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The conformation response of calf thymus DNA and β-lactoglobulin (BLG) to solvent conditions altered by varying amounts of ethanol (EtOH) and tert-butanol (TBA) has been monitored by viscosimetry and circular dichroism measurements. A correlation between the effects of EtOH and TBA on DNA condensation and BLG denaturation clearly appears from the data, suggesting that a similar molecular mechanism is responsible for the alcohol effects on these two very different systems and processes. These alcohol-induced transitions appear in the concentration range (alcohol mole fraction X = 0.22 and X = 0.07 for EtOH and TBA, respectively) where changes in the association state of the alcohol molecule occur (see compressibility and IR data).

Photon correlation spectroscopy and circular dichroism have been used to study the role of hydration in the structure and thermostability of the model protein lysozyme in water-glycerol mixtures. Two cases have been considered: water-rich and glycerol-rich regimes of concentrations. We follow the thermal denaturation both by optical spectral changes and hydrodynamic radius variations. This methodology allows us to emphasize the relevant role played by hydrophobic interactions during the process in aqueous solutions and, in glycerol, to distinguish the non-cooperative melting of secondary structure, supporting the view of a protein transition to a molten globule-like state.

The influence of methanol on the activity, stability and internal dynamics of myoglobin (Mb) has been investigated to obtain information about the effect of alcohol on protein behaviour. Spectroscopic investigations show that there are no significant changes in conformational structures of the protein within the range of alcohol concentrations where the catalytic activity ( k cat ) and thermal stability ( T m ) of Mb decrease. Neutron scattering measurements indicate that the characteristic times related to protein internal fluctuations increase when the methanol molar fraction in the mixtures increases. This suggests a direct relationship between the protein internal motion rate and the catalytic activity.

A recent neutron scattering investigation on lysozyme embedded in glycerol–water mixtures has shown that solvent dynamics is crucial in determining the dynamical properties of the biomolecule itself (Biophys. J. 83 (2002) 1157). To better understand the role played by solvent, we have performed an elastic incoherent neutron scattering (INS) experiment as a function of the temperature on pure glycerol. To directly compare the dynamics of the solvated protein and that of the pure solvent, we settled the same experimental conditions and applied the same data analysis procedure as in Paciaroni et al. (Biophys. J. 83 (2002) 1157). By using a double-well model and taking into account for the global molecular diffusion, we exploited the measured intensity to estimate the mean square displacements (MSD) of glycerol hydrogen atoms. We found that the total MSD deviate from the low-temperature vibrational harmonic trend at approximately T =235 K, consistent with the value of the critical temperature reported in literature (Phys. Rev. E 55 (1997) 3183). The present investigation suggests that the internal dynamics of glycerol molecules, i.e. the vibrations and reorientations of hydrogen atoms relative to the molecular centre of mass (c.o.m.), can be put in relationship with the protein dynamics.

We performed an inelastic and quasielastic neutron scattering investigation of the molecular dynamics of lysozyme solvated in glycerol, at different water contents h (g water/g lysozyme). At low temperature, dry lysozyme solvated with glycerol shows a low-frequency vibrational bump located at around 4 meV. Contrary to the behaviour of strongly hydrated protein powders, this peak is well visible also at room temperature and persists in the experimental spectra at all the hydration degrees. The quasielastic contribution increases remarkably with h, thus suggesting that water molecules perform their plasticizing action by allowing the onset of confined diffusive motions of protein groups. The quasielastic signal could be decomposed in two Lorentzian components, representing motions with characteristic times of, respectively, 15 and 0.8 ps. The Lorentzian curves exhibit constant widths but variable intensities as a function of the hydration degree. The trend of the estimated quasielastic structure factors suggests that a preferential hydration effect may take place in lysozyme solvated with glycerol and water.

We performed an elastic neutron scattering investigation of the molecular dynamics of lysozyme solvated in glycerol, at different water contents h (grams of water/grams of lysozyme). The marked non-Gaussian behavior of the elastic intensity was studied in a wide experimental momentum transfer range, as a function of the temperature. The internal dynamics is well described in terms of the double-well jump model. At low temperature, the protein total mean square displacements exhibit an almost linear harmonic trend irrespective of the hydration level, whereas at the temperature T(d) a clear changeover toward an anharmonic regime marks a protein dynamical transition. The decrease of T(d) from approximately 238 K to approximately 195 K as a function of h is reminiscent of that found in the glass transition temperature of aqueous solutions of glycerol, thus suggesting that the protein internal dynamics as a whole is slave to the environment properties. Both T(d) and the total mean square displacements indicate that the protein flexibility strongly rises between 0.1 and 0.2h. This hydration-dependent dynamical activation, which is similar to that of hydrated lysozyme powders, is related to the specific interplay of the protein with the surrounding water and glycerol molecules.

A highly sensitive scanning microcalorimeter and a low scanning rate (0.1 K/min) has been used to determine the thermodynamic properties of the main phase transition of distearoylphosphatidylcholine (DSPC) in presence of ethanol in the 0–0.20 ethanol mole fraction (x2) range. These measurements revealed previously unreported features of DSPC/water/ethanol phase behavior and visualized distinct changes in the main phase transition mechanism induced by addition of ethanol. It is found that the well known interdigitated phase in DSPC induced by ethanol above x2 =0.01 abruptly disappears at x2 =0.12. The abrupt change in the DSPC phase behavior at x2 = 0.12 shows some analogies with the observed one relative to the conformation response of DNA molecule to solvent condition altered by varying amounts of ethanol. As inferred from previous adiabatic compressibility and IR data in water/ethanol mixtures, a correlation between changes in properties of the solvent, and the effect of ethanol on both the conformational properties of DNA and the main phase transition of DSPC clearly appears from the data. © 2002 Elsevier Science B.V. All rights reserved.

The ferricytochrome-c (cyt-c) shows a complex unfolding pathway characterized by a series of stable partially folded states. When titrated with HCl at low ionic strength, two transitions are detected. At pH 2, cyt-c assumes the U1 unfolded state, whereas the successive addition of Cl− ion from either HCl or NaCl induces the recompaction to a molten globule conformation (A1 and A2 states, respectively). A second unfolded state (U2) is also observed at pH 12. Recent data evidence different features for the local structure of the heme in the different states. To derive relationships between local and overall conformations, we analyzed the structural characteristics of the different states by synchrotron small angle x-ray scattering. The results show that in the acidic-unfolded U1 form the protein assumes a worm-like conformation, whereas in the alkaline-unfolded U2 state, the cyt-c is globular. Moreover, the molten globule states induced by adding HCl or NaCl to U1 appear structurally different: in the A1 state cyt-c is dimeric and less compact, whereas in the A2 form the protein reverts to a globular-like conformation. According to the local heme structure, a molecular model for the different forms is derived.

This work deals with a study of alkaline transition of ferricytochrome-c in water and in water−trehalose solutions using two different techniques: spectrophotometry in the region of the heme absor...

The thermal denaturation of calf thymus total chromatin and of fractions enriched in heterochromatin or euchromatin, has been investigated by differential scanning calorimetry and compared to that of calf thymus DNA and DNA-histone complexes. In our experimental conditions, chromatin melts in three thermal transitions: the main one, assigned to separation of the DNA double helix, occurs at 83 °C, while the other two occur at 63 °C and 74 °C. The data show that: (a) the transition enthalpy for denaturation of DNA in the total chromatin and in DNA-histone complexes is nearly the same as that of DNA in solution; (b) the transition at 63 °C is present in the thermogram of the heterocromatin enriched fraction, while it is completely absent in that of the euchromatin enriched one. The results suggest that this transition can be attributed to the higher order structures of heterochromatin.

Previous studies from our laboratory demonstrated the existence of at least two levels of structural complexity in E. coli 70S ribosomes. Ribosomal RNA seems to be principally involved in the overall stability of these structures. In this paper we present an investigation of ribosomes subjected to treatment with RNase. The study is based on both differential scanning microcalorimetry and dielectric spectroscopy. In the thermograms obtained on treated ribosomes only the low temperature peak of the two typical denaturation events observed in native ribosomes, is promptly eliminated by the enzyme treatment. Dielectric spectroscopy measurements carried out on the same samples indicate an alteration of the dielectric behavior previously shown to consist of two subsequent relaxation processes. In fact, only the low frequency relaxation is affected by the treatment. The second one, observed at higher frequency, remains unaltered. The same effect on the dielectric parameters is observed if the ribosome particles are heated and then cooled prior to measurement. These results are consistent with the idea that two different structures are present within the ribosome. One is very stable and withstands both temperature and RNase treatment while the second is promptly abolished by both treatments. Data presented here strongly suggest that the RNA domains exposed to the solvent play a fundamental role in the stability of the 3-D structure of the ribosome particle.

The effect of monohydric alcohols on the micellization of sodium dodecyl sulphate (SDS) and on the thermal unfolding of lysozyme has been studied by DSC as a function of alcohol concentration in the water-rich region of composition. The results show that the effects due to alcohols on these very different systems and processes are strikingly similar and are closely linked with structural and dynamical properties of water–alcohol mixtures themselves. The data have been interpreted on the basis of the assumption that the addition of short chain alcohol affects both the thermal unfolding of proteins as the micellization process modifying the extent of enthalpy and entropy contribution associated with structural reorganization of water in these processes.

We investigated the thermal degradation of E. coli ribosomes by differential scanning microcalorimetry. The 70S particles show two distinctive and irreversible peaks upon thermal degradation. Free rRNA in solution produces, on the contrary, an unstructured denaturation profile. The thermal analysis of 50S particles shows a profile substantially identical to that observed in 70S, while 30S particles produce an unstructured denaturation pattern. Therefore the thermal behavior of the 70S particle is essentially attributable to the denaturation of the 50S subunit. Our data validate previous observations that the 50S has a more rigid structure as compared to 30S, which behaves as a 'floppy' particle. In addition our data suggest that protein/RNA interactions play a significant role to stabilize three-dimensional structures of the ribosome.

Thermal denaturation of lysozyme has been studied at pH = 3 in water/ethanol and water/tert-butyl alcohol mixtures in the water rich region of composition (mole fraction of cosolvent x2 < 0.12) by high-sensitivity differential scanning calorimetry. The results show that on increasing alcohol concentration, the enthalpy and entropy of denaturation of lysozyme first reach a maximum at an intermediate composition x2 = typical for each alcohol ( ≅ 0.06 for ethanol and ≅ 0.02 for tert-butyl alcohol) and then decrease with increasing x2. In addition, two enthalpy−entropy compensation patterns each having its own compensation temperature (Tc) clearly appear from the data: a compensation data line obtained with rising x2 in the 0− range (with Tc = 281 ± 6 K) followed by a compensation line with Tc = 403 ± 14 K after x2 passes the value. The value of is close to that at which a change in the nature of solvent component interaction occurs as inferred from compressibility and IR absorption measurements. The data ha...

We have performed a study of protein dynamics in native and partially denatured horse-heart met-myoglobin (Mb-met) diluted in D2O. Protein dynamics is shown to be strongly solvent-dependent; in particular, higher degrees of macromolecular motions have been observed in the denatured states of Mb-met.

We provide a quantitative description of the solvation properties of lysozyme in water/ethanol mixtures, which has been obtained by a simultaneous analysis of small-angle neutron scattering and differential scanning calorimetry experiments. All data sets were analyzed by an original method, which integrates the exchange equilibrium model between water and ethanol molecules at the protein surface and activity coefficients data of water/ethanol binary mixtures. As a result, the preferential binding of ethanol molecules at the protein surface was obtained for both native and thermal unfolded protein states. Excess solvation numbers reveal a critical point at ethanol molar fraction ≈0.06, corresponding to the triggering of the hydrophobic clustering of alcohol molecules detected in water/ethanol binary mixtures.

In the present study, the thermal unfolding of lysozyme in D2O and D2O/CH3CH2OD solutions is analyzed by means of FTIR spectroscopy. A detailed investigation of the conformational rearrangement of the protein upon heating is achieved by inspection of the amide bands. The effects of partial and total deuteration on amide groups are also investigated for they suggest important information about exposure to the solvent. Finally, a comparison between the characteristics of the unfolding process of lysozyme in water and in ethanol/water solutions is performed to clarify some misinterpretation about the possible formation of intermediates.

The influence of short-chain alcohols and osmolytes on the structural properties, catalytic activity and thermal stability of myoglobin (Mb) has been investigated. Results show that in the presence of a cosolvent, the catalytic activity of Mb decrease as the concentration increase, starting when the concentration was low. Spectroscopic investigations show that changes in catalytic activity are not due to protein conformational changes. Otherwise, no significant correlation between the thermal stability and the catalytic activity is evident from the data. Our measurements show a correlation between the effect of cosolvents on catalytic activity and changes in the microstructure of solvent, as inferred from previous IR data on these mixtures.

"Folded protein stabilization or destabilization induced by cosolvent in mixed aqueous solutions has been studied by differential scanning microcalorimetry and related to difference in preferential solvation of native and denatured states. In particular, the thermal denaturation of a model system formed by lysozyme dissolved in water in the presence of the stabilizing cosolvent glycerol has been considered. Transition temperatures and enthalpies, heat capacity, and standard free energy changes have been determined when applying a two-state denaturation model to microcalorimetric data. Thermodynamic parameters show an unexpected, not linear, trend as a function of solvent composition; in particular, the lysozyme thermodynamic stability shows a maximum centered at water molar fraction of about 0.6. Using a thermodynamic hydration model based on the exchange equilibrium between glycerol and water molecules from the protein solvation layer to the bulk, the contribution of protein-solvent interactions to the unfolding free energy and the changes of this contribution with solvent composition have been derived. The preferential solvation data indicate that lysozyme unfolding involves an increase in the solvation surface, with a small reduction of the protein-preferential hydration. Moreover, the derived changes in the excess solvation numbers at denaturation show that only few solvent molecules are responsible for the variation of lysozyme stability in relation to the solvent composition. (c) 2008 American Institute of Physics."

The adsorption of myoglobin (Mb) onto phosphate grafted-zirconia (ZrO2-P) nanoparticles was studied in terms of conformational studies and thermal stability, determined by circular dichroism (CD), differential scanning calorimetry (DSC), and atomic force microscopy (AFM). The changes in protein structure have been correlated with the catalytic activity of free and adsorbed Mb. CD and DSC studies indicate marked rearrangements in Mb structure upon adsorption onto phosphate-grafted zirconia nanoparticles. These structural rearrangements of Mb could be responsible for the loss of catalytic activity observed for the adsorbed Mb. In particular, the conformational changes due to the adsorption process induced a reduction of kcat and KM. AFM measurements indicate that the interaction with the grafted-zirconia nanoparticles also affects the morphology of the bound protein, inducing the nucleation of prefibrillar-like aggregates.

Mixtures containing lysozyme, LYSO, and a fully fluorinated surfactant, lithium perfluorononanoate, LiPFN, were investigated in a wide range of concentrations and mole ratios. To ensure consistency to the data, a comparison was made, when possible, with the more conventional SDS as surfactant. Molecular solutions, precipitates, and micellar phases have been observed. The region of existence for each phase depends on the LiPFN/LYSO mole ratios, r, and was determined by different experimental methods. Optical absorbance, CD, F-19 NMR, viscosity, electrical conductivity, and dielectric relaxation methods were used. Some methods give information on the protein conformation, others on the state of the surfactant or on the collective system properties, respectively. Addition of LiPFN gives rise to a solution, a poly phase dispersion (at low surfactant to protein ratios) and to a micelle-mediated redissolution of the precipitates. Concomitant to the above macroscopic properties, peculiar effects in the state of LYSO are observed. Low amounts of surfactant reduce significantly the amount of alpha-helix in favor of the beta-sheet conformation of the protein. The former is almost completely regained once micelle-assisted redissolution of the complex occurs. The tertiary structure of the protein, conversely, is lost at low surfactant content and never recovered. Such evidence suggests the occurrence of a molten globule conformation for LYSO in micellar media.

In solution small-angle neutron scattering has been used to study the solvation properties of lysozyme dissolved in water/glycerol mixtures. To detect the characteristics of the protein-solvent interface, 35 different experimental conditions (i.e., protein concentration, water/glycerol fraction in the solvent, content of deuterated compounds) have been considered and a suitable software has been developed to fit simultaneously the whole set of scattering data. The average composition of the solvent in the close vicinity of the protein surface at each experimental condition has been derived. In all the investigated conditions, glycerol resulted especially excluded from the protein surface, confirming that lysozyme is preferentially hydrated. By considering a thermodynamic hydration model based on an equilibrium exchange between water and glycerol from the solvation layer to the bulk, the preferential binding coefficient and the excess solvation number have been estimated. Results were compared with data previously derived for ribonuclease A in the same mixed solvent: even if the investigated solvent compositions were very different, the agreement between data is noticeable, suggesting that a unique mechanism presides over the preferential hydration process. Moreover, the curve describing the excess solvation number as a function of the solvent composition shows the occurrence of a region of maximal hydration, which probably accounts for the changes in protein stability detected in the presence of cosolvents. (c) 2007 American Institute of Physics.

We have investigated the effect of a cationic lipid [DOTAP] on both the thermotropic phase behavior and the structural organization of aqueous dispersions of dipalmitoyl-phosphatidylcholine [DPPC] by means of high-sensitivity differential scanning calorimetry and dynamic light scattering measurements. We find that the incorporation of increasing quantities of DOTAP progressively reduces the temperature and the enthalpy of the gel-to-liquid crystalline transition. We are further showing that, in mixed DOTAP-DPPC systems, the reduction of the phase transition temperature is accompanied by a reduction of the average size of the structures present in the aqueous mixtures, whatever the DOTAP concentration is. These results, which extend a previous investigation by Campbell et al. (Campbell, R. B.; Balasubramanian, S. V.; Straubinger, R. M.; Biochim. Biosphys. Acta 2001, 27, 1512.) limited to a DOTAP concentration below 20 mol %, confirm that the insertion of cationic head groups in zwitterionic phosphatidylcholine bilayers facilitates the formation of stable, relatively small, unilamellar vesicles. This self-assembling restructuring from an aqueous multilamellar structure toward a liposomal phase is favored by decreasing the phospholipid phase transition temperature and by increasing the temperature of the system. This reduction of the average size and the appearance of a stable liposomal phase is also promoted by a heating and cooling thermal treatment.

We have investigated how the internal dynamics of two different macromolecules is affected by hydration, to understand if there are common features related to the plasticizing role of water. To this purpose, elastic and quasielastic incoherent neutron scattering spectra of AOT (sodium bis(2-ethylhexyl) sulfosuccinate) reverse micelles at different hydration degrees W=[H2O]/[AOT] have been compared with elastic neutron scattering data of lysozyme in deuterated glycerol, as a function of increasing water content h (h=grams of water/grams of lysozyme) in the mixture. The elastic and quasielastic data on AOT micelles provide a coherent description of a hydration-dependent intrinsic micelle dynamics, which is activated above a threshold W∼1 and approaches to a saturation limit for W>6. This dynamics essentially involves the hydrogen atoms belonging to AOT hydrocarbon tails and appears to be strongly correlated to the fully hydrated AOT head groups mobility. For lysozyme in glycerol, at room temperature the total hydrogen mean square displacement (MSD) 〈u2〉 strongly rises above h∼0.1 and tends to saturate at higher hydration contents. The striking similarity between the dynamical behaviour of these two systems as a function of their progressive hydration confirms that water molecules generally play a plasticizer role independent of the intrinsic nature of the system they interact with.

An elastic neutron scattering investigation of the molecular dynamics of hydrated lysozyme powders has been undertaken for different water contents h (g water/g Lysozyme). The dry sample exhibits a harmonic behaviour in the whole temperature range, while anharmonic motions arise on hydrated samples at a temperature Td. Both Td and the magnitude of the anharmonic motions are markedly hydration dependent. On increasing water content the crossing barrier entropy change increases, while the enthalpy change keeps constant. The estimated average rigidity of the protein structure decreases abruptly immediately below the onset of the enzymatic activation at around 0.2h.

This work deals with a dielectric study at radio frequencies of the influence at room temperature of two organic molecules, known as cryo-protectants, ethylene-glycol and glycerol, on conformational and dynamic properties of two model proteins, lysozyme (lys) from chicken egg-white and ferricytochrome-c (cyt-c) from horse heart. Cyt-c is a compact globular protein whereas lys is composed of two structural domains, separated by the active site cleft. Measurements were carried out at the fixed temperature of 20°C varying the concentration of the cosolvent up to 90% w/w. From the analysis of the dielectric relaxation of the protein solution, the effective hydrodynamic radius and the electric dipole moment of the protein were calculated as a function of the cosolvent concentration. The data show that glycerol does not modify significantly the conformation of both proteins and cyt-c is also stable in the presence of ethylene-glycol. On the contrary ethylene-glycol strongly affects the dielectric response of lysozyme denoting a specific effect on its conformation and dynamics. The data are coherently interpreted hypothesizing that glycol molecule wedges between and separates the two domains of lys making them rotationally independent.

A differential scanning micro-calorimetric (DSC) investigation has been performed to study the thermal stability of lysozyme solvated in glycerol as a function of the water content h (grams of water/grams of lysozyme). The unfolding process is strongly dependent on h, as it is witnessed by the behavior of the melting temperature Tm which shows a significant drop in the hydration range from 0 h to 0.4/0.5 h. The specific heat difference ΔCp between denatured and native state also displays an important variation for water amounts lower than ca. 0.5 h. For higher water amounts, both Tm and ΔCp seem to attain constant values. Such hydration dependent behavior is reminiscent of the trend exhibited by some quantities characterizing the protein internal dynamics on the pico- and nano-second timescale, as estimated by elastic neutron scattering. Also the protein mobility, which is measured through mean square displacements (MSD), increases mainly for water amounts lower than ca. 0.5 h, in the same range where the protein molecular rigidity rapidly drops down. This behaviour emphasizes the crucial role played by hydration water in determining both the protein thermodynamic and dynamic quantities.

Highly sensitive differential scanning microcalorimetry (DSC) has been used to investigate the phase transition properties of lipid vesicles prepared from 1,2-distearoyl-L-3-glyceryl-phosphatidylcholine (DSPC) in H(2)O and D(2)O. The data show that the response of pre-transition properties to D(2)O--H(2)O substitution is stronger than the main transition properties. We find that there is a small increase in the phase transition temperature (DeltaT approximately 0.5 K) and in the co-operative unit in the main transition. The increase in enthalpy (DeltaH congruent with1 kJ(.)mol(-1)) and in transition temperature (DeltaT congruent with2 K) observed in the pre-transition is comparable with that observed in quite different processes and systems, i.e. melting of nucleic acids and proteins and gel formation. It is suggested that D(2)O--H(2)O substitution affects the thermal transition in these systems in such a way that the contributions of enthalpy and entropy to structural reorganization of water in these processes is modified.

In this paper we show a microcalorimetric investigation carried out on the so-called cores, i. e. ribosomes deprived of select proteins by LiCl treatment. Thermal degradation of native ribosomes gives rise to two thermal transitions occurring at different temperatures. In the cores the high temperature peak persists even after treatment at very high ion strength (2 м LiCl). This strongly suggests the existence of a very stable structure that was previously observed also in particles treated with agents that hydrolyze the RNA moiety. The low temperature peak gradually but dramatically decreases even though it never disappears completely This indicates that the treatment to obtain ribosomal cores does not cause complete unfolding of the particle but only the destabilization of a structural three-dimensional domain present in native ribosomes. These data are discussed in the light of previous results obtained by dielectric spectroscopy and microcalorimetric studies on ribosomal particles.

Different structural probes following the unfolding process of a protein may evidence the existence of stable intermediates from the differences in the unfolding curves. In this work, we analyze the thermal unfolding of chicken egg lysozyme in the presence of 8 M urea at pH 5 combining dielectric spectroscopy in the radiofrequency region, UV absorbance and circular dichroism in the far and near UV regions. The data are consistent with a two-state model of unfolding equilibrium and do not provide support for the presence of a significantly populated intermediate state.

A neutron-scattering investigation of the internal picosecond dynamics of lysozyme solvated in glycerol as a function of temperature in the range 200-410 K has been undertaken. The inelastic contribution to the measured intensity is characterized by the presence of a bump generally known as "boson peak", clearly distinguishable at low temperature. When the temperature is increased the quasielastic component of the spectrum becomes more and more intrusive and progressively overwhelms the vibrational bump. This happens especially for T345 K when the protein goes through an unfolding process, which leads to the complete denaturation. The quasielastic term is the superposition of two components whose intensities and linewidths have been studied as a function of temperature. The slower component describes motions with characteristic times of approximately 4 ps corresponding to reorientations of polypeptide side chains. Both the intensity and linewidth of this kind of relaxations show two distinct regimes with a crossover in the temperature range where the melting process occurs, thus suggesting the presence of a dynamical transition correlated to the protein unfolding. Conversely the faster component might be ascribed to the local dynamics of hydrogen atoms caged by the nearest neighbors with characteristic time of approximately 0.3 ps.