Viscosity-Dependent Kinetics of Protein Conformational Exchange: Microviscosity Effects and the Need for a Small Viscogen

Effects of Macromolecular Cosolutes on the Kinetics of Huntingtin Aggregation Monitored by NMR Spectroscopy

The effects of two macromolecular cosolutes, specifically the polysaccharide dextran-20 and the protein lysozyme, on the aggregation kinetics of a pathogenic huntingtin exon-1 protein (hhtex1) with a 35 polyglutamine repeat, httex1Q35, are described. A unified kinetic model that establishes a direct connection between reversible tetramerization occurring on the microsecond time scale and irreversible fibril formation on a time scale of hours/days forms the basis for quantitative analysis of httex1Q35 aggregation, monitored by measuring cross-peak intensities in a series of 2D 1H-15N NMR correlation spectra acquired during the course of aggregation. The primary effects of the two cosolutes are associated with shifts in the prenucleation tetramerization equilibrium resulting in substantial changes in concentration of "preformed" httex1Q35 tetramers. Similar effects of the two cosolutes on the tetramerization equilibrium observed for a shorter, nonaggregating huntingtin variant with a 7-glutamine repeat, httex1Q7, lend confidence to the conclusions drawn from the fits to the httex1Q35 aggregation kinetics.

The role of memory-dependent friction and solvent viscosity in isomerization kinetics in viscogenic media

Molecular isomerization kinetics in liquid solvent depends on a complex interplay between the solvent friction acting on the molecule, internal dissipation effects (also known as internal friction), the viscosity of the solvent, and the dihedral free energy profile. Due to the absence of accurate techniques to directly evaluate isomerization friction, it has not been possible to explore these relationships in full. By combining extensive molecular dynamics simulations with friction memory-kernel extraction techniques we consider a variety of small, isomerising molecules under a range of different viscogenic conditions and directly evaluate the viscosity dependence of the friction acting on a rotating dihedral. We reveal that the influence of different viscogenic media on isomerization kinetics can be dramatically different, even when measured at the same viscosity. This is due to the dynamic solute-solvent coupling, mediated by time-dependent friction memory kernels. We also show that deviations from the linear dependence of isomerization rates on solvent viscosity, which are often simply attributed to internal friction effects, are due to the simultaneous violation of two fundamental relationships: the Stokes-Einstein relation and the overdamped Kramers prediction for the barrier-crossing rate, both of which require explicit knowledge of friction.

Beyond slow two-state protein conformational exchange using CEST: applications to three-state protein interconversion on the millisecond timescale

Although NMR spectroscopy is routinely used to study the conformational dynamics of biomolecules, robust analyses of the data are challenged in cases where exchange is more complex than two-state, such as when a 'visible' major conformer exchanges with two 'invisible' minor states on the millisecond timescale. It is becoming increasingly clear that chemical exchange saturation transfer (CEST) NMR experiments that were initially developed to study systems undergoing slow interconversion are also sensitive to intermediate-fast timescale biomolecular conformational exchange. Here we investigate the utility of the amide 15N CEST experiment to characterise protein three-state exchange occurring on the millisecond timescale by studying the interconversion between the folded (F) state of the FF domain from human HYPA/FBP11 (WT FF) and two of its folding intermediates I1 and I2. Although 15N CPMG experiments are consistent with the F state interconverting with a single minor state on the millisecond timescale, 15N CEST data clearly establish an exchange process between F and a pair of minor states. A unique three-state exchange model cannot be obtained by analysis of 15N CEST data recorded at a single temperature. However, including the relative sign of the difference in the chemical shifts of the two minor states based on a simple two-state analysis of CEST data recorded at multiple temperatures, results in a robust three-state model in which the F, I1 and I2 states interconvert with each other on the millisecond timescale ( k e x , F I 1 ~ 550 s-1, k e x , F I 2 ~ 1200 s-1, k e x , I 1 I 2 ~ 5000 s-1), with I1 and I2 sparsely populated at ~ 0.15% and ~ 0.35%, respectively, at 15 °C. A computationally demanding grid-search of exchange parameter space is not required to extract the best-fit exchange parameters from the CEST data. The utility of the CEST experiment, thus, extends well beyond studies of conformers in slow exchange on the NMR chemical shift timescale, to include systems with interconversion rates on the order of thousands/second.

NMR Provides Unique Insight into the Functional Dynamics and Interactions of Intrinsically Disordered Proteins

Intrinsically disordered proteins are ubiquitous throughout all known proteomes, playing essential roles in all aspects of cellular and extracellular biochemistry. To understand their function, it is necessary to determine their structural and dynamic behavior and to describe the physical chemistry of their interaction trajectories. Nuclear magnetic resonance is perfectly adapted to this task, providing ensemble averaged structural and dynamic parameters that report on each assigned resonance in the molecule, unveiling otherwise inaccessible insight into the reaction kinetics and thermodynamics that are essential for function. In this review, we describe recent applications of NMR-based approaches to understanding the conformational energy landscape, the nature and time scales of local and long-range dynamics and how they depend on the environment, even in the cell. Finally, we illustrate the ability of NMR to uncover the mechanistic basis of functional disordered molecular assemblies that are important for human health.

Temperature Dependence of Internal Friction of Peptides

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

Poly(acrylamide-co-acrylic acid) gel polymer electrolyte incorporating with water-soluble sodium sulfide salt for quasi-solid-state quantum dot-sensitized solar cell

Rapid decay of photoanode, leakage from sealant, and evaporation of electrolyte are always the major concerns of quantum dot-sensitized solar cells (QDSCs) based on liquid electrolyte. Subsequently, gel polymer electrolyte (GPE) appears as an attractive solution in addition to lower cost, lighter weight, and flexibility. Poly(acrylamide- co-acrylic acid) (PAAm-PAA) is of special interest to act as a polymer host to entrap liquid electrolyte because it provides high transparency, good gelatinizing properties, and excellent compatibility with the liquid electrolyte. In this work, the electrical and transport properties of PAAm-PAA GPE incorporating with water-soluble sodium sulfide were characterized by impedance spectroscopy. An increment of ionic conductivity was observed with the incorporation of ethylene carbonate (EC) and potassium chloride (KCl). The highest room temperature ionic conductivity of PAAm-PAA GPE is 70.82 mS·cm−1. QDSC based on PAAm-PAA GPE with the composition of 1.3 wt% of KCl, 0.9 wt% of EC, 55.3 wt% of PAAm-PAA, 38.5 wt% of sodium sulfide, and 4.0 wt% of sulfur can present up to 1.80% of light-to-electricity conversion efficiency.

A Unified Description of Intrinsically Disordered Protein Dynamics under Physiological Conditions Using NMR Spectroscopy

Intrinsically disordered proteins (IDPs) are flexible biomolecules whose essential functions are defined by their dynamic nature. Nuclear magnetic resonance (NMR) spectroscopy is ideally suited to the investigation of this behavior at atomic resolution. NMR relaxation is increasingly used to detect conformational dynamics in free and bound forms of IDPs under conditions approaching physiological, although a general framework providing a quantitative interpretation of these exquisitely sensitive probes as a function of experimental conditions is still lacking. Here, measuring an extensive set of relaxation rates sampling multiple-time-scale dynamics over a broad range of crowding conditions, we develop and test an integrated analytical description that accurately portrays the motion of IDPs as a function of the intrinsic properties of the crowded molecular environment. In particular we observe a strong dependence of both short-range and long-range motional time scales of the protein on the friction of the solvent. This tight coupling between the dynamic behavior of the IDP and its environment allows us to develop analytical expressions for protein motions and NMR relaxation properties that can be accurately applied over a vast range of experimental conditions. This unified dynamic description provides new insight into the physical behavior of IDPs, extending our ability to quantitatively investigate their conformational dynamics under complex environmental conditions, and accurately predicting relaxation rates reporting on motions on time scales up to tens of nanoseconds, both in vitro and in cellulo.

A Threshold-Limited Fluorescence Probe for Viscosity

Viscosity of body fluid is an established biomarker of pathological conditions. Abnormality of cellular viscosity occurs when cells are challenged with external stresses. Small molecule probes to assess the viscosity are sought after for both disease diagnostics and basic studies. Fluorescence based probes are particular attractive due to their potentials for convenient and high spatiotemporal resolution microscopic monitoring of biological samples. The dyes with a floppy push-pull backbone or dyes with a rotatable substituent exhibits a viscosity responsive fluorescence enhancement and therefore viable viscosity probes. The scaffold of the existing viscosity probes contains typically one such floppy site. Therefore, they typically linearly respond to log(viscosity). We argue that minor viscosity fluctuation could potentially be physiological as the biological system is dynamic. We wish to develop a type of conceptually-new, threshold-limited viscosity probes, to complement the existing probes. Such probes do not exhibit a fluorescence enhancement when challenged with minor and presumably physiological enhancement of viscosity. When the viscosity is higher than a certain threshold, their fluorescence turns on. We hypothesize that a dye with two far-apart floppy sites could potentially yield such a threshold-limited signal and designed VPZ2 and VPZ3. Through spectral titration, VPZ3 was found to yield the desired threshold-limited signal. VPZ3 was suitable for in vitro bioimaging of viscosity under one-photon or two-photon excitation. VPZ3 is potentially useful in many downstream applications. Future work includes fine-tune of the threshold to allow tailored limit for fluorescence turn-on to better meet the need of different applications. Besides the implications in the real-world applications, the design concept could also be translated to design of alternative substrates.

A Simple and Noninvasive DOSY NMR Method for Droplet Size Measurement of Intact Oil-In-Water Emulsion Drug Products

In a typical oil-in-water emulsion drug product, oil droplets with varied sizes are dispersed in a water phase and stabilized by surfactant molecules. The size and polydispersity of oil droplets are critical quality attributes of the emulsion drug product that can potentially affect drug bioavailability. More critically, to ensure accuracy in characterization of the finished drug product, analytical methods should introduce minimal physical perturbation (e.g., temperature variation or dilution) before the analysis. The classical methods of dynamic light scattering or electron microscopy can be used but they generally require sample dilution or harsh preparation conditions, respectively. By contrast, the size distribution of emulsion formulations can be assessed with a simple and noninvasive solution nuclear magnetic resonance method, namely, two-dimensional Diffusion Ordered SpectroscopY. The two-dimensional Diffusion Ordered SpectroscopY method probed signal decay of methyl resonances from oil and sorbate molecules and was applied to 3 types of U.S.-marketed emulsion drug products, that is, difluprednate, cyclosporine, and propofol, yielding measured droplet sizes of 40-280 nm in diameter. The high precision of ±6 nm of the new nuclear magnetic resonance method allows analytical differentiation of lot-to-lot and brand-to-brand droplet size differences in emulsion drug products, critical for drug-quality development, control, and surveillance.

Spectroscopic methods for assessing the molecular origins of macroscopic solution properties of highly concentrated liquid protein solutions

In cases of subcutaneous injection of therapeutic monoclonal antibodies, high protein concentrations (>50 mg/ml) are often required. During the development of these high concentration liquid formulations (HCLF), challenges such as aggregation, gelation, opalescence, phase separation, and high solution viscosities are more prone compared to low concentrated protein formulations. These properties can impair manufacturing processes, as well as protein stability and shelf life. To avoid such unfavourable solution properties, a detailed understanding about the nature of these properties and their driving forces are required. However, the fundamental mechanisms that lead to macroscopic solution properties, as above mentioned, are complex and not fully understood, yet. Established analytical methods for assessing the colloidal stability, i.e. the ability of a native protein to remain dispersed in solution, are restricted to dilute conditions and provide parameters such as the second osmotic virial coefficient, B₂₂, and the diffusion interaction coefficient, k_D. These parameters are routinely applied for qualitative estimations and identifications of proteins with challenging solution behaviours, such as high viscosities and aggregation, although the assays are prepared for low protein concentration conditions, typically between 0.1 and 20 mg/ml ("ideal" solution conditions). Quantitative analysis of samples of high protein concentration is difficult and it is hard to obtain information about the driving forces of such solution properties and corresponding protein-protein self-interactions. An advantage of using specific spectroscopic methods is the potential of directly analysing highly concentrated protein solutions at different solution conditions. This allows for collecting/gaining valuable information about the fundamental mechanisms of solution properties of the high protein concentration regime. In addition, the derived parameters might be more predictive as compared to the parameters originating from assays which are optimized for the low protein concentration range. The provided information includes structural data, molecular dynamics at various timescales and protein-solvent interactions, which can be obtained at molecular resolution. Herein, we provide an overview about spectroscopic techniques for analysing the origins of macroscopic solution behaviours in general, with a specific focus on pharmaceutically relevant high protein concentration and formulation conditions.

Molecular motion regulates the activity of the Mitochondrial Serine Protease HtrA2

HtrA2 (high-temperature requirement 2) is a human mitochondrial protease that has a role in apoptosis and Parkinson's disease. The structure of HtrA2 with an intact catalytic triad was determined, revealing a conformational change in the active site loops, involving mainly the regulatory LD loop, which resulted in burial of the catalytic serine relative to the previously reported structure of the proteolytically inactive mutant. Mutations in the loops surrounding the active site that significantly restricted their mobility, reduced proteolytic activity both in vitro and in cells, suggesting that regulation of HtrA2 activity cannot be explained by a simple transition to an activated conformational state with enhanced active site accessibility. Manipulation of solvent viscosity highlighted an unusual bi-phasic behavior of the enzymatic activity, which together with MD calculations supports the importance of motion in the regulation of the activity of HtrA2. HtrA2 is an unusually thermostable enzyme (T_M=97.3 °C), a trait often associated with structural rigidity, not dynamic motion. We suggest that this thermostability functions to provide a stable scaffold for the observed loop motions, allowing them a relatively free conformational search within a rather restricted volume.

Protein folding by NMR

Protein folding is a highly complex process proceeding through a number of disordered and partially folded nonnative states with various degrees of structural organization. These transiently and sparsely populated species on the protein folding energy landscape play crucial roles in driving folding toward the native conformation, yet some of these nonnative states may also serve as precursors for protein misfolding and aggregation associated with a range of devastating diseases, including neuro-degeneration, diabetes and cancer. Therefore, in vivo protein folding is often reshaped co- and post-translationally through interactions with the ribosome, molecular chaperones and/or other cellular components. Owing to developments in instrumentation and methodology, solution NMR spectroscopy has emerged as the central experimental approach for the detailed characterization of the complex protein folding processes in vitro and in vivo. NMR relaxation dispersion and saturation transfer methods provide the means for a detailed characterization of protein folding kinetics and thermodynamics under native-like conditions, as well as modeling high-resolution structures of weakly populated short-lived conformational states on the protein folding energy landscape. Continuing development of isotope labeling strategies and NMR methods to probe high molecular weight protein assemblies, along with advances of in-cell NMR, have recently allowed protein folding to be studied in the context of ribosome-nascent chain complexes and molecular chaperones, and even inside living cells. Here we review solution NMR approaches to investigate the protein folding energy landscape, and discuss selected applications of NMR methodology to studying protein folding in vitro and in vivo. Together, these examples highlight a vast potential of solution NMR in providing atomistic insights into molecular mechanisms of protein folding and homeostasis in health and disease.

Numerical Treatment of Stokes Solvent Flow and Solute-Solvent Interfacial Dynamics for Nonpolar Molecules

We design and implement numerical methods for the incompressible Stokes solvent flow and solute-solvent interface motion for nonpolar molecules in aqueous solvent. The balance of viscous force, surface tension, and van der Waals type dispersive force leads to a traction boundary condition on the solute-solvent interface. To allow the change of solute volume, we design special numerical boundary conditions on the boundary of a computational domain through a consistency condition. We use a finite difference ghost fluid scheme to discretize the Stokes equation with such boundary conditions. The method is tested to have a second-order accuracy. We combine this ghost fluid method with the level-set method to simulate the motion of the solute-solvent interface that is governed by the solvent fluid velocity. Numerical examples show that our method can predict accurately the blow up time for a test example of curvature flow and reproduce the polymodal (e.g., dry and wet) states of hydration of some simple model molecular systems.

Effect of viscogens on the kinetic response of a photoperturbed allosteric protein

By covalently binding a photoswitchable linker across the binding groove of the PDZ2 domain, a small conformational change can be photo-initiated that mimics the allosteric transition of the protein. The response of its binding groove is investigated with the help of ultrafast pump-probe IR spectroscopy from picoseconds to tens of microseconds. The temperature dependence of that response is compatible with diffusive dynamics on a rugged energy landscape without any prominent energy barrier. Furthermore, the dependence of the kinetics on the concentration of certain viscogens, sucrose, and glycerol, has been investigated. A pronounced viscosity dependence is observed that can be best fit by a power law, i.e., a fractional viscosity dependence. The change of kinetics when comparing sucrose with glycerol as viscogen, however, provides strong evidence that direct interactions of the viscogen molecule with the protein do play a role as well. This conclusion is supported by accompanying molecular dynamics simulations.

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.

STABILITY OF A CYLINDRICAL SOLUTE-SOLVENT INTERFACE: EFFECT OF GEOMETRY, ELECTROSTATICS, AND HYDRODYNAMICS

The solute-solvent interface that separates biological molecules from their surrounding aqueous solvent characterizes the conformation and dynamics of such molecules. In this work, we construct a solvent fluid dielectric boundary model for the solvation of charged molecules and apply it to study the stability of a model cylindrical solute-solvent interface. The motion of the solute-solvent interface is defined to be the same as that of solvent fluid at the interface. The solvent fluid is assumed to be incompressible and is described by the Stokes equation. The solute is modeled simply by the ideal-gas law. All the viscous force, hydrostatic pressure, solute-solvent van der Waals interaction, surface tension, and electrostatic force are balanced at the solute-solvent interface. We model the electrostatics by Poisson's equation in which the solute-solvent interface is treated as a dielectric boundary that separates the low-dielectric solute from the high-dielectric solvent. For a cylindrical geometry, we find multiple cylindrically shaped equilibrium interfaces that describe polymodal (e.g., dry and wet) states of hydration of an underlying molecular system. These steady-state solutions exhibit bifurcation behavior with respect to the charge density. For their linearized systems, we use the projection method to solve the fluid equation and find the dispersion relation. Our asymptotic analysis shows that, for large wavenumbers, the decay rate is proportional to wavenumber with the proportionality half of the ratio of surface tension to solvent viscosity, indicating that the solvent viscosity does affect the stability of a solute-solvent interface. Consequences of our analysis in the context of biomolecular interactions are discussed.

NMR studies of protein folding and binding in cells and cell-like environments

Proteins function in cells where the concentration of macromolecules can exceed 300g/L. The ways in which this crowded environment affects the physical properties of proteins remain poorly understood. We summarize recent NMR-based studies of protein folding and binding conducted in cells and in vitro under crowded conditions. Many of the observations can be understood in terms of interactions between proteins and the rest of the intracellular environment (i.e. quinary interactions). Nevertheless, NMR studies of folding and binding in cells and cell-like environments remain in their infancy. The frontier involves investigations of larger proteins and further efforts in higher eukaryotic cells.

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.