Crowding, Sticking, and Partial Folding of GTT WW Domain in a Small Cytoplasm Model.

Recent experimental data has shown that protein folding in the cytoplasm can differ from in vitro folding with respect to speed, stability, and residual structure. Here we investigate the all-atom molecular dynamics (MD) simulations of 9 copies of the model protein GTT WW domain in a small bacterial cytoplasm model using three force fields. GTT has been well-studied by MD in aqueous solution for comparison. We find that folded copies remain folded for up 25 µs, whereas unfolded copies do not fold for up to 190 µs. Unfolded GTT in our cytoplasm model does populate partly folded intermediates with one of the two hairpins formed. Relative to aqueous solution, GTT gets stuck in metastable states with a small RMSD and radius of gyration and extensive burial of surface area against other macromolecules. In particular, GTT is even able to form transient intermolecular ß-sheets with other proteins, resulting in a "chimeric structure" that could be a precursor to oligomeric ß-aggregates. We conclude that sticking, enhanced by the non-native mutations of GTT, is largely responsible, and we propose, on the basis of our result as well as recent experiments, that coevolution of protein surfaces with their solvation environment (including chaperones) is important for folding and diffusion of proteins in the cytoplasm.

Multi-scale dynamics at the glassy silica surface.

Silica-based glass is a household name, providing insulation for windows to microelectronics. The debate over the types of motions thought to occur in or on SiO2 glass well below the glass transition temperature continues. Here, we form glassy silica films by oxidizing the Si(100) surface (from 0.5 to 1.5 nm thick, to allow tunneling). We then employ scanning tunneling microscopy in situ to image and classify these motions at room temperature on a millisecond to hour time scale and 50-pm to 5-nm length scale. We observe two phenomena on different time scales. Within minutes, compact clusters with an average diameter of several SiO2 glass-forming units (GFUs) hop between a few (mostly two) configurations, hop cooperatively (facilitation), and merge into larger clusters (aging) or split into smaller clusters (rejuvenation). Within seconds, Si-O-Si bridges connect two GFUs within a single cluster flip, providing a vibrational fine structure to the energy landscape. We assign the vibrational fine structure using electronic structure calculations. Calculations also show that our measured barrier height for whole cluster hopping at the glass surface (configurational dynamics) is consistent with the configurational entropy predicted by thermodynamic models of the glass transition and that the vibrational entropy for GFU flipping and configurational entropy for cluster hopping are comparable (on a per GFU basis).

Competition of individual domain folding with inter-domain interaction in WW domain engineered repeat proteins.

Engineered repeat proteins have proven to be a fertile ground for studying the competition between folding, misfolding and transient aggregation of tethered protein domains. We examine the interplay between folding and inter-domain interactions of engineered FiP35 WW domain repeat proteins with n = 1 through 5 repeats. We characterize protein expression, thermal and guanidium melts, as well as laser T-jump kinetics. All experimental data is fitted by a global fitting model with two states per domain (U, N), plus a third state M to account for non-native states due to domain interactions present in all but the monomer. A detailed structural model is provided by coarse-grained simulated annealing using the AWSEM Hamiltonian. Tethered FiP35 WW domains with n = 2 and 3 domains are just slightly less stable than the monomer. The n = 4 oligomer is yet less stable, its expression yield is much lower than the monomer's, and depends on the purification tag used. The n = 5 plasmid did not express at all, indicating the sudden onset of aggregation past n = 4. Thus, tethered FiP35 has a critical nucleus size for inter-domain aggregation of n ≈ 4. According to our simulations, misfolded structures become increasingly prevalent as one proceeds from monomer to pentamer, with extended inter-domain beta sheets appearing first, then multi-sheet 'intramolecular amyloid' structures, and finally novel motifs containing alpha helices. We discuss the implications of our results for oligomeric aggregate formation and structure, transient aggregation of proteins whilst folding, as well as for protein evolution that starts with repeat proteins.

Plasmonic support-mediated activation of 1 nm platinum clusters for catalysis.

Nanometer-sized metal clusters are prime candidates for photoactivated catalysis, based on their unique tunable optical and electronic properties, combined with a large surface-to-volume ratio. Due to the very small optical cross sections of such nanoclusters, support-mediated plasmonic activation could potentially make activation more efficient. Our support is a semi-transparent gold film, optimized to work in a back-illumination geometry. It has a surface plasmon resonance excitable in the 510-540 nm wavelength range. Ptn clusters (size distribution peaked at n = 46 atoms) have been deposited onto this support and investigated for photoactivated catalytic performance in the oxidative decomposition of methylene blue. The Pt cluster catalytic activity under illumination exceeds that of the gold support by more than an order of magnitude per active surface area. To further investigate the underlying mechanism of plasmon-induced catalysis, the clusters have been imaged with optically-assisted scanning tunneling microscopy under illumination. The photoactivation of the Pt clusters via plasmonic excitation of the support and subsequential electronic excitation of the clusters can be imaged with nanometer resolution. The light-induced tunneling current on the clusters is enhanced relative to the gold film support.

Filling up the heme pocket stabilizes apomyoglobin and speeds up its folding.

Wild type apomyoglobin folds in at least two steps: the ABGH core rapidly, followed much later by the heme-binding CDEF core. We hypothesize that the evolved heme-binding function of the CDEF core frustrates its folding: it has a smaller contact order and is no more complex topologically than ABGH, and thus, it should be able to fold faster. Therefore, filling up the empty heme cavity of apomyoglobin with larger, hydrophobic side chains should significantly stabilize the protein and increase its folding rate. Molecular dynamics simulations allowed us to design four different mutants with bulkier side chains that increase the native bias of the CDEF region. In vitro thermal denaturation shows that the mutations increase folding stability and bring the protein closer to two-state behavior, as judged by the difference of fluorescence- and circular dichroism-detected protein stability. Millisecond stopped flow measurements of the mutants exhibit refolding kinetics that are over 4 times faster than the wild type's. We propose that myoglobin-like proteins not evolved to bind heme are equally stable, and find an example. Our results illustrate how evolution for function can force proteins to adapt frustrated folding mechanisms, despite having simple topologies.

A thermodynamic derivation of the reciprocal relations.

Starting with the continuity and Smoluchowski equations, we write the mass flux for a system out of equilibrium in terms of the physicochemical potential µ(g). µ(g) is a coarse-grained analog of the chemical potential in the presence of forces that drive the system out of equilibrium. The expression for flux in terms of µ(g) allows for a macroscopic derivation of the Onsager reciprocal relations for the case of transport by diffusion and drift in single or multi-component systems, without recourse to microscopic fluctuations or equations of motion. Transport coefficients for any time reversal-invariant properties now are expressed in terms of only partial molar derivatives and mobilities (diffusion coefficients). The thermodynamic derivation cannot treat time reversal.

Microsecond folding experiments and simulations: a match is made.

For the past two decades, protein folding experiments have been speeding up from the second or millisecond time scale to the microsecond time scale, and full-atom simulations have been extended from the nanosecond to the microsecond and even millisecond time scale. Where the two meet, it is now possible to compare results directly, allowing force fields to be validated and refined, and allowing experimental data to be interpreted in atomistic detail. In this perspective we compare recent experiments and simulations on the microsecond time scale, pointing out the progress that has been made in determining native structures from physics-based simulations, refining experiments and simulations to provide more quantitative underlying mechanisms, and tackling the problems of multiple reaction coordinates, downhill folding, and complex underlying structure of unfolded or misfolded states.

Temperature-dependent two-state dynamics of individual cooperatively rearranging regions on a glass surface.

Cooperatively rearranging regions (CRRs) play a central role in the temperature dependence of glass dynamics. We record real-time atomic resolution movies of individual CRRs, while ramping their temperature. Between 295 and 326 K, well below the bulk glass transition temperature T(g), the rate coefficient for two-state hopping of CRRs increases over tenfold, yielding an Arrhenius activation barrier of ≈10k(B)T(g). By time resolving the dynamics of many individual CRRs, we show that highly stretched dynamics of the CRR ensemble results mainly from spatial heterogeneity, less from temporal heterogeneity of individual CRRs.

Communication: An obligatory glass surface.

Theory predicts, and experiments have shown, that dynamics is faster at glass surfaces than in the bulk, allowing the glass to settle into deeper energy landscape minima, or "age more." Is it possible that a glass surface could survive at temperatures where the bulk crystallizes, or that it could remain glassy after the bulk is heated all the way to its melting temperature and re-cooled? We image in real-time and with sub-nanometer resolution the two-state surface dynamics on a cerium-based glass surface, from deep within the glassy regime to above the crystallization temperature. Unlike other surfaces that we have studied, this glass surface remains amorphous even after the bulk re-crystallizes. The surface retains non-crystalline structure and two state dynamics of cooperatively rearranging regions even after heat annealing to just below the bulk melting temperature. The heat-annealed cooperatively rearranging regions are larger than originally, a sign that the surface is well aged. The surface dynamics depends weakly on temperature, showing no sign of the superexponential increase in bulk dynamics expected near T(g).

Protein stability and folding kinetics in the nucleus and endoplasmic reticulum of eucaryotic cells.

We measure the stability and folding relaxation rate of phosphoglycerate kinase (PGK) Förster resonance energy transfer (FRET) constructs localized in the nucleus or in the endoplasmic reticulum (ER) of eukaryotic cells. PGK has a more compact native state in the cellular compartments than in aqueous solution. Its native FRET signature is similar to that previously observed in a carbohydrate-crowding matrix, consistent with crowding being responsible for the compact native state of PGK in the cell. PGK folds through multiple states in vitro, but its folding kinetics is more two-state-like in the ER, so the folding mechanism can be modified by intracellular compartments. The nucleus increases PGK stability and folding rate over the cytoplasm and ER, even though the density of crowders in the nucleus is no greater than in the ER or cytoplasm. Nuclear folding kinetics (and to a lesser extent, thermodynamics) vary less from cell to cell than in the cytoplasm or ER, indicating a more homogeneous crowding and chemical environment in the nucleus.

Direct imaging of two-state dynamics on the amorphous silicon surface.

Amorphous silicon is an important material, amidst a debate whether or not it is a glass. We produce amorphous Si surfaces by ion bombardment and vapor growth, and image discrete Si clusters which hop by two-state dynamics at 295 K. Independent of surface preparation, these clusters have an average diameter of ∼5 atoms. Given prior results for metallic glasses, we suggest that this cluster size is a universal feature. The hopping activation free energy of 0.93±0.15 eV is rather small, in agreement with a previously untested surface glass model. Hydrogenation quenches the two-state dynamics, apparently by increasing surface crystallinity.

Freezing vibrational energy flow: a fitness function for interchangeable computational and experimental control.

We develop a fitness functional for freezing molecular energy flow that relies only on experimental observables. The functional allows us to implement a modular control algorithm where simulation data and experimental data can be used interchangeably. This interchangeability could be useful as a spectroscopic tool and for reactive control because the controllability of the experimental system and its model can be compared directly. The fitness functional performs as well as functionals based on complete knowledge of the wave function. We compare our simulation results with an analytical theory of control, and find good agreement between the simulated and predicted times over which the system can be controlled.

Size and energy scaling of nonstatistical vibrational quantum states.

Polyatomic molecules are generally believed to behave more statistically as the number of vibrational modes increases. We show that even at the dissociation energy, low mode populations result in many nonstatistical quantum states. We derive a scaling relation for the number of nonstatistical states as a function of molecular size. In molecules with more than 6 atoms this model predicts that the majority of states are nonstatistical at dissociation.

Quantizing Ulam's control conjecture.

Like classically chaotic systems, can quantum systems be nudged from a given initial state to any other by arbitrarily weak control fields? We explore a scaling theory that sets fundamental limits on the time required for population transfer with weak control fields. Our results depend on the size of the quantum state space and on the rate and extent of energy flow within the system. When the unperturbed dynamics is quantum localized, the total distance in state space over which control can be achieved grows linearly with the number of photons that are expended.

Multiple probes reveal a native-like intermediate during low-temperature refolding of ubiquitin.

We investigate the refolding of ubiquitin Phe45Trp/Ile61Ala (Ub(*)I61A) in a low-temperature, high-viscosity buffer, where folding is slowed so that apparent two-state and three-state mechanisms are readily distinguishable. Ub(*)I61A forms a compact ensemble rapidly (as judged from stopped-flow, small-angle X-ray scattering) with a secondary structure signature similar to that of the native state (as judged from stopped-flow circular dichroism from 215 nm to 250 nm), but the fluorescence signature still resembles the guanidinium-denatured state. The compact ensemble forms over a range of solvent and temperature conditions. The native fluorescence signature, which requires the tryptophan residue to be packed tightly, is acquired at least 500 times more slowly. Molecular dynamics simulations at 495 K show no contraction of the backbone in ethylene glycol buffer compared to pure aqueous buffer, and no significant effect on the local backbone structure of the unfolded protein. Only at higher simulation temperature does a backbone contraction appear. Thus, it appears unlikely that the aqueous ethylene glycol buffer fundamentally changes the folding mechanism of ubiquitin. We suggest that ubiquitin forms a compact ensemble with native-like secondary structure, but without tight packing, long before the native state.

Vibrational energy flow and chemical reactions.

How vibrational energy flows in molecules has recently become much better understood through the joint efforts of theory, experiment, and computation. The phenomenology of energy flow is much richer than earlier thought. We now know energy flow depends on the local structure of molecular vibrational state space. The details of the theoretically predicted transition from localized vibrations to free flow, where the molecule can act as its own heat bath, are now well-established experimentally. Energy flow is a quantum diffusive process leading to nonexponential decays, also seen in experiment. The slowness of energy flow in activated molecules causes substantial deviation from statistical Rice-Ramsperger-Kassel-Marcus (RRKM) theories for low barrier rate processes, such as isomerization. Quantitative calculations of rates in those cases are now possible.

Quantifying protein folding transition States with φ(t).

A number of reaction coordinates have been proposed for reduced-dimensionalityrepresentations of a protein's folding free energy surface. We discuss in detail the entropic reaction coordinate Φ(T) = Δ S(†)ΔS, recently introduced to quantify the conservation of mutations and the location of the folding transition state based on experimental temperature-tuning data. Numerical simulations illustrate the advantages as well as the limitations of Φ(T). Φ(T) can be determined from experiment,computation, and analytical theory; Φ(T) can also be used to investigate structurally localized perturbations of the free energy surface. However, Φ(T) is only a relative reaction cordinate; furthermore, proteins undergo cold denaturation at sufficiently low temperatures, and care must be taken ininterpreting Φ(T) near the region where ∂ΔG/∂T = 0, particularly if the heat capacity change upon folding is small.

The folding mechanism of a beta-sheet: the WW domain.

The folding thermodynamics and kinetics of the Pin WW domain, a three-stranded antiparallel beta-sheet, have been characterized extensively. Folding and activation free energies were determined as a function of temperature for 16 mutants, which sample all strands and turns of the molecule. The mutational phi value (Phi(m)) diagram is a smooth function of sequence, indicating a prevalence of local interactions in the transition state (TS). At 37 degrees C, the diagram has a single pronounced maximum at turn 1: the rate-limiting step during folding is the formation of loop 1. In contrast, key residues for thermodynamic stability are located in the strand hydrophobic clusters, indicating that factors contributing to protein stability and folding kinetics are not correlated. The location of the TS along the entropic reaction coordinate Phi(T), obtained by temperature-tuning the kinetics, reveals that sufficiently destabilizing mutants in loop 2 or in the Leu7-Trp11-Tyr24-Pro37 hydrophobic cluster can cause a switch to a late TS. Phi(m) analysis is usually applied "perturbatively" (methyl truncation), but with Phi(T) to quantitatively assess TS shifts along a reaction coordinate, more severe mutations can be used to probe regions of the free energy surface beyond the TS.

Mapping the transition state of the WW domain beta-sheet.

The folding kinetics of a three-stranded antiparallel beta-sheet (WW domain) have been measured by temperature jump relaxation. Folding and activation free energies were determined as a function of temperature for both the wild-type and the mutant domain, W39F, which modifies the beta(2)-beta(3) hydrophobic interface. The folding rate decreases at higher temperatures as a result of the increase in the activation free energy for folding. Phi-Values were obtained for thermal perturbations allowing the primary features of the folding free energy surface to be determined. The results of this analysis indicate a significant shift from an "early" (Phi(T)=0. 4) to a "late" (Phi(T)=0.8) transition state with increasing temperature. The temperature-dependent Phi-value analysis of the wild-type WW domain and of its more stable W39F hydrophobic cluster mutant reveals little participation of residue 39 in the transition state at lower temperature. As the temperature is raised, hydrophobic interactions at the beta(2)-beta(3) interface gain importance in the transition state and the barrier height of the wild-type, which contains the larger tryptophan residue, increases more slowly than the barrier height of the mutant.

Submicrosecond real-time fluorescence sampling: application to protein folding.

Time-resolved fluorescence detection has become a central tool in the study of protein folding. This article briefly reviews modern fluorescence techniques and then focuses on recent improvements made possible by array photomultipliers, computer-controlled data gating, and long-memory multi-channel digitizers. It is now possible to detect fluorescence wavelength profiles and/or fluorescence decay transients very cost effectively with sub-microsecond kinetic time resolution out to long times. Folding kinetics can be analyzed by singular value decomposition (SVD) or chi-analysis. The latter provides an objective method for detecting nonexponential kinetics in two-state systems.