Diffusional Barrier in the Unfolding of a Small Protein

Physical properties of the cytoplasm modulate the rates of microtubule polymerization and depolymerization

The cytoplasm is a crowded, visco-elastic environment whose physical properties change according to physiological or developmental states. How the physical properties of the cytoplasm impact cellular functions in vivo remains poorly understood. Here, we probe the effects of cytoplasmic concentration on microtubules by applying osmotic shifts to fission yeast, moss, and mammalian cells. We show that the rates of both microtubule polymerization and depolymerization scale linearly and inversely with cytoplasmic concentration; an increase in cytoplasmic concentration decreases the rates of microtubule polymerization and depolymerization proportionally, whereas a decrease in cytoplasmic concentration leads to the opposite. Numerous lines of evidence indicate that these effects are due to changes in cytoplasmic viscosity rather than cellular stress responses or macromolecular crowding per se. We reconstituted these effects on microtubules in vitro by tuning viscosity. Our findings indicate that, even in normal conditions, the viscosity of the cytoplasm modulates the reactions that underlie microtubule dynamic behaviors.

Structural dynamics of the chromo-shadow domain and chromodomain of HP1 bound to histone H3K9 methylated peptide, as measured by site-directed spin-labeling EPR spectroscopy

The structural dynamics of the chromo-shadow domain (CSD) and chromodomain (CD) of human HP1 proteins essential for heterochromatin formation were investigated at the nanosecond and nanometer scales by site-directed spin labeling electron paramagnetic resonance and pulsed double resonance spectroscopy. Distance measurements showed that the spin-labeled CSD of human HP1α and HP1γ tightly dimerizes. Unlike CD-CD interaction observed in fission yeast HP1 in an inactivated state (Canzio et al., 2013), the two CDs of HP1α and HP1γ were spatially separated from each other, dynamically mobile, and ready for a Brownian search for H3K9-tri-methyl(me3) on histones. Complex formation of the CD with H3K9me3 slowed dynamics of the domain due to a decreased diffusion constant. CSD mobility was significantly (∼1.3-fold) lower in full-length HP1α than in HP1γ, suggesting that the immobilized conformation of human HP1α shows an auto-inactivated state. Differential properties of HP1α and HP1γ to form the inactive conformation could be relevant to its physiological role in the heterochromatin formation in a cell.

High resolution ensemble description of metamorphic and intrinsically disordered proteins using an efficient hybrid parallel tempering scheme

Mapping free energy landscapes of complex multi-funneled metamorphic proteins and weakly-funneled intrinsically disordered proteins (IDPs) remains challenging. While rare-event sampling molecular dynamics simulations can be useful, they often need to either impose restraints or reweigh the generated data to match experiments. Here, we present a parallel-tempering method that takes advantage of accelerated water dynamics and allows efficient and accurate conformational sampling across a wide variety of proteins. We demonstrate the improved sampling efficiency by benchmarking against standard model systems such as alanine di-peptide, TRP-cage and β-hairpin. The method successfully scales to large metamorphic proteins such as RFA-H and to highly disordered IDPs such as Histatin-5. Across the diverse proteins, the calculated ensemble averages match well with the NMR, SAXS and other biophysical experiments without the need to reweigh. By allowing accurate sampling across different landscapes, the method opens doors for sampling free energy landscape of complex uncharted proteins.

Structure and Dynamics of Ribonuclease A during Thermal Unfolding: The Failure of the Zimm Model

Disordered regions as found in intrinsically disordered proteins (IDP) or during protein folding define response time to stimuli and protein folding times. Neutron spin-echo spectroscopy is a powerful tool to directly access the collective motions of the unfolded chain to enlighten the physical origin of basic conformational relaxation. During the thermal unfolding of native ribonuclease A, we examine the structure and dynamics of the disordered state within a two-state transition model using polymer models, including internal friction, to describe the chain dynamics. The presence of four disulfide bonds alters the disordered configuration to a more compact configuration compared to a Gaussian chain that is defined by the additional links, as demonstrated by coarse-grained simulation. The dynamics of the disordered chain is described by Zimm dynamics with internal friction (ZIF) between neighboring amino acids. Relaxation times are dominated by mode-independent internal friction. Internal friction relaxation times show an Arrhenius-like behavior with an activation energy of 33 kJ/mol. The Zimm dynamics is dominated by internal friction and suggest that the characteristic motions correspond to overdamped elastic modes similar to the motions observed for folded proteins but within a pool of disordered configurations spanning the configurational space. For IDP, internal friction dominates while solvent friction and hydrodynamic interactions are smaller corrections.

Kramers’ Theory and the Dependence of Enzyme Dynamics on Trehalose-Mediated Viscosity

The disaccharide trehalose is accumulated in the cytoplasm of some organisms in response to harsh environmental conditions. Trehalose biosynthesis and accumulation are important for the survival of such organisms by protecting the structure and function of proteins and membranes. Trehalose affects the dynamics of proteins and water molecules in the bulk and the protein hydration shell. Enzyme catalysis and other processes dependent on protein dynamics are affected by the viscosity generated by trehalose, as described by the Kramers’ theory of rate reactions. Enzyme/protein stabilization by trehalose against thermal inactivation/unfolding is also explained by the viscosity mediated hindering of the thermally generated structural dynamics, as described by Kramers’ theory. The analysis of the relationship of viscosity–protein dynamics, and its effects on enzyme/protein function and other processes (thermal inactivation and unfolding/folding), is the focus of the present work regarding the disaccharide trehalose as the viscosity generating solute. Finally, trehalose is widely used (alone or in combination with other compounds) in the stabilization of enzymes in the laboratory and in biotechnological applications; hence, considering the effect of viscosity on catalysis and stability of enzymes may help to improve the results of trehalose in its diverse uses/applications.

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.

Transition between protein-like and polymer-like dynamic behavior: Internal friction in unfolded apomyoglobin depends on denaturing conditions

Equilibrium dynamics of different folding intermediates and denatured states is strongly connected to the exploration of the conformational space on the nanosecond time scale and might have implications in understanding protein folding. For the first time, the same protein system apomyoglobin has been investigated using neutron spin-echo spectroscopy in different states: native-like, partially folded (molten globule) and completely unfolded, following two different unfolding paths: using acid or guanidinium chloride (GdmCl). While the internal dynamics of the native-like state can be understood using normal mode analysis based on high resolution structural information of myoglobin, for the unfolded and even for the molten globule states, models from polymer science are employed. The Zimm model accurately describes the slowly-relaxing, expanded GdmCl-denaturated state, ignoring the individuality of the different aminoacid side chain. The dynamics of the acid unfolded and molten globule state are similar in the framework of the Zimm model with internal friction, where the chains still interact and hinder each other: the first Zimm relaxation time is as large as the internal friction time. Transient formation of secondary structure elements in the acid unfolded and presence of α-helices in the molten globule state lead to internal friction to a similar extent.

How cooperative are protein folding and unfolding transitions?

A thermodynamically and kinetically simple picture of protein folding envisages only two states, native (N) and unfolded (U), separated by a single activation free energy barrier, and interconverting by cooperative two-state transitions. The folding/unfolding transitions of many proteins occur, however, in multiple discrete steps associated with the formation of intermediates, which is indicative of reduced cooperativity. Furthermore, much advancement in experimental and computational approaches has demonstrated entirely non-cooperative (gradual) transitions via a continuum of states and a multitude of small energetic barriers between the N and U states of some proteins. These findings have been instrumental towards providing a structural rationale for cooperative versus noncooperative transitions, based on the coupling between interaction networks in proteins. The cooperativity inherent in a folding/unfolding reaction appears to be context dependent, and can be tuned via experimental conditions which change the stabilities of N and U. The evolution of cooperativity in protein folding transitions is linked closely to the evolution of function as well as the aggregation propensity of the protein. A large activation energy barrier in a fully cooperative transition can provide the kinetic control required to prevent the accumulation of partially unfolded forms, which may promote aggregation. Nevertheless, increasing evidence for barrier-less "downhill" folding, as well as for continuous "uphill" unfolding transitions, indicate that gradual non-cooperative processes may be ubiquitous features on the free energy landscape of protein folding.

Viscosity Dependence of Some Protein and Enzyme Reaction Rates: Seventy-Five Years after Kramers

Kramers rate theory is a milestone in chemical reaction research, but concerns regarding the basic understanding of condensed phase reaction rates of large molecules in viscous milieu persist. Experimental studies of Kramers theory rely on scaling reaction rates with inverse solvent viscosity, which is often equated with the bulk friction coefficient based on simple hydrodynamic relations. Apart from the difficulty of abstraction of the prefactor details from experimental data, it is not clear why the linearity of rate versus inverse viscosity, k ∝ η(-1), deviates widely for many reactions studied. In most cases, the deviation simulates a power law k ∝ η(-n), where the exponent n assumes fractional values. In rate-viscosity studies presented here, results for two reactions, unfolding of cytochrome c and cysteine protease activity of human ribosomal protein S4, show an exceedingly overdamped rate over a wide viscosity range, registering n values up to 2.4. Although the origin of this extraordinary reaction friction is not known at present, the results indicate that the viscosity exponent need not be bound by the 0-1 limit as generally suggested. For the third reaction studied here, thermal dissociation of CO from nativelike cytochrome c, the rate-viscosity behavior can be explained using Grote-Hynes theory of time-dependent friction in conjunction with correlated motions intrinsic to the protein. Analysis of the glycerol viscosity-dependent rate for the CO dissociation reaction in the presence of urea as the second variable shows that the protein stabilizing effect of subdenaturing amounts of urea is not affected by the bulk viscosity. It appears that a myriad of factors as diverse as parameter uncertainty due to the difficulty of knowing the exact reaction friction and both mode and consequences of protein-solvent interaction work in a complex manner to convey as though Kramers rate equation is not absolute.

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.

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.

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

The elongated three-helix bundle domains spectrin R16 and R17 fold some two to three orders of magnitude more slowly than their homologue R15. We have shown that this slow folding is due, at least in part, to roughness in the free-energy landscape of R16 and R17. We have proposed that this roughness is due to a frustrated search for the correct docking of partly preformed helices. However, this accounts for only a small part of the slowing of folding and unfolding. Five residues on the A helix of R15, when inserted together into R16 or R17, increase the folding rate constants, reduce landscape roughness, and alter the folding mechanism to one resembling R15. The effect of each of these mutations individually is investigated here. No one mutation causes the behavior seen for the five in combination. However, two mutations, E18F and K25V, significantly increase the folding and unfolding rates of both R16 and R17 but without a concomitant loss in landscape roughness. E18F has the greatest effect on the kinetics, and a Φ-value analysis of the C helix reveals that the folding mechanism is unchanged. For both E18F and K25V the removal of the charge and resultant transition state stabilization is the main origin of the faster folding. Consequently, the major cause of the unusually slow folding of R16 and R17 is the non-native burial of the two charged residues in the transition state. The slowing due to landscape roughness is only about fivefold.

Co-solvent mediated thermal stabilization of chondroitinase ABC I form Proteus vulgaris

Chondroitinase ABC I (cABC I) from Proteus vulgaris cleaves glycosaminoglycan chains which are responsible for most of the inhibition of axon regrowth in spinal cord injury. The clinical utilization of this enzyme is mainly limited by its thermal instability. This study has been undertaken to determine the effects of glycerol, sorbitol and trehalose on cABC I activity and thermal stability. The results indicated that the enzyme catalytic activity and intrinsic fluorescence intensity increased in the presence of these cosolvents whereas no considerable conformational changes observed in far-UV CD spectra. Thermal CD experiment revealed an increase in T(m) of cABC I in the presence of cosolvents which was significant for trehalose. Our results support the idea that cABC I has stabilized in the presence of glycerol, sorbitol and trehalose. Therefore, the use of these cosolvents seems to be promising for improvement in shelf-life and clinical applications of this drug enzyme.

Periodic force induced stabilization or destabilization of the denatured state of a protein

We have studied the effects of an external sinusoidal force in protein folding kinetics. The externally applied force field acts on the each amino acid residues of polypeptide chains. Our simulation results show that mean protein folding time first increases with driving frequency and then decreases passing through a maximum. With further increase of the driving frequency the mean folding time starts increasing as the noise-induced hoping event (from the denatured state to the native state) begins to experience many oscillations over the mean barrier crossing time period. Thus unlike one-dimensional barrier crossing problems, the external oscillating force field induces both stabilization or destabilization of the denatured state of a protein. We have also studied the parametric dependence of the folding dynamics on temperature, viscosity, non-Markovian character of bath in presence of the external field.

A kinetic study of the interaction of DNA with gold nanoparticles: mechanistic aspects of the interaction

A kinetic study of the interaction of gold nanoparticles capped with N-(2-mercaptopropionyl)glycine with double stranded DNA was carried out in water and in salt (NaCl) solutions. The kinetic curves are biexponential and reveal the presence of three kinetic steps. The dependence of the reciprocal fast and slow relaxation time, on the DNA concentration, is a curve and tends to a plateau at high DNA concentrations. The simplest mechanism consistent with the kinetic results involves a simple three-step series mechanism reaction scheme. The first step corresponds to a very fast step that is related to a diffusion controlled formation of an external precursor complex (DNA, AuNPs); the second step involves the formation of a (DNA/AuNPs)(I) complex, as a result of the binding affinity between hydrophilic groups of the tiopronin and the DNA grooves. Finally, the third step has been interpreted as a consequence of a conformational change of the (DNA/AuNPs)(I) complex formed in the second step, to a more compacted form (DNA/AuNPs)(II). The values of the rate constants of each step decrease as NaCl concentration increases. The results have been discussed in terms of solvation of the species and changes in the viscosity of the solution.

Experimental evidence for a frustrated energy landscape in a three-helix-bundle protein family

Energy landscape theory is a powerful tool for understanding the structure and dynamics of complex molecular systems, in particular biological macromolecules. The primary sequence of a protein defines its free-energy landscape and thus determines the folding pathway and the rate constants of folding and unfolding, as well as the protein's native structure. Theory has shown that roughness in the energy landscape will lead to slower folding, but derivation of detailed experimental descriptions of this landscape is challenging. Simple folding models show that folding is significantly influenced by chain entropy; proteins in which the contacts are local fold quickly, owing to the low entropy cost of forming stabilizing, native contacts during folding. For some protein families, stability is also a determinant of folding rate constants. Where these simple metrics fail to predict folding behaviour, it is probable that there are features in the energy landscape that are unusual. Such general observations cannot explain the folding behaviour of the R15, R16 and R17 domains of alpha-spectrin. R15 folds approximately 3,000 times faster than its homologues, although they have similar structures, stabilities and, as far as can be determined, transition-state stabilities. Here we show that landscape roughness (internal friction) is responsible for the slower folding and unfolding of R16 and R17. We use chimaeric domains to demonstrate that this internal friction is a property of the core, and suggest that frustration in the landscape of the slow-folding spectrin domains may be due to misdocking of the long helices during folding. Theoretical studies have suggested that rugged landscapes will result in slower folding; here we show experimentally that such a phenomenon directly influences the folding kinetics of a 'normal' protein, that is, one with a significant energy barrier that folds on a relatively slow, millisecond-second, timescale.

Solvent friction changes the folding pathway of the tryptophan zipper TZ2

Because the rate of a diffusional process such as protein folding is controlled by friction encountered along the reaction pathway, the speed of folding is readily tunable through adjustment of solvent viscosity. The precise relationship between solvent viscosity and the rate of diffusion is complex and even conformation-dependent, however, because both solvent friction and protein internal friction contribute to the total reaction friction. The heterogeneity of the reaction friction along the folding pathway may have subtle consequences. For proteins that fold on a multidimensional free-energy surface, an increase in solvent friction may drive a qualitative change in folding trajectory. Our time-resolved experiments on the rapidly and heterogeneously folding beta-hairpin TZ2 show a shift in the folding pathway as viscosity increases, even though the energetics of folding is unaltered. We also observe a nonlinear or saturating behavior of the folding relaxation time with rising solvent viscosity, potentially an experimental signature of the shifting pathway for unfolding. Our results show that manipulations of solvent viscosity in folding experiments and simulations may have subtle and unexpected consequences on the folding dynamics being studied.

Trehalose-mediated thermal stabilization of glucose oxidase from Aspergillus niger

Thermal inactivation and enzyme kinetics of glucose oxidase (a FAD dependent enzyme) were studied in the absence and presence of trehalose. The inactivation rate constant decreased by up to 50% at temperatures between 50 and 70 degrees C in the presence of 0.6M trehalose; as a consequence the glucose oxidase half-life increased. Intrinsic fluorescence spectra showed a maximum center of spectral mass (CSM) red shift of 6.5nm. Therefore, major structural changes seem to be related to glucose oxidase thermal inactivation. Trehalose decreased the rate constant for unfolding as monitored by CSM red shift kinetics indicating that this disaccharide favors the most compact folded state. The E(a) for unfolding was increased from 204 to 221kJ mol(-1). It is proposed that FAD dissociation is preceded by the exposition of hydrophobic regions, while the presence of trehalose was able to hinder the release of FAD. Enzyme kinetics analysis showed that trehalose does not affect V(max) but instead decreases K(m); as a result enzyme efficiency was increased. The stabilizing effect of trehalose in a cofactor-dependent enzyme has not been tested to date. In addition, glucose oxidase has an enormous commercial importance and therefore, the use of trehalose to stabilize glucose oxidase in its multiple applications seems to be promising.

Measuring internal friction of an ultrafast-folding protein

Nanosecond laser T-jump was used to measure the viscosity dependence of the folding kinetics of the villin subdomain under conditions where the viscogen has no effect on its equilibrium properties. The dependence of the unfolding/refolding relaxation time on solvent viscosity indicates a major contribution to the dynamics from internal friction. The internal friction increases with increasing temperature, suggesting a shift in the transition state along the reaction coordinate toward the native state with more compact structures, and therefore, a smaller diffusion coefficient due to increased landscape roughness. Fitting the data with an Ising-like model yields a relatively small position dependence for the diffusion coefficient. This finding is consistent with the excellent correlation found between experimental and calculated folding rates based on free energy barrier heights using the same diffusion coefficient for every protein.

Viscosity scaling for the glassy phase of protein folding

Although commendable progress has been made in the understanding of the physics of protein folding, a key unresolved issue is whether Kramers' diffusion model of chemical reactions is generally applicable to activated barrier crossing events during folding. To examine the solvent viscosity effect on the folding transition of native-like trapped intermediates, laser flash photolysis has been used to measure the microsecond folding kinetics of a natively folded state of CO-liganded ferrocytochrome c (M-state) in the 1-250 cP range of glycerol viscosity at pH 7.0, 20 degrees C. The single rate coefficient for the folding of the M-state to the native state of the protein (i.e., the M --> N folding process) decreases initially when the solvent viscosity is low (<10 cP), but saturates at higher viscosity, indicating that Kramers model is not general enough for scaling the viscosity dependence of post-transition folding involving glassy dynamics. Analysis based on the Grote-Hynes idea of time dependent friction in conjunction with defect diffusion dynamics can account for the observed non-Kramers scaling.

Hydration dynamics in a partially denatured ensemble of the globular protein human alpha-lactalbumin investigated with molecular dynamics simulations

Atomistic molecular dynamics simulations are used to probe changes in the nature and subnanosecond dynamical behavior of solvation waters that accompany partial denaturation of the globular protein, human alpha-lactalbumin. A simulated ensemble of subcompact conformers, similar to the molten globule state of human alpha-lactalbumin, demonstrates a marginal increase in the amount of surface solvation relative to the native state. This increase is accompanied by subtle but distinct enhancement in surface water dynamics, less favorable protein-water interactions, and a marginal decrease in the anomalous behavior of solvation water dynamics. The extent of solvent influx is not proportional to the increased surface area, and the partially denatured conformers are less uniformly solvated compared to their native counterpart. The observed solvation in partially denatured conformers is lesser in extent compared to earlier experimental estimates in molten globule states, and is consistent with more recent descriptions based on nuclear magnetic relaxation dispersion studies.

Minimizing frustration by folding in an aqueous environment

Although life as we know it evolved in an aqueous medium, the properties of water are not completely understood. In this review, we focus on the role of water in guiding protein folding and stability. Specifically, we discuss the mechanisms of protein folding in an aqueous environment, the effects of water on the folding energy landscape as well as the transition state ensemble, and interactions of water with the folded state. We show that water cannot be viewed as a passive solvent, but rather, plays a very active role in the life of a protein.