Inhomogeneity of viscous aqueous solutions

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.

Local and Large-Scale Conformational Dynamics in Unfolded Proteins and IDPs. I. Effect of Solvent Viscosity and Macromolecular Crowding

Protein/solvent interactions largely influence protein dynamics, particularly motions in unfolded and intrinsically disordered proteins (IDPs). Here, we apply triplet-triplet energy transfer (TTET) to investigate the coupling of internal protein motions to solvent motions by determining the effect of solvent viscosity (η) and macromolecular crowding on the rate constants of loop formation (kc) in several unfolded polypeptide chains including IDPs. The results show that the viscosity dependence of loop formation depends on amino acid sequence, loop length, and co-solute size. Below a critical size (rc), co-solutes exert a maximum effect, indicating that under these conditions microviscosity experienced by chain motions matches macroviscosity of the solvent. rc depends on chain stiffness and reflects the length scale of the chain motions, i.e., it is related to the persistence length. Above rc, the effect of solvent viscosity decreases with increasing co-solute size. For co-solutes typically used to mimic cellular environments, a scaling of kc ∝ η-0.1 is observed, suggesting that dynamics in unfolded proteins are only marginally modulated in cells. The effect of solvent viscosity on kc in the small co-solute limit (below rc) increases with increasing chain length and chain flexibility. Formation of long and very flexible loops exhibits a kc ∝ η-1 viscosity dependence, indicating full solvent coupling. Shorter and less flexible loops show weaker solvent coupling with values as low as kc ∝ η-0.75 ± 0.02. Coupling of formation of short loops to solvent motions is very little affected by amino acid sequence, but solvent coupling of long-range loop formation is decreased by side chain sterics.

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.

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.

Self-Healable, Fast Responsive Poly(ω-Pentadecalactone) Thermogelling System for Effective Liver Cancer Therapy

A polyurethane based thermogelling system comprising poly(ω-pentadecalactone) (PPDL), poly(ethylene glycol) (PEG), and poly(propylene glycol) (PPG), termed as PDEP, was synthesized. The incorporation of PPDL lowers critical micelle concentration (CMC) as well as critical gelation concentration (CGC) of the novel copolymers compared to commercial Pluronic® F127. The thermogels showed excellent thermal stability at high temperature up to 80°C, fast response to temperature change in a time frame of less than second, as well as remarkable self-healing properties after being broken at high strain. In vitro drug release studies using docetaxel (DTX) and cell uptake studies using doxorubicin (DOX) show high potential of the hydrogel as drug reservoir for sustainable release profile of payloads, while the in vivo anti-tumor evaluation using mice model of hepatocellular carcinoma further demonstrated the significant inhibition on the growth of tumor. Together with its excellent biocompatibility in different organs, the novel PDPE thermogelling copolymers reported in this work could potentially be utilized as in situ-forming hydrogels for liver cancer therapy.

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.

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.

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.

Contraction behaviors of Vorticella sp. stalk investigated using high-speed video camera. II: Viscosity effect of several types of polymer additives

The contraction process of living Vorticella sp. in polymer solutions with various viscosities has been investigated by image processing using a high-speed video camera. The viscosity of the external fluid ranges from 1 to 5mPa·s for different polymer additives such as hydroxypropyl cellulose, polyethylene oxide, and Ficoll. The temporal change in the contraction length of Vorticella sp. in various macromolecular solutions is fitted well by a stretched exponential function based on the nucleation and growth model. The maximum speed of the contractile process monotonically decreases with an increase in the external viscosity, in accordance with power law behavior. The index values approximate to 0.5 and this suggests that the viscous energy dissipated by the contraction of Vorticella sp. is constant in a macromolecular environment.

Effect of macromolecular crowding on protein folding dynamics at the secondary structure level

Macromolecular crowding is one of the key characteristics of the cellular environment and is therefore intimately coupled to the process of protein folding in vivo. While previous studies have provided invaluable insight into the effect of crowding on the stability and folding rate of protein tertiary structures, very little is known about how crowding affects protein folding dynamics at the secondary structure level. In this study, we examined the thermal stability and folding-unfolding kinetics of three small folding motifs (i.e., a 34-residue alpha-helix, a 34-residue cross-linked helix-turn-helix, and a 16-residue beta-hairpin) in the presence of two commonly used crowding agents, Dextran 70 (200 g/L) and Ficoll 70 (200 g/L). We found that these polymers do not induce any appreciable changes in the folding kinetics of the two helical peptides, which is somewhat surprising as the helix-coil transition kinetics have been shown to depend on viscosity. Also to our surprise and in contrast to what has been observed for larger proteins, we found that crowding leads to an appreciable decrease in the folding rate of the shortest beta-hairpin peptide, indicating that besides the excluded volume effect, other factors also need to be considered when evaluating the net effect of crowding on protein folding kinetics. A model considering both the static and the dynamic effects arising from the presence of the crowding agent is proposed to rationalize these results.

Macrocyclic beta-sheet peptides that mimic protein quaternary structure through intermolecular beta-sheet interactions

This paper reports the design, synthesis, and characterization of a family of cyclic peptides that mimic protein quaternary structure through beta-sheet interactions. These peptides are 54-membered-ring macrocycles comprising an extended heptapeptide beta-strand, two Hao beta-strand mimics [JACS 2000, 122, 7654] joined by one additional alpha-amino acid, and two delta-linked ornithine beta-turn mimics [JACS 2003, 125, 876]. Peptide 3a, as the representative of these cyclic peptides, contains a heptapeptide sequence (TSFTYTS) adapted from the dimerization interface of protein NuG2 [PDB ID: 1mio]. 1H NMR studies of aqueous solutions of peptide 3a show a partially folded monomer in slow exchange with a strongly folded oligomer. NOE studies clearly show that the peptide self-associates through edge-to-edge beta-sheet dimerization. Pulsed-field gradient (PFG) NMR diffusion coefficient measurements and analytical ultracentrifugation (AUC) studies establish that the oligomer is a tetramer. Collectively, these experiments suggest a model in which cyclic peptide 3a oligomerizes to form a dimer of beta-sheet dimers. In this tetrameric beta-sheet sandwich, the macrocyclic peptide 3a is folded to form a beta-sheet, the beta-sheet is dimerized through edge-to-edge interactions, and this dimer is further dimerized through hydrophobic face-to-face interactions involving the Phe and Tyr groups. Further studies of peptides 3b-3n, which are homologues of peptide 3a with 1-6 variations in the heptapeptide sequence, elucidate the importance of the heptapeptide sequence in the folding and oligomerization of this family of cyclic peptides. Studies of peptides 3b-3g show that aromatic residues across from Hao improve folding of the peptide, while studies of peptides 3h-3n indicate that hydrophobic residues at positions R3 and R5 of the heptapeptide sequence are important in oligomerization.

Picosecond-time-scale fluctuations of proteins in glassy matrices: the role of viscosity

Through elastic neutron scattering we investigated the fast dynamics of lysozyme in hydrated powder form or embedded in glycerol-water and glucose-water matrices. We calculated the relaxational contribution to the mean square displacements of protein hydrogen atoms. We found that the inverse of this quantity is linearly proportional to the logarithm of the viscosity of the solvent glassy matrix. This relationship suggests a close connection between the picosecond-time-scale dynamics of protein side chains and the solvent structural relaxation.

The effect of water on the rate of conformational change in protein allostery

The influence of solvation on the rate of quaternary structural change is investigated in human hemoglobin, an allosteric protein in which reduced water activity destabilizes the R state relative to T. Nanosecond absorption spectroscopy of the heme Soret band was used to monitor protein relaxation after photodissociation of aqueous HbCO complex under osmotic stress induced by the nonbinding cosolute poly(ethylene glycol) (PEG). Photolysis data were analyzed globally for six exponential time constants and amplitudes as a function of osmotic stress and viscosity. Increases in time constants associated with geminate rebinding, tertiary relaxation, and quaternary relaxation were observed in the presence of PEG, along with a decrease in the fraction of hemes rebinding CO with the slow rate constant characteristic of the T state. An analysis of these results along with those obtained by others for small cosolutes showed that both osmotic stress and solvent viscosity are important determinants of the microscopic R --> T rate constant. The size and direction of the osmotic stress effect suggests that at least nine additional water molecules are required to solvate the allosteric transition state relative to the R-state hydration, implying that the transition state has a greater solvent-exposed area than either end state.

Microscopic viscosity and rotational diffusion of proteins in a macromolecular environment

The Stokes-Einstein-Debye equation is currently used to obtain information on protein size or on local viscosity from the measurement of the rotational correlation time. However, the implicit assumptions of a continuous and homogeneous solvent do not hold either in vivo, because of the high density of macromolecules, or in vitro, where viscosity is adjusted by adding viscous cosolvents of various size. To quantify the consequence of nonhomogeneity, we have measured the rotational Brownian motion of three globular proteins with molecular mass from 66 to 4000 kD in presence of 1.5 to 2000 kD dextrans as viscous cosolvents. Our results indicate that the linear viscosity dependence of the Stokes-Einstein relation must be replaced by a power law to describe the rotational Brownian motion of proteins in a macromolecular environment. The exponent of the power law expresses the fact that the protein experiences only a fraction of the hydrodynamic interactions of macromolecular cosolvents. An explicit expression of the exponent in terms of protein size and cosolvent's mass is obtained, permitting definition of a microscopic viscosity. Experimental data suggest that a similar effective microviscosity should be introduced in Kramers' equation describing protein reaction rates.