Analyzing Demicellization Data from Isothermal Titration Calorimetry

Surfactants such detergents are indispensable compounds that are often used in biochemical and industrial applications. They are essential for processes such as purification, extraction and handling membrane proteins. Detergents are amphiphilic by nature meaning they offer a membrane-like environment. Integral membrane proteins need a membrane-like environment to preserve their native functions and structures when in aqueous solutions.

It is important to determine which detergent is appropriate for the stabilization, solubilization and reconstitution of the preferred protein as well as its structural, biochemical and biophysical analysis.

As a result, it is essential to screen different types of detergents. For each process, the suitability is governed by the membrane protein of interest and this choice relies on a number of physicochemical properties such as polarity, chain length, headgroup charge or headgroup size. Conversely, an optimal detergent deemed for membrane protein separation may not be the best choice for in vitro analyses and downstream purification.

SDS is a harsh detergent which can denature proteins, rendering them inactive; ionic detergents cannot be used for ion-exchange chromatography or isoelectric focusing; and Triton-X 100 detergents absorb the UV range and impede with spectroscopic studies. While dialysis is often used for removing detergents to achieve protein reconstitution, detergents of a low critical micellar concentration (CMC) need a long analysis duration.

A basic property of a surfactant is it's CMC, the critical micelle concentration. When the concentration of surfactants in aqueous solutions surpasses the CMC, they form micelles or colloidal aggregates. Changes occurring in different physical properties can be seen at or around this concentration of detergent.

While these changes occur, the detergent can be experimentally established using a range of techniques such as nuclear magnetic resonance spectroscopy, conductivity and surface tension measurements and dye binding experiments.

However, isothermal titration calorimetry (ITC) is a suitable technique that allows an accurate determination of the CMC. This method offers high reproducibility, has excellent sensitivity and delivers unparalleled resolution. It also eliminates the need for sample labeling and gives a comprehensive thermodynamic profile for experiments including the molar entropy and enthalpy changes that accompany micellization.

As a result, the ITC method is often used for measuring the CMCs for different types of surfactants such as bile salts, alkyl phenol ethoxylates, tritons and alkylpyrinidinium halides to name a few. CMCs of block copolymers, fluorinated surfactants, proteins, surface-active peptides and more are also determined with the ITC method.

Two strategies for data analysis are often employed when using ITC to acquire the heat of demicellization of surfactants and the CMC. In the first approach, the initial derivative of the heat of demicellization regarding surfactant concentration is measured, and in the second method the demicellization isotherm is applied with a general sigmoidal fit.

This article shows how both strategies can be effectively integrated to give a data-analysis approach that provides excellent reproducibility, without any user bias.

Models of Micelle Formation

When the ITC technique is used for CMC analysis, a suspension of surfactant in a solvent, such as water or a buffer, is titrated into the same solvent which contains no surfactant. The concentration of the surfactant in the suspension added is far greater than the CMC.

The following ranges define the isotherm of this demicellization titration:

  • Micelles break down into monomers at surfactant concentrations less than the CMC
  • The first micelles emerge when the concentration of the surfactant nears the transition point near the CMC
  • Micelles dilute at nearly constant monomer concentration when more micellar surfactant is added

In ITC experiments, the demicellization process determined is the opposite of micelle formation, and this can be elucidated with different types of thermodynamic models. Under  standard models, it is presumed that only micelles and detergent monomers exist throughout the process, similar to the pseudophase separation and the closed-association models shown in Figure 1A and Figure 1B respectively.

Alternatively, models can also consider the population of detergent assemblies of intermediate aggregation numbers, similar to the isodesmic and the cooperative aggregation models shown in Figure 1C and Figure 1D respectively.

Thermodynamic models of micelle formation. (A) Pseudophase separation model. (B) Closed association model. (C) Isodesmic model. (D) Cooperative aggregation model.

Figure 1. Thermodynamic models of micelle formation. (A) Pseudophase separation model. (B) Closed association model. (C) Isodesmic model. (D) Cooperative aggregation model.

The demicellization isotherm analysis is based on the pseudophase separation model, which assumes micelles and monomers to be separate pseudophases in equilibrium with one another. The pseudophase separation model does not make any precise assumptions regarding the micelles’ structure or size, however the closed-association model makes specific assumptions regarding the micelles’ size. Here, micellization is also considered as a stoichiometric association reaction.

When the detergent concentration approaches the CMC, both the pseudophase separation and the closed-association models predict rapid changes in the sample’s physicochemical properties. This happens for standard aggregation numbers of greater than 50.

In contrast, the cooperative aggregation and isodesmic models reproduce steady changes in a better way. The former assumes that the formation of dimers is relatively more complex than the following association steps, while the latter assumes the formation of stepwise aggregates, with each and every association step defined by the same association constant.

While these two models are more practical when compared to the pseudophase separation and closed-association models, they need more fitting parameters, and resultantly are unstable for studying demicellization data or experimental micellization. The pseudophase separation model is more reliable so it can be used for studying the demicellization isotherms acquired from ITC.

Facile Data Analysis of Demicellization Isotherms

In most surfactants, the demicellization thermogram is combined to acquire a sigmoidal isotherm. The isotherm’s transition range is defined by a sudden decrease in the recorded heat. The isotherm produces the CMC and Qdemic, which is the heat of demicellization, using the following methods:

  • The extremum in the initial isotherm derivative regarding the surfactant concentration in the transition range is assumed to be the CMC. THe Qdemic is  derived from the variation in heat between both the linear pre- and post-transition baselines at the CMC
  • The isotherm is fitted with a common sigmoidal function to obtain the Qdemic and CMC via nonlinear least-squares fitting.

Both of these methods can be integrated to get a simple, unbiased examination of demicellization isotherms. In the first step, the parameters illustrating the isotherm are calculated and in the second step these calculations are employed as initial values for a nonlinear least-squares fit to the demicellization isotherm. This is done due to a common sigmoidal function as per the equation given below:

Where, Q represents the standardized heat of reaction and c_D denotes the concentration of the surfactant in the calorimeter cell.

Excel sheet provided for analysis of ITC demicellization isotherms. After isotherm data has been loaded and the total concentration of surfactant in the syringe has been provided by the user (1)., estimate values of all fitting parameters are displayed immediately (2). After a nonlinear leastsquares fit (3), fitting parameters are available (4) and can be assessed with regard to precision by means of confidence intervals (5). Additional checkboxes provide more options as specified in the text (0). Only values of orange cells should be modified.

Figure 2. Excel sheet provided for analysis of ITC demicellization isotherms. After isotherm data has been loaded and the total concentration of surfactant in the syringe has been provided by the user (1)., estimate values of all fitting parameters are displayed immediately (2). After a nonlinear leastsquares fit (3), fitting parameters are available (4) and can be assessed with regard to precision by means of confidence intervals (5). Additional checkboxes provide more options as specified in the text (0). Only values of orange cells should be modified.

In Figure 2, more checkboxes give more choices as given in the text (0). Changes should be made only to values of orange cells. The following steps should be followed for demicellization isotherm analysis using the Microsoft Excel worksheet:

  • Demicellization information should be loaded in a standardized form within the worksheet.
  • Once the data is loaded the approximate values for parameters are quickly determined.
  • The estimates in the blue box, as well as their graphical representation in the plot, should be checked. At this stage, if the estimates are insignificant, users should enter their own estimate into the subsequent cell in the red box and must make sure that the checkbox is unchecked for the subsequent parameter to reject it as an inconsistent parameter from the fit to be carried out in the following step.
  • A nonlinear least-square fit to the data should be carried out by clicking the “Fit” button.
  • The ensuing best-fit values in the red box as well as the fit in the plot should be checked. In case a specific value does not result in a good agreement of the fit with the data, the subsequent parameter should be changed and unchecked to keep it fixed and the fit should be repeated.
  • The fitting accuracy of a best-fit value can be evaluated by selecting the preferred parameter in the dropdown menu over the “Confidence Interval” button and clicking the latter. The results of the confidence interval estimates update the “Confidence Interval” sheet. Confidence intervals of other parameters must then be repeated. The “Keep CI Sheet” button given on the “Confidence Interval” sheet can be clicked, if the parameter results need to be maintained.

Case Studies: CMC Determination for DM and CHAPSO

In order to demonstrate the method, demicellization experiments were performed for the zwitterionic detergent 3 ([3 cholamidopropyl]dimethylammonio)-2 hydroxy-1 propanesulfonate (CHAPSO) and the nonionic detergent n decyl-β D maltoside (DM).

A VP-ITC instrument was used to carry out both titrations for a filter period of 2 seconds and a stirrer speed of 310 rpm. In the case of DM demicellization, about 24 mM of detergent was titrated into triple-distilled water with 18 MΩ resistivity. The experiment was performed at 25°C temperature with a reference power of 63 µJ per second, with a spacing of 300 seconds and an injection volume of 10 µL. In the case of CHAPSO demicellization, about 120 mM of detergent was titrated into 20 mM of a sodium phosphate buffer at 7.0 pH.

The experiment was performed at 35°C temperature with the reference power at 13 µJ per second, with a spacing of 750 seconds and aninjection volume on 5 µL. NITPIC was employed for assigning baselines and for combining thermogram peaks by singular value decomposition for data analysis.

Certain measures were undertaken during sample preparation to acquire accurate results from demicellization titrations. Before use, water was filtered, and the same was applied for both set of samples in the cell and the syringe.

Both detergents and hygroscopic compounds were allowed to equilibrate to room temperature and then weighed on a highly accurate microbalance to prevent errors in stock concentrations. Foam can be removed by centrifuging the samples at low speeds. If the quantity of the detergent is adequate, then an ITC system with the VP-ITC can be used to achieve a higher signal-to-noise ratio.

Representative analysis of the demicellization of DM and CHAPSO as monitored by ITC. (A,B) Isotherms depicting integrated heats of reaction, Q, versus titrant concentration and (C,D) confidence interval for the adjustable parameters ΔH°mic and CMC are shown for the demicellization of (A,C) DM and (B,D) CHAPSO. (A,B) Experimental data (black solid circles), generic sigmoidal fit according to Eq. (1) (red open circles), pre-transition and post-transition baselines of initial estimate and fit (dotted and dashed blue and red lines, respectively), Qdemic at the CMC as derived from initial estimate and fit (blue and red solid lines, respectively), and estimated boundaries of transition region (vertical blue dashed lines). (C,D).

Figure 3. Representative analysis of the demicellization of DM and CHAPSO as monitored by ITC. (A,B) Isotherms depicting integrated heats of reaction, Q, versus titrant concentration and (C,D) confidence interval for the adjustable parameters ΔH°mic and CMC are shown for the demicellization of (A,C) DM and (B,D) CHAPSO. (A,B) Experimental data (black solid circles), generic sigmoidal fit according to Eq. (1) (red open circles), pre-transition and post-transition baselines of initial estimate and fit (dotted and dashed blue and red lines, respectively), Qdemic at the CMC as derived from initial estimate and fit (blue and red solid lines, respectively), and estimated boundaries of transition region (vertical blue dashed lines). (C,D).

As shown in Figure 3A, upon testing the DM demicellization, initial estimates were obtained that were similar to the final best-fit values. This is because an adequate number of injections was used in the experimental data which showed a good signal-to-noise ratio. This led to narrow confidence intervals for the preferred fit parameters as shown in Figure 3C.

However, CHAPSO demicellization resulted in a relatively complex isotherm. Due to the sharp increase of initial heats the pre-transition baseline slope (m1) has been overestimated.

As a result, impractical parameter values are obtained. One way to overcome this problem is to fix m1 and m2 to zero and to repeat the fit. In case proper values are not found, the estimates can be used, and these can be obtained by checking the “Use estimates as values for fixed parameters” option. Figure 3B shows the outcome of this approach.

The confidence intervals are asymmetric and wider for the DM dataset and yet are still narrow (Figure 3D). Therefore, in the most challenging situations, user intervention is kept to a minimum and a reliable analysis of ITC demicellization data can be obtained. The solution can also be identified easily. For additional analysis, permanent values can be used by unchecking the “Use estimates as values for fixed parameters“option.

Conclusion

The article has shown how a two-step method offers the ΔH°mic and CMC quickly with no user input. This approach simply uses the surfactant concentration and the standardized and combined isotherm in the syringe.

The analysis of demicellization data was adapted as a Microsoft Excel spreadsheet, which helps in assessing the fit with respect to confidence intervals. With the aid of this analysis strategy, both ΔH°mic and CMC are effectively extracted from demicellization isotherms, and hence, fast, accurate, and reproducible results are obtained.

This information has been sourced, reviewed and adapted from materials provided by Malvern Panalytical.

For more information on this source, please visit Malvern Panalytical.

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