Conductometric and Fluorescence Probe Analysis to Investigate the Interaction between Bioactive Peptide and Bile Salts: A Micellar State Study

The present work deals with the micellar state study of sodium cholate and sodium deoxycholate in the aqueous solution of a bioactive peptide, namely glycyl dipeptide, having different concentrations through conductivity and fluorescence methods at different temperatures. The data obtained from conductivity is plotted against the concentration of Bile salts, and CMC (critical micelle concentration) values are calculated. The results realized have been elucidated with reference to Glycyl dipeptide–bile salts hydrophobic/hydrophilic interactions existing in solution. In addition, the CMC values converted to mole fraction (Xcmc) values have been used to evaluate the standard thermodynamic factors of micellization viz., enthalpy H, free energy ΔGm0, and entropy (ΔSm0) which extract information regarding thermodynamic feasibility of micellar state, energy alteration, and the assorted interactions established in the existing (bile salts–water–glycyl dipeptide) system. Furthermore, the pyrene fluorescence spectrum has also been utilized to study the change in micro polarity induced by the interactions of bile salts with glycyl dipeptide and the aggregation action of bile salts. The decrease in modification in the ratio of intensities of first and third peaks i.e., (I1/I3) for the pyrene molecules in aqueous bile salts solution by the addition of dipeptide, demonstrates that the micelle polarity is affected by glycyl dipeptide. This ratio has also been utilized to determine CMC values for the studied system, and the results have been found to be in good correlation with observations made in conductivity studies.


Introduction
Biologically significant macromolecules are the building blocks of living organisms and are prerequisites for all forms of life. As the research related to new chemical and pharmaceutical formulations has grown extensively in recent years, the industries are turning more progressively towards biologically active compounds such as peptides/proteins in search for better drug formulation [1]. In this regard, a considerable impetus is driven by the unique requirement of proteins/peptides, because they provide procedures that are more unwavering and have effectual bioavailability, and facilitate the sound development of drugs. Peptides are short polymers formed by the connection of (≤100) amino acids which encompass a few of the indispensable components of various biological processes of living beings, such as enzymes, antibodies, sundry hormones, etc. They are the significant Furthermore, in contradiction to conventional surfactants, bio surfactants (bile salts) possess a particular structure and stiff steroid backbone with an extended alkyl chain of numerous lengths ending with the carboxylic acid group, which leads to a distinctive aggregation behavior of bile salts and features which are more advantageous than conven-  measurements [23][24][25][26]. Moreover, the micelle formation of bile salts is affected by their external conditions, including the presence of co-solutes [27][28][29][30][31]. Thus, it is imperative to study the micellization properties of these surfactants that accommodate to manage the potency of various interactions affecting protein-surfactant systems. Scheme 1. Schematic presentation of micelle formation.

Chemicals
Distilled solvent water, used for the entire experiment, was obtained from a Millipore-Elix system with conductivity (2 to 3) µS•cm −1 and pH~6.8−7.0 at temperature 298.15 K. Analytical grade NaC and NaDC were purchased from Himedia Pvt. Ltd. (Mumbai, India) and recrystallized from ethanol as per the method conveyed in our previous studies [29].The glycyl dipeptide was obtained from Spectrochem Pvt. Ltd. (Mumbai, India) and was utilized by itself without applying any supplementary action. Pyrene of A.R. grade, used as a fluorescent probe, was obtained from Merck (Darmstadt, Germany) and utilized without passing through any treatment. Molecular weight, purity, and sources of the chemicals used in our study are provided in Table 1.

Conductivity Measurements
The desired solutions of sodium cholate (NaC) (1-20 mmol•kg −1 ) and sodium deoxycholate (NaDC) (1-10 mmol•kg −1 ) were made in aqueous stock mixture of Glycyl dipeptide (0.001, 0.005, and 0.010 mol•kg −1 ). The chemicals were weighed using a Shimadzu scalewith the precision of ±0.0001 g. Conductivity was measured via digital conductivity meter Cyberscan CON 510, whose procedure and principle of working has been eluci-Scheme 1. Schematic presentation of micelle formation. Furthermore, in contradiction to conventional surfactants, bio surfactants (bile salts) possess a particular structure and stiff steroid backbone with an extended alkyl chain of numerous lengths ending with the carboxylic acid group, which leads to a distinctive aggregation behavior of bile salts and features which are more advantageous than conventional surfactants [16,17]. They are small aggregates which help to solubilize and disperse hydrolyzed fat and lipids that are derived from food. Bio-surfactants have a lesser amount of toxicity and are formed from renewable substrates, and many display stabilities under some conditions, viz. pH, temperatures, and ionic strength [18,19]. Interestingly, studies on micellar aggregates of bile salts help us to understand the interactions of biological membranes, hydrolysis, biliary secretion, and solubilization of cholesterol and hence are able to disclose certain physiological processes [20][21][22]. In this paper, we intend to investigate the micellar action of bile salts, viz., sodium cholate (NaC) (C 24 H 39 O 5 Na) and sodium deoxycholate (NaDC) (C 24 H 39 O 4 Na), in aqueous glycyl dipeptide, for attaining the proper understanding of their properties and applications in various fields viz. chemical, biochemical, pharmaceutical and industrial fields. The system has been analyzed in terms of variation in the micellar behavior of NaC and NaDC in the presence of glycyl dipeptide, by investigating critical micelle concentration (CMC) and related parameters. The analyzed system consists glycyl dipeptide, which may be considered to be the model component of enzyme and may further give valuable information on the interactive nature of biologically important compounds consisting of protein-bile salt. The study may further lend a hand in understanding the self-aggregation mechanism of bile salts in the presence of proteins/enzymes, which may be helpful in explaining the several biological interactions and processes. The molecular structures of these compounds are shown in Figure 1. Several physicochemical properties, for instance CMC, aggregation number, degree of dissociation, thermodynamic parameters, and micellar properties of bile salts, etc., have been frequently analyzed with the support of various investigating approaches, for instance, conductivity, density, fluorescence, surface tension, viscosity, diffusion, lightscattering, electron (nuclear) spin resonance methods (E(N)SR), osmometry, and refractive index measurements [23][24][25][26]. Moreover, the micelle formation of bile salts is affected by their external conditions, including the presence of co-solutes [27][28][29][30][31]. Thus, it is imperative to study the micellization properties of these surfactants that accommodate to manage the potency of various interactions affecting protein-surfactant systems.

Chemicals
Distilled solvent water, used for the entire experiment, was obtained from a Millipore-Elix system with conductivity (2 to 3) µS·cm −1 and pH~6.8−7.0 at temperature 298.15 K. Analytical grade NaC and NaDC were purchased from Himedia Pvt. Ltd. (Mumbai, India) and recrystallized from ethanol as per the method conveyed in our previous studies [29].The glycyl dipeptide was obtained from Spectrochem Pvt. Ltd. (Mumbai, India) and was utilized by itself without applying any supplementary action. Pyrene of A.R. grade, used as a fluorescent probe, was obtained from Merck (Darmstadt, Germany) and utilized without passing through any treatment. Molecular weight, purity, and sources of the chemicals used in our study are provided in Table 1. The desired solutions of sodium cholate (NaC) (1-20 mmol·kg −1 ) and sodium deoxycholate (NaDC) (1-10 mmol·kg −1 ) were made in aqueous stock mixture of Glycyl dipeptide (0.001, 0.005, and 0.010 mol·kg −1 ). The chemicals were weighed using a Shimadzu scalewith the precision of ±0.0001 g. Conductivity was measured via digital conductivity meter Cyberscan CON 510, whose procedure and principle of working has been elucidated earlier [32]. The temperature was upheld constantly at ±0.1 K by flowing thermostated water through a double-walled conductivity vessel containing the solution. The reproductivity of the conductivity measurements was assessed to be ±15 µS·cm −1 .

Fluorescence Measurements
The fluorescence spectral analysis was completed with an LS-55 Perkins Elmer Fluorescence Spectrophotometer. The principle of working and procedure isdescribed in our prior study [31]. The samples were analyzed by using a quartz cuvette with a 10 mm path length. The wavelength for excitation was set aside at 334 nm and for the emission at 373 and 384 nm. The excitation slit was managed at 8.0 nm while the emission slit was kept at 2.5 nm. The pyrene solutions (2 µmol kg −1 ) utilized as a probe were prepared by following the procedure documented in the literature [31].

Micellization of Bile Salts in Aqueous Medium of Glycyl Dipeptide
This section employs the conductivity method to analyze the effect of micellization on the interaction of NaC and NaDC with glycyl dipeptide in an aqueous medium at fluctuating amounts (0.001, 0.005 and 0.010 mol·kg −1 ) and temperatures (from 293.15 K up to 313.15 K). The conductivity data of NaC and NaDC in the aqueous solution of glycyl dipeptide at different temperatures are encapsulated in Table S1 in the supporting data. The illustrative plots between κ [NaC/NaDC] are presented in Figure 2. The plot displays a kink at the point of aggregation i.e., critical micelle concentration (CMC). The (CMC) values of NaC as well as NaDC have been extracted and are then turned into their mole fraction unit, X cmc , before exposing these values for a discussion of energetic micelle formation. However, it is important to mention that the κ values increase linearly as a function of bile salt content, prior (i.e., pre-micellar) and subsequently (i.e., post-micellar) to the point of aggregation, i.e., critical micelle concentration (CMC), for all studied temperatures, as shown in Figure 2. However, the CMC in the conductivity curves for NaC and NaDC cannot be identified clearly as the change in conductivity near the CMC region is not very fine, which has a characteristic quality when coupled with bile salts [33,34] and with some binary mixtures of conventional ionic surfactants. The elevation in κ values occurs more in pre-micellar than post-micellar regions, because the conductivity of bile salts solution results from the dependence of conductivity upon ions present on surfactants' heads as well as the mobility of ions. At lower concentrations, NaC and NaDC act as strong electrolytes and undergo complete dissociation into ions and are free to move, therefore contributing significantly toward conductivity value. Furthermore, as the bile salts content increases, the association of bile salt initiates leads to the construction of self-organized molecular assemblies called micelles [35]. The aggregation and incorporation of counter-ions into these aggregates cause a diminishment in the number of free ions and hence a smaller increment in conductivity values [36,37]. However, the conductivity κ values are of higher magnitude for sodium cholate (NaC) in contrast to sodium deoxycholate (NaDC) for all the experimented systems. This can be explained by considering the structural relationship between NaC and NaDC, as NaDC has one less -OH group and hence lesser number of ions will be present for the movement, resulting in lower conductivity values. Moreover, the conductivity values escalate with the concentration of glycyl dipeptide for both the bile salts, and have been found to increase with bile salt concentration. The increase in conductivity values with bile salt concentration may be attributed to the fact that the number of charge carriers (ions) increases with addition of bile salts as well as glycyl dipeptide [37].

Critical Micelle Concentration (CMC)
Furthermore, on the investigation of CMC values from Table 2, we infer that values for bile salts in pure water are similar to those in the literature [38][39][40][41], decreasing while proceeding towards higher concentrations of glycyl dipeptide. This leads to the following outcomes on the addition of glycyl dipeptide: 1. There is a decrease in the thickness of the solvation layer surrounding the (ionic) head groups of the bile salts. 2. The electrostatic repulsive kind of interactions are also lessened amongst the negatively charged part of the bile salts.
These two outcomes are responsible for the net diminution in the hydrophilicity of NaC and NaDC, i.e., their adsorption on the surface is increased and molecules assemble effortlessly on the surface and within the solution and hence CMC values decrease. Herein, it is imperative to remark that the dipeptides typically occur in the zwitterion and diffuse into ions alike amino acids, for the reason that dipeptide bonds do not detach. This may firmly lead towards the formation of ion pairs among differently-charged head assemblies of bile salts and molecules of glycyl dipeptide, by means of electrostatic interactions triggering solubilization of the glycyl dipeptide. Nevertheless, it has been noticed that the solubilization for the ion-pairs interaction of the glycyl dipeptide is privileged for

Critical Micelle Concentration (CMC)
Furthermore, on the investigation of CMC values from Table 2, we infer that values for bile salts in pure water are similar to those in the literature [38][39][40][41], decreasing while proceeding towards higher concentrations of glycyl dipeptide. This leads to the following outcomes on the addition of glycyl dipeptide: 1.
There is a decrease in the thickness of the solvation layer surrounding the (ionic) head groups of the bile salts.

2.
The electrostatic repulsive kind of interactions are also lessened amongst the negatively charged part of the bile salts.
These two outcomes are responsible for the net diminution in the hydrophilicity of NaC and NaDC, i.e., their adsorption on the surface is increased and molecules assemble effortlessly on the surface and within the solution and hence CMC values decrease. Herein, it is imperative to remark that the dipeptides typically occur in the zwitterion and diffuse into ions alike amino acids, for the reason that dipeptide bonds do not detach. This may firmly lead towards the formation of ion pairs among differently-charged head assemblies of bile salts and molecules of glycyl dipeptide, by means of electrostatic interactions triggering solubilization of the glycyl dipeptide. Nevertheless, it has been noticed that the solubilization for the ion-pairs interaction of the glycyl dipeptide is privileged for NaC compared to NaDC; this can be attributed to the lack of -OH group in the latter, which makes it more hydrophobic. Precisely, glycyl dipeptide has been known to play a dual role, as it also reinforces the arranged solvent molecules surrounding the steroidal backbone of bile salt monomers with water molecules [38] or else the adding of glycyl dipeptide molecules lessens the electrostatic repulsive-type interactions among polar head parts of NaC/NaDC molecules and the ionic group of glycyl dipeptides. Moreover, the structured water surrounding of the steroidal backbone of bile salt monomers may have been ruptured withthe addition of glycyl dipeptide molecules [39]. This fortifies the solvophobicity of the studied bile salts system and establishes an easier micelle formation, thus, a steady decrease was observed for the CMC values. The uncertainty in the CMC values was ±0.03 × 10 −3 and ±0.02 × 10 −3 for NaC and NaDC, respectively. The variations of X cmc (or CMC) with temperature sheds light on micelle formation and micellar transitions to a large extent, and helps to identify the effect on the CMC of the amphiphiles. The X cmc values of bile salts in the considered solvent systems are recorded in Table 3 and displayed against temperatures in Figure 3. A careful scrutiny of these plots reveals that the values of X cmc confirm a deep minimum at around 298.15-308.15 K for NaC as well as for NaDC, and then escalate with rise in temperature. The variation in the X cmc values for NaC shows a typical U-type curve at the studied temperature range. However, for NaDC, a sheer decrease can be observed from Figure 3.The steepness in the X cmc curves for NaC and NaDC clearly expose that the micellization behavior of these bile salts is affected by temperature for all the concentrations. The larger diminishment in the X cmc values for NaDC along with temperature is the manifestation of the more hydrophobic character of NaDC. These types of characteristics for several ionic and non-ionic surfactants have already been suggested in the literature [40][41][42]. The temperature dependence on the values of X cmc for these bio-surfactants in aqueous systems can be construed as hydrophobic and likewise hydrophilic hydrations [43][44][45]. In the pre-micellar region, both the hydrations (i.e., hydrophobic along with hydrophilic hydrations) are equally important, whilst the hydrophilic hydrations are feasible in the post-micellar region of amphiphilic systems. After micellization, hydrophobic and hydrophilic hydrations decrease with temperature [43]. A lessening of hydrophilic hydration promotes the formation of aggregates (micelles), whereas the lessening of hydrophobic hydration demotes the selfassembling of amphiphilic molecules on escalating temperatures [45]. Subsequently, the supremacy of these two outcomes will be decisive factors for governing the magnitude of the CMC (or X cmc ) values in the studied temperature range. The uncertainty in the X CMC values was ±0.0002 × 10 −3 and ±0.0001 × 10 −3 for NaC and NaDC, respectively.   Alternatively, the increase in CMC values for studied bile salts in aqueous solutions of glycyl dipeptide could also be ascribed to the thermal motion of existing species in the ternary solution. It has also been observed that, with escalation in temperature, the kinetic energy of the molecules (bile salts and solvent) piles up, owing to the upsurge in the thermal motion of these molecules which ensures that the rupture of the water structure and the formation of micelles becomes intricated. Thus, with the elevation in temperature, disaggregation of micelles occurs; consequently, there is an increase in the CMC X or CMC values for the studied system.

Thermodynamics of Micellization of NaC and NaDC in Aqueous Glycyl Dipeptide
The distinctive thermodynamic parameters in relation to the micellization process of NaC and NaDC in analyzed solvent system have been calculated using the data summarized in Table 3. The standard enthalpy for the formation of micelles, ∆ 0 for NaC and NaDC have been estimated by using the Equation (1) [46,47]: is the slope of lnXCMC versus T plots and implies the degree of counter-ion dissociation, given as (2). Alternatively, the increase in CMC values for studied bile salts in aqueous solutions of glycyl dipeptide could also be ascribed to the thermal motion of existing species in the ternary solution. It has also been observed that, with escalation in temperature, the kinetic energy of the molecules (bile salts and solvent) piles up, owing to the upsurge in the thermal motion of these molecules which ensures that the rupture of the water structure and the formation of micelles becomes intricated. Thus, with the elevation in temperature, disaggregation of micelles occurs; consequently, there is an increase in the X CMC or CMC values for the studied system.

Thermodynamics of Micellization of NaC and NaDC in Aqueous Glycyl Dipeptide
The distinctive thermodynamic parameters in relation to the micellization process of NaC and NaDC in analyzed solvent system have been calculated using the X CMC data summarized in Table 3. The standard enthalpy for the formation of micelles, ∆H 0 m for NaC and NaDC have been estimated by using the Equation (1) [46,47]: where d(lnX CMC /dT) is the slope of lnX CMC versus T plots and α implies the degree of counter-ion dissociation, given as (2).
where S1 and S2 signifies the slopes before and after the CMC region, respectively, calculated by subjecting conductivity data to linear regression, and having a correlation factor greater than 0.998. The standard free energy of micellization, (∆G 0 m ) nd entropy of micellization, (∆S 0 m , have been calculated from the following equations [46]: The values of ∆H 0 m , ∆G 0 m , and ∆S 0 m for NaC and NaDC in different concentrations of glycyl dipeptide are tabulated in Table 4. In addition, their variations with temperature are shown in Figure 4.  A fascinating feature about the data related to Table 4 is that the values of ∆ 0 are endothermic (i.e., positive) at a lower temperature up to 303.15 K for both bile salts, and then turn to exothermic (i.e., negative) with a rise in temperatures for all the studied systems of glycyl dipeptide, irrespective of the variation in concentration. The larger lack of the -OH group in NaDC compared to NaC can be clearly noticed from more positive ∆ 0 values for NaDC for all the concentrations of glycyl dipeptide. The micellization process becomes more entropy-controlled for NaDC than that of NaC, as revealed by the fact that the transferring of NaDC molecules is associated with more breakages of the solvent structure to the micellar region, altogether explaining (for NaDC) > ∆ 0 (for NaC). This seems to be steady with the actuality that the solubilization of glycyl dipeptide in NaDC is more than NaC, and thus, signifying larger involvement of glycyl dipeptide towards the thermodynamics process of micellization for NaDC. Figure 4 depicts that the ∆ 0 and ∆ 0 values in aqueous and various concentrations of glycyl dipeptidedecline with an upsurge in temperature. This behavior is vindicated by the fact that the hydrophobic dehydration (being accountable for more positive ∆ 0 values at low temperatures) displays the role of hydrophobic type interactions in micellization. Similar results have been found for bile salts in binary solvent mixtures in aqueous systems [49]. This effect remains more effective for NaDC as attributed to larger positive ∆ 0 values. Further, the decrease in ∆ 0 values with the rise in temperatures can be manifested by the lessening of hydrogen bonding in spatial structures of water. Subsequently, when the temperature is elevated, less energy is needed in the disruption of spatial arrangements, owing to which more negative ∆ 0 values being observed [49]. Both the bile salts seem to add their existence to this outcome, as recognized by more negative ∆ 0 values in the presence and absence of glycyl dipeptide (Table 4). Similar outcomes have been revealed by others [50] which suggested that the dispersion forces of interactions responsible for negative ∆ 0 values, which characterize the foremost attrac-     A fascinating feature about the data related to Table 4 is that the values of ∆H 0 m are endothermic (i.e., positive) at a lower temperature up to 303.15 K for both bile salts, and then turn to exothermic (i.e., negative) with a rise in temperatures for all the studied systems of glycyl dipeptide, irrespective of the variation in concentration. The larger lack of the -OH group in NaDC compared to NaC can be clearly noticed from more positive ∆H 0 m values for NaDC for all the concentrations of glycyl dipeptide. The micellization process becomes more entropy-controlled for NaDC than that of NaC, as revealed by the fact that the transferring of NaDC molecules is associated with more breakages of the solvent structure to the micellar region, altogether explaining (for NaDC) > ∆S 0 m (for NaC). This seems to be steady with the actuality that the solubilization of glycyl dipeptide in NaDC is more than NaC, and thus, signifying larger involvement of glycyl dipeptide towards the thermodynamics process of micellization for NaDC. Figure 4 depicts that the ∆H 0 m and ∆S 0 m values in aqueous and various concentrations of glycyl dipeptidedecline with an upsurge in temperature. This behavior is vindicated by the fact that the hydrophobic dehydration (being accountable for more positive ∆S 0 m values at low temperatures) displays the role of hydrophobic type interactions in micellization. Similar results have been found for bile salts in binary solvent mixtures in aqueous systems [49]. This effect remains more effective for NaDC as attributed to larger positive ∆S 0 m values. Further, the decrease in ∆S 0 m values with the rise in temperatures can be manifested by the lessening of hydrogen bonding in spatial structures of water. Subsequently, when the temperature is elevated, less energy is needed in the disruption of spatial arrangements, owing to which more negative ∆H 0 m values being observed [49]. Both the bile salts seem to add their existence to this outcome, as recognized by more negative ∆H 0 m values in the presence and absence of glycyl dipeptide (Table 4). Similar outcomes have been revealed by others [50] which suggested that the dispersion forces of interactions responsible for negative ∆H 0 m values, which characterize the foremost attractive force in the process of micellization.
The ∆S 0 m values become positive under the examined experimental temperature, which makes the process of micellization for bile salts entropically favorable. As we know, micellization is a process where the system endures transformation from a monomeric state to micellar state, and thus a decline in ∆S 0 m values have been observed. However, more positive ∆S 0 m values have been observed due to breakage in the arranged structure of solvents around the hydrophobic chains, leading to more randomness in the mixture [51]. However, the decline in ∆S 0 m values with temperature may be explained in terms of the enhanced randomness of hydrophobic chains in mixture solution as a result of breakage of the ordered structure of solvent molecules [48].
In view of the evidence reported above, it is definite that, during the micelle formation of bile salts, entropy driven at lower temperatures and enthalpy controlled at higher temperatures occurs in different investigated concentrations of glycyl dipeptide. It was also observed that hydrophobic as well as electrostatic interactions between bile salts and glycyl dipeptide seem to be the outcomes of the temperature effect on ∆H 0 m and ∆S 0 m values. A similar effect has also been reported in the literature [52,53] for ∆H 0 m and ∆S 0 m values for ionic surfactants It can be inferred from Table 4 that ∆G 0 m , values seem to be negative and lie within the range of −23 to −42 kJ·mol −1 for diverse surfactants other those non-ionic in nature [53]. This displays the feasibility for spontaneous process at all the studied temperature ranges for the formation of micelles of NaC and NaDC in the studied system. The negative values of ∆G 0 m do not virtually depend on temperature orthe nature of glycyl dipeptide. This behavior is accountable for the compensation among ∆S 0 m and ∆H 0 m values and parting ∆G 0 m values nearly unaffected. ∆G 0 m is the summation of the (∆H 0 m ) and (−T∆S 0 m ) contributions, but as the temperature escalates, the enthalpy influence to the free energy rises, while the entropic influence declines, as revealed in Figure 4. Thus, the supremacy of entropy is shifted to enthalpy at the mid-temperature range analyzed for both bile salts.
The above discussions on thermodynamic parameters have given an indication of a significant contribution towards the micellization process by the size of the hydrophobic assemblies. Thus, it is possible that the typical characteristic behaviors of glycyl dipeptide in the presence of NaC and NaDC has been observed, as a result of the hydrophobicity in the −R group as well as the hydrophilicity as a consequence of -NH 3 + and -COO − groups present in the glycyl dipeptide. This may be the prime aspect in estimating the energetic micelle formation of studied bile salts in aqueous glycyl dipeptide.

Enthalpy-Entropy Compensation for Micelle Formation
Enthalpy-entropy recompense stretches linear reliance amidst the variation in enthalpy (∆H 0 m ) and variation in entropy (∆S 0 m ) and acts as a basic foundation for the thermodynamic investigation of the scarce and associated properties of micellization in numerous solvent systems [29,54]. The process of micellization was studied as an influence of following two consequences: (a) the "de-solvation" part, i.e., the dehydration of the hydrocarbon tail of surfactant molecules, and (b) the "chemical" part, i.e., the accretion of the hydrocarbon tails of surfactant molecules in the process of micelle formation [55].
Basically, the recompense phenomenon amid ∆H 0 m and ∆S 0 m in the numerous procedures is as follows [56]: where T c is the compensation temperature and signifies the slope of the ∆H 0 m versus ∆S 0 m curve, and can be construed as solute-solvent interactions, i.e., anticipated as a degree of the "de-solvation" part in the process of self-aggregation. The intercept ∆H 0 m symbolizes the solute-solute interaction and is considered as per an index of the "chemical" part during micelle formation In the present study, there seems to be an excellent relationship between the ∆H 0 m and ∆S 0 m values for NaC and NaDC at all the concentrations, with the correlation constantly falling within the range of 0.997 to 0.999, as revealed by Figure 5. The plots divulge that the compensation temperature T c (277.15-303.15 K) lies in a close conformity with the values given in the literature (270.15-300.15 K) [57], which recognize solvent structural deviations accompanying the process of micelle formation etc. [57][58][59]. The intercept ∆H * m decreased to some extent as we moved from values in water to aqueous glycyl dipeptide was at a smaller proportion in aqueous NaDC than the NaC system, i.e., ∆H * m values are more negative for NaDC than NaC at all studied solvent systems. The factor ∆H * m is the enthalpy at ∆S 0 m = zero and points to the steadiness of micelles, thus, the higher the value of ∆H * m , the lesser the firmness of the micelles [57]. Hence, the obtained results specify the involvement of chemical parts in micellization, and the stability of the micelle formed is improved with the addition of glycyl dipeptides, and this is more distinct with NaDC than NaC. Analogous enthalpy-entropy recompense has also been reported in the case of SDS-amino acid systems [60]. of ∆ * , the lesser the firmness of the micelles [57]. Hence, the obtained results specify the involvement of chemical parts in micellization, and the stability of the micelle formed is improved with the addition of glycyl dipeptides, and this is more distinct with NaDC than NaC. Analogous enthalpy-entropy recompense has also been reported in the case of SDSamino acid systems [60].

Fluorescence Probe Studies of NaC and NaDC
In this section, we explain fluorescence spectra for bile salts viz. NaC and NaDC for the estimation of the CMC values in aqueous and aqueous solutions of glycyl dipeptide at room temperature.
Pyrene, being a colorless solid used for the spectral measurements, is comprised of four fused rings (benzene), which results in a flat aromatic arrangement. Pyrene is prepared in partial organic complexes. The fluorescence spectrum of pyrene is quite sensitive to the polarity of the solvent system, so it is used as a probe to assess the environments of the solvent. This is because its excited state has non-planar shape, unlike that of the ground state. Definite emission bands remain unaffected, but others may vary in intensity owing to the strength of various interactions with the solvent.
The I1/I3dependence of pyrene on the content of NaC and NaDC is demonstrated in Figure 6. The I1/I3 remains unchanged up to a definite concentration of bile salts and then drops down abruptly above it. The first break points in the fluorescence spectra investigation by using pyrene solution as a probe are due to the solvent reliance of the vibrational band intensities of the pyrene fluorescence spectra. The fluorescence spectra of pyrene display five emission peaks at 373, 379, 383, 389, and 393 nm, detected for pyrene solution (2 µ mol·kg −1 ) and fluorescence spectra in water [61]. It has been perceived for pyrene that the fraction of intensity of I1to I3 at 373 and 384 nm, respectively, is a sensitive parameter to characterize the polarity around the probe's environment. The lower value of the I1/I3point to a polar environment [62][63][64] since pyrene has a lesser solubility in aqueous mediums (~10 −7 mol·kg −1 ) than that of hydrophobic solvent (0.075 mol·kg −1 ). It is powerfully dispersed into micelles as quickly as they are formed, and since the conversion can be observed by a rapid decline in the ratio of I1/I3, we can assume the commencement of the micelle formation when the bile salts are mixed in the pyrene solution.

Fluorescence Probe Studies of NaC and NaDC
In this section, we explain fluorescence spectra for bile salts viz. NaC and NaDC for the estimation of the CMC values in aqueous and aqueous solutions of glycyl dipeptide at room temperature.
Pyrene, being a colorless solid used for the spectral measurements, is comprised of four fused rings (benzene), which results in a flat aromatic arrangement. Pyrene is prepared in partial organic complexes. The fluorescence spectrum of pyrene is quite sensitive to the polarity of the solvent system, so it is used as a probe to assess the environments of the solvent. This is because its excited state has non-planar shape, unlike that of the ground state. Definite emission bands remain unaffected, but others may vary in intensity owing to the strength of various interactions with the solvent.
The I 1 /I 3 dependence of pyrene on the content of NaC and NaDC is demonstrated in Figure 6. The I 1 /I 3 remains unchanged up to a definite concentration of bile salts and then drops down abruptly above it. The first break points in the fluorescence spectra investigation by using pyrene solution as a probe are due to the solvent reliance of the vibrational band intensities of the pyrene fluorescence spectra. The fluorescence spectra of pyrene display five emission peaks at 373, 379, 383, 389, and 393 nm, detected for pyrene solution (2 µmol·kg −1 ) and fluorescence spectra in water [61]. It has been perceived for pyrene that the fraction of intensity of I 1 to I 3 at 373 and 384 nm, respectively, is a sensitive parameter to characterize the polarity around the probe's environment. The lower value of the I 1 /I 3 point to a polar environment [62][63][64] since pyrene has a lesser solubility in aqueous mediums (~10 −7 mol·kg −1 ) than that of hydrophobic solvent (0.075 mol·kg −1 ). It is powerfully dispersed into micelles as quickly as they are formed, and since the conversion can be observed by a rapid decline in the ratio of I 1 /I 3 , we can assume the commencement of the micelle formation when the bile salts are mixed in the pyrene solution. The plots of I1/I3 versus the amount of NaC and NaDC in water and aqueous glycyl dipeptide are illustrated in Figure 6. When the micelles are not formed, i.e., below CMC pyrene undergoes the polarity from the environment around the water molecules that ultimately result in higher values of the I1/I3 ratio. However, when the micelles are formed, i.e., above the CMC, pyrene molecules are solubilized into the interior part of the micelle due to their more hydrophobic nature. Thus, the environment around the pyrene senses a hydrophobic solvent, which has smaller polarity owning to a decrease of I1/I3 values. It has been observed from the plots of I1/I3 that the values follow the sequence water > NaC > NaDC, which reflects the increasing nature of the hydrophobicity in the solvent system.
The values for CMC have been computed by plotting the ratio of I1/I3against the concentration of bile salts by using the sigmoidal Boltzman equation (SBE) [64], where all the plots display sigmoidal nature. The CMC values for NaC and NaDC at lab temperature for the considered solvent systems are presented in Table 5. The CMC values measured by this method were also in a similar fashion to those found by conductance measurements. The results corroborate the observations obtained from the conductance measurements.

Conclusions
The conductivity studies lead to a clear picture of the thermodynamic behavior of dipeptides; eventually the polypeptide and hence protein interactions in aqueous environment will also be estimated easily. As shown in the present case, the interaction The plots of I 1 /I 3 versus the amount of NaC and NaDC in water and aqueous glycyl dipeptide are illustrated in Figure 6. When the micelles are not formed, i.e., below CMC pyrene undergoes the polarity from the environment around the water molecules that ultimately result in higher values of the I 1 /I 3 ratio. However, when the micelles are formed, i.e., above the CMC, pyrene molecules are solubilized into the interior part of the micelle due to their more hydrophobic nature. Thus, the environment around the pyrene senses a hydrophobic solvent, which has smaller polarity owning to a decrease of I 1 /I 3 values. It has been observed from the plots of I 1 /I 3 that the values follow the sequence water > NaC > NaDC, which reflects the increasing nature of the hydrophobicity in the solvent system.
The values for CMC have been computed by plotting the ratio of I 1 /I 3 against the concentration of bile salts by using the sigmoidal Boltzman equation (SBE) [64], where all the plots display sigmoidal nature. The CMC values for NaC and NaDC at lab temperature for the considered solvent systems are presented in Table 5. The CMC values measured by this method were also in a similar fashion to those found by conductance measurements. The results corroborate the observations obtained from the conductance measurements.

Conclusions
The conductivity studies lead to a clear picture of the thermodynamic behavior of dipeptides; eventually the polypeptide and hence protein interactions in aqueous environment will also be estimated easily. As shown in the present case, the interaction strength of dipeptide with bio-surfactants increases with concentration increments but decreases with temperature, showing a strong dependence on these parameters. However, NaDC appears to decrease the CMC values to larger extent compared to NaC, due to its more hydrophobic nature and hence promotion of micellization. Furthermore, the results obtained from fluorescence spectroscopic studies corroborate with results obtained from conductivity studies. The aforementioned studies on Glycylglycine and NaC/NaDC thus seem to reveal the underlying facts about the micellar structures and the role played by them in physiological systems.