Dielectric relaxation in an enzyme active site: molecular dynamics simulations interpreted with a macroscopic continuum model.

Dielectric relaxation plays an important role in many chemical processes in proteins, including acid-base titration, ligand binding, and charge transfer reactions. Its complexity makes experimental characterization difficult, and so, theoretical approaches are valuable. The comparison of molecular dynamics free energy simulations with simpler models such as a dielectric continuum model is especially useful for obtaining qualitative insights. We have analyzed a charge insertion process that models deprotonation or mutation of an important side chain in the active site of the enzyme aspartyl-tRNA synthetase. Complexes with the substrate aspartate and the analogue asparagine were studied. The resulting dielectric relaxation was found to involve both ligand and side chain rearrangements in the active site and to account for a large part of the overall charging free energy. With the continuum model, charge insertion is performed along a two-step pathway: insertion into a static environment, followed by relaxation of the environment. These correspond to different physical processes and require different protein dielectric constants. A low value of approximately 1 is needed for the static step, consistent with the parametrization of the molecular mechanics charge set used. A value of 3-6 (depending on the exact insertion site and the nature of the ligand) is needed to describe the dielectric relaxation step. This moderate value indicates that, for this system, the local protein polarizability in the active site is within at most a factor of 2 of that expected at nonspecific positions in a protein interior.     

Freezing of low energy excitations in charge density wave glasses

Thermally stimulated discharge current measurements were performed to study slow relaxation processes in two canonical charge density wave systems K(0.3)MoO(3) and o-TaS(3). Two relaxation processes were observed and characterized in each system, corroborating the results of dielectric spectroscopy. Our results are consistent with the scenario of the glass transition on the charge density wave superstructure level. In particular, the results directly prove the previously proposed criterion of charge density wave freezing based on the interplay of charge density wave pinning by impurities and screening by free carriers. In addition, we obtained new information on distribution of relaxation parameters, as well as on nonlinear dielectric response both below and above the threshold field for charge density wave sliding.     

Molecular motion and relaxation studies of aliphatic polyureas by thermal windowing thermally stimulated depolarization current technique

Molecular motion and relaxation studies using a thermal windowing thermally stimulated depolarization current (TW‐TSDC) were performed for aliphatic polyureas 7 and 9. Global thermally stimulated depolarization current gave three characteristic major peaks corresponding to the α, β, and γ relaxation modes at 78.5, −44, and −136°C for polyurea 7 and at 80, −50, and −134°C for polyurea 9, respectively. The α relaxation is related to the large‐scale molecular motion due to micro‐Brownian motion of long‐range segments. This relaxation is significantly related to the glass‐transition temperature. The β relaxation is caused by the local thermal motion of long‐chain segments. The γ relaxation is caused by the limited local motion of hydrocarbon sections. Temperature dependence of relaxation times was expressed well using Vogel–Tammann–Fulcher (VTF) expression. 3‐D simulation of dielectric constants of dielectric strength and loss factor were performed in the frequency range from 10⁻⁶ to 10⁴ Hz and temperature range from −150 to 250°C, using the relaxation parameters obtained from the TW‐TSDC method. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 88–94, 2000     

Molecular dynamics in ion‐irradiated poly(ether ether ketone) investigated by two‐dimensional correlation dielectric relaxation spectroscopy

This paper reports the first use of temperature–temperature 2D correlation dielectric relaxation spectroscopy (2D COS‐DRS) to study the molecular relaxation dynamics in ion‐irradiated poly(ether ether ketone) (PEEK). With the help of the high resolution and high sensitivity of 2D COS‐DRS, it was possible to locate the position of the motion of water molecules in the dielectric spectrum of PEEK. This occurred at −20°C and increased in intensity on increasing water contents. On irradiation, a new relaxation was observed at −75°C and −85°C for proton and helium ion‐irradiated samples, respectively. This increased in intensity on increasing radiation dose and was assigned to main‐chain phenyl motions of the cross‐linked units of the polymer. 2D COS‐DRS was also successfully applied to resolve the overlap in molecular events in the region of glass transition. Three processes that change in different directions with respect to ion irradiation dose were identified. These were at 160°C, 175°C, and 240°C and were assigned to the α relaxation, second α relaxation, and the onset of conductivity, respectively. In addition, hybrid 2D COS‐DRS was used to investigate the effect of the so‐called linear energy transfer effect, and the results showed that helium ions were more effective in cross‐linking PEEK. Copyright © 2013 John Wiley & Sons, Ltd.     

Biocatalytic Intramolecular C−H aminations via Engineered Heme Proteins: Full Reaction Pathways and Axial Ligand Effects

Engineered heme protein biocatalysts provide an efficient and sustainable approach to develop amine-containing compounds through C−H amination. A quantum chemical study to reveal the complete heme catalyzed intramolecular C−H amination pathway and protein axial ligand effect was reported, using reactions of an experimentally used arylsulfonylazide with hemes containing L=none, SH⁻, MeO⁻, and MeOH to simulate no axial ligand, negatively charged Cys and Ser ligands, and a neutral ligand for comparison. Nitrene formation was found as the overall rate-determining step (RDS) and the catalyst with Ser ligand has the best reactivity, consistent with experimental reports. Both RDS and non-RDS (nitrene transfer) transition states follow the barrier trend of MeO⁻<SH⁻<MeOH<None due to the charge donation capability of the axial ligand to influence the key charge transfer process as the electronic driving forces. Results also provide new ideas for future biocatalyst design with enhanced reactivities.     

Dehydration-induced structural relaxation effects in poly(methyl methacrylate)

The Thermally Stimulated Depolarization (TSD) dielectric technique and Dielectric Relaxation Spectroscopy (DRS) have been used in order to investigate aging phenomena in poly(methyl methacrylate) (PMMA). Earlier TSD studies on amorphous PMMA report peculiar dielectric relaxation signals within the range of the glass transition (at ∼378 K) and the secondary relaxation (∼230 K). In the present study, an intense TSD current relaxation band maximizing around 310 K is tentatively attributed to the molecular mobility due to a residual free volume below the glass transition temperature, T_g, that allows structural recovery at the free volume released from the desorption of H₂O molecules during evacuation. Limited motions in the main backbone provoke dipole (re)orientation of the ester carbonyl pendant groups with an activation energy E=0.85±0.05 eV, being responsible for the latter dielectric relaxation effect. Alternative attributions based on the short-range jump relaxation of electric charges and boundary effects are also discussed.     

Temperature Dependent Dielectric Relaxation in Solvent Mixtures at Microwave Frequencies

By the use of time domain reflectometry method, dielectric measurements were carried out on dimethylformamide‐2‐nitrotoluene solvent mixtures in the frequency range 10 MHz‐20 GHz, at various temperatures from 15 °C to 45 °C. These solvent mixtures as well as pure solvents display a Debye type dispersion. Their frequency dependent dielectric properties can be summarized by the three parameters in the Debye equation: a static permittivity, permittivity at high frequency and a dielectric relaxation time constant. The free energy of activation for dipolar relaxation process and the Kirkwood correlation factor were determined using these fitting parameters for these solvent mixtures at various concentrations and temperatures. By using these dielectric parameters, the excess permittivity and excess inverse relaxation time is obtained. The excess permittivity is found to be positive for all concentrations and temperatures whereas the excess inverse relaxation time is negative.     

Molecular dynamics study on the solvent dependent heme cooling following ligand photolysis in carbonmonoxy myoglobin

The time scale and mechanism of vibrational energy relaxation of the heme moiety in myoglobin was studied using molecular dynamics simulation. Five different solvent models, including normal water, heavy water, normal glycerol, deuterated glycerol and a nonpolar solvent, and two forms of the heme, one native and one lacking acidic side chains, were studied. Structural alteration of the protein was observed in native myoglobin glycerol solution and native myoglobin water solution. The single-exponential decay of the excess kinetic energy of the heme following ligand photolysis was observed in all systems studied. The relaxation rate depends on the solvent used. However, this dependence cannot be explained using bulk transport properties of the solvent including macroscopic thermal diffusion. The rate and mechanism of heme cooling depends upon the detailed microscopic interaction between the heme and solvent. Three intermolecular energy transfer mechanisms were considered: (i) energy transfer mediated by hydrogen bonds, (ii) direct vibration-vibration energy transfer via resonant interaction, and (iii) energy transfer via vibration-translation or vibration-rotation interaction, or in other words, thermal collision. The hydrogen bond interaction and vibration-vibration interaction between the heme and solvent molecules dominates the energy transfer in native myoglobin aqueous solution and native myoglobin glycerol solutions. For modified myoglobin, the vibration-vibration interaction is also effective in glycerol solution, different from aqueous solution. Thermal collisions form the dominant energy transfer pathway for modified myoglobin in water solution, and for both native myoglobin and modified myoglobin in a nonpolar environment. For native myoglobin in a nonpolar solvent solution, hydrogen bonds between heme isopropionate side chains and nearby protein residues, absent in the modified myoglobin nonpolar solvent solution, are key interactions influencing the relaxation pathways.     

Relaxation behavior of acrylate and methacrylate polymers containing dioxacyclopentane rings in the side chains

The synthesis of poly[(2,2‐dimethyl‐1,3‐dioxolan‐4‐yl) methyl acrylate)] (PACGA) and poly[(2,2‐dimethyl‐1,3‐dioxolan‐4‐yl) methyl methacrylate] (PMCGA) is reported. Both polymers present dielectric and mechanical β subglass absorptions at −128 and −115 °C, respectively, at 1 Hz, followed by ostensible glass–rubber or α relaxations centered in the vicinity of 0 and 67 °C, respectively, at the same frequency. The values of the activation energy of both the mechanical and dielectric β absorptions lie in the vicinity of 10 kcal mol⁻¹. The critical interpretation of the relaxation behavior of PMCGA suggests that dipolar intramolecular correlations play a dominant role in the response of the polymer to an electric field. The subglass relaxations of PACGA and PMCGA are further compared with the relaxation behavior of poly(1,3‐dioxane acrylate), poly(1,3‐dioxane methacrylate), and other polymers in the glassy state. The strong conductive processes observed in PMCGA at low frequencies and high temperatures were studied under the assumption that that these processes arise from Maxwell–Wagner–Sillars effects occurring in the bulk combined with Nernst–Planckian electrodynamic effects caused by interfacial polarization in the films. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 286–299, 2001     

Influence of oxycycloaliphatic groups in the relaxation behavior of acrylic polymers

A comparative study on the mechanical and dielectric relaxation behavior of poly(5‐acryloxymethyl‐5‐methyl‐1,3‐dioxacyclohexane) (PAMMD), poly(5‐acryloxymethyl‐5‐ethyl‐1,3‐dioxacyclohexane) (PAMED), and poly(5‐methacryloxymethyl‐5‐ethyl‐1,3‐dioxacyclohexane) (PMAMED) is reported. The isochrones representing the mechanical and dielectric losses present prominent mechanical and dielectric β relaxations located at nearly the same temperature, approximately −80°C at 1 Hz, followed by ostensible glass–rubber or α relaxations centered in the neighborhood of 27, 30, and 125°C for PAMMD, PAMED, and PMAMED, respectively, at the same frequency. The values of the activation energy of the β dielectric relaxations of these polymers lie in the vicinity of 10 kcal mol⁻¹, ∼ 2 kcal mol⁻¹ lower than those corresponding to the mechanical relaxations. As usual, the temperature dependence of the mean‐relaxation times associated with both the dielectric and mechanical α relaxations is described by the Vogel–Fulcher–Tammann–Hesse (VFTH) equation. The dielectric relaxation spectra of PAMED and PAMMD present in the frequency domain, at temperatures slightly higher than T_g, the α and β relaxations at low and high frequencies, respectively. The high conductive contributions to the α relaxation of PMAMED preclude the possibility of isolating the dipolar component of this relaxation in this polymer. Attempts are made to estimate the temperature at which the α and β absorptions merge together to form the αβ relaxation in PAMMD and PAMED. Molecular Dynamics (MD) results, together with a comparative analysis of the spectra of several polymers, lead to the conclusion that flipping motions of the 1,3‐dioxacyclohexane ring may not be exclusively responsible for the β‐prominent relaxations that polymers containing dioxane and cyclohexane pendant groups in their structure present, as it is often assumed. The diffusion coefficient of ionic species, responsible for the high conductivity exhibited by these polymers in the α relaxation, is semiquantitatively calculated using a theory that assumes that this process arises from MWS effects, taking place in the bulk, combined with Nernst–Planckian electrodynamic effects, due to interfacial polarization in the films. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2486–2498, 1999     

Free energy of charge transfer and intraprotein electric field: method of calculation depends on the charge state of protein at a given structure.

Free energy of charge transfer presents a basic characteristic of reactions such as protonation, oxido-reduction and similar. Evaluation of this quantity requires calculation of charging energy. Proteins are structured dielectrics, and a consistent incorporation of their structure into calculation of intraprotein electric field results in expression for charging energy of an active group in protein, which is essentially different from that for a simple dielectric. An algorithm for semi-continuum calculation of relevant free energies is described. First of the two components of charging energy in protein, energy of the medium response to charge redistribution in reactants, should be always calculated as the charging energy by the charge redistribution using the static dielectric constant of protein. The second term is interaction energy of the charge redistribution with the 'frozen' electric field of the system before reaction. Charges of protein groups, at which the protein structure has been determined, are often different from those before reaction of charge transfer, so is the corresponding intraprotein field. The field is expressed through either both the optical and static dielectric constants of protein or only optical one depending on whether the charges of protein groups before reaction and upon structural analysis are the same or not. Proper allowance for difference in charges of reacting groups before reaction and upon structural analysis of protein is thermodynamically necessary and quantitatively important. The expression for activation free energy for charge transfer in proteins is derived in the form presenting explicitly an invariant contribution of protein structure.     

On the dielectric glass relaxation process of polymers: Ball-like labels in polystyrene

Ball-like molecules with strong dipoles (labels) were mixed with technical polystyrene (PS168N) in low concentrations (<0.5% wt) and measured dielectrically in the frequency range 10^–2–10⁷ Hz, and the temperature range 100°–135°C (glass relaxation region). The measurements showed that these ball-like molecules relax cooperatively with the polymeric segments with relaxation times lying at the high-frequency tail of the glass process. The activation energy of the main label process is found to be very similar to that of the glass process of the polystyrene segments and also has the same temperature dependence. This finding implies the existence of an additional mode of relaxation in the dielectric spectrum of the glass process of polystyrene (compared to polyisoprene). Considering the different behavior of the ball-like molecules in polystyrene and polyisoprene and the temperature dependence of the half-width of dielectric loss peak in different polymers, we suggest that the polymers could be classified into three classes according to the available dielectric relaxation modes in the glass process. In addition, the label molecules showed a high-frequency local relaxation process. The relaxation strength ratio of the local process (X _local) to the total relaxation strength of the label was found to be dependent on the volume of the label. This phenomenon could supply a new method for the determination of the mean size of the holes (voids) representing the free volume of the host matrix.     

Ultrafast Vibrational Dynamics of Membrane‐Bound Peptides at the Lipid Bilayer/Water Interface

Vibrational energy transfer (VET) of proteins at cell membrane plays critical roles in controlling the protein functionalities, but its detection is very challenging. By using a surface‐sensitive femtosecond time‐resolved sum‐frequency generation vibrational spectroscopy with infrared pump, the detection of the ultrafast VET in proteins at cell membrane has finally become possible. The vibrational relaxation time of the N−H groups is determined to be 1.70(±0.05) ps for the α‐helix located in the hydrophobic core of the lipid bilayer and 0.9(±0.05) ps for the membrane‐bound β‐sheet structure. The N−H groups with strong hydrogen bonding gain faster relaxation time. By pumping the amide A band and probing amide I band, the vibrational relaxation from N−H mode to C=O mode through two pathways (direct coupling and through intermediate states) is revealed. The ratio of the pathways depends on the NH⋅⋅⋅O=C hydrogen‐bonding strength. Strong hydrogen bonding favors the coupling through intermediate states.     

Competition between protein ligands and cytoplasmic inorganic anions for the metal cation: a DFT/CDM study

Many of the essential metalloproteins are located in the cell, whose cytoplasmic fluid contains several small inorganic anions, such as Cl-, NO2-, NO3-, H2PO4-, and SO4(2-), that play an indispensable role in determining the cell's volume, regulating the cell's pH, signal transduction, muscle contraction, as well as cell growth and metabolism. However, the physical principles governing the competition between these abundant, intracellular anions and protein or nucleic acid residues in binding to cytoplasmic metal cations such as Na+, K+, Mg2+, and Ca2+ are not well understood; hence, we have delineated the physicochemical basis for this competition using density functional theory in conjunction with the continuum dielectric method. The results show that the metal cation can bind to its target protein against a high background concentration of inorganic anions because (i) desolvating a negatively charged Asp/Glu carboxylate in a protein cavity costs much less than desolvating an inorganic anion in aqueous solution and (ii) the metal-binding site acts as a polydentate ligand that uses all its ligating entities to bind the metal cation either directly or indirectly. The results also show that the absolute hydration free energy of the "alien" anion as well as the net charge and relative solvent exposure of the metal-binding protein cavity are the key factors governing the competition between protein and inorganic ligands for a given cytoplasmic metal cation. Increasing the net negative charge of the protein cavity, while decreasing the number of available amide groups for metal binding, protects the metal-bound ligands from being dislodged by cellular anions, thus revealing a "protective" role for carboxylate groups in a protein cavity, in addition to their role in high affinity metal-binding.     

Dielectric relaxation spectroscopy in poly(ethylene oxide)/water systems

The dielectric properties of poly(ethylene oxide) (PEO) are studied by dielectric relaxation spectroscopy measurements in wide ranges of frequency (5–2×10⁹ Hz) and temperature (193 − 300 K). PEO/water systems are also studied in a wide range of water content h (0 − 0.85 grams of water per grams of dry PEO). The measurements allow to distinguish between the dipolar secondary mechanism γ and effects related to free charge motion. The data are analyzed within the formalisms of permittivity, ϵ*, and electric modulus, M*. The water has been found to plasticize the dipolar process and to affect strongly the conduction process. A critical water content h_c, h_c = 0.13, has been found for the mechanism of charge transport.     

WATsite: Hydration site prediction program with PyMOL interface

Water molecules that mediate protein–ligand interactions or are released from the binding site on ligand binding can contribute both enthalpically and entropically to the free energy of ligand binding. To elucidate the thermodynamic profile of individual water molecules and their potential contribution to ligand binding, a hydration site analysis program WATsite was developed together with an easy‐to‐use graphical user interface based on PyMOL. WATsite identifies hydration sites from a molecular dynamics simulation trajectory with explicit water molecules. The free energy profile of each hydration site is estimated by computing the enthalpy and entropy of the water molecule occupying a hydration site throughout the simulation. The results of the hydration site analysis can be displayed in PyMOL. A key feature of WATsite is that it is able to estimate the protein desolvation free energy for any user specified ligand. The WATsite program and its PyMOL plugin are available free of charge from http://people.pnhs.purdue.edu/~mlill/software . © 2014 Wiley Periodicals, Inc.     

Dielectric relaxation and AC conductivity of modified polysulfones with chelating groups

The frequency-dependent dielectric properties and conductivity of partially quaternized polysulfones, quaternized polysulfones containing chelating groups, and chelated quaternized polysulfones with Cu²⁺ have been studied. The permittivity has low values and is dependent on the chemical characteristic of samples, in relation with the charge transfer complex and free volume and, consequently, with packing of the polymer chains and of the polarizable groups per volume units. At temperatures below 150 °C, all polysulfone films develop two relaxation processes, i.e., γ and β relaxation, involving different enthalpy and entropy contributions induced by their chemical structures. Frequency–temperature-dependent conductivity showed that conductivity increased with frequency, while the values of thermal activation energy of electrical conduction, lower that 1, suggest that a model based on energy bandgap representation could be suitable for explaining the temperature influence on AC conductivity for all samples. In addition, enhancement of mobility of the charge carrier upon complexation was observed for chelated quaternized polysulfones with Cu²⁺. All these typical semiconducting properties recommend the studied polymers as potential candidates for use in various applications in electrotechnical industry.     

Temperature-dependent studies of NO recombination to heme and heme proteins

The rebinding kinetics of NO to the heme iron of myoglobin (Mb) is investigated as a function of temperature. Below 200 K, the transition-state enthalpy barrier associated with the fastest (approximately 10 ps) recombination phase is found to be zero and a slower geminate phase (approximately 200 ps) reveals a small enthalpic barrier (approximately 3 +/- 1 kJ/mol). Both of the kinetic rates slow slightly in the myoglobin (Mb) samples above 200 K, suggesting that a small amount of protein relaxation takes place above the solvent glass transition. When the temperature dependence of the NO recombination in Mb is studied under conditions where the distal pocket is mutated (e.g., V68W), the rebinding kinetics lack the slow phase. This is consistent with a mechanism where the slower (approximately 200 ps) kinetic phase involves transitions of the NO ligand into the distal heme pocket from a more distant site (e.g., in or near the Xe4 cavity). Comparison of the temperature-dependent NO rebinding kinetics of native Mb with that of the bare heme (PPIX) in glycerol reveals that the fast (enthalpically barrierless) NO rebinding process observed below 200 K is independent of the presence or absence of the proximal histidine ligand. In contrast, the slowing of the kinetic rates above 200 K in MbNO disappears in the absence of the protein. Generally, the data indicate that, in contrast to CO, the NO ligand binds to the heme iron through a "harpoon" mechanism where the heme iron out-of-plane conformation presents a negligible enthalpic barrier to NO rebinding. These observations strongly support a previous analysis (Srajer et al. J. Am. Chem. Soc. 1988, 110, 6656-6670) that primarily attributes the low-temperature stretched exponential rebinding of MbCO to a quenched distribution of heme geometries. A simple model, consistent with this prior analysis, is presented that explains a variety of MbNO rebinding experiments, including the dependence of the kinetic amplitudes on the pump photon energy.     

Effect of side-chain length on charge mobilities in neutral poly(3-alkylthiophene)s: Determination from dielectric measurement

For neutral poly(3-alkylthiophene)s (P3ATs), the electric modulus formalism of dielectric relaxation measurement together with the use of nonexponential decay function can be applied to describe the behavior of conductivity relaxation and carrier transport. The charge mobilities of neutral P3ATs calculated from conductivity relaxation with the use of the defect-diffusion model are in agreement with the data from field-effect transistor measurement. The temperature dependence of charge mobility exhibits a local maximum right after the end of glass transition region, which can be attributed to the transition of soft conformons in the disordered phase to localized conformons. The charge mobilities and activation energies of mobilities for P3ATs are dependent on conjugation length and volume fraction of conducting units. © 1994 John Wiley & Sons, Inc.     

Ultrafast Heme Dynamics of Ferric Cytochrome c in Different Environments: Electronic,Vibrational, and Conformational Relaxation

The excited‐state dynamics of ferric cytochrome c (Cyt c), an important electron‐transfer heme protein, in acidic to alkaline medium and in its unfolded form are investigated by using femtosecond pump–probe spectroscopy, exciting the heme and Tryptophan (Trp) to understand the electronic, vibrational, and conformational relaxation of the heme. At 390 nm excitation, the electronic relaxation of heme is found to be ≈150 fs at different pH values, increasing to 480 fs in the unfolded form. Multistep vibrational relaxation dynamics of the heme, including fast and slow processes, are observed at pH 7. However, in the unfolded form and at pH 2 and 11, fast phases of vibrational relaxation dominate, revealing the energy dissipation occurring through the covalent bond interaction between the heme and the nearest amino acids. A significant shortening of the excited‐state lifetime of Trp is observed at various pH values at 280 nm excitation due to resonance energy transfer to the heme. The longer time constant (25 ps) observed in the unfolded form is attributed to a complete global conformational relaxation of Cyt c.