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Keywords:

  • pH titration;
  • titration;
  • Gran plots;
  • equivalence point;
  • amino acid titration

Abstract

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS AND DISCUSSION
  5. CONCLUSIONS
  6. LIST OF RELEVANT WEBSITES
  7. REFERENCES

The quantitative character of biochemistry imposes some familiarization of the student with analytical practice in laboratory work and data analysis. This article describes the application of an inexpensive home-made precision titrator for titrant standardizations, introducing the students to amino acid and protein pH titrations and data analysis.

pH titration is not only a very useful tool for the quantification of inorganic and organic analytes from pollutants to medicines, but it is also a powerful tool for the investigation of the ionic state of amino acid side chains of proteins and enzymes. However, the stability of proteins, for instance, can also be investigated by comparing the proton binding to the native and unfolded states of these macromolecules. To enable the students to handle the more elaborate pH titrations, including those applied to proteins [1, 2] and other titratable molecules, they were first trained on the standard HCl and NaOH titrant solution preparation as a preceding step for more complex titrations. The analytical thought developed during the initial steps of the equivalence point determination by Gran plot [3] and its comparison to the value calculated by the first derivative method was further extended to an approach to non-linear regression of amino acids and gelatin titration data as the basis for the comprehension of protein titration curve calculations and analysis.

MATERIALS AND METHODS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS AND DISCUSSION
  5. CONCLUSIONS
  6. LIST OF RELEVANT WEBSITES
  7. REFERENCES

The titrator (Fig. 1) was constructed by mounting a syringe (inner diameter = 5 mm) on a 25-mm micrometer. The linear displacement of the syringe piston was produced by the micrometer coupled to a stepper motor (1.8°/step) purchased from Jameco Electronics (Belmont, CA). A polytetrafluoroethylene dispensing tube (0.1-mm inner diameter) was adapted at the syringe tip to avoid undesirable titrant diffusion. The delivered volume by the micrometric linear displacement was calibrated gravimetrically using a 0.0001-g precision balance.

The schedule of experiments included two full periods divided into two steps. The first step included the preparation of primary standard preparations with their respective HCl and NaOH titrations and equivalence point calculations. The second step included the titration of the analytes and the lengthy determination of pK, volume subtractions, and equivalence volume.

The solvent we used for all solutions was double distilled water, collected and stored in an N2 atmosphere. The primary standard solutions 0.100 M Tris (analytical grade, Merck) and 0.100 M potassium hydrogen phthalate (ACS Standard, Sigma) were also prepared in an N2 atmosphere. The HCl titrant was prepared in a fume hood by transferring ∼2 ml of concentrated HCl to a graduated cylinder containing ∼100 ml of water, and the volume was completed to 250 ml (stock solution). The NaOH standard was prepared by fast washing of NaOH (∼12 g) and dissolving the remaining carbonate-free lentils in 20 ml of CO2-free double distilled water. Immediately before the standard titrations, proper dilutions of HCl and NaOH stock solutions were prepared. The Tris and the biphthalate standards were diluted to 1:50 and 1:5, respectively. The amino acids β-alanine (Sigma) and aspartic acid (Carlo Erba) were both prepared at 10 mM. Gelatin (0.200 g) was dissolved in 20 ml of boiling water, cooled, and then sonicated, and the volume was completed to 100 ml. The titration vessel was kept CO2-free by continuous nitrogen flushing and magnetic stirring with titrations performed at 25 °C. The standard solutions were volumetrically (4 ml) transferred to the titration vessel, the syringe and dispensing tube were carefully filled with titrant, avoiding air bubbles in the dispensing path, and afterward the titrator was zeroed. The same procedure was used for the analytes and their respective blank solutions. Finally, for each titration, the pH meter (Micronal, model B474) equipped with a combined glass electrode was calibrated with standards of pH 7.00 and pH 4.00, the RS232 output of the instrument was connected to the serial port of a computer, and the titration was performed using SoftwareWedge (Tal Technologies, Inc.) for data collection. As the linear displacement rate of the syringe piston was kept constant, the final volume was determined by the gravimetrically calibrated data (Fig. 2) using the unitary density for the water. The final titration volume was divided by the total number of records. This average value corresponding to the first dispensed volume was used as the increment for generating the titration volume (v) data, each item having its respective pH value. For the primary standards and for each analyte titration, the students were instructed in computer table construction (e.g. Microsoft Excel) containing the following:

(v) the titrant added volume,

pH,

(V + v) V initial volume (4 ml) + (v),

10−pH representing [H+math image with unitary γmath image for practical purposes, and

ϕ the product (V + v) × 10−pH.

The standard NaOH solution was used to bring the amino acids and gelatin close to the completely ionized state immediately before each titration with standard HCl solution and to adjust, nearly as possible, the pH of the blanks to the initial pH value of the amino acids and gelatin. Finally, amino acids, gelatin, and blank volume values were numerically treated by polynomial interpolation to the same pH values to subtract from the amino acids and gelatin titration volumes their respective blank volume titrations.

RESULTS AND DISCUSSION

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS AND DISCUSSION
  5. CONCLUSIONS
  6. LIST OF RELEVANT WEBSITES
  7. REFERENCES

A simple plot of the collected values is shown in Fig. 3, IA and IIA. Fig. 3, IB and IIB, shows the first derivative (Δvolume/ΔpH × volume) of the whole data since a software utility (GraFit from Erithacus Software, Ltd.) was used for this purpose.

In general, if any software is available, the use of manual chronometric registers and data plotting is recommended to the students. In this case, the data collection will take longer, the number of points plotted will be fewer, and the number of students participating will be proportionally reduced. Thus, the use of a computer is strongly recommended. To save time, the weighing of the standards and analyte samples on the day before the experiment as well as a short review of the least squares statistics is also suggested.

For the standards, the equivalence estimated visually and calculated by linear regression of the side of the Gran plot (Fig. 3, IC and IIC), where v > equivalence volume, was compared with the value found by the first derivative. As observed, they were always identical within the limits of experimental error. For example, the HCl titrant equivalence volume calculated by Gran plot and first derivative, as shown in Fig. 3, B and C, were 0.3524 and 0.3518 ml, respectively. The value estimated visually is close to 0.35 ml. Asking about which method should be chosen, the general consensus was for Gran plots since few data values are sufficient and these plots deal with straight lines. An alternative to the Gran plot for equivalence point determinations is to plot the calculated activity coefficient γmath imageversus titration volume as shown in Fig. 4. The activity coefficient γmath image can be calculated by the extended Debye-Hückel equation transformed to Equation 1,

  • equation image(1)

where μ is the ionic strength of the H+ ion throughout the titration. The 0.51 parameter comes from the original equation as does the 2.95 parameter, which corresponds to the quotient of 900 (the size in picometers of the H+ ion) by 305, another parameter from the Debye-Hückel equation. As observed in Fig. 4, the activity coefficient γmath image expressed as 10−pH/[H]+ remains practically unitary throughout the titration as mentioned above.

Once the equivalent volume of the titrant was known, its concentration in the stock solution was calculated by Equation 2,

  • equation image(2)

where MTitrant is the molar concentration of the titrant, V is the volume of the primary standard (Tris or biphthalate), veq is the equivalence volume, and fd Titrant and fd Standard are the dilutions of titrant (HCl or NaOH) and the primary standard, respectively.

At this point, we have to remark that Gran plots and/or the derivative methods can be used for amino acid titrations if they are applied to the equivalence point determination of the titratable group, which is more distant from the other group(s) on the pH scale (see Fig. 5). This group, as we know, consumes the same titrant equivalent of each other group that has pK values closer to one another if more than two titratable groups are present. This allows us to estimate, by extrapolation, the equivalence point of the next titratable group. It is also useful to remember that for monoamino-monocarboxyl amino acids the first equivalence point corresponds to the isoelectric point.

The pK values of β-alanine (Fig. 6A) and the closer pK values of aspartic acid, viz. α-COOH and β-COOH (Fig. 6B), were more precisely determined by plotting a curve to fit the titration data to Equation 3,

  • equation image(3)

where y is the volume (or any proportional data), and LL, IL, and UL are the lower limit, the intermediate limit, and the upper limit of the titration volume, respectively. The variable x is represented by the pH values, and the unknown parameters are the pK values. Strong emphasis is given to the use of Equation 3 since the same approach and few mathematical derivations of this equation can be extended to the analysis of the amino acid side chain ionization pattern on protein titrations [4]. For a single pK molecule or for a range in which a single group of a more complex molecule dissociates, the two limit equation (Equation 4) can also be used.

  • equation image(4)

where y is the volume (or any proportional data), LL and UL are the lower limit and upper limit of the titration volume, respectively, the variable x is represented by the pH values, and the unknown parameter is the pK value.

The pK values of β-alanine were: pKαCOOH = 3.61 and pKmath image = 10.48 (Fig. 6A). For the aspartic acid the values were: pKαCOOH = 1.87, pKβCOOH = 3.86, and pKmath image = 10.2 (Fig. 6B). All these values are comparable to those listed in the literature taking into account the fact that the curves were not corrected for the alkaline error of the electrode, that hysteresis due to KCl diffusion from the electrode to the solution was present, and also that some CO2 absorption was expected to occur at higher pH values. To prevent these possibilities in more elaborate titrations such as those of proteins, the students were advised to use solvents of higher ionic strength and to use permanent pure nitrogen flushing.

A short discussion was proposed about the influence of a proton acceptor and a proton donor group bound to the same carbon (α-carbon) on their respective dissociation constants as observed in aspartic acid. The pK references used were those of β-alanine, bearing in mind the fact that this amino acid only differs from aspartic acid with regard to the β-carbon substituents: hydrogen in β-alanine and carboxyl in aspartic acid.

Finally, the results of gelatin titrations (Fig. 7) were briefly discussed. The same reasoning applied to the titrated amino acids was used with gelatin as an example of a “complex” titration. Equations 3 and 4 were respectively applied to the pH ranges 7.5–12 and 3–4.5. The calculated pK values for the basic group region were 8.41 and 10.80. In the carboxyl region, the pK value was 3.51.

CONCLUSIONS

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS AND DISCUSSION
  5. CONCLUSIONS
  6. LIST OF RELEVANT WEBSITES
  7. REFERENCES

This practical study is suitable for two full periods of lab work, being applicable to either individual or group training. It has the advantage of covering all steps of typical lab work from preparation of standard solutions to analytic titrations, data analysis, and interpretation of final results, including some graphical alternatives for the equivalence point determination as well as some rudiments of instrument calibrations and data acquisition.

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Figure FIGURE 1.. Sketch of the micrometric titrator showing the syringe and the stepper motor.

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Figure FIGURE 2.. Calibration curve of the dispensed volume. The weight of water was recorded at increments of 0.5 mm on the linear displacement of the syringe piston. The syringe has a 5-mm inner diameter, and the slope and the intercept of the linear fit of three independent measures on a 0.0001-g precision balance were 1.96 × 10−2 and 1.88 × 10−5, respectively. The registers were performed at sea level at 25 °C. For practical purposes, the unitary density of water was considered.

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Figure FIGURE 3.. Titration curve of 2.0 × 10−3M Tris and 2.0 × 10−2M potassium hydrogen phthalate.Graphs IA and IIA show the whole titration curve represented as pH versus titrant (HCl) volume. On graphs IB and IIB, the first derivative (Δvolume/ΔpH versus volume) of the titration data shows the minimal value corresponding to the equivalence volume of 0.352 and 0.193 ml, respectively, for HCl and NaOH. The Gran plot ϕ [(V + v) × 10−pH] as a function of the titrant volume is shown in graphs IC and IIC, which present the same equivalence volumes. Observe the line passing through the equivalence volume in all graphs.

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Figure FIGURE 4.. Titration curve of 2.0 × 10−3M Tris expressed as activity coefficient versus titrant volume. The activity coefficient γmath image was calculated by the extended Debye-Hückel equation (see text). Observe that the activity coefficient γmath image expressed as 10−pH/[H]+ remains practically unitary throughout the titration.

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Figure FIGURE 5.. Titration curve of aspartic acid. The concept of equivalence was explored with the first derivative and with the Gran plot. This approach is useful for the estimation of the other equivalence volume(s) provided the determined equivalence is of an isolated titratable group as seen for the α-amino of aspartic acid. Thus, as the equivalence of this group was 0.022 ml, one can estimate 0.044 and 0.066 ml for the respective equivalence volumes of β- and α-carboxyls.

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Figure FIGURE 6.. Titration curves of β-alanine (graph A) and aspartic acid (graph B). The curves using the equations for one or two pK values (see text) were fitted to the experimental data. The calculated pK values are marked with triangles. The squares represent the experimental data, and some values were suppressed for clarity.

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Figure FIGURE 7.. Titration curve of gelatin. The triangles mark the pK values. Two classes of basic groups were observed in the alkaline range of the pH scale, and a typical carboxylate (pK = 3.51) was titrated in the acid range.

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REFERENCES

  1. Top of page
  2. Abstract
  3. MATERIALS AND METHODS
  4. RESULTS AND DISCUSSION
  5. CONCLUSIONS
  6. LIST OF RELEVANT WEBSITES
  7. REFERENCES