of the biogenesis and folding of outer membrane proteins in vitro and in vivo: what have we learned to date?

Research into the mechanisms by which proteins fold into their native structures has been on-going since the work of Anfinsen in the 1960s. Since that time, the folding mechanisms of small, water-soluble proteins have been well characterised. By contrast, progress in understanding the biogenesis and folding mechanisms of integral membrane proteins has lagged significantly because of the need to create a membrane mimetic environment for folding studies in vitro and the difficulties in finding suitable conditions in which reversible folding can be achieved. Improved knowledge of the factors that promote membrane protein folding and disfavour aggregation now allows studies of folding into lipid bilayers in vitro to be performed. Consequently, mechanistic details and structural information about membrane protein folding are now emerging at an ever increasing pace. Using the panoply of methods developed for studies of the folding of water-soluble proteins. This review summarises current knowledge of the mechanisms of outer membrane protein biogenesis and folding into lipid bilayers in vivo and in vitro and discusses the experimental techniques utilised to gain this information. The emerging knowledge is beginning to allow comparisons to be made between the folding of membrane proteins with current understanding of the mechanisms of folding of water-soluble proteins.

Folding pathway of a multidomain protein depends on its topology of domain connectivity

How do the folding mechanisms of multidomain proteins depend on protein topology? We addressed this question by developing an Ising-like structure-based model and applying it for the analysis of free-energy landscapes and folding kinetics of an example protein, Escherichia coli dihydrofolate reductase (DHFR). DHFR has two domains, one comprising discontinuous N- and C-terminal parts and the other comprising a continuous middle part of the chain. The simulated folding pathway of DHFR is a sequential process during which the continuous domain folds first, followed by the discontinuous domain, thereby avoiding the rapid decrease in conformation entropy caused by the association of the N- and C-terminal parts during the early phase of folding. Our simulated results consistently explain the observed experimental data on folding kinetics and predict an off-pathway structural fluctuation at equilibrium. For a circular permutant for which the topological complexity of wild-type DHFR is resolved, the balance between energy and entropy is modulated, resulting in the coexistence of the two folding pathways. This coexistence of pathways should account for the experimentally observed complex folding behavior of the circular permutant.

Frustration in biomolecules

Biomolecules are the prime information processing elements of living matter. Most of these inanimate systems are polymers that compute their own structures and dynamics using as input seemingly random character strings of their sequence, following which they coalesce and perform integrated cellular functions. In large computational systems with finite interaction-codes, the appearance of conflicting goals is inevitable. Simple conflicting forces can lead to quite complex structures and behaviors, leading to the concept of frustration in condensed matter. We present here some basic ideas about frustration in biomolecules and how the frustration concept leads to a better appreciation of many aspects of the architecture of biomolecules, and especially how biomolecular structure connects to function by means of localized frustration. These ideas are simultaneously both seductively simple and perilously subtle to grasp completely. The energy landscape theory of protein folding provides a framework for quantifying frustration in large systems and has been implemented at many levels of description. We first review the notion of frustration from the areas of abstract logic and its uses in simple condensed matter systems. We discuss then how the frustration concept applies specifically to heteropolymers, testing folding landscape theory in computer simulations of protein models and in experimentally accessible systems. Studying the aspects of frustration averaged over many proteins provides ways to infer energy functions useful for reliable structure prediction. We discuss how frustration affects folding mechanisms. We review here how the biological functions of proteins are related to subtle local physical frustration effects and how frustration influences the appearance of metastable states, the nature of binding processes, catalysis and allosteric transitions. In this review, we also emphasize that frustration, far from being always a bad thing, is an essential feature of biomolecules that allows dynamics to be harnessed for function. In this way, we hope to illustrate how Frustration is a fundamental concept in molecular biology.

Single-molecule force spectroscopy of rapidly fluctuating, marginally stable structures in the intrinsically disordered protein α-synuclein

Intrinsically disordered proteins form transient, fluctuating structures that are difficult to observe directly. We used optical tweezers to apply force to single α-synuclein molecules and measure their extension, characterizing the resulting conformational transitions. Force-extension curves revealed rapid fluctuations at low force, arising from the folding of two different classes of structure that were only marginally stable. The energy landscape for these transitions was characterized via the force-dependent kinetics derived from correlation analysis of the extension trajectories. The barriers were small, only a few kBT, but the diffusion was slow, revealing a landscape that is flat but rough.

The folding of a family of three-helix bundle proteins: spectrin R15 has a robust folding nucleus, unlike its homologous neighbours

Three homologous spectrin domains have remarkably different folding characteristics. We have previously shown that the slow-folding R16 and R17 spectrin domains can be altered to resemble the fast folding R15, in terms of speed of folding (and unfolding), landscape roughness and folding mechanism, simply by substituting five residues in the core. Here we show that, by contrast, R15 cannot be engineered to resemble R16 and R17. It is possible to engineer a slow-folding version of R15, but our analysis shows that this protein neither has a rougher energy landscape nor does change its folding mechanism. Quite remarkably, R15 appears to be a rare example of a protein with a folding nucleus that does not change in position or in size when its folding nucleus is disrupted. Thus, while two members of this protein family are remarkably plastic, the third has apparently a restricted folding landscape.

Assessment of local friction in protein folding dynamics using a helix cross-linker

Internal friction arising from local steric hindrance and/or the excluded volume effect plays an important role in controlling not only the dynamics of protein folding but also conformational transitions occurring within the native state potential well. However, experimental assessment of such local friction is difficult because it does not manifest itself as an independent experimental observable. Herein, we demonstrate, using the miniprotein trp-cage as a testbed, that it is possible to selectively increase the local mass density in a protein and hence the magnitude of local friction, thus making its effect directly measurable via folding kinetic studies. Specifically, we show that when a helix cross-linker, m-xylene, is placed near the most congested region of the trp-cage it leads to a significant decrease in both the folding rate (by a factor of 3.8) and unfolding rate (by a factor of 2.5 at 35 °C) but has little effect on protein stability. Thus, these results, in conjunction with those obtained with another cross-linked trp-cage and two uncross-linked variants, demonstrate the feasibility of using a nonperturbing cross-linker to help quantify the effect of internal friction. In addition, we estimate that a m-xylene cross-linker could lead to an increase in the roughness of the folding energy landscape by as much as 0.4-1.0k(B)T.

How well does a funneled energy landscape capture the folding mechanism of spectrin domains?

Three structurally similar domains from α-spectrin have been shown to fold very differently. First, there is a contrast in the folding mechanism, as probed by Φ-value analysis, between the R15 domain and the R16 and R17 domains. Second, there are very different contributions from internal friction to folding: the folding rate of the R15 domain was found to be inversely proportional to solvent viscosity, showing no apparent frictional contribution from the protein, but in the other two domains, a large internal friction component was evident. Non-native misdocking of helices has been suggested to be responsible for this phenomenon. Here, I study the folding of these three proteins with minimalist coarse-grained models based on a funneled energy landscape. Remarkably, I find that, despite the absence of non-native interactions, the differences in folding mechanism of the domains are well captured by the model, and the agreement of the Φ-values with experiment is fairly good. On the other hand, within the context of this model, there are no significant differences in diffusion coefficient along the chosen folding coordinate, and the model cannot explain the large differences in folding rates between the proteins found experimentally. These results are nonetheless consistent with the expectations from the energy landscape perspective of protein folding, namely, that the folding mechanism is primarily determined by the native-like interactions present in the Gō-like model, with missing non-native interactions being required to explain the differences in "internal friction" seen in experiment.

Membrane proteins can have high kinetic stability

Approximately 10% of water-soluble proteins are considered kinetically stable with unfolding half-lives in the range of weeks to millenia. These proteins only rarely sample the unfolded state and may never unfold on their respective biological time scales. It is still not known whether membrane proteins can be kinetically stable, however. Here we examine the subunit dissociation rate of the trimeric membrane enzyme, diacylglycerol kinase, from Escherichia coli as a proxy for complete unfolding. We find that dissociation occurs with a half-life of at least several weeks, demonstrating that membrane proteins can remain locked in a folded state for long periods of time. These results reveal that evolution can use kinetic stability to regulate the biological function of membrane proteins, as it can for soluble proteins. Moreover, it appears that the generation of kinetic stability could be a viable target for membrane protein engineering efforts.

Frustration-induced protein intrinsic disorder

Spontaneous folding into a specific native structure is the most important property of protein to perform their biological functions within organisms. Spontaneous folding is understood on the basis of an energy landscape picture based on the minimum frustration principle. Therefore, frustration seemingly only leads to protein functional disorder. However, frustration has recently been suggested to have a function in allosteric regulation. Functional frustration has the possibility to be a key to our deeper understanding of protein function. To explore another functional frustration, we theoretically examined structural frustration, which is designed to induce intrinsic disorder of a protein and its function through the coupled folding and binding. We extended the Wako-Saitô-Muñoz-Eaton model to take into account a frustration effect. With the model, we analyzed the binding part of neuron-restrictive silencer factor and showed that designed structural frustration in it induces intrinsic disorder. Furthermore, we showed that the folding and the binding are cooperative in interacting with a target protein. The cooperativity enables an intrinsically disordered protein to exhibit a sharp switch-like folding response to binding chemical potential change. Through this switch-like response, the structural frustration may contribute to the regulation function of interprotein interaction of the intrinsically disordered protein.

Analyzing the effect of homogeneous frustration in protein folding

The energy landscape theory has been an invaluable theoretical framework in the understanding of biological processes such as protein folding, oligomerization, and functional transitions. According to the theory, the energy landscape of protein folding is funneled toward the native state, a conformational state that is consistent with the principle of minimal frustration. It has been accepted that real proteins are selected through natural evolution, satisfying the minimum frustration criterion. However, there is evidence that a low degree of frustration accelerates folding. We examined the interplay between topological and energetic protein frustration. We employed a Cα structure-based model for simulations with a controlled nonspecific energetic frustration added to the potential energy function. Thermodynamics and kinetics of a group of 19 proteins are completely characterized as a function of increasing level of energetic frustration. We observed two well-separated groups of proteins: one group where a little frustration enhances folding rates to an optimal value and another where any energetic frustration slows down folding. Protein energetic frustration regimes and their mechanisms are explained by the role of non-native contact interactions in different folding scenarios. These findings strongly correlate with the protein free-energy folding barrier and the absolute contact order parameters. These computational results are corroborated by principal component analysis and partial least square techniques. One simple theoretical model is proposed as a useful tool for experimentalists to predict the limits of improvements in real proteins.

Localizing internal friction along the reaction coordinate of protein folding by combining ensemble and single-molecule fluorescence spectroscopy

Theory, simulations and experimental results have suggested an important role of internal friction in the kinetics of protein folding. Recent experiments on spectrin domains provided the first evidence for a pronounced contribution of internal friction in proteins that fold on the millisecond timescale. However, it has remained unclear how this contribution is distributed along the reaction and what influence it has on the folding dynamics. Here we use a combination of single-molecule Förster resonance energy transfer, nanosecond fluorescence correlation spectroscopy, microfluidic mixing and denaturant- and viscosity-dependent protein-folding kinetics to probe internal friction in the unfolded state and at the early and late transition states of slow- and fast-folding spectrin domains. We find that the internal friction affecting the folding rates of spectrin domains is highly localized to the early transition state, suggesting an important role of rather specific interactions in the rate-limiting conformational changes.

Take home lessons from studies of related proteins

The 'Fold Approach' involves a detailed analysis of the folding of several topologically, structurally and/or evolutionarily related proteins. Such studies can reveal determinants of the folding mechanism beyond the gross topology, and can dissect the residues required for folding from those required for stability or function. While this approach has not yet matured to the point where we can predict the native conformation of any polypeptide chain in silico, it has been able to highlight, amongst others, the specific residues that are responsible for nucleation, pathway malleability, kinetic intermediates, chain knotting, internal friction and Paracelsus switches. Some of the most interesting discoveries have resulted from the attempt to explain differences between homologues.

Protein folding: adding a nucleus to guide helix docking reduces landscape roughness

The elongated three-helix‐bundle spectrin domains R16 and R17 fold and unfold unusually slowly over a rough energy landscape, in contrast to the homologue R15, which folds fast over a much smoother, more typical landscape. R15 folds via a nucleation–condensation mechanism that guides the docking of the A and C-helices. However, in R16 and R17, the secondary structure forms first and the two helices must then dock in the correct register. Here, we use variants of R16 and R17 to demonstrate that substitution of just five key residues is sufficient to alter the folding mechanism and reduce the landscape roughness. We suggest that, by providing access to an alternative, faster, folding route over their landscape, R16 and R17 can circumvent their slow, frustrated wild-type folding mechanism.