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A Comparative Study of the Influence of Sugars Sucrose, Trehalose and Maltose on the Hydration and Diffusion of DMPC Lipid Bilayer at Complete Hydration: Investigation of Structural and Spectroscopic Aspect of Lipid-Sugar Interaction Arpita Roy, Rupam Dutta, Niloy Kundu, Debasis Banik, and Nilmoni Sarkar Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b01115 • Publication Date (Web): 01 May 2016 Downloaded from http://pubs.acs.org on May 4, 2016
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A Comparative Study of the Influence of Sugars Sucrose, Trehalose and Maltose on the Hydration and Diffusion of DMPC Lipid Bilayer at Complete Hydration: Investigation of Structural and Spectroscopic Aspect of Lipid-Sugar Interaction
Arpita Roy, Rupam Dutta, Niloy Kundu, Debasis Banik and Nilmoni Sarkar*
Department of Chemistry, Indian Institute of Technology, Kharagpur 721302, WB, India E-mail:
[email protected] Fax: 91-3222-255303 Abstract It is well known that sugars protect membrane structures against fusion and leakage. Here, we have investigated the interaction between different sugars (sucrose, trehalose and maltose) and phospholipid membrane of 1,2-dimyristoyl-sn-glycero-3-phoshpocholine (DMPC) using dynamic light scattering (DLS), transmission electron microscopy (TEM) and other various spectroscopic techniques. DLS measurement reveals that the addition of sugar molecule results a significant increase of the average diameter of DMPC membrane. We have also noticed that in presence of different sugars the rotational relaxation and solvation time of coumarin 480 (C480) and coumarin 153 (C153) surrounding DMPC membrane increases, suggesting a marked reduction of the hydration behavior at the surface of phospholipid membrane. In addition, we have also investigated the effect of sugar molecules on the lateral mobility of phospholipids. Interestingly, the relative increase in rotational, solvation and lateral diffusion is more prominent for C480 than that of C153 because of their different location in lipid bilayer. It is because of preferential location of comparatively hydrophilic probe C480 in the interfacial region of the lipid bilayer. Sugars intercalate with the phospholipid head group through hydrogen bonding and replace smaller sized water molecules from the membrane surface. Therefore, overall, we have monitored a comparative analysis regarding the interaction of different sugar molecules (sucrose, trehalose and 1 ACS Paragon Plus Environment
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maltose) with the DMPC membrane through DLS, TEM, solvation dynamics, time resolved anisotropy and fluorescence correlation spectroscopy (FCS) measurements to explore the structural and spectroscopic aspect of lipid-sugar interaction. Keywords: Lipid bilayer, Sugar, Solvation Dynamics, Time Resolved Anisotropy and Fluorescence Correlation Spectroscopy (FCS).
1. Introduction: The orientation of water molecules at the lipid membrane interface is of certain interest, as it determines essential functional characteristics of a biomembrane, such as the hydration forces, excluded volume, and the dipole potential.1–3 The excluded volume imparts towards the permeability barrier and also the structural aspect of membrane.2 The hydration water also influence the repulsion forces between membrane surface, which can contribute to prevent the adhesion adsorption, or aggregation phenomenon.1,3 Herein, a glycerophospholipid (1,2dimyristoyl-sn-glycero-3-phoshpocholine, DMPC) has been chosen as a model membrane system that forms spherical aggregates of small unilamellar and multilamellar vesicles. These self-assemblies are considered as the ideal models for the microenvironments in which molecules can be categorized in the two distinct aqueous environments.4 Generally, phospholipid molecules form onion like multilamellar vesicular aggregates in aqueous medium. However, on extensive sonication these multilamellar vesicles are transformed into small unilamellar ones.5 Lipid membranes can undergo a structural transition from an organized to disorganized assemblies at a particular temperature designated as phase transition temperature (Tm). At a temperature less than that of Tm, lipids are in the solid phase having reduced fluidity, whereas, lipids are in liquid phase having greater fluidity at the temperature above Tm. The phase transition temperature (Tm) of DMPC (Tm=23.90C) is lower than our body temperature.6
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Disaccharides are build up by many organisms7 from nature against various stresses, like temperature8, osmotic9, and oxidative stress.10 Trehalose is accumulated by various organisms to preserve both lipid membranes and proteins against cold and drought stress.11,12 Higher plants generally accumulate sucrose instead of trehalose.13 The preservation of biological entities by disaccharides has many applications in the broad fields of food preservation and cryoconservation of eukaryotic cell lines.14 It is established through various studies that during freezing and drying condition, the lipid bilayer and proteins are protected by many sugars.11,12 During the drying process, lipids having low phase transition temperature (Tm), undergo a transition from the liquid crystalline to the gel phase. The preservative action of disaccharides are of two types: i) the formulation of a glassy matrix, and ii) direct interactions between the lipids and the carbohydrates.15–17 The development of a glassy matrix is associated with the glass transition temperature (Tg) of the disaccharides. Sugars having high Tg generally have better protection capacity than those with a low Tg.13,16,17 Dehydration of lipids enhances the Tm of the membranes and results the phase transition from liquid crystalline to gel. This phase transition of lipids in its dry state, can be prevented by the formation of hydrogen bond between the sugar molecules and the lipid head groups which reduces the enhancement of Tm.12,15–17 Investigation of fully hydrated membrane falls into two category having mutually contradictory conclusions. Various studies have proposed favourable interaction between the sugars and the interfacial region of bilayer membrane.18–23 Several number of lipid molecules are interlocked simultaneously by hydrogen bonding to the sugar molecules.24 This is interpreted as the “interaction hypothesis.” However, other investigations suggest that the sugar molecules are evacuated from the hydration layer of lipid membrane. Due to the interaction of sugars with lipid membrane, the local osmotic balance is affected and as a consequence the interfacial free energy is increased.25,26 This is known as the “exclusion
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hypothesis”. When sugar molecules are introduced into the aqueous subphase in a LangmuirBlodgett trough, it results in lateral expansion of lipid monolayers. This is the most explicit support for the interaction hypothesis.18,27 The proper interpretation of the above phenomenon is that the sugar molecules intercalated into the head groups of lipid membrane and increased its area. The experimental investigations also supported the similar conclusions regarding the interaction of sugars with the lipid bilayers.20,24,28 Recently, molecular dynamics (MD) simulations studies also support the interaction hypothesis between sugars and lipid molecules at the interface of the membrane bilayer.19,21,22,24 Kapla et al. investigated the lipidsugar interaction by means of molecular dynamics simulations and monitored the replacement of water molecules by sugar (trehalose) at bilayer surface.29 Recently, Dzuba et al. also indicated that sugars are directly bonded to the bilayer surface (one sugar molecule per lipid), which is in favour of the water replacement hypothesis. Again, the electron spin echo envelope modulation (ESEEM) spectroscopy studies suggested that direct sugarmolecule bonding takes place with the bilayer surface.30 In the present study, we have investigated the structural and spectroscopic aspect of membrane-sugar interactions using DLS, TEM, time-resolved anisotropy, solvation dynamics, and fluorescence correlation spectroscopy (FCS) measurements. Till now, very little is known about the interactions between lipids and the sugars in the fully hydrated state, while most of the studies on the interactions between phospholipid membranes and sugars emphasize either on the phase transition temperature (Tm) or on the preservation against solute leakage and fusion of liposomes or whole cells. In solution, carbohydrates interact directly with phospholipid bilayer as indicated by the earlier studies.20 Sugars also protect the liposome surface from protein adsorption, liposome aggregation and encapsulated dye leakage.31–33 It is indicated that the disaccharide molecules associate with the lipid membrane34 and forms hydrogen bonding network with the phosphate groups;35
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consequently, water molecules are replaced from the membrane surface.20,36 In the course of our study, we have employed DLS analysis to study the size of the vesicular systems, TEM and fluorescence-lifetime imaging microscopy (FLIM) measurements to investigate the morphological changes in the lipid bilayer in presence of different sugar molecules. Here, FCS technique was also used to measure the influence of different sugars (sucrose, trehalose and maltose) on the lateral diffusion of fully hydrated lipids using two different fluorescence probe, coumarin 153 (C153) and coumarin 480 (C480) having different hydrophobicity. Moreover, we have mainly focused on the changes in the hydration properties of water molecules which are taking place in the lipid bilayer in presence of different sugar molecules. The dynamics of water molecules and their influence on chemical and biological processes has always gain importance in science.37–49 Previously, Hof and co-workers have studied solvation dynamics of different probes inside various lipid vesicular systems.45,46,49 The water molecules have important role in accordance to their reactivity, structure and dynamics of biological systems.50,51 Again, Bhattacharyya et al. have also monitored solvation dynamics of probes inside lipid vesicles. They have emphasized on the hydrogen bonding interaction which is the main cause behind the slowing down of the solvation process inside a microheterogeneous system, like lipid vesicles. The ultraslow component of solvation dynamics in organized assemblies arises from hydrogen bonding (“bound water”) to the polar head groups.38,41,47,48,52,53 Likewise, in our system, the main role played in slowing down the dynamics of solvation is the hydrogen bonding interaction. However, in our study, we have emphasized on the fate of the hydrophobic and hydrophilic molecules inside DMPC vesicles intercalated by the sugar molecules undergoing solvation dynamics. The properties and functions of various bioassemblies significantly depend upon their hydration behavior.54,55 Previously, Andersen et al. have observed the influence of sugars on the lipid bilayer through Small-angle neutron scattering (SANS) and thermodynamic measurements.56 To the best of
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our knowledge, no such fluorescence spectroscopic based study has been carried out to explore lipid-sugar interaction using two different solvatochromic probe molecules (C153 and C480) having different hydrophobicity. Hence, we are very keen to observe the dynamical behavior of two different probes inside the lipid bilayer in presence of different sugar molecules. Moreover, to explore the morphological property of such a system, we have performed systematic TEM and FLIM measurements. Therefore, our present study may reveal some interesting aspects towards the overall effect of sucrose, trehalose and maltose on the lipid bilayer in fully hydrated state. 2. Experimental Section: 2.1. Materials and Method: The lipid, 1,2-dimyristoyl-sn-glycero-3-phoshpocholine (DMPC) was purchased from SigmaAldrich. The sugars (sucrose, trehalose and maltose) were purchased from Sisco Research Laboratories Pvt. Ltd. (SRL), India. The dye molecules, coumarin 153 (C153) and coumarin 480 (C480) were purchased from Exciton. All these materials were used as received. The experiments were executed at 298 K. The concentration of sugars used in the experiments is 1M. The structures of DMPC, C153, C480, sucrose, trehalose and maltose are given in Scheme 1. 2.2. Preparation of Solutions. For the preparation of small unilamellar vesicles of DMPC molecules, sonication method was used. Initially, required amount of phospholipid (12 mM of DMPC) was taken in a roundbottom flask and dissolved in 1:1 (v/v) methanol-chloroform mixture. After complete solubilization of DMPC in methanol-chloroform mixture, the solvent mixture was evaporated using rotary evaporator. A thin dry lipid film was noticed after evaporation of solvent at bottom of the flask and it was kept in a vacuum desiccator for overnight. Finally, this thin lipid film was hydrated using tris-buffer (20 mM, pH=~7.4) and vortex the mixture for
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complete dispersion. To prepare small unilamellar vesicle, the suspension of large DMPC vesicle was sonicated by an ultrasonic probe sonicator of frequency ~20±3 kHz for 15 minutes (Processor SONOPROS PR-250 MP, Oscar Ultrasonics Pvt. Ltd. India). 2.5. Steady-State and Time-Resolved Fluorescence Studies. The emission spectra of C480 and C153 were monitored using Shimadzu (model number UV-2450) spectrophotometer and a Hitachi (model number F-7000) spectrofluorimeter, respectively. We have used time correlated single photon counting (TCSPC) picosecond spectrometer to record the time resolved decay of the fluorophores in solution. The detailed of TCSPC set-up was depicted in our earlier publication.57 Generally, picosecond diode lasers (IBH, UK, Nanoled) were utilized as excitation source and the emission decays were detected in magic angle (54.70) polarization by Hamamatsu microchannel plate photomultiplier tube (MCP PMT) (3809U). The picosecond diode laser of 408 nm was used as excitation source. The instrument response function of TCSPC set up is ~100 ps. During the analysis of time resolved decays, we have used IBH DAS-6 decay analysis software. Similarly, the anisotropy decays were measured using the same TCSPC instrument. During anisotropy measurements, the motorized polarizer in the emission side was utilized to collect the emission decays at parallel, ∥ (t) and perpendicular, (t) polarizations alternatively using
vertically polarized excitation source until a certain peak difference between ∥ (t) and (t)
decays were reached. The anisotropy decay function, was defined as:58 =
∥ .
∥ .
1
Here, G is the correction factor and for our set up is 0.6. 2.6. Fluorescence Correlation Spectroscopy (FCS): The DCS 120 confocal Laser Scanning Microscope (LSM) system (Becker & Hickl DCS 120) setup was used for FCS measurements. The instrument was equipped with an inverted 7 ACS Paragon Plus Environment
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optical microscope of zeiss (Carl Zeiss, Germany) and a 40X water emulsion objective (NA=1.2). During FCS measurements, membrane solution containing C153 and C480 were placed onto the glass coverslip and picosecond diode laser (bh BDL-SMC) of 408 nm was utilized at excitation source. In FCS, the temporal fluctuation of fluorescence intensity was used to obtained the correlation function G(τ) defined as58,59 =
〈 + 〉 2 〈〉
Here, denotes the fluctuation of fluorescence signal as deviations from the temporal average of the signal 〈〉 at time t. Therefore, = − 〈〉.
The detailed descriptions of the instrumental section are given in the Supporting Information. 3. Results and Discussion: 3.1. Structural Characterization of DMPC vesicle in presence and absence of Sugar molecules. To investigate the influence of different sugar molecules (sucrose, maltose and trehalose) on the size of unilamellar DMPC vesicles, we have performed dynamic light scattering (DLS) measurement. The intensity-size distribution profiles of neat DMPC vesicle and DMPC vesicles in presence of different sugar molecules have been shown in Figure 1. DLS measurements indicate that size of DMPC aggregate is ∼110 nm (diameter). Further, we have also investigated the effect of sugar molecule binding on lipid surfaces. It involves intercalation of sugars with the head group region of the DMPC membrane. Therefore, the head groups are separated and as a result, the lateral area is increased which is reflected in both the DLS and TEM measurements. This general behavior is typical for the interfacial binding of small molecules to membranes.60,61 Moreover, the extent of enhancement of lateral area is not same for different sugar molecules (i.e. Sucrose, Trehalose and Maltose). The
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different extent of hydrogen bonding interactions between various sugar molecules with lipid bilayer is responsible for this difference. In presence of sucrose, maximum increase in size of DMPC vesicles is observed. This observation is considered to be an indication of most favorable hydrogen bond formation by sucrose with the membrane surface. According to the molecular dynamics simulations, sucrose molecules can form more than 10% hydrogen bonds with the head groups of phospholipid membrane than trehalose.24 Therefore, the interaction of sucrose is more effective as it is interacting with more number of lipid head groups simultaneously than other sugar molecule does. Simulation study also suggested that the increased cross-linking of lipid bilayer with sugars, causes greater reduction of the diffusion coefficient.24 During lipid-sugar interactions, majority of hydrogen bonds are formed involving the phosphate oxygens. In comparison with other sugars, more numbers of sucrose molecules are involved in hydrogen bonding with the lipid bilayer. Similarly in average, greater numbers of lipids are also involved in hydrogen bonding interaction with sucrose than trehalose and maltose. Hence, sucrose molecules are more effective than other sugars in increasing the size of the DMPC vesicle by cross-linking with the phospholipid head groups. Anderson et al. showed that the interactions of sugar with lipid includes intercalation and separates the head groups of lipids which in turn increases the lateral area.56 Very recently, Dzuba et al. also provided information regarding the direct interaction of sugars with lipid membrane by spin-label electron paramagnetic resonance (EPR) technique.30 Therefore, sucrose molecules interact with more number of lipid molecules compared to trehalose and maltose. As more number of sucrose molecules interact with the lipid bilayer more effectively than trehalose or maltose, the increase in size of the DMPC vesicles is larger in presence of sucrose. To get an idea regarding the shape and morphology of DMPC vesicles in absence and presence of sugar molecules, we have performed TEM measurements. It becomes to some
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extent difficult to dry the samples completely in presence of sugars. Hence, for the TEM measurements, we have diluted the samples to overcome the difficulty of sample drying. Moreover, by dilution one can be able to get more clear images of lipid vesicles well separated with each other. The TEM images of neat DMPC vesicles and in presence of sugar molecules are shown in Figure 2. These TEM images indicate the vesicles are spherical, unilamellar with a distinct bilayer region. The TEM images also suggest that the size of vesicle increases significantly in presence of sugars. The extent of increase in the size of DMPC vesicle is higher with the addition of sucrose compared to trehalose which is well correlated with the DLS findings. As TEM measurements are done in dry state, therefore, to further convince our observation, we have performed FLIM measurements. Moreover, the FLIM measurements are performed in the liquid state of the sample that excludes the possibility of the change in the samples property during the process of drying. In principle, it is not possible to spatially resolve different regions of dimension ∼110 nm in a microscope of spatial resolution ∼200 nm (for 408 nm excitation). Hence, it is not possible to obtain the FLIM images of neat DMPC vesicles. However, in presence of the sugar, the size of the DMPC vesicles enhances as detected in previous DLS study and it comes in the microscope spatial resolution of ∼200 nm (for 408 nm excitation). This observation is a concrete prove that the size of the DMPC vesicle increases as a result of the hydrogen bonding interaction with the phosphate head group region of the DMPC vesicles (Figure S1,a,b,c, Supporting Information). Confocal images of single sugar intercalated DMPC vesicle at two different heights (z) have also been shown (Figure S2,a,b, Supporting Information). 3.2. Spectroscopic Study to Probe the Microstructural Difference between DMPC Vesicle and DMPC-Sugar Containing Vesicle:
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Understanding the differences between DMPC lipid membranes in presence and absence of different carbohydrates seems to be an essential part to compare the rigidity and hydration properties of lipid vesicles from the point of fluorescence spectroscopic techniques. Hence, to observe the rigidity and hydration behavior of lipid bilayer in presence of sugars, we have used C480 and C153 as probe molecules. In presence of sugars, the shape of lipid vesicles remains spherical. Therefore, the findings of rotational, solvation and lateral diffusion properties of C480 and C153 can provide the important aspects regarding the structural heterogeneity of DMPC vesicles and sugar decorated DMPC vesicles. 3.2.1. Steady-State Emission Measurements: The steady-state fluorescence spectra of C480 and C153 in neat DMPC and in presence of different sugars (sucrose, maltose and trehalose) are given in Figure S3,a,b (Supporting Information). In neat DMPC vesicle, the emission maxima of C480 and C153 appear at ~480 nm and ~526 nm, respectively. However, with addition of sucrose, maltose and trehalose in individual DMPC vesicle solution, the emission spectra of both the probes (i.e., C480 and C153) are blue-shifted. This indicates that the hydrophobicity of the surrounding microenvironment increases. This blue shift in fluorescence spectra suggests that due to the hydrogen bonding between the sugar and the head groups of lipid molecules, water molecules are replaced from vesicle surface. Kapla et al. investigated the lipid-sugar interaction by means of molecular dynamics (MD) simulations.29 According to their molecular dynamics simulations study, smaller sized water molecules are replaced by sugar (trehalose) molecules from the bilayer interface.29 Besides, Dzuba et al. also indicated that sugars are directly bonded to the bilayer surface (one sugar molecule per lipid), which is in favour of the water replacement hypothesis.30 Besides, the electron spin echo envelope modulation (ESEEM) spectroscopy proposed that direct sugar molecule bonding takes place to the membrane surface. Therefore, we can conclude that the interaction of sugar molecules with the surface
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of lipid bilayer renders it more hydrophobic in nature which induces blue shift in emission maxima of C153 and C480 molecules. Moreover, the extent of blue shift in emission maxima in sugar containing DMPC solution is more pronounced for C480 than that of C153. This scenario can be explained by considering hydrophobicity of coumarin molecules (C153 and C480) and their different locations in DMPC vesicles. As C153 is comparatively more hydrophobic than C480, majority of C153 molecules reside into the hydrophobic chain of lipid bilayer region of DMPC vesicle and
little population is also there, towards the
interfacial region of the lipid bilayer.62,63 However, comparatively hydrophilic C480 molecules reside in the interfacial region of the DMPC membrane and also in water pool of the lipid vesicles.62 Again, it is notable to mention that we have found more significant change in emission spectral profiles of both coumarin molecules in DMPC-sucrose vesicles than DMPC-trehalose or DMPC-maltose containing vesicles. As sucrose molecules interact with the head groups of DMPC more efficiently than the other does. Therefore, the extent of blue shift in emission spectra of C153 and C480 are more pronounced in sucrose containing DMPC vesicle solution. 3.2.3. Time-Resolved Anisotropy Measurements of C153 and C480. Time resolved anisotropy measurement provides helpful information concerning the location and interaction of probe molecules in organized assemblies. The interaction of probe molecules with surrounding microenvironments can influence their rotational motion.57,63 Therefore, the correlation of rotational dynamics is a useful technique to monitor the interaction and hydration properties surrounding the probe molecules in the confined microenvironments. However, there are no reports considering the rotational dynamics of probe molecules inside the lipid bilayer in presence of different sugars. The steady state emission spectral profiles of C153 and C480 provide an initial idea regarding the interaction of these probe molecules with DMPC vesicles in presence of sugar molecules. Hence, to
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provide quantitative information about the changes in microheterogeneity, rigidity and hydrophobicity of the surrounding microenvironment of probe molecules as a result of interaction between lipid bilayer and different sugars, the anisotropy decays of C153 and C480 have been monitored both in neat DMPC and DMPC-sugar containing vesicles. The changes in anisotropy decays of C153 and C480 in neat DMPC vesicles and in presence of different sugars have been depicted in Figure 3 (a), (b). In bulk water, the anisotropy decays of C480 and C153 are single exponential with reorientation time constant of ~70 ps and ~100 ps, respectively.64,65 However, the anisotropy decays of both C153 and C480 in neat DMPC vesicle and also in presence of different sugars are biexponential in nature and the corresponding decay parameters of C480 and C153 are given in Table 1 and Table 2, respectively. This observation indicates that due to the solubilization of both coumarin molecules in vesicular aggregates, the rotational motion of both of these dyes hindered significantly inside the lipid vesicle with respect to that of the bulk water. Interestingly, with the addition of sugars into DMPC vesicular solution, further increase of the rotational time constant is observed. This confirms that with the incorporation of different sugar molecules, the smaller water molecules are replaced by the larger disaccharides and the surrounding confined microenvironments of probe molecules become more rigid and hydrophobic in DMPC-sugar containing aggregates compared to neat DMPC vesicles. The carbohydrates form hydrogen bonding with the phosphate moiety in the head group region of the DMPC vesicles and as a consequence, water molecules are replaced from the interfacial region of lipid membrane.24,30 Again if we compare the relative change in rotational time constant of both the coumarin molecules in DMPC-sugar systems, maximum increase in rotational time constant is observed in DMPC-sucrose containing membrane solution. In neat DMPC vesicular solution, the average rotational time () of C153 is ~1.28 ns and that of C480 is ~0.92 ns. However, in DMPC-sucrose containing vesicle, the average rotational time of C153
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is increased to ~1.40 ns and that of C480 is ~1.35 ns. As described earlier that the extend of hydrogen bonding with the phospholipid head group is greater for sucrose followed by trehalose and maltose.24 Therefore, the reduction of the rotational motion of C480 and C153 by the carbohydrates follows the same order. If we keep closer look into the rotational motion of C480 and C153 in DMPC-sugar containing membrane solution, the rotational motion of C480 is more affected by the carbohydrates than the rotational motion of C153. This is due to the different location of the two probes in DMPC vesicle. As C153 is a hydrophobic molecule, most of it would prefer the hydrophobic chain region of the bilayer and a little proportion would reside towards the interfacial region of the membrane.63 In contrast, the hydrophilic C480 mainly located in the head group region of the lipid bilayer where the carbohydrate affects mostly as described previously.62 3.2.4. Solvation Dynamics Studies. Solvation dynamics study has been used as a sensitive technique to understand the hydration behavior of various self-assembled organized as well as biological systems.38,42–44 In this particular study, the changes in hydration properties of lipid membrane in presence of three different sugars have been investigated using C480 and C153 as solvatochromic probes.66 To monitor the solvation dynamics, individually the emission decays of C153 and C480 have been collected at different wavelengths over the entire range of steady state fluorescence spectra. Finally, using the best fitting parameters of emission decays, we have constructed the time-resolved emission spectra (TRES) following the procedure of Fleming and Maroncelli.40 The TRES at a particular time t, S(λ;t), is obtained by the fitted decays, D(t;λ), by relative normalization to the steady-state spectrum S0(λ), as follows ; =
;
∞ "!
!
; #
3
Every TRES was fitted by “log-normal line shape function”. The function is defined as follows: 14 ACS Paragon Plus Environment
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+, [1 + 2/& − &0 /2] % & = %! '() *−+,2 4 5 4 / where g0, b, νp and ∆ are the peak height, asymmetric parameter, peak frequency, and width parameter, respectively. The peak frequency has been estimated from the log-normal fitting of TRES. This calculated peak frequency is utilized to construct the decay of the solvent correlation function, C(t). The solvent correlation function, C(t) is defined as: 7 =
& − &∞ 5 &0 − &∞
Here, υ(0), υ(t) and υ( ) represent the peak frequency at time zero, t and infinity. The decays of C(t) are fitted using the following bi-exponential function: 7 = :; '()
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