SO32 - American Chemical Society

Article pubs.acs.org/JPCA

Periodic Changes in the Distribution of Species Observed in the Ni2+−Histidine Equilibrium Coupled to the BrO3−−SO32− pH Oscillator Eszter Poros, Krisztina Kurin-Csörgei, István Szalai, Viktor Horváth, and Miklós Orbán* Department of Analytical Chemistry, Institute of Chemistry, L. Eötvös University, P.O. Box 32, H-1518 Budapest 112, Hungary

ABSTRACT: The dynamical behavior of the system comprising of the pH-dependent complex formation between histidine and Ni(II) ions coupled to the BrO3−−SO32− pH oscillator was studied. The pH oscillator was demonstrated to be capable of forcing the pH-sensitive nickel ion−histidine equilibrium to alternate periodically between the unreacted and the fully complexed states. The periodic interconversions gave rise to an oscillatory distribution of the species that participate in the equilibrium and resulted in oscillations in the free [Ni2+], [NiHis+], and [Ni(His)2]. The preconditions of the successful coupling of metal ion−amino acid complexes to a primary pH oscillator are briefly discussed. Model calculations were performed to simulate the dynamics observed in the BrO3−−SO32− − Ni2+−His CSTR system. formation or to the Ca2+ + F− precipitation process in a flow reactor.3 Oscillatory pulses of some divalent metal ions were induced in the BS−M2+ systems (M2+ = Cd2+, Ni2+, and Zn2+) due to the formation of a sparingly soluble sulfite precipitate (MSO3) at high pHs and its dissolution when the pH dropped to its minimum value.4 In this study, our aim was to extend the variety of the combined systems listed above by using more complicated equilibrium processes. The complex formation that takes place between amino acids and metal ions was considered as equilibrium in this case. Significant changes in the distribution of the species concentrations are expected to occur periodically when high amplitude pH oscillations are imposed on a properly chosen metal ion−amino acid reaction. Selection of the Subsystems. For a primary oscillator, to which the complexation equilibrium is to be coupled, the BrO3−−SO32− CSTR system reported by Szántó and Rábai5 was chosen. Among the known oscillatory reactions, this one exhibits the largest amplitude pH oscillations. At a typical composition described in the Experimental Section ([BrO3−]0 = 0.15 M, [SO32−]0 = 0.175 M, and [H+]0 = 7.5 × 10−3 M), the changes in the pH exceed 4 pH units; it spans from 2.6 to 7.5. Beside the large ΔpH during the oscillatory cycle, the

1. INTRODUCTION The coupling of pH oscillatory reaction to a pH-sensitive equilibrium process offers a route to generate periodic pulses in the concentration of species which, due to their chemical properties, are otherwise unable to participate directly in any known oscillatory cycle. This method has already been successfully applied to induce oscillations in the concentration of several nonredox inorganic cations and anions.1 In all known examples, appropriate complex formation or precipitation reactions, in which these ions are involved, were identified and linked to high amplitude [H+] oscillations produced by a pH oscillator operated in a CSTR (continuously flowed stirred tank reactor). In such a combined system, the periodic pH changes affect the equilibrium, forcing it to shift repeatedly both in the forth and back directions, which give rise to oscillations in the concentration of all components of the equilibrium, including the target species. In the induced concentration oscillations reported so far, the BrO3−−SO32−− Fe(CN)64− (abbreviated as BSF), the BrO3−−SO32−−Mn2+ (BSM), and the BrO3−−SO32− (BS) systems served as a core or primary pH oscillator. When the Ca2+ + EDTA reaction was coupled to the BSF oscillator, the oscillations in the unbound [Ca2+] exceeded 2 orders of magnitude.2 The hydrated [Al3+] oscillated with the amplitude of 9 orders of magnitude when a solution of Al(NO3)3 was introduced into the BSF CSTR system. Sustained oscillations in the [F−] were generated when the BSM oscillator was linked either to the Al3+ + F− complex © 2014 American Chemical Society

Received: May 19, 2014 Revised: July 25, 2014 Published: July 29, 2014 6749

dx.doi.org/10.1021/jp504902v | J. Phys. Chem. A 2014, 118, 6749−6756

The Journal of Physical Chemistry A

Article

form in the presence of histidine. This way the two subsystems can simultaneously function in the coupled BrO3−−SO32−− Ni2+−His (abbreviated as BSNH) CSTR system.

additional advantage of using the BS reaction as a core system is that the oscillatory mixture is colorless, which allows spectrophotometric methods to be used to estimate the quantity of the colored species of the equilibrium reaction. However, the very long time period, exceeding 3 h at room temperature, makes the BS oscillator inconvenient to use. This drawback was diminished by choosing a working temperature of T = 45 °C, where the period time is only about 40 min. In selection of an appropriate metal ion−amino acid complex equilibrium, several points should be taken into account. We have to seek a system of simple stoichiometry, in which only 1:1 and 1:2 metal-to-ligand complexes are formed, the 1:1 and 1:2 species possess different colors or well-separated light absorption bands for their easy observation, detection, or quantification, and the complexation equilibrium should display a strong dependency on the [H+] in the pH range where the pH oscillator operates. First, the relevant literature information relating to the stability of the metal ion−amino acid complexes6 was surveyed, and then preliminary test tube reactions were carried out and absorption spectra in the mixtures of amino acids (glycine, cysteine, aspartic acid, and histidine) and metal ions (Cu2+, Ni2+, Co2+, Zn2+, and Mn2+) were taken. We have concluded that the complex formation between nickel(II) ions and histidine (His) can be a proper partner reaction of the BS oscillator in studying the effect of the periodical pH changes on the position of an amino acid−metal ion equilibrium in a dynamical system. This equilibrium reaction seems to meet all necessary criteria listed above. In the aqueous mixture of Ni2+ and histidine only two dominant species, the NiHis+ (log K1 = 8.9) and Ni(His)2 (log K2 = 6.9), are present, and their proportion depends on the pH of the medium; the NiHis+ is greenish blue, the Ni(His)2 has a bluish-violet color, and the two complexes show well-distinguished absorption bands. Other metal ion−amino acid equilibria were also considered; however, most of them were ruled out of use as a suitable subsystem. For example, the presence of Cu2+ ions was found to destroy the pH oscillations in the BS system by speeding up greatly the H+-producing autocatalytic composite reaction. The Zn2+ and Cd2+ complexes are colorless, and their presence can not be detected by optical spectroscopy. The complexes of Co2+ are known to be highly sensitive to the air oxygen. Mn2+ ions form low stability complexes with histidine (log K1 = 3.3 and log K2 = 2.4). The Ni2+−aspartic acid reaction is seemingly usable. Calculations based on the stepwise stability constants (log K1 = 6.8 and log K2 = 5.3) and the protonation constants of the aspartic acid (pK1= 9.5 and pK2 = 3.8) predict the formation of mainly a 1:1 complex at a pH above 4 and the presence of only a 1:2 complex above pH 6, but the two complexes absorb light roughly in the same wavelength region. In some cases the BS oscillator prevents fitting together a proper coupled system. For example, the BS−Ni2+−glycine or the BS−Ni2+−cysteine systems represent poor combinations. The BS system can not provide the high pHs (pH about 8) needed by the Ni2+−glycine complex formation to reach sufficient extent due to the lower stability constants (log K1 = 5.7 and log K2 = 4.9). The cysteine complexes of Ni2+ have an intense brown color; the equilibria show the right pH sensitivity, but the cysteine undergoes easy oxidation by the oxidant of the BS oscillator. The components of the BrO3−−SO32− pH oscillator and the Ni2+−His complex equilibrium tolerate the presence of each other. The BrO3− ions do not oxidize the histidine at the pH values occurring in the BS system; NiSO3 precipitate does not

2. EXPERIMENTAL SECTION 2.1. Materials. The chemicals used to make stock solutions [NaBrO3 (Aldrich), Na2SO3 (Sigma-Aldrich), L-histidine (Sigma-Aldrich), NiSO4·7H2O (Reanal)] were of analytical grade. The NaBrO3 solution can be stored indefinitely, but the solution of Na2SO3 must be freshly prepared due to its sensitivity to air oxygen. The mixtures containing the Ni2+ and histidine at different molar ratios (1:1, 1:2, and 1:4) were prepared before use. 2.2. Apparatus and Methods. The components of the two subsystems, the BS pH oscillator and the Ni2+−His equilibrium reaction were mixed in a thermally regulated CSTR of a volume of 25 cm3 thermostated at T = 45 °C. The reactor was fed through 4 input tubes by a Gilson Minipulse type peristaltic pump. The tubes carried the stock solutions of bromate (NaBrO3), sulfite (Na2SO3), sulfuric acid, and the mixture of nickel ions and histidine. [NaBrO3] = 0.60 M and [Na2SO3] = 0.90 M were most frequently used in the CSTR runs. The concentration of the H2SO4 varied between 0.06 and 0.02 M depending on the need of the input [H+]0 to generate pH oscillations in the CSTR. The mixtures of [NiSO4] = 0.020−0.040 M and [His] = 0.012−0.080 M were introduced into the reactor at a composition where the metal-to-ligand ratio was 1:1, 1:2, and 1:4. Reagent concentrations in the CSTR at the start were a quarter of the input ones. The reactor was hermetically sealed with a Teflon cap. The combined glass electrode and the input and output tubes were in contact with the reaction mixture through holes in the cap. The excess solution was removed from the CSTR through an output tube connected to another peristaltic pump. The reactor was placed in the compartment of an Agilent 89090A stopped flow spectrophotometer operated in the kinetic mode. The reactor served also as an optical cell with a path length of 3.21 cm (the inner diameter of the reactor) for the spectrophotometric measurements. The pH in the reactor and the light absorbance of the reaction mixtures at selected wavelengths were simultaneously recorded as a function of time. The efficient mixing of the reactor content was ensured with an ultraflat IKA lab disc magnetic stirrer fitted in the cell compartment of the spectrophotometer. The dependence of the extent of the Ni2+− His equilibrium reaction on the pH was studied under batch conditions. Light absorbance spectra were taken in the solutions where the molar ratio of [Ni2+] to [His] was similar to that in the CSTR experiments (1:1, 1:2, or 1:4), and the pH varied from 3 to about 8. In these experiments, a diode array spectrophotometer (Milton Roy Spectronic 3000) was used. The absorbances were measured in the wavelength range of λ = 300−800 nm. The optical cell (l = 1.00 cm) was thermostated to T = 25 °C. Despite this temperature differing significantly from the working temperature of T = 45 °C used in the CSTR experiments, the spectra measured at room and elevated temperatures are comparable because the extent of the Ni2+− His equilibrium is almost independent from the temperature. This statement was verified both experimentally (the light absorption spectra of the Ni2+−His systems taken at T = 25 and 45 °C were identical) and by the reported literature data (the stepwise stability constants of the Ni(His) 2 complex determined in the temperature range between T = 15 and 40 °C are almost the same).7 6750



Article

3. RESULTS In order to obtain information about the response of the Ni2+− His equilibrium to the periodic changes of the environmental pH, the following working steps were completed. First, the composition of the Ni2+−His system as a function of the pH was established by calculations, after which efforts have been made to identify experimentally the species whose presence was predicted by calculations. Finally, we looked for changes in the distribution of the species in the oscillatory BSNH flow system. The species distribution in the solution that contained nickel(II) ions and histidine at a different metal-to-ligand ratio as a function of pH was calculated by using MEDUSA.8 Figure 1 (panels a−c) shows the results of calculations at the initial ratios of [Ni2+]0 to [His]0 = 1:1, 1:2, and 1:4. These ratios of the reactants were used in the coupled BSNH CSTR system. As it is seen from the distribution diagrams in the aqueous solution of NiSO4 and histidine, three predominant species the aquated Ni2+, the 1:1 nickel-to-histidine complex, NiHis+, and

the bis(histidine) complex Ni(His)2 are present in the ratio that depends strongly on the initial concentrations of the reagents and the pH. Figure 1 (panels a−c) indicates no complex formation at a pH below 3 at any composition. Complexes start to form above pH 3 both in the 1:1, 1:2, and 1:4 initial ratios of metal-to-ligand solutions. At the initial ratio of 1:1 (Figure 1a), the dominant species is NiHis+ at the pH values above 4.3 but some amount of Ni(His)2 also forms. At an initial ratio of 1:2 (Figure 1b), as the pH increases, first the NiHis+ complex starts to appear and its concentration reaches a maximum at around pH 4.7 then it sharply decreases. In parallel with the decline, the 1:2 complex forms and accumulates and almost all nickel ions (∼80%) are bound into bis-complex at pH above 7. The same scenario prevails if the ratio of [Ni2+]0 to [His]0 equals 1:4 (Figure 1c), but the transformation of the free Ni2+ ions to Ni(His)2 is complete already at a pH around 6. In the BS pH oscillator, the periodic pH changes cover the range from 3 to 7 which makes it well-suited to play the role of core oscillator in the BSNH coupled system. Spectrophotometric measurements were performed to identify the free Ni2+, NiHis+ and Ni(His)2 complexes predicted by the calculations shown in Figure 1. Three sets of light absorption spectra are depicted in Figure 2 (panels a− c) taken in the mixtures of Ni2+ and His at 1:1, 1:2, and 1:4 initial ratios of metal-to-ligand in the pH range of 3−8. Figure 2a displays the spectra recorded in the histidine-free [Ni2+]0 = 2 × 10−2 M solution at pH = 3.26 (black curve) and in the mixture of initial [Ni2+]0 = [His]0 = 2 × 10−2 M at pHs 3.98, 5.05, 6.15, and 7.31. A similar set of spectra was measured in a solution of [Ni2+]0 = 2 × 10−2 M and [His]0 = 4 × 10−2 M (Figure 2b) and in the mixture of [Ni2+]0 = 2 × 10−2 M and [His]0 = 8 × 10−2 M (Figure 2c). In each figure, the spectrum taken at the lowest pH is identical to that measured in the aqueous Ni2+ solution, confirming no complex formation at this pH. When the pH increases, characteristic bands centered at λ = 610 nm (Figure 2a) and at λ = 557 nm [Figure 2 (panels b− c)] develop. These correspond to the existence of the NiHis+ and Ni(His)2 species. An increasing absorption with the increasing pH appears at λ > 720 nm in Figure 2 (panels b and c), where the ratio of [Ni2+]0 to [His]0 was 1:2 and 1:4. This section of the spectra is supposed to be part of the absorption of the Ni(His)2 species. The shape of the bands is not symmetrical, which is a sign of an overlapping in the absorption of the free Ni2+, NiHis+, and Ni(His)2 complexes. An apparent absorption coefficient (ε) of about 2.3, 5.0, and 7.5 M−1 cm−1 for the Ni2+, NiHis+, and Ni(His)2, respectively, were estimated from the absorption maxima at the wavelengths of λ = 720, 610, and 557 nm on the assumption that only one species is present. This assumption is not fully true, there is some overlapping of the absorption bands, but using these ε values allows us to make approximate calculations of the concentration of species Ni2+, NiHis+, and Ni(His)2 at the maximum pH provided by the BS oscillator. The same procedure but different molar ratios were applied by Valentini et al.9 in their study of binding Ni2+ to histidine and hexahistidine to obtain ε values of 9.3 M−1 cm−1 at λ = 557 nm for the Ni(His)2 species, but no ε value and absorption maximum were established for the 1:1 complex. Neither the presence of the components of the pH oscillator nor the elevated temperature (T = 45 °C) applied in the BSNH system influenced the traces of the spectra shown in Figure 2. The BrO3− and SO32− ions have zero absorption at λ above 400 nm. No changes were observed in the spectra of the mixture of Ni2+ and His for hours when the histidine complexes were in

Figure 1. Calculated distribution of the species in the Ni2+−His system as a function of the pH. (a) [Ni2+]0 = 10−2 M and [His]0 = 10−2 M (molar ratio 1:1); (b) [Ni2+]0 = 10−2 M and [His]0 = 2 × 10−2 M (molar ratio 1:2); (c) [Ni2+]0 = 5 × 10−3 M and [His]0 = 2 × 10−2 M (molar ratio 1:4). 6751



Article

decreases in the concentration of the species present in the Ni2+−His equilibrium were expected to be observed in the BSNH dynamical system. To prove this assumption, the time evolution of the light absorption bands that corresponds to the [Ni(His)2], [NiHis+], and [Ni2+] were recorded in a system where the two subsystems, the BS oscillator and the Ni2+−His equilibrium reaction were linked in a CSTR. The light absorbance versus time curves taken at λ = 557, 610, and 720 nm in the solutions at the initial metal-to-ligand ratios of 1:2, 1:1, and 1:4 are shown in Figure 3 (panels b, c, and d). Red (taken at λ = 557 nm), green (λ = 610 nm), and black (λ = 720 nm) traces in the figures correspond to the changes in the [Ni(His)2], [NiHis+], and the free [Ni2+], respectively, as a function of time. Figure 3a presents the pH oscillations in time recorded simultaneously with the light absorbance measurements at the initial concentration of [Ni2+]0 = 10−2 M and [His]0 = 2 × 10−2 M, shown in Figure 3b. [Ni2+]0 = 0.01 M was chosen for use in most of our experiments. This concentration does not influence the parameters of the BS oscillator; it is high enough to provide well measurable absorbance for the NiHis+ and Ni(His)2 complexes without serious overlap between the absorption bands but low enough to avoid the risk of formation of the NiSO3 precipitate when a high concentration of Ni2+ and SO32− was present in the BSNH system. The traces in Figure 3 (panels b−d) exhibit the time variation of the concentration of the components in the BSNH system, but these curves do not allow for the derivation of quantitative data regarding the real values of [Ni(His)2], [NiHis+], and [Ni2+] due mainly to the uncertainty in the ε values calculated from the overlapped absorption bands in Figure 2. However, from the position of the red, green, and black curves, the relative quantity of the species in the BSNH system can be estimated at any pH. For example, when the 1:1 ratio of initial concentration of Ni2+ to His was used (Figure 3c), the [NiHis+] (green line) significantly exceeds the [Ni(His)2] (red line) in the entire range of the pH oscillations as it is expected from the [species] versus pH curves shown in Figure 1a. When the pH reached the maximum pH of 6.7 in the CSTR, [NiHis+] ∼ 6.2 × 10−3 M, and [Ni(His)2] ∼ 2.5 × 10−3 M were calculated from the changes in the absorbance, using the apparent ε values and taking the cell length as 3.21 cm. At feed concentrations of [Ni2+]0 = 1 × 10−2 M and [His]0 = 2 × 10−2 M (Figure 3b), the order in which the species appear in the CSTR as the pH changes from the minimum of 2.9 to the maximum of 6.3 is the following: no or only a negligible amount of complexes form at pH ∼ 3. Here, the free [Ni2+] must be close to its input concentrations. NiHis+ is the dominant species until the pH reaches a value of about 5, and mainly Ni(His)2 is present at the largest pH ∼ 6.3, where [NiHis+] ∼ 4.3 × 10−3 M and [Ni(His)2] ∼ 7.4 × 10−3 M were estimated from the maximum and minimum values of the green and red traces in Figure 3b. No further increase in the [Ni(His)2] to [NiHis+] is observed if the ratio of metal-toligand is 1:4 (Figure 3d), which is attributed to the high stability of both Ni2+−His complexes. It is also seen from Figure 3 that the maximum concentrations of the Ni2+−His complexes are accompanied by the minimum concentrations of the free Ni2+ ions and vice versa. It was of interest to notice that the Ni2+−His equilibrium slightly acted on the BS oscillator. Ni2+ ions do not influence the parameters of the oscillations, but the addition of His or Ni2+−His complexes were found to affect the dynamics of the BS flow system. Both the amplitude and the frequency of the

Figure 2. Light absorption spectra taken in the mixture of Ni2+ and His at initial molar ratios of 1:1, 1:2, and 1:4 at different pHs. Cell length: 1.00 cm, T = 25 °C. (a) [Ni2+]0 = 2 × 10−2 M and [His]0 = 2 × 10−2 M; (b) [Ni2+]0 = 2 × 10−2 M and [His]0 = 4 × 10−2 M; (c) [Ni2+]0 = 2 × 10−2 M and [His]0 = 8 × 10−2 M.

contact with excess BrO3− at pH ∼3 (oxidation of histidine by bromate did not occur). Figure 2 and the observations above confirm that the absorptions measured in the BSNH CSTR system at λ = 557, 610, and 720 nm are attributed to the presence of Ni(His)2, NiHis+, and Ni2+ species, respectively. The strong dependence of the species distribution on the pH that exists in the nickel(II) ions−histidine batch systems was clearly demonstrated by the information derived from Figures 1 and 2. The oscillatory changes in the environmental pH were supposed to bring about a similar effect. Periodic increases and 6752



Article

Figure 3. continued 0.025 M, k0 = 0.0048 s−1 (the pH vs time curve is not shown, pHmin = 2.99, pHmax = 6.71). (d) Light absorbances vs time measured at the initial ratio of metal-to-ligand 1:4, experimental conditions: [Ni2+]0 = 5 × 10−3 M, [His]0 = 2 × 10−2 M, [H+]0 = 0.038 M, k0 = 0.0058 s−1 (pHmin = 3.10, pHmax = 6.22).

pH oscillations were influenced. The ΔpH just slightly decreased (a few tenth of a pH unit), but a significant decrease in the period of the oscillations (τ) was observed when Ni2+− His complexes were present. In the absence of the complexes, the τ is about 40 min at T = 45 °C. When the mixture of [Ni2+]0 = 10−2 M and [His]0 = 10−2 M or [Ni2+]0 = 10−2 M and [His]0 = 2 × 10−2 M were introduced, τ = 12 and 9 min, respectively, were measured. Even the histidine alone decreased the period. In the presence of [His] = 3 × 10−3 or 10−2 M, τ = 30 and 18 min, respectively, were obtained. When Ni2+−His complexes formed in the CSTR, lower input [H+]0 and/or higher input [SO32−]0 were required to restore the original high amplitude oscillatory state. If only His were introduced, the input [H+]0 had to be increased to keep the system in the oscillatory regime. Occasionally, a slight adjustment of the flow rate (k0) was also necessary to maintain sustained high amplitude pH oscillations in the combined system. When the composition in the BSNH system was changed, we looked for k0, where the largest ΔpH could be observed. Within the oscillatory range of k0, the amplitude and frequency of the pH oscillations increased with increasing the flow rate before the system approached the high pH steady state.

4. DISCUSSION The large amplitude pH oscillations that appear in the BrO3−− SO32−−(H+) flow system were first observed by Szántó and Rábai.5 The oscillations in this reaction are attributed to the interplay of three basic processes, namely, the protonation equilibria of the SO32− and HSO3−, the total oxidation of the SO32− to SO42−, which produces H+ in an autocatalytic way, and the partial oxidation of the SO32− to S2O62− (this step consumes H+). The most important composite reactions are shown in eqs 1−5. SO32 − + H+ ↔ HSO3−

(1)

HSO3− + H+ ↔ H 2SO3

(2)

3HSO3− + BrO3− → 3H+ + 3SO4 2 − + Br −

(3)

3H 2SO3 + BrO3− → 6H+ + 3SO4 2 − + Br −

(4)

6SO32 − + BrO3− + 6H+ → 3S2 O6 2 − + Br− + 3H 2O (5)

Figure 3. pH vs time and the light absorbance vs time curves recorded simultaneously in the BSNH CSTR system. The concentrations of the components of the BS oscillator at the start: [BrO3−]0 = 0.15 M and [SO32−]0 = 0.225M; T = 45 °C. (a) pH oscillations in the BSNH CSTR system when [Ni2+]0 = 10−2 M and [His]0 = 2 × 10−2 M, [H+]0 = 0.038M, k0 = 0.01 s−1 (pHmin = 2.85, pHmax = 6.34). (b) Light absorbances taken at λ = 557 nm (red), λ = 610 nm (green), and λ = 720 nm (black) characteristic for the absorption maxima of Ni(His)2, NiHis+, and Ni2+ ions, respectively, vs time measured at the initial ratio of metal-to-ligand 1:2, experimental conditions as in (a). (c) Light absorbances vs time measured at the initial ratio of metal-to-ligand 1:1, experimental conditions: [Ni2+]0 = 10−2 M, [His]0 = 10−2 M, [H+]0 =

SO32−

HSO3−

The major route of the oxidation of and leads to the formation of SO42− in reactions 1−4, providing the (+)-feedback in the pH oscillatory cycle. Reaction 5 represents the delayed (−)-feedback in which only 1−2% of the initial SO32− is oxidized to S2O62−. This low conversion is the main reason for the high sensitivity of the oscillations to the input [H+]0. Equations 1−5 were used to simulate the pH oscillations in the BS, BSH, and BSHN systems. Histidine is a tridentate ligand toward the Ni2+ with the binding groups of −COOH, −NH2, and N in the imidazol 6753



Article

Table 1. Model and Rate Constants Used in the Simulation of the Dynamics in the BSNH Coupled System reactions

rate constants k1 = 2 × 10 M 10

−1

−1

k−1 = 2 × 103 s−1

(1)

SO3

(2)

HSO3− + H+ ↔ H 2SO3

k2 = 1.2 × 1010 M−1 s−1

(3)

3HSO3− + BrO3− → 3H+ + 3SO4 2 − + Br −

k3 = 0.13 M−1 s−1

(4)

3H 2SO3 + BrO3− → 6H+ + 3SO4 2 − + Br −

k4 = 30 M−1 s−1

(5)

6H 2SO3 + BrO3− → 6H+ + 3S2 O6 2 − + Br − + 3H 2O

k5 = 2 M−1 s−1

(6)

H+ + OH− ↔ H 2O

k6 = 1.4 × 1011 M−1 s−1

k−6 = 1.4 × 10−3 s−1

(7)

His− + H+ ↔ His

k7 = 1 × 1010 M−1 s−1

k−7 = 6.6 s−1

(8)

+

2−

+

+H ↔

HSO3−

His + H ↔ His

k8 = 1 × 10 M

−1 −1

10

+

s

s

k−2 = 2 × 108 s−1

−1

k−8 = 1.26 × 104 s−1

−1

k−9 = 1.7 × 108 s−1

(9)

His+ + H+ ↔ His2 +

k9 = 1 × 10 M

(10)

His− + Ni 2 + ↔ NiHis+

k10 = 1 × 1010 M−1 s−1

k−10 = 21.9 s−1

(11)

His− + NiHis+ ↔ Ni(His)2

k11 = 1 × 1010 M−1 s−1

k−11 = 1.3 × 103 s−1

10

s

Figure 4a presents the pH oscillations calculated with the same parameters ([BrO3−]0, [SO32−]0, [H+]0, k0), as in Figure 3a. Figure 4b shows the calculated absorbances in the BSNH CSTR system as a function of time for the species of Ni2+ (black), NiHis+ (green), and Ni(His)2 (red) at the initial metal-

ring. The molecule is fully protonated at pH < 1.7 but unprotonated at pH > 9.2, as shown in the diagram below. In the operational pH range of the BS oscillator, the histidine is present in the forms of His+ and His. The Ni2+ ions bind the deprotonated His− species, therefore, the formation of 1:1 and 1:2 complexes is accompanied by production of 1 to 4 H+. The oscillations in the BS flow reaction occur only in a narrow range of the input [H+]0, where the higher [H+]0 results in a shorter time period. The protons liberated when the Ni2+−His complexes form increase the frequency of the oscillations; even they can make the original BS system slip out of the oscillatory domain. This explains the need for using lower [H+]0 and/or higher [SO32−]0 to keep the oscillations going in the total BSNH system. On the contrary, higher input [H+]0 had to be used when only His was present because its protonation below pH ∼ 5 reduces the actual H+ level in the reactor. Model calculations were performed to simulate the dynamical behavior observed in the complex BSNH system. First, we tested the simple model based on eqs 1−5 as suggested in ref 5 to describe the pH oscillations in the BS CSTR reaction under the conditions used in our experiments. Then the model was supplemented with the processes and data (protonation, stepwise complex formation) characteristic of the Ni2+−His equilibrium. The full model is shown in Table 1. The composite reactions of the BS oscillator, the rate equations, the corresponding rate laws, and the rate constants (k1−k6) were taken from ref 5. The k1−k6 values for T = 45 °C were estimated from average activation energies. Steps 7−11 were supposed to be diffusion controlled. The rate constants of k−7−k−9 and of k−10−k−11 were derived from the protonation constants of His and the stability constants of Ni2+−His complexes, respectively.6 The calculations were made with XPPAUT by using the CVODE integrator10 and MATLABR2013.

Figure 4. (a) pH vs time and (b) absorbances vs time curves simulated with the model of Table 1. The concentration of the components in the BSNH CSTR system as in Figure 3a but [Ni2+]0 = 5 × 10−3 M, [His]0 = 10−2 M, k0 = 0.0045 s−1 (for ε values see text, optical length: 3.21 cm). 6754



Article

to-ligand ratio of 1:2 using the rate constants listed in Table 1 and [BrO3−]0, [SO32−]0, and [H+]0, as in Figure 3a. Two peaks appear in the simulated absorption of NiHis+ (green) because the pH of its optimal formation (pH 4−5) is reached twice during an oscillatory cycle. The numerical model of steps 1−11 in Table 1 is too simple to yield quantitative agreement with the experimental results, but it seems to be capable of providing a qualitative description of the dynamics observed in the BSNH CSTR system. The model simulates the oscillations in the pH when the input [BrO3−]0 and [SO32−]0 exceeded significantly the concentrations used in the source article5 (the use of the higher [BrO3−]0 and [SO32−]0 was needed to ensure high capacity of the oscillator to tolerate the presence of His or Ni2+−His complexes). The position of the calculated oscillatory traces and the amplitude of the pH oscillations are similar to that measured in the experiments. The pH oscillatory curve simulated with the experimental parameters is somewhat shifted toward the lower pH region, which may be a reason for calculating a higher ratio of [NiHis+] to [Ni(His)2] at the maximum pH than what was measured and shown in Figure 3b (using lower [H+]0 than in the experiments would result in higher oscillatory pHs). The analysis of the model revealed further similarities between the experimental and simulated results. For example, the oscillations appeared only in a narrow range of the input [H+]0 or the calculated time period (τ) was longest in the (Ni2+−His)-free BS oscillator (25 min) and shorter in the presence of His and even shorter in the BSNH system (8 min), like in the experiments. The sensitivity of the model in Table 1 on variation of the experimental parameters and the rate constants was also tested. It is of interest to note that an almost perfect replica of Figure 3 (panels a and b) could be simulated when the initial concentrations only slightly differred from the values used in the experiments, but the rate constants of the complex formation (k10 and k11) were drastically reduced. The use of lower k10 and k11 in the simulations may be more reasonable than considering steps 10 and 11 to be diffusion controlled. In accordance with the review paper of Eigen and Wilkins,11 the rate of the complex formation that takes place between metal ion and ligand is roughly equal to the rate of the exchange of the water molecule in the hydrated metal ion. For the formation of Ni2+- complexes, a value of 3 × 104 s−1 was estimated. Simulations have been done with replacing k10 = k11 = 1010 M−1 s−1 with k10 = k11 = 3 × 104 s−1 and slightly adjusting the value of rate constants k3 and k4 recommended in ref 5 in order to obtain simulated curves which better match the experimental ones. From the results of the simulations, we have concluded that the rate constants k3 and k4 in Table 1 need to be improved. Figure 5 depicts the simulated (a) pH versus time and (b) absorbance versus time traces using k10 = k11 = 3 × 104 s−1 and the parameters listed in the figure caption. The simulated Figure 5 strongly resembles the measured Figure 3: the shape and ΔpH of the pH oscillations in Figure 5a look like those in Figure 3a, only one peak appears in the time evolution of [NiHis+], and the ratio of [Ni(His)2] to [NiHis+] at the maximum pH is similar.

Figure 5. (a) pH vs time and (b) absorbances (red: λ = 557 nm; green: λ = 610 nm; black: λ = 720 nm) vs time traces simulated with the model of Table 1 but k10 = k11 = 3 × 104 s−1 and k3, k4 slightly adjusted. The other parameters in the simulations: [BrO3−]0 = 0.15 M, [SO32−]0 = 0.225 M, [H+]0 = 0.04 M, [Ni2+]0 = 10−2 M, [His]0 = 2 × 10−2 M, and k0 = 1.2 × 10−3 s−1.

reaction to alternate periodically between two states resulting in an oscillatory distribution of the species in the BSNH flow system. In the present case the periodic interconversions in the concentration of the aquated Ni2+ ions and the fully complexed ones took place which gave rise to oscillations in the free [Ni2+], [NiHis+], and [Ni(His)2]. This mechanism may represent a way to generate oscillations in the concentration of ions or molecules not only in the relatively simple chemical systems but in the more complicated biological organisms as well. It was demonstrated that the successful coupling of a pHdependent metal ion−amino acid complex formation to a pH oscillator requires numerous prerequisites to be fulfilled. It was also pointed out that such dynamical behavior that appears in the complex systems can be predicted by numerical calculations if the properties and peculiarities of the individual subsystems are sufficiently known.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +36-1-372-2542. Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by grants from the Hungarian Academy of Sciences (OTKA K100891).

5. CONCLUSIONS In the work discussed here, two subsystems, the BS CSTR pH oscillator and the Ni2+−His equilibrium reaction, were linked through a common species, the H+ ions. The subsystems mutually affected each other, but the BS pH oscillator was capable of forcing the pH-dependent Ni2+−His complexation

REFERENCES

(1) Kurin-Csörgei, K.; Epstein, I. R.; Orban, M. Systematic Design of Chemical Oscillators Using Complexation and Precipitation Equilibria. Nature 2005, 443, 139−142. 6755



Article

(2) Kurin-Csörgei, K.; Epstein, I. R.; Orban, M. Periodic Pulses of Calcium Ions in a Chemical System. J. Phys. Chem. A 2006, 110, 7588−7592. (3) Horvath, V.; Kurin-Csörgei, K.; Epstein, I. R.; Orban, M. Oscillations in the Concentration of Fluoride Ions Induced by a pHOscillator. J. Phys. Chem. A 2008, 112, 4271−4276. (4) Horvath, V.; Kurin-Csörgei, K.; Epstein, I. R.; Orban, M. Oscillatory Concentration Pulses of Some Divalent Metal Ions Induced by a Redox Oscillator. Phys. Chem. Chem. Phys. 2010, 12, 1207−1217. (5) Szántó, T. G.; Rábai, G. pH-Oscillations in the BrO3−− SO32−/ HSO3− Reaction in a CSTR. J. Phys. Chem. A 2005, 109, 5398−5402. (6) Stability Constants of Metal-ion Complexes: Part B, Organic Ligands, 2nd ed.; Perrin, D. D., Ed.; Pergamon Press, Oxford, 1979. (7) Rajn, E. V.; Mathur, H. B. Thermochemical Studies: The Heats and Entropies of Reactions of Transition Metal Ions with Histidine. J. Inorg. Nucl. Chem. 1969, 31, 425−432. (8) Puigdomenech, I. Chemical Equilibrium Software, version 2, Chemistry Department, School of Chemical Sciences and Engineering, KTH Royal Institute of Technology, Sweden, 2013. (9) Valentini, L. E.; De Pauli, C. P.; Giacomelli, C. E. The Binding of Ni(II) ions to Hexahistidine as a Model System of the Interaction between Nickel and His-tagged Proteins. J. Inorg. Biochem. 2006, 100, 192−200. (10) Ermentrout, B. Simulating, Analyzing and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students; Software, Environment and Tools Series; Society for Industrial and Applied Mathematics: Philadelphia, PA, 2002. (11) Eigen, M.; Wilkins, R. G. Mechanism of Inorganic Reactions; Kleinberg, J., Murmann, R. K., Bauman, J., Eds.; Advances of Chemical Series, No. 49; American Chemical Society: Washington, D.C., 1965.

6756


SO32 - American Chemical Society

Recommend Documents