Udo Kaatze

Titration is a common analytical procedure used in modern laboratories. One of the first types of titration was invented by Joseph Louis Gay-Lussac, known as an author of "The Law of Combining Volumes." Today, titration is an analytical method that allows quantitative determination of a specific substance (analyte) in a sample by adding to it a second reactant solution of known concentration in carefully measured amounts until the reaction of definite and known proportion is completed. To be suitable for a determination, the end of the titration reaction must be observable. This means that the reaction should be monitored by an appropriate detection technique, for example, potentiometry, color indicators, pH, and so forth.  

One of the important applications of titration is analysis of molecular binding. In this case, an appropriate detection system provides quantitative information on the amount of titrant bound to its target and the nature of the binding. This allows the measurement of the binding isotherm, which represents the dependence of concentration of bound titrant on the total or free concentration of the titrant in solution. The binding isotherm then is used to calculate binding constants, stoichiometry, and the free energy of binding. Temperature dependence of the free energy is used to calculate the entropy and enthalpy of binding.  

The key element of titration analysis is the selection of an appropriate detector, which can provide quantitative information on the amount of titrant bound or reacted with the analyte. A range of techniques can be employed in titration analysis. The list of these techniques includes potentiometry, voltametry, electrical conductivity, isothermal titration calorimetery, UV/Vis absorbance, fluorescence, and others. However, none of these methods can serve as a universal detector for the binding of titrant to analyte. For example, fluorescence and UV/Vis absorbance require a change in optical activity of titrant or analyte in the binding as well as optical transparency of the solution. Therefore, titrations often require a complex sample preparation procedure such as extraction of analyte to make a solution with required optical transparency or other procedures such as attaching optical markers to titrant molecules, etc.  

High-resolution ultrasonic spectroscopy (HR-US) is an analytical technique based upon precision measurements of parameters (velocity and attenuation) of ultrasonic compression wave propagating through the analyzed sample. This technique allows direct probing of intermolecular forces and therefore can be used as a universal detector for titration analysis. Any change in molecular structure upon the binding affects intermolecular interactions in the sample and therefore can be detected with ultrasonic measurements. The measured ultrasonic titration profile can be recalculated into the binding isotherm. This technology is extremely sensitive, requires no markers, and can be used in non-transparent samples such as cell cultures or dispersions (for example, blood or milk). Another advantage of the HR-US titration technique is its ability to analyze molecules in their original state without immobilizing procedures or transferring into another environment. 

The key factor responsible for "ultrasonic visibility" of molecular processes is the resolution of the ultrasonic measuring devices, similar to a magnification power of telescopes in astronomy, which determines the visibility of stars. Novel principles of ultrasonic detection utilized in high-resolution ultrasonic spectrometers allow a tremendous increase in the resolution of ultrasonic instrumentation by several orders of magnitude when compared with the traditional ultrasonic techniques. Current applications of this technique include analysis of chemical reactions, conformational transitions in polymers and biopolymers, aggregation and gelation phenomena, particle sizing, phase transitions, stability of emulsions and suspensions, formation of micelles, ligand binding, composition analysis, and many others. 

Recently, capabilities of the HR-US technique have been expanded to titration analysis. HR-US titration spectrometers allow analysis of most chemical reactions and molecular bindings without or with minimum sample preparation. They do not require optical markers and optical transparency and use only a small volume of sample (down to 0.04 mL).  

 Figure 1. The HR-US Titration system: Titration module and HR-US 102 spectrometer are controlled by a PC using HR-US Titration Analysis software. 			

In this example, the Ultrasonic Titration system (Ultrasonic Scientific, Dublin, Ireland) (Figure 1) was used to analyze the binding of alamethicin to unilamellar DMPC (1,2-dimyristoyl-3-

-glycero-phosphocholine) vesicles. Alamethicin is a peptide antibiotic that forms transmembrane channels and regulates membrane permeability by acting as a monovalent cation ionophore. However, while the primary mechanism of antibacterial activity is not yet known, it is generally agreed that binding of peptide monomers to the surface of the target cells causes disruption, permeabilization, or disintegration of cytoplasmic membranes. It was proposed that depending upon the conditions, the peptides associate with membranes in two ways: they either adsorb parallel to the membrane surface (at low peptide/lipid ratios, P/L) or insert perpendicularly into the bilayer (at high peptide ratios), as illustrated in Figure 2. 

Figure 2. Ultrasonic titration profile of unilamellar vesicles of DMPC with pore forming peptide alamethicin in water. Change in ultrasonic velocity in solution caused by addition of the peptide is plotted as function of the molar ratio of alamethicin to DMPC (P/L). The curve for 17 Â°C corresponds to the binding with the gel membrane and for 33 Â°C, with the fluid membrane. (The gel to fluid transition temperature for DMPC membranes was about 23 Â°C.) 			

Binding of alamethicin depends upon the state of the lipid membrane, which could be in a fluid (at high temperature) or gel state (at low temperature). The transition temperature between the fluid and the gel states for the DMPC membranes is about 23 °C. In the current example, the binding was analyzed at two temperatures, 17 °C (gel state) and 33 °C (fluid state).  

The DMPC vesicles in water were prepared by extrusion and 1 mL of 7.54 mM DMPC suspension was loaded into the sample cell of the ultrasonic analyzer. The reference cell was filled with water. Solution of 5 mM alamethicin in ethanol was used as a titrant. The titrant solution was injected to the sample automatically in 1-μL steps. After each injection, the sample was mixed using double stirring systems that provided effective mixing within seconds. Ultrasonic velocity and attenuation in the suspension were monitored over the course of the titration. The same titration of DMPC vesicles was performed with just ethanol as titrant to determine the contribution of ethanol to ultrasonic parameters. The data were subtracted from the original titration curve and was corrected for dilution using Titration Analysis software (Ultrasonic Scientific). The resulting titration curves at two temperatures are given in Figure 2.  

The titration curve at 17 °C (gel state of the membrane) reveals two major stages of binding. The first stage is observed at low peptide to lipid (P/L) ratios, up to 0.0026 (or 1 peptide molecule per 380  lipid molecules). This stage shows a significant increase in ultrasonic velocity and therefore a decrease in compressibility of the system. This can be explained by adsorption of alamethicin molecules on the membrane surface. Molecular dynamic simulations (1) show that the helical structure of alamethicin is stabilized by the hydration water of the membrane. It is known that the strong binding of hydration water leads to a decrease in the compressibility. The adsorption of alamethicin molecules on the membrane surface also can reduce the movements of molecules of lipid, which will reduce compressibility of the membrane. 

Figure 3. Differential ultrasonic titration profile of unilamellar vesicles of DMPC with pore forming peptide alamethicin in water. The slope of the ultrasonic velocity curves (change in velocity per unit of P/L ratio) is plotted as function of the molar ratio of alamethicin to DMPC (P/L). The curve for 17 Â°C corresponds to the binding with the gel membrane and for 33 Â°C, with the fluid membrane. (The gel to fluid transition temperature for DMPC membranes occurs at 23 Â°C.)			

At high alamethicin concentration, P/L > 0.0085, the sound velocity shows a slow linear increase in the velocity with peptide concentration. This stage can be attributed to a solubilization (insertion) of alamethicin in the membranes. The change in the velocity upon the insertion is less in comparison with those for the adsorption when calculated per mole of peptide bound. This is seen clearly in Figure 3, which represents the slope of ultrasonic titration curve (change of ultrasonic velocity per unit of P/L ratio). The lower slope of velocity curve at the second stage can be attributed to a dehydration of peptide upon the insertion. In addition, the effect of peptide on compressibility of membrane also can be different compared with the first stage. Assuming that the initial (at P/L = 0/0.0015) and final (at P/L > 0.01) slopes of the ultrasonic velocity curve (Figure 2) correspond to the adsorption and insertion modes of the peptide binding, respectively, the percentage of alamethicin bound to the surface of the membrane and incorporated in the membrane was calculated and plotted in Figure 4. Figure 4 allows an estimation of the concentration corresponding to the beginning of incorporation of alamethicin into the membrane, the critical concentration for insertion or CCI, which is approximately 20 μM (at P/L = 0.0026) at 17 °C. 

Figure 4. Distribution of bound alamethicin molecules between the adsorbed onto the surface of DMPC membrane and the inserted into the membrane states at 17 Â°C as calculated from the slope of ultrasonic velocity. 			

At 33 °C (fluid membrane), ultrasonic titration curves (Figures 2 and 3) show a more complex profile of binding of alamethicin. The beginning of the binding is significantly different compared with the gel membrane, however, the last binding stage is the nearly the same for both fluid and gel membranes. A significant decrease in ultrasonic velocity in a narrow range of alamethicin concentration (2 m/s within the P/L range of 0–0.04) is an indication of a cooperative change in the lipid structure upon the peptide binding. One of possible reasons could be a fusion of lipid vesicles induced by the peptide. However, further studies of the binding process in a wider concentration range of lipids and at different temperatures could be essential to clarifying the mechanism of this process. These analytical tasks can be performed using the HR-US technique with expanded titration capabilities. 

HR-US titration analysis is a new, powerful tool in research and analytical laboratory work for quantitative measurements of different processes and compounds. This technique provides universal detection capabilities for molecular binding, as any binding affects intermolecular forces in the sample, and therefore, can be detected with ultrasonic measurements. Because the measurements do not require any optical transparency, molecular markers or other properties of solution and solutes, the complex sample preparation procedures in many cases become obsolete. 

1. P.D. Tieleman, H.J.C. Berendsen, and M.S.P. Sansom, 

 are with Arbeitsgruppe Komplexe Fluide, III Physikalisches Institut, Georg-August-Universitaet Goettingen (Goettingen, Germany).			

 are with Ultrasonic Scientific (Dublin, Ireland). E-Mail 

 is with the Department of Chemistry at University College Dublin (Dublin, Ireland).			

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