Peptide chain dynamics in light and heavy water: zooming in on internal friction

Frictional effects due to the chain itself, rather than the solvent, may have a significant effect on protein dynamics. Experimentally, such "internal friction" has been investigated by studying folding or binding kinetics at varying solvent viscosity; however, the molecular origin of these effects is hard to pinpoint. We consider the kinetics of disordered glycine-serine and α-helix forming alanine peptides and a coarse-grained protein folding model in explicit-solvent molecular dynamics simulations. By varying the solvent mass over more than two orders of magnitude, we alter only the solvent viscosity and not the folding free energy. Folding dynamics at the near-vanishing solvent viscosities accessible by this approach suggests that solvent and internal friction effects are intrinsically entangled. This finding is rationalized by calculation of the polymer end-to-end distance dynamics from a Rouse model that includes internal friction. An analysis of the friction profile along different reaction coordinates, extracted from the simulation data, demonstrates that internal as well as solvent friction varies substantially along the folding pathways and furthermore suggests a connection between friction and the formation of hydrogen bonds upon folding.     

Solvent viscosity dependence of the protein folding dynamics

Solvent viscosity has been frequently adopted as an adjustable parameter in various computational studies (e.g., protein folding simulations) with implicit solvent models. A common approach is to use low viscosities to expedite simulations. While using viscosities lower than that of aqueous is unphysical, such treatment is based on observations that the viscosity affects the kinetics (rates) in a well-defined manner as described by Kramers' theory. Here, we investigate the effect of viscosity on the detailed dynamics (mechanism) of protein folding. On the basis of a simple mathematical model, we first show that viscosity may indeed affect the dynamics in a complex way. By applying the model to the folding of a small protein, we demonstrate that the detailed dynamics is affected rather pronouncedly especially at unphysically low viscosities, cautioning against using such viscosities. In this regard, our model may also serve as a diagnostic tool for validating low-viscosity simulations. It is also suggested that the viscosity dependence can be further exploited to gain information about the protein folding mechanism.     

A limiting speed for protein folding at low solvent viscosity

Because protein folding dynamics are heavily overdamped, Kramers theory predicts the rate of folding to scale inversely with the reaction friction, which is usually interpreted to mean the solvent viscosity. This does not mean, however, that the speed of folding can increase without limit as solvent viscosity decreases. We show that, in a sufficiently fast-folding protein, the folding speed approaches a finite limit at low solvent viscosity, indicating a reaction controlled by internal friction.     

Numerical simulation of the effect of solvent viscosity on the motions of a beta-peptide heptamer

This report examines the effect of a decrease in solvent viscosity on the simulated folding behaviour of a beta-peptide heptamer in methanol. Simulations of the molecular dynamics of the heptamer H-beta3-HVal-beta3-HAla-beta3-HLeu-(S,S)-beta3-HAla(alphaMe)-beta3-HVal-beta3-HAla-beta3-HLeu-OH in methanol, with an explicit representation of the methanol molecules, were performed for 80 ns at various solvent viscosities. The simulations indicate that at a solvent viscosity of one third of that of methanol, only the dynamic aspects of the folding process are altered, and that the rate of folding is increased. At a viscosity of one tenth of that of methanol, insufficient statistics are obtained within the 80 ns period. We suggest that 80 ns is an insufficient time to reach conformational equilibrium at very low viscosity because the dependence of the folding rate of a beta-peptide on solvent viscosity has two regimes; a result that was observed in another computational study for alpha-peptides.     

Numerical Simulation of the Effect of Solvent Viscosity on the Motions of a β‐Peptide Heptamer

This report examines the effect of a decrease in solvent viscosity on the simulated folding behaviour of a β‐peptide heptamer in methanol. Simulations of the molecular dynamics of the heptamer H‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐(S,S)‐β³‐HAla(αMe)‐β³‐HVal‐β³‐HAla‐β³‐HLeu‐OH in methanol, with an explicit representation of the methanol molecules, were performed for 80 ns at various solvent viscosities. The simulations indicate that at a solvent viscosity of one third of that of methanol, only the dynamic aspects of the folding process are altered, and that the rate of folding is increased. At a viscosity of one tenth of that of methanol, insufficient statistics are obtained within the 80 ns period. We suggest that 80 ns is an insufficient time to reach conformational equilibrium at very low viscosity because the dependence of the folding rate of a β‐peptide on solvent viscosity has two regimes; a result that was observed in another computational study for α‐peptides.     

A second generation mesoscopic lipid bilayer model: connections to field-theory descriptions of membranes and nonlocal hydrodynamics

A new mesoscopic membrane model is developed in order to examine long-wavelength structural and dynamical membrane phenomena. Two different explicit mesoscopic solvent models are employed. The first mesoscopic solvent is denoted the big liquid oscillating blob system, which is parametrized to model water at a coarse-grained level and is motivated by a Langevin-like approach; the resulting membrane dynamics predict a solvent viscosity dependence consistent with the known viscosity of water. The second mesoscopic solvent is a Weeks-Chandler-Anderson model. Here, it is found that the correct mesoscopic hydrodynamic scaling of the membrane undulation dynamics is still preserved, although accelerated. When the behavior of the two membranes in close proximity to one another is examined, very little correlated motion is observed. However, the theoretically predicted scaling of the entropic undulation energy is confirmed, demonstrating that the entropic interaction between two membranes becomes increasingly repulsive with decreasing separation.     

A molecular dynamics study of the correlations between solvent-accessible surface, molecular volume, and folding state

We analyzed the correlations between molecular volume, solvent-accessible surface, and folding state (secondary structure content) for unfolded conformers of alpha (holo- and apomyoglobin) and beta (retinal-binding protein) proteins and a small water-soluble alanine-rich alpha-helical peptide. Conformers with different degrees of folding were obtained using molecular dynamics at constant temperature and pressure with implicit solvent (dielectric constant adjustment) for all four systems and with explicit solvent for the single helix peptide. Our results support the view that unfolded conformations are not necessary extended, that volume variation is not a good indication of folding state and that the simple model of water penetrating the interior of the protein does not explain the increase in volume upon unfolding.     

Bimolecular self-reactions of 2-arylindandione- 1,3-yl radicals studied by flash photolysis

Kinetic and thermodynamic data for reaction (1) of certain C-centered aromatic radicals (referred to in this paper by the numbers I to X) in chlorobenzene: have been obtained. The k₁ values of radicals varied between (1.1 ± 0.2) × 10⁶M^?1·sec^?1 (radical VIII) and (3.6 ± 0.7) × 10⁹M^?1 sec^?1 (radical VI) at 20°C. An investigation of the relationship between the recombination rates of radicals I–VIII and X and the solvent viscosity (mixture of toluene and dibutylphthalate, 0.6 < η < 18.4 cP) has shown that the recombination reactions involving radicals I–IV are limited by diffusion in solvents having a viscosity η> 10 cP and are activation reactions in solvents having a viscosity η < 10 cP. The recombination of radicals VIII and IX is an activation reaction, while that of radicals V–VII is diffusion-controlled in the entire viscosity range. The recombination of radical X is limited, in the viscosity range of 18.4 to 2 cP, by intrusion into the first coordination sphere of the partner, the effect of viscosity on the radical X recombination rate in the specified range being the same as its effect on diffusion-controlled reactions. The possible reasons of the discrepancies between the experimental fast recombination rate constants and the theoretical values calculated by the Debye–Smoluchowski theory are discussed. The equilibrium constant depends strongly on the nature of the substituent in the phenyl fragment: the substituents which increase unpaired electron delocalization in the radical intensify the dissociation of the respective dimer. Long-wave absorption bands have been recorded for radicals I–X and their extinction coefficients obtained. Dimers I–V are thermo- and photochromic compounds.     

Fluorescence probe for microenvironments: anomalous viscosity dependence of the fluorescence quantum yield of p-N,N-dialkylaminobenzylidenemalononitrile in 1-alkanols

The effect of solvent viscosity on the fluorescence quantum yield of p-N,N-dialkylaminobenzylidenemalononitrile has been studied in alcoholic solvents with viscosities ranging from 0.55 to 115 cP. The observed effect is shown to be a direct consequence of the molecular rotation of surrounding solvent molecules.     

Site-specific hydration dynamics in the nonpolar core of a molten globule by dynamic nuclear polarization of water

Water-protein interactions play a direct role in protein folding. The chain collapse that accompanies protein folding involves extrusion of water from the nonpolar core. For many proteins, including apomyoglobin (apoMb), hydrophobic interactions drive an initial collapse to an intermediate state before folding to the final structure. However, the debate continues as to whether the core of the collapsed intermediate state is hydrated and, if so, what the dynamic nature of this water is. A key challenge is that protein hydration dynamics is significantly heterogeneous, yet suitable experimental techniques for measuring hydration dynamics with site-specificity are lacking. Here, we introduce Overhauser dynamic nuclear polarization at 0.35 T via site-specific nitroxide spin labels as a unique tool to probe internal and surface protein hydration dynamics with site-specific resolution in the molten globular, native, and unfolded protein states. The (1)H NMR signal enhancement of water carries information about the local dynamics of the solvent within ～10 ? of a spin label. EPR is used synergistically to gain insights on local polarity and mobility of the spin-labeled protein. Several buried and solvent-exposed sites of apoMb are examined, each bearing a covalently bound nitroxide spin label. We find that the nonpoloar core of the apoMb molten globule is hydrated with water bearing significant translational dynamics, only 4-6-fold slower than that of bulk water. The hydration dynamics of the native state is heterogeneous, while the acid-unfolded state bears fast-diffusing hydration water. This study provides a high-resolution glimpse at the folding-dependent nature of protein hydration dynamics.     

Human telomere sequence DNA in water-free and high-viscosity solvents: g-quadruplex folding governed by kramers rate theory

Structures formed by human telomere sequence (HTS) DNA are of interest due to the implication of telomeres in the aging process and cancer. We present studies of HTS DNA folding in an anhydrous, high viscosity deep eutectic solvent (DES) comprised of choline choride and urea. In this solvent, the HTS DNA forms a G-quadruplex with the parallel-stranded ("propeller") fold, consistent with observations that reduced water activity favors the parallel fold, whereas alternative folds are favored at high water activity. Surprisingly, adoption of the parallel structure by HTS DNA in the DES, after thermal denaturation and quick cooling to room temperature, requires several months, as opposed to less than 2 min in an aqueous solution. This extended folding time in the DES is, in part, due to HTS DNA becoming kinetically trapped in a folded state that is apparently not accessed in lower viscosity solvents. A comparison of times required for the G-quadruplex to convert from its aqueous-preferred folded state to its parallel fold also reveals a dependence on solvent viscosity that is consistent with Kramers rate theory, which predicts that diffusion-controlled transitions will slow proportionally with solvent friction. These results provide an enhanced view of a G-quadruplex folding funnel and highlight the necessity to consider solvent viscosity in studies of G-quadruplex formation in vitro and in vivo. Additionally, the solvents and analyses presented here should prove valuable for understanding the folding of many other nucleic acids and potentially have applications in DNA-based nanotechnology where time-dependent structures are desired.     

Foldamer simulations: novel computational methods and applications to poly-phenylacetylene oligomers

We apply several methods to probe the ensemble kinetic and structural properties of a model system of poly-phenylacetylene (pPA) oligomer folding trajectories. The kinetic methods employed included a brute force accounting of conformations, a Markovian state matrix method, and a nonlinear least squares fit to a minimalist kinetic model used to extract the folding time. Each method gave similar measures for the folding time of the 12-mer chain, calculated to be on the order of 7 ns for the complete folding of the chain from an extended conformation. Utilizing both a linear and a nonlinear scaling relationship between the viscosity and the folding time to correct for a low simulation viscosity, we obtain an upper and a lower bound for the approximate folding time within the range 70 ns相似文献   

Solvation dynamics of a protein in the pre molten globule state

The nature of solvent molecules around proteins in native and different non-native states is crucial for understanding the protein folding problem. We have characterized two compact denatured states of glutaminyl-tRNA synthetase (GlnRS) under equilibrium conditions in the presence of a naturally occurring osmolyte, l-glutamate. The solvation dynamics of the compact denatured states and the fully unfolded state has been studied using a covalently attached probe, acrylodan, near the active site. The solvation dynamics progressively becomes faster as the protein goes from the native to the molten globule to the pre molten globule to the fully unfolded state. Anisotropy decay measurements suggest that the pre-molten-globule intermediate is more flexible than the molten globule although the secondary structure is largely similar. Dynamic light scattering studies reveal that both the compact denatured states are aggregated under the measurement conditions. The implications of solvation dynamics in aggregated compact denatured states have been discussed.     

Concepts and misconcepts in the analysis of simple kinetics of protein folding

Unusually simple two-state kinetics characterizes the folding of a number of small proteins possessing a variety secondary structures. This limits dramatically the number of experimentally resolvable parameters that may characterize this process and also suggests the possibility to describe it based on simple theories borrowed from the field of ordinary chemical reactions. An attempt is made to critically evaluate the basic concepts, which are in the background of this approach. We demonstrate their limitations, which may cast doubt on the interpretation of experimental data. It is shown also that, in contrast to provisions of transition state theory, the simple kinetics of protein folding does not correlate with folded state stability or with the size of the folding unit. Moreover, the folding kinetics exhibits anomalous dependence on temperature and pressure and surprisingly strong dependence on solvent viscosity. The possible role in folding of fluctuations, relaxations and gradient dynamics is discussed. Being overlooked or underestimated, these mechanisms may determine the rate and specificity of the process.     

Diffusive dynamics on multidimensional rough free energy surfaces

The dynamics of processes relevant to chemistry and biophysics on rough free energy landscapes is investigated using a recently developed algorithm to solve the Smoluchowski equation. Two different processes are considered: ligand rebinding in MbCO and protein folding. For the rebinding dynamics of carbon monoxide (CO) to native myoglobin (Mb) from locations around the active site, the two-dimensional free energy surface (FES) is constructed using extensive molecular dynamics simulations. The surface describes the minima in the A state (bound MbCO), CO in the distal pocket and in the Xe4 pocket, and the transitions between these states and allows to study the diffusion of CO in detail. For the folding dynamics of protein G, a previously determined two-dimensional FES was available. To follow the diffusive dynamics on these rough free energy surfaces, the Smoluchowski equation is solved using the recently developed hierarchical discrete approximation method. From the relaxation of the initial nonequilibrium distribution, experimentally accessible quantities such as the rebinding time for CO or the folding time for protein G can be calculated. It is found that the free energy barrier for CO in the Xe4 pocket and in the distal pocket (B state) closer to the heme iron is approximately 6 kcal/mol which is considerably larger than the inner barrier which separates the bound state and the B state. For the folding of protein G, a barrier of approximately 10 kcal/mol between the unfolded and the folded state is consistent with folding times of the order of milliseconds.     

The Trp cage: folding kinetics and unfolded state topology via molecular dynamics simulations

Using over 75 mus of molecular dynamics simulation, we have generated several thousand folding simulations of the 20-residue Trp cage at experimental temperature and solvent viscosity. A total of 116 independent folding simulations reach RMSDcalpha values below 3 A RMSDcalpha, some as close as 1.4 A RMSDcalpha. We estimate a folding time of 5.5+/-3.5 mus, a rate that is in reasonable agreement with experimental kinetics. Finally, we characterize both the folded and unfolded ensemble under native conditions and note that the average topology of the unfolded ensemble is very similar to the topology of the native state.     

Viscosity dependence of the kinetic parameters of the radical ion pair in homogeneous solution determined by optically detected X- and ku-band electron spin resonance

We investigated the dynamics of the radical ion pairs formed by photoinduced electron-transfer reaction from zinc tetraphenyl porphyrin to 2-methyl-1,4-naphthoquinone in mixtures of 2-propanol and cyclohexanol. By the irradiation of a resonant X- (9.16 GHz) or Ku-band (17.41 GHz) microwave pulse, the time profiles of the transient absorptions was modified and the yields of escaping radical ions decreased. From these experiments, we determined the kinetic parameters of the radical ion pairs at various solvent viscosities. The recombination rates of the singlet pairs were (4 +/- 4), (8 +/- 3), and (16 +/- 3) x 10(6) s(-1) at 5, 10, and 15 cP, respectively. The escape rates were (1.7 +/- 0.2), (1.4 +/- 0.1), and (0.9 +/- 0.2) x 10(6) s(-1) at 5, 10, and 15 cP, respectively. The viscosity dependence of the kinetic parameters was followed by the simple continuum diffusion model.     

Conformational dependence of hemoglobin reactivity under high viscosity conditions: the role of solvent slaved dynamics

The concept of protein dynamic states is introduced. This concept is based on (i) protein dynamics being organized hierarchically with respect to solvent slaving and (ii) which tier of dynamics is operative over the time window of a given measurement. The protein dynamic state concept is used to analyze the kinetic phases derived from the recombination of carbon monoxide to sol-gel-encapsulated human adult hemoglobin (HbA) and select recombinant mutants. The temperature-dependent measurements are made under very high viscosity conditions obtained by bathing the samples in an excess of glycerol. The results are consistent with a given tier of solvent slaved dynamics becoming operative at a time delay (with respect to the onset of the measurement) that is primarily solvent- and temperature-dependent. However, the functional consequences of the dynamics are protein- and conformation-specific. The kinetic traces from both equilibrium populations and trapped allosteric intermediates show a consistent progression that exposes the role of both conformation and hydration in the control of reactivity. Iron-zinc symmetric hybrid forms of HbA are used to show the dramatic difference between the kinetic patterns for T state alpha and beta subunits. The overall results support a model for allostery in HbA in which the ligand-binding-induced transition from the deoxy T state to the high -affinity R state proceeds through a progression of T state intermediates.     

Synthesis of Low‐Viscosity Ionic Liquids for Application in Dye‐Sensitized Solar Cells

Two types of ionic liquids (ILs), 1‐(3‐hexenyl)‐3‐methyl imidazolium iodide and 1‐(3‐butenyl)‐3‐methyl imidazolium iodide, are synthesized by introducing an unsaturated bond into the side alkyl chain of the imidazolium cation. These new ionic liquids exhibit high thermal stability and low viscosity (104 cP and 80 cP, respectively). The molecular dynamics simulation shows that the double bond introduced in the alkane chain greatly changes the molecular system space arrangement and diminishes the packing efficiency, leading to low viscosity. The low viscosity of the synthesized ionic liquids would enhance the diffusion of redox couples. This enhancement is detected by fabricating dye‐sensitized solar cells (DSSCs) with electrolytes containing the two ILs and I₂. The highest efficiency of DSSCs is 6.85 % for 1‐(3‐hexenyl)‐3‐methyl imidazolium iodide and 5.93 % for 1‐(3‐butenyl)‐3‐methyl imidazolium iodide electrolyte, which is much higher than that of 5.17 % with the counterpart 1‐hexyl‐3‐methyl imidazolium iodide electrolyte.