Limited internal friction in the rate-limiting step of a two-state protein folding reaction

Macromolecular Crowding and DNA: Bridging the Gap between In Vitro and In Vivo

The cellular environment is highly crowded, with up to 40% of the volume fraction of the cell occupied by various macromolecules. Most laboratory experiments take place in dilute buffer solutions; by adding various synthetic or organic macromolecules, researchers have begun to bridge the gap between in vitro and in vivo measurements. This is a review of the reported effects of macromolecular crowding on the compaction and extension of DNA, the effect of macromolecular crowding on DNA kinetics, and protein-DNA interactions. Theoretical models related to macromolecular crowding and DNA are briefly reviewed. Gaps in the literature, including the use of biologically relevant crowders, simultaneous use of multi-sized crowders, empirical connections between macromolecular crowding and liquid-liquid phase separation of nucleic materials are discussed.

Probing the Internal Dynamics and Shape of Simple Peptides in Urea, Guanidinium Hydrochloride, and Proline Solutions with Time-Resolved Fluorescence Anisotropy and Atomistic Cosolvent Simulations

Picosecond time-resolved fluorescence anisotropy was used to measure the effect of denaturants and osmolytes on the reorientation dynamics of the simplest dipeptide. The solvent denaturants guanidinium hydrochloride (gdm), urea, and the osmolyte proline were used at several concentrations. Analysis of the concentration dependence of denaturants at a fixed temperature showed faster and slower reorientation time in two different denaturants at a nearly identical solvent viscosity (η). The reorientation time τ significantly deviates from Kramers' theory (τ ∝ η¹) in the high friction limit for guanidinium and urea with r ≈ 0.4 and r ≈ 0.6 at pH 7.2, respectively. In proline, τ is nearly proportional to η. Atomistic molecular dynamics simulations of the dipeptide in identical cosolvents showed excellent agreement with the measured rotational orientation time. The dipeptide dihedral (ϕ, ψ) isomerization times in water and 6 M urea are almost identical and significantly slower in guanidinium. If a faster and slower reorientation time can be associated with the compact and expanded shapes, the fractional viscosity dependence for guanidinium and urea may result from the fact that internal dynamics of peptides in these cosolvents involve higher and lower internal friction within the dynamic elements.

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.

DsbA is a redox-switchable mechanical chaperone

DsbA is a ubiquitous bacterial oxidoreductase that associates with substrates during and after translocation, yet its involvement in protein folding and translocation remains an open question. Here we demonstrate a redox-controlled chaperone activity of DsbA, on both cysteine-containing and cysteine-free substrates, using magnetic tweezers-based single molecule force spectroscopy that enables independent measurements of oxidoreductase activity and chaperone behavior. Interestingly we found that this chaperone activity is tuned by the oxidation state of DsbA; oxidized DsbA is a strong promoter of folding, but the effect is weakened by the reduction of the catalytic CXXC motif. We further localize the chaperone binding site of DsbA using a seven-residue peptide which effectively blocks the chaperone activity. We found that the DsbA assisted folding of proteins in the periplasm generates enough mechanical work to decrease the ATP consumption needed for periplasmic translocation by up to 33%.

Does Electric Friction Matter in Living Cells?

The thermal motion of charged proteins causes randomly fluctuating electric fields inside cells. According to the fluctuation-dissipation theorem, there is an additional friction force associated with such fluctuations. However, the impact of these fluctuations on the diffusion and dynamics of proteins in the cytoplasm is unclear. Here, we provide an order-of-magnitude estimate of this effect by treating electric field fluctuations within a generalized Langevin equation model with a time-dependent friction memory kernel. We find that electric friction is generally negligible compared to solvent friction. However, a significant slowdown of protein diffusion and dynamics is expected for biomolecules with high net charges such as intrinsically disordered proteins and RNA. The results show that direct contacts between biomolecules in a cell are not necessarily required to alter their dynamics.

Capacities and efficient computation of first-passage probabilities

A reversible diffusion process is initialized at position x_{0} and run until it first hits any of several targets. What is the probability that it terminates at a particular target? We propose a computationally efficient approach for estimating this probability, focused on those situations in which it takes a long time to hit any target. In these cases, direct simulation of the hitting probabilities becomes prohibitively expensive. On the other hand, if the timescales are sufficiently long, then the system will essentially "forget" its initial condition before it encounters a target. In these cases the hitting probabilities can be accurately approximated using only local simulations around each target, obviating the need for direct simulations. In empirical tests, we find that these local estimates can be computed in the same time it would take to compute a single direct simulation, but that they achieve an accuracy that would require thousands of direct simulation runs.

The non-classical kinetics and the mutual information of polymer loop formation

The loop formation of a single polymer chain has served as a model system for various biological and chemical processes. Theories based on the Smoluchowski equation proposed that the rate constant (k_loop) of the loop formation would be inversely proportional to viscosity (η), i.e., k_loop ∼ η^-1. Experiments and simulations showed, however, that k_loop showed the fractional viscosity dependence of k_loop ∼ η^-β with β < 1 either in glasses or in low-viscosity solutions. The origin of the fractional viscosity dependence remains elusive and has been attributed to phenomenological aspects. In this paper, we illustrate that the well-known failure of classical kinetics of the loop formation results from the breakdown of the local thermal equilibrium (LTE) approximation and that the mutual information can quantify the breakdown of the LTE successfully.

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.

Considerations on Protein Stability During Freezing and Its Impact on the Freeze-Drying Cycle: A Design Space Approach

Freezing is widely used during the manufacturing process of protein-based therapeutics, but it may result in undesired loss of biological activity. Many variables come into play during freezing that could adversely affect protein stability, creating a complex landscape of interrelated effects. The current approach to the selection of freezing conditions is however nonsystematic, resulting in poor process control. Here we show how mathematical models, and a design space approach, can guide the selection of the optimal freezing protocol, focusing on protein stability. Two opposite scenarios are identified, suggesting that the ice-water interface is the dominant cause of denaturation for proteins with high bulk stability, while the duration of the freezing process itself is the key parameter to be controlled for proteins that are susceptible to cold denaturation. Experimental data for lactate dehydrogenase and myoglobin as model proteins support the model results, with a slow freezing rate being optimal for lactate dehydrogenase and the opposite being true for myoglobin. A possible application of the calculated design space to the freezing and freeze-drying of biopharmaceuticals is finally described, and some considerations on process efficiency are discussed as well.

The effect of macromolecular crowding on single-round transcription by Escherichia coli RNA polymerase

Previous works have reported significant effects of macromolecular crowding on the structure and behavior of biomolecules. The crowded intracellular environment, in contrast to in vitro buffer solutions, likely imparts similar effects on biomolecules. The enzyme serving as the gatekeeper for the genome, RNA polymerase (RNAP), is among the most regulated enzymes. Although it was previously demonstrated that macromolecular crowding affects association of RNAP to DNA, not much is known about how crowding acts on late initiation and promoter clearance steps, which are considered to be the rate-determining steps for many promoters. Here, we demonstrate that macromolecular crowding enhances the rate of late initiation and promoter clearance using in vitro quenching-based single-molecule kinetics assays. Moreover, the enhancement's dependence on crowder size notably deviates from predictions by the scaled-particle theory, commonly used for description of crowding effects. Our findings shed new light on how enzymatic reactions could be affected by crowded conditions in the cellular milieu.

Dynamics of Disordered Proteins under Confinement: Memory Effects and Internal Friction

Many proteins are disordered under physiological conditions. How efficiently they can search for their cellular targets and how fast they can fold upon target binding is determined by their intrinsic dynamics, which have thus attracted much recent attention. Experiments and molecular simulations show that the inherent reconfiguration timescale for unfolded proteins has a solvent friction component and an internal friction component, and the microscopic origin of the latter, along with its proper mathematical description, has been a topic of considerable debate. Internal friction varies across different proteins of comparable length and increases with decreasing denaturant concentration, showing that it depends on how compact the protein is. Here we report on a systematic atomistic simulation study of how confinement, which induces a more compact unfolded state, affects dynamics and friction in disordered peptides. We find that the average reconfiguration timescales increase exponentially as the peptide's spatial dimensions are reduced; at the same time, confinement broadens the spectrum of relaxation timescales exhibited by the peptide. There are two important implications of this broadening: First, it limits applicability of the common Rouse and Zimm models with internal friction, as those models attempt to capture internal friction effects by introducing a single internal friction timescale. Second, the long-tailed distribution of relaxation times leads to anomalous diffusion effects in the dynamics of intramolecular distances. Analysis and interpretation of experimental signals from various measurements that probe intramolecular protein dynamics (such as single-molecule fluorescence correlation spectroscopy and single-molecule force spectroscopy) rely on the assumption of diffusive dynamics along the distances being probed; hence, our results suggest the need for more general models allowing for anomalous diffusion effects.

The folding pathways and thermodynamics of semiflexible polymers

Inspired by the protein folding and DNA packing, we have systematically studied the thermodynamic and kinetic behaviors of single semiflexible homopolymers by Langevin dynamics simulations. In line with experiments, a rich variety of folding products, such as rod-like bundles, hairpins, toroids, and a mixture of them, are observed in the complete diagram of states. Moreover, knotted structures with a significant population are found in a certain range of bending stiffness in thermal equilibrium. As the solvent quality becomes poorer, the population of the intermediate occurring in the folding process increases, which leads to a severe chevron rollover for the folding arm. However, the population of the intermediates in the unfolding process is very low, insufficient to induce unfolding arm rollover. The total types of folding pathways from the coil state to the toroidal state for a semiflexible polymer chain remain unchanged by varying the solvent quality or temperature, whereas the kinetic partitioning into different folding events can be tuned significantly. In the process of knotting, three types of mechanisms, namely, plugging, slipknotting, and sliding, are discovered. Along the folding evolution, a semiflexible homopolymer chain can knot at any stage of folding upon leaving the extended coil state, and the probability to find a knot increases with chain compactness. In addition, we find rich types of knotted topologies during the folding of a semiflexible homopolymer chain. This study should be helpful in gaining insight into the general principles of biopolymer folding.

Butane dihedral angle dynamics in water is dominated by internal friction

The dihedral dynamics of butane in water is known to be rather insensitive to the water viscosity; possible explanations for this involve inertial effects or Kramers' turnover, the finite memory time of friction, and the presence of so-called internal friction. To disentangle these factors, we introduce a method to directly extract the friction memory function from unconstrained simulations in the presence of an arbitrary free-energy landscape. By analysis of the dihedral friction in butane for varying water viscosity, we demonstrate the existence of an internal friction contribution that does not scale linearly with water viscosity. At normal water viscosity, the internal friction turns out to be eight times larger than the solvent friction and thus completely dominates the effective friction. By comparison with simulations of a constrained butane molecule that has the dihedral as the only degree of freedom, we show that internal friction comes from the six additional degrees of freedom in unconstrained butane that are orthogonal to the dihedral angle reaction coordinate. While the insensitivity of butane's dihedral dynamics to water viscosity is solely due to the presence of internal friction, inertial effects nevertheless crucially influence the resultant transition rates. In contrast, non-Markovian effects due to the finite memory time are present but do not significantly influence the dihedral barrier-crossing rate of butane. These results not only settle the character of dihedral dynamics in small solvated molecular systems such as butane, they also have important implications for the folding of polymers and proteins.

The dock-and-coalesce mechanism for the association of a WASP disordered region with the Cdc42 GTPase

Intrinsically disordered proteins (IDPs) play key roles in signaling and regulation. Many IDPs undergo folding upon binding to their targets. We have proposed that coupled folding and binding of IDPs generally follow a dock-and-coalesce mechanism, whereby a segment of the IDP, through diffusion, docks to its cognate subsite and, subsequently, the remaining segments coalesce around their subsites. Here, by a combination of experiment and computation, we determined the precise form of dock-and-coalesce operating in the association between the intrinsically disordered GTPase-binding domain (GBD) of the Wiskott-Aldrich Syndrome protein and the Cdc42 GTPase. The association rate constants (k_a ) were measured by stopped-flow fluorescence under various solvent conditions. k_a reached 10⁷ m^-1 ·s^-1 at physiological ionic strength and had a strong salt dependence, suggesting that an electrostatically enhanced, diffusion-controlled docking step may be rate limiting. Our computation, based on the transient-complex theory, identified the N-terminal basic region of the GBD as the docking segment. However, several other changes in solvent conditions provided strong evidence that the coalescing step also contributed to determining the magnitude of k_a . Addition of glucose and trifluoroethanol and an increase in temperature all produced experimental k_a values much higher than expected from the effects on the docking rate alone. Conversely, addition of urea led to k_a values much lower than expected if only the docking rate was affected. These results all pointed to k_a being approximately two-thirds of the docking rate constant under physiological solvent conditions.

Fractional Viscosity Dependence of Reaction Kinetics in Glass-Forming Liquids

The diffusion of molecules in complex systems such as glasses and cell cytoplasm is slow, heterogeneous, and sometimes nonergodic. The effects of such intriguing diffusion on the kinetics of chemical and biological reactions remain elusive. In this Letter, we report that the kinetics of the polymer loop formation reaction in a Kob-Andersen (KA) glass forming liquid is influenced significantly by the dynamic heterogeneity. The diffusion coefficient D of a KA liquid deviates from the Stokes-Einstein relation at low temperatures and D shows a fractional dependence on the solvent viscosity η_{s}, i.e., D∼η_{s}^{-ξ_{D}} with ξ_{D}=0.85. The dynamic heterogeneity of a KA liquid affects the rate constant k_{rxn} of the loop formation and leads to the identical fractional dependence of k_{rxn} on η_{s} with k_{rxn}∼η_{s}^{-ξ} and ξ=ξ_{D}, contrary to reactions in dynamically homogeneous solutions where k_{rxn}∼η_{s}^{-1}.

Integrated view of internal friction in unfolded proteins from single-molecule FRET, contact quenching, theory, and simulations

Internal friction is an important contribution to protein dynamics at all stages along the folding reaction. Even in unfolded and intrinsically disordered proteins, internal friction has a large influence, as demonstrated with several experimental techniques and in simulations. However, these methods probe different facets of internal friction and have been applied to disparate molecular systems, raising questions regarding the compatibility of the results. To obtain an integrated view, we apply here the combination of two complementary experimental techniques, simulations, and theory to the same system: unfolded protein L. We use single-molecule Förster resonance energy transfer (FRET) to measure the global reconfiguration dynamics of the chain, and photoinduced electron transfer (PET), a contact-based method, to quantify the rate of loop formation between two residues. This combination enables us to probe unfolded-state dynamics on different length scales, corresponding to different parts of the intramolecular distance distribution. Both FRET and PET measurements show that internal friction dominates unfolded-state dynamics at low denaturant concentration, and the results are in remarkable agreement with recent large-scale molecular dynamics simulations using a new water model. The simulations indicate that intrachain interactions and dihedral angle rotation correlate with the presence of internal friction, and theoretical models of polymer dynamics provide a framework for interrelating the contribution of internal friction observed in the two types of experiments and in the simulations. The combined results thus provide a coherent and quantitative picture of internal friction in unfolded proteins that could not be attained from the individual techniques.

Integrated view of internal friction in unfolded proteins from single-molecule FRET, contact quenching, theory, and simulations

Internal friction is an important contribution to protein dynamics at all stages along the folding reaction. Even in unfolded and intrinsically disordered proteins, internal friction has a large influence, as demonstrated with several experimental techniques and in simulations. However, these methods probe different facets of internal friction and have been applied to disparate molecular systems, raising questions regarding the compatibility of the results. To obtain an integrated view, we apply here the combination of two complementary experimental techniques, simulations, and theory to the same system: unfolded protein L. We use single-molecule Förster resonance energy transfer (FRET) to measure the global reconfiguration dynamics of the chain, and photoinduced electron transfer (PET), a contact-based method, to quantify the rate of loop formation between two residues. This combination enables us to probe unfolded-state dynamics on different length scales, corresponding to different parts of the intramolecular distance distribution. Both FRET and PET measurements show that internal friction dominates unfolded-state dynamics at low denaturant concentration, and the results are in remarkable agreement with recent large-scale molecular dynamics simulations using a new water model. The simulations indicate that intrachain interactions and dihedral angle rotation correlate with the presence of internal friction, and theoretical models of polymer dynamics provide a framework for interrelating the contribution of internal friction observed in the two types of experiments and in the simulations. The combined results thus provide a coherent and quantitative picture of internal friction in unfolded proteins that could not be attained from the individual techniques.

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.

Infrared and Fluorescence Assessment of Protein Dynamics: From Folding to Function

While folding or performing functions, a protein can sample a rich set of conformational space. However, experimentally capturing all of the important motions with sufficient detail to allow a mechanistic description of their dynamics is nontrivial since such conformational events often occur over a wide range of time and length scales. Therefore, many methods have been employed to assess protein conformational dynamics, and depending on the nature of the conformational transition in question, some may be more advantageous than others. Herein, we describe our recent efforts, and also those of others, wherever appropriate, to use infrared- and fluorescence-based techniques to interrogate protein folding and functional dynamics. Specifically, we focus on discussing how to use extrinsic spectroscopic probes to enhance the structural resolution of these techniques and how to exploit various cross-linking strategies to acquire dynamic and mechanistic information that was previously difficult to attain.

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.

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.

Dependence of internal friction on folding mechanism

An outstanding challenge in protein folding is understanding the origin of "internal friction" in folding dynamics, experimentally identified from the dependence of folding rates on solvent viscosity. A possible origin suggested by simulation is the crossing of local torsion barriers. However, it was unclear why internal friction varied from protein to protein or for different folding barriers of the same protein. Using all-atom simulations with variable solvent viscosity, in conjunction with transition-path sampling to obtain reaction rates and analysis via Markov state models, we are able to determine the internal friction in the folding of several peptides and miniproteins. In agreement with experiment, we find that the folding events with greatest internal friction are those that mainly involve helix formation, while hairpin formation exhibits little or no evidence of friction. Via a careful analysis of folding transition paths, we show that internal friction arises when torsion angle changes are an important part of the folding mechanism near the folding free energy barrier. These results suggest an explanation for the variation of internal friction effects from protein to protein and across the energy landscape of the same protein.

Dissipative dynamics of enzymes

We explore enzyme conformational dynamics at sub-Å resolution, specifically, temperature effects. The ensemble-averaged mechanical response of the folded enzyme is viscoelastic in the whole temperature range between the warm and cold denaturation transitions. The dissipation parameter γ of the viscoelastic description decreases by a factor of 2 as the temperature is raised from 10 to 45 °C; the elastic parameter K shows a similar decrease. Thus, when probed dynamically, the enzyme softens for increasing temperature. Equilibrium mechanical experiments with the DNA spring (and a different enzyme) also show, qualitatively, a small softening for increasing temperature.

The osmotic resistance, and zeta potential responses of human erythrocytes to transmembrane modification of Ca2+ fluxes in the presence of the imposed low rate radiation field of 90Sr

PURPOSE

To investigate the effects of the imposed low dose rate ionizing field on membrane stability of human erythrocytes under modulation of transmembrane exchange of Ca(2+).

MATERIALS AND METHODS

Osmotic resistance of human erythrocytes was determined by a measure of haemoglobin released from erythrocytes when placed in a medium containing serial dilutions of Krebs isotonic buffer. The zeta potential as indicator of surface membrane potential was calculated from value of the cellular electrophoretic mobility. The irradiation of erythrocyte suspensions carried out by applying suitable aliquots of (90)Sr in incubation media.

RESULTS

Irradiation of human erythrocytes by (90)Sr (1.5-15.0 μGy·h(-1)) induced a reversible increase of hyposmotic hemolysis and negative charge value on the outer membrane surface as well as changed responses these parameters to modification of Ca(2+) fluxes with calcimycin and nitrendipine.

CONCLUSIONS

Findings indicate that the low dose rate radionuclides ((90)Sr) field modifies both Ca(2+)-mediated, and Ca(2+)-independent cellular signalling regulating mechanical stability of erythrocyte membrane. A direction of that modification presumably depends on the initial structure of membranes, and it is determined by the quality and quantitative parameters of changes in membrane structure caused by concrete operable factors.

Molecular origins of internal friction effects on protein-folding rates

Recent experiments on protein folding dynamics have revealed strong evidence for internal friction effects. That is, observed relaxation times are not simply proportional to the solvent viscosity as might be expected if the solvent were the only source of friction. However, a molecular interpretation of this remarkable phenomenon is currently lacking. Here, we use all-atom simulations of peptide and protein folding in explicit solvent, to probe the origin of the unusual viscosity dependence. We find that an important contribution to this effect, explaining the viscosity dependence of helix formation and the folding of a helix-containing protein, is the insensitivity of torsion angle isomerization to solvent friction. The influence of this landscape roughness can, in turn, be quantitatively explained by a rate theory including memory friction. This insensitivity of local barrier crossing to solvent friction is expected to contribute to the viscosity dependence of folding rates in larger proteins.

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.

Understanding the mechanism of proteasome 20S core particle gating

The 20S core particle proteasome is a molecular machine playing an important role in cellular function by degrading protein substrates that no longer are required or that have become damaged. Regulation of proteasome activity occurs, in part, through a gating mechanism controlling the sizes of pores at the top and bottom ends of the symmetric proteasome barrel and restricting access to catalytic sites sequestered in the lumen of the structure. Although atomic resolution models of both open and closed states of the proteasome have been elucidated, the mechanism by which gates exchange between these states remains to be understood. Here, this is investigated by using magnetization transfer NMR spectroscopy focusing on the 20S proteasome core particle from Thermoplasma acidophilum. We show from viscosity-dependent proteasome gating kinetics that frictional forces originating from random solvent motions are critical for driving the gating process. Notably, a small effective hydrodynamic radius (EHR; <4Å) is obtained, providing a picture in which gate exchange proceeds through many steps involving only very small segment sizes. A small EHR further suggests that the kinetics of gate interconversion will not be affected appreciably by large viscogens, such as macromolecules found in the cell, so long as they are inert. Indeed, measurements in cell lysate reveal that the gate interconversion rate decreases only slightly, demonstrating that controlled studies in vitro provide an excellent starting point for understanding regulation of 20S core particle function in complex, biologically relevant environments.

Effects of desolvation barriers and sidechains on local–nonlocal coupling and chevron behaviors in coarse-grained models of protein folding

Coarse-grained protein chain models with desolvation barriers or sidechains lead to stronger local–nonlocal coupling and more linear chevron plots.

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.

Defining a length scale for millisecond-timescale protein conformational exchange

Although atomic resolution 3D structures of protein native states and some folding intermediates are available, the mechanism of interconversion between such states remains poorly understood. Here we study the four-helix bundle FF module, which folds via a transiently formed and sparsely populated compact on-pathway intermediate, I. Relaxation dispersion NMR spectroscopy has previously been used to elucidate the 3D structure of this intermediate and to establish that the conformational exchange between the I and the native, N, states of the FF domain is driven predominantly by water dynamics. In the present study we use NMR methods to define a length scale for the FF I-N transition, namely the effective hydrodynamic radius (EHR) that provides an average measure of the size of the structural units participating in the transition at any given time. Our experiments establish that the EHR is less than 4 Å, on the order of the size of one to two amino acid side chains, much smaller than the FF domain hydrodynamic radius (13 Å). The small magnitude of the EHR provides strong evidence that the I-N interconversion does not proceed via the synchronous motion of large clusters of amino acid residues, but rather by the exposure/burial of one or two side chains from solvent at any given time. Because the hydration of small hydrophobic solutes (< 4 Å) does not involve considerable dewetting or disruption of the water-hydrogen bonding network, the FF domain I-N transition does not require appreciable changes to the structure of the surrounding water.

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.

Confinement-dependent friction in peptide bundles

Friction within globular proteins or between adhering macromolecules crucially determines the kinetics of protein folding, the formation, and the relaxation of self-assembled molecular systems. One fundamental question is how these friction effects depend on the local environment and in particular on the presence of water. In this model study, we use fully atomistic MD simulations with explicit water to obtain friction forces as a single polyglycine peptide chain is pulled out of a bundle of k adhering parallel polyglycine peptide chains. The whole system is periodically replicated along the peptide axes, so a stationary state at prescribed mean sliding velocity V is achieved. The aggregation number is varied between k = 2 (two peptide chains adhering to each other with plenty of water present at the adhesion sites) and k = 7 (one peptide chain pulled out from a close-packed cylindrical array of six neighboring peptide chains with no water inside the bundle). The friction coefficient per hydrogen bond, extrapolated to the viscous limit of vanishing pulling velocity V → 0, exhibits an increase by five orders of magnitude when going from k = 2 to k = 7. This dramatic confinement-induced friction enhancement we argue to be due to a combination of water depletion and increased hydrogen-bond cooperativity.

Folding of the four-helix bundle FF domain from a compact on-pathway intermediate state is governed predominantly by water motion

Friction plays a critical role in protein folding. Frictional forces originating from random solvent and protein fluctuations both retard motion along the folding pathway and activate protein molecules to cross free energy barriers. Studies of friction thus may provide insights into the driving forces underlying protein conformational dynamics. However, the molecular origin of friction in protein folding remains poorly understood because, with the exception of the native conformer, there generally is little detailed structural information on the other states participating in the folding process. Here, we study the folding of the four-helix bundle FF domain that proceeds via a transiently formed, sparsely populated compact on-pathway folding intermediate whose structure was elucidated previously. Because the intermediate is stabilized by both native and nonnative interactions, friction in the folding transition between intermediate and folded states is expected to arise from intrachain reorganization in the protein. However, the viscosity dependencies of rates of folding from or unfolding to the intermediate, as established by relaxation dispersion NMR spectroscopy, clearly indicate that contributions from internal friction are small relative to those from solvent, so solvent frictional forces drive the folding process. Our results emphasize the importance of solvent dynamics in mediating the interconversion between protein configurations, even those that are highly compact, and in equilibrium folding/unfolding fluctuations in general.

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.

Worm-like Ising model for protein mechanical unfolding under the effect of osmolytes

We show via single-molecule mechanical unfolding experiments that the osmolyte glycerol stabilizes the native state of the human cardiac I27 titin module against unfolding without shifting its unfolding transition state on the mechanical reaction coordinate. Taken together with similar findings on the immunoglobulin-binding domain of streptococcal protein G (GB1), these experimental results suggest that osmolytes act on proteins through a common mechanism that does not entail a shift of their unfolding transition state. We investigate the above common mechanism via an Ising-like model for protein mechanical unfolding that adds worm-like-chain behavior to a recent generalization of the Wako-Saitô-Muñoz-Eaton model with support for group-transfer free energies. The thermodynamics of the model are exactly solvable, while protein kinetics under mechanical tension can be simulated via Monte Carlo algorithms. Notably, our force-clamp and velocity-clamp simulations exhibit no shift in the position of the unfolding transition state of GB1 and I27 under the effect of various osmolytes. The excellent agreement between experiment and simulation strongly suggests that osmolytes do not assume a structural role at the mechanical unfolding transition state of proteins, acting instead by adjusting the solvent quality for the protein chain analyte.