Kinetic estimation of hydrogen isotope exchange reaction between tritiated-water (HTO) vapor and each amino acid in a heterogeneous system

Abstract

The hydrogen isotope exchange reaction between HTO vapor and each amino acid has been observed in order to establish a method of estimation of the internal exposure of organically bound tritium in a heterogeneous system at 25∼70°C. Rate constants (k) for the amino acids have been obtained by applying the A″-McKay plot method. Using these k values, Arrhenius plots for both the COOH and NH₂ groups are drawn, and linearity was obtained over the range of 25∼70°C. Comparing the rate constants, the following four statements can be made regarding the T-for-H exchange reaction. (1) The reactivity of the functional groups in amino acids increases with increasing temperature. (2) Applying Taft's equation, the ratio of polar effect to steric effect is 2:8 in the COOH group and 9:1 in the NH₂ group at 25°C. (3) The A″-McKay plot method is useful for studying the reactivity of materials, not only with one (or the same kind of) functional group(s) but also with two different kinds of functional groups. (4) The method used in this work may be useful to investigate the behavior of organically bound tritium, quantitatively.

Keywords:

• T-for-H exchange reaction
• the A″-McKay plot method
• amino acids
• Taft plot
• exchangeable organically bound tritium

1. Introduction

The external exposure from tritium (T) can be neglected because the maximum energy of the emitted  β ⁻-ray is very low (18.6 keV). In the case of tritiated-water (HTO), T can be incorporated into the body and behaves as free water tritium (FWT) [1]. T also causes a hydrogen isotope exchange reaction [2] (T-for-H exchange reaction) that can be divided into exchangeable organically bound tritium (OBT) and non-exchangeable OBT [3]. Exchangeable OBT behaves as FWT in the body, and the dose coefficient of T in FWT is unity. On the other hand, the dose coefficient of T in non-exchangeable OBT is 2.3 [4]. This is a key distinction that makes the study on the internal exposure of T and is very important. The T concentration in the atmosphere will increase as more reprocessing plants for spent nuclear fuel come online and nuclear fusion research continues. Thus, the study on exchangeable OBT and non-exchangeable OBT is more important.

Previously [5], we have studied the T-for-H exchange reaction over the range of 50∼70°C using the A″-McKay plot method, and the rate constants (k) of the materials were obtained. We also have estimated the reactivity of functional groups using k. Considering the evaluation of internal exposure, it is found that observing the T-for-H exchange reaction under the biological temperature (≈ 36°C) in a heterogeneous system is necessary [6].

Taking into account the above background information, the T-for-H exchange reaction (gas–solid reaction) between HTO vapor and each amino acid having two different kinds of functional groups (i.e. COOH and NH₂ groups) is observed at 36°C and 25°C. The observed data were applied to the A″-McKay plot method to obtain the k for the functional groups in each amino acid. Each Taft plot was also drawn by using these k values. Consequently, the ratio of the polar effect to the steric effect in the reaction can be estimated. Observing the reaction at various temperatures, the temperature dependence is clarified. From these experiments, the effect of T on the human body can be estimated.

2. Theoretical background

As mentioned in previous literature [6–11], the A″-McKay plot is described by the following equation.

where k is rate constant, t is time, x is activity observed (for the solid sample in the reaction) and x _∞(F) is the calculated activity (for the solid sample)

This method has three characteristics: (1) The value of the slope equals k when the plot of −log₁₀[1 − x/x _∞(F)] vs. t is drawn. (2) k can be also obtained in a heterogeneous system. (3) It is possible to study the reactivity of the materials not only having one (or the same kind of) functional group(s), but having three different kinds of functional groups.

3. Experiment

Using a vacuum line [12], each T-for-H exchange reaction was observed between HTO vapor and several amino acids at 25, 36, 50, 60, or 70°C. Each solid sample was sufficiently powdered in an agate mortar, then dried and sieved to obtain a grain size between 53 and 75 μ m in diameter [12]. For each reaction run, both 7.22 mg of HTO water as a gas sample (whose specific activity was 8 × 10⁵ Bq g⁻¹) and 15.0 mg of each solid material were used. The method of observation was the same as previously reported [12]. After the reaction, the solid sample was dissolved in 3.00 ml of water, and the activity of 1.00 ml of the solution was measured with a liquid scintillation counter. Because the half-life of T is 12.3 years, the activity was corrected by a calculation every three months.

In order to apply the obtained data to the A″-McKay plot method in the gas–solid reaction, the excess experiment [13,14] was performed. From the experiment, it is found that the total number of ¹H atoms and T atoms in this HTO vapor are much larger than the total number of H atoms at the solid sample surface contributing to the reaction. In other words, we changed the mass of the solid samples in order to use the analysis method of pseudo first order reaction.

Based on the two previous reports [15,16], ¹H atoms directly bonded to the carbon atom cannot participate in the reaction. Accordingly, it is found that the exchange ¹H atoms are the only ¹H atoms in the COOH and NH₂ groups under the conditions in this work.

4. Results and discussion

4.1. Applicability of the A″-McKay plot method

Based on the former section, the excess experiment was carried out. If the excess condition is satisfied, total activity of each solid sample material is proportional to the mass in the reaction. Figure 1 shows the excess experiment of the l-aminobutylic acid at 70°C. This figure shows a linear relationship between the activity and mass. That is, the number of reactions per unit is constant in the mass range of 5∼60 mg and the quantity of the HTO vapor is much in excess to the l-aminobutylic acid. The results obtained by using other sample materials were similar to that of the amino acid.

Figure 1. Activity of l-aminobutyric acid vs. mass of the material for the reaction. Gas sample material: HTO vapor; Reaction temp: 70°C; Reaction time: 1.0 h.

4.2. Reactivity of each material

The T-for-H exchange reaction between HTO vapor and each amino acid was observed. The relation between reaction time and the specific activity of l-aminobutylic acid at 25°C was drawn (Figure 2). It is found that the reaction occurred because the specific activity of T increased with time. From the previous report [17], it can be assumed that the reactivity of the COOH group is larger than that of the NH₂ group in the same molecule. Therefore, it is found that the three following reactions occurred in this figure.

Figure 2. T specific activity vs. time for the reaction between l-aminobutyric acid and HTO vapor. Reaction temp: 25°C.

Part (1): From the origin to (A)

Both the COOH group and NH₂ group at the surface of l-aminobutylic acid react with HTO vapor, and a reaction at the surface of the COOH group reaches equilibrium at (A).

Part (2): From (A) to (B)

Only the NH₂ group at the surface of l-aminobutylic acid reacts with HTO vapor and a reaction at the surface of the NH₂ group reaches equilibrium at (B).

Part (3): After (B)

T on the solid surface diffuses to the inside.

4.3. Reactivity of COOH and NH₂ groups in each material

In Figure 2, the data obtained from Part (1) was applied to the A″-McKay plot method to obtain the rate constant (k _NH2) [18]. Figure 3 shows the A″-McKay plot of the NH₂ group, and the slope of the straight line of the NH₂ group is equal to k _NH2. In order to obtain the rate constant (k _COOH), the reaction value of the NH₂ group in Part (1) was calculated from the broken line. Then the reaction value of the NH₂ group thus obtained was subtracted from the total reaction value. Each data thus obtained was applied to the A″-McKay plot method in order to obtain k _COOH. The slope of the straight line of the COOH group in Figure 3 is equal to k _COOH. For other materials, the values of k for the COOH and NH₂ groups are shown in Table 1. The table shows that the reactivity of each group increases with increasing temperature. In this way, the A″-McKay plot method is useful to analyze two steps of a simultaneous reaction.

Figure 3. A″-McKay plots for l-aminobutyric acid in the reaction at 25°C. ▴: COOH group, •: NH₂ group.

Table 1. Rate constants (k) for COOH and NH₂ groups in each sample material and activation energy (E _a).

Material	Structural formula		k/10^−2 h^−1					E a
			25°C	36°C	50°C	60°C	70°C	kJ · mol^−1
l-glycine [15]		k NH2	3.3	3.9	5.9	7.2	8.2	18
		k COOH	3.9	5.4	10	11	13	24
l-α-alanine [15]		k NH2	3.1	3.7	5.3	8.4	12.5	26
		k COOH	3.8	5.3	14	20	37	44
l-aminobutyric acid		k NH2	2.7	3.5	5.6	7.3	8.5	23
		k COOH	3.7	5.1	12	17	21	35
l-norvaline [17]		k NH2	2.5	3.3	5.5	7.3	7.9	23
		k COOH	3.6	4.8	11	16	20	35
l-valine		k NH2	2.3	3.0	5.3	6.7	7.5	24
		k COOH	3.3	4.2	10	15	17	34
l-leucine		k NH2	2.4	3.2	5.4	6.9	7.7	24
		k COOH	3.5	4.5	11	16	19	35
l-2-phenylglycine [18]		k NH2	3.5	4.0	6.0	7.6	8.7	18
		k COOH	3.7	5.6	14	17	18	33
l-2-phenylalanine [18]		k NH2	3.4	4.0	5.8	7.6	8.2	18
		k COOH	3.9	5.6	14	16	18	33

Using these k values, Arrhenius plots for both the COOH and NH₂ groups are shown in Figure 4. The correlation coefficients of the straight lines in the figure satisfy the condition of significance at the 1% level. As previously reported [18], linearity was seen in the range of 50∼70°C. However, such linearity was not obtained at low temperature. In this work, linearity was obtained over the range of 25∼70°C, that is, the reactivity at biological temperature can be clarified. In addition, activation energies (E _a) for both COOH and NH₂ groups were obtained from Figure 4 and shown in Table 1.

Figure 4. Arrhenius plots for the COOH and NH₂ groups in l-aminobutyric acid. ▵: COOH group, ○: NH₂ group.

4.4. Applicability of Taft's equation

In order to quantitatively estimate the reactivity, we applied the k values to Taft's equation [19]. Taft's equation is generally expressed as follows:

In this work, k ₀ is the rate constant for glycine; k is a rate constant for each amino acid; ρ* equals the reaction constant for amino acids; σ* equals the polar substituent constant; E _s equals the steric substituent constant; δ is a measure of the steric effect. The following two operations were carried out: (1) the value of ρ* was changed from 0.0 to 1.0 at 0.1 intervals; (2) inversely, δ was changed from 1.0 to 0.0 at 0.1 intervals. As a result, 11 figures for the COOH group (or the NH₂ group) can be obtained at each temperature. One line was obtained in each figure, and the line having the largest correlation coefficient out of the 11 lines was selected as the ratio of ρ* to δ for the functional group at each temperature. These ratios for the COOH and NH₂ groups at 25°C, 36°C, and 50°C are shown in Table 2, and the plots having the largest correlation coefficient for COOH and NH₂ groups at 25°C are shown in Figures 5 and 6. It is fairly certain that (1) the reactivity of amino acids follows Taft's equation in gas–solid reaction, (2) the COOH group is strongly influenced by the steric effect, and (3) the NH₂ group is strongly influenced by the polar effect. Consequently, the effect of “the ratio of the polar effect to the steric effect” on the reactivity of the materials has been clarified at each temperature.

Figure 5. A plot (based on Taft's equation) of COOH group for each amino acid. Reaction temp: 25°C. ×: l-aminobutyric acid (obtained in this work), *: l-valine (obtained in this work), □: l-2-phenylglycine, ⋄: l-phenylalanine, ▵: l-α-alanine, ○: l-norvaline.

Figure 6. A plot (based on Taft's equation) of NH₂ group for each amino acid. Reaction temp: 25°C. ×: l-aminobutyric acid, *: l-valine, ▪: l-2-phenylglycine, ♦: l-phenylalanine, ▴: l-α-alanine, •: l-norvaline.

Table 2. The ratio of the reaction constant (ρ*) to the steric effect (δ).

Temperature	Functional group	ρ*	δ
25°C	COOH	2	8
	NH2	9	1
36°C	COOH	4	6
	NH2	8	2
50°C	COOH	3	7
	NH2	10	0
60°C	COOH	3	7
	NH2	10	0
70°C	COOH	3	7
	NH2	10	0

4.5. Comparison of the reactivity of NH₂ group in each amino acid

Comparing the structures of the various amino acids having two functional groups (COOH and NH₂), the number of carbon or benzene rings is different in l-glycine as shown Table 1. Based on Taft's equation mentioned in the former section, the NH₂ group can be considered as having some polar effect. The CH₃ group is an electron-donative substituent (−I effect [18]) and the effect increases with increasing carbon chain. If electron density of the functional group becomes large, the reactivity generally diminishes. Therefore, the reactivity of the NH₂ group of l-norvaline diminishes because it has the longest carbon chains in the sample materials. In addition, by comparison between l-norvaline and l-valine, it is found that the reactivity tends to diminish by existing carbon near the functional group. However, the C₆H₅ group is an electron attractive substituent (+I effect). So, electron density of the functional group diminishes, and the reactivity of the NH₂ group of l-phenylalanine or l-phenylglycine is larger than that of l-glycine.

On the other hand, the COOH group is also influenced by the steric effect. Based on the influence of steric effect of the substituent, the reactivity of the COOH group is diminished. Because the +I effect of the benzene ring is larger than the −I effect of CH₃ group, the reactivity of l-phenylalanine or l-phenylglycine is similar to that of l-glycine (in spite of having the polar effect). That is, the reactivity of the COOH group diminishes because the volume of the substituent becomes large.

5. Conclusions

The T-for-H exchange reaction (gas–solid reaction) between HTO vapor and each amino acid was observed and the reactivity of the amino acid was quantitatively analyzed. The Arrhenius plots showed good linear behavior over the range of 25∼70°C. Based on these results we can make the following statements. (1) The reactivity at biological temperature was clarified. (2) Applying Taft's equation, the ratio of polar effect to steric effect was clarified at each temperature (i.e. 25°C and 36°C). (3) The method used in this work can quantitatively clarify the reactivity of the T-for-H exchange reaction, and can be useful to estimate the internal exposure of exchangeable OBT.