Reagents
l-α-amino acids: asparagine, pure, Sigma Chemical Co., histidine, pure (≥99.0%), Fluka Chemie GmbH, alanine, pure, International Enzymes Limited; polymeric [Co(imid)2]n complex prepared by A. Vogt, Faculty of Chemistry, University of Wrocław [27, 38, 45]; potassium nitrate (V), p.a., P.O.Ch. Gliwice; nitric (V) acid, p.a., P.O.Ch. Lublin; sodium hydroxide—0.5021 M solution determined by potassium hydrogen phthalate; acetone, p.a., P.O.Ch. Gliwice; oxygen pure medical (99.7–99.8%); argon, p.a. (99.999%) from Linde Gas (Poland).
Apparatus
An isobaric laboratory set for volumetric and pH-metric measurements (see Additional file 3: Figure S3), composed of the following elements: a double-walled thermostated glass vessel of volume ca 80 mL, tightly closed with a silicon stopper and equipped with a burette nozzle supplying the 4 M HNO3; a combination pH glass electrode C2401, Radiometer (Copenhagen); a Radiometer Analytical 101 temperature sensor; a gas inlet tube (dioxygen) connected with the gas burette; outlet tube; a glass rode to hang a small glass vessel with the [Co(imid)2]n polymer. A PHM 85 Precision pH Meter Radiometer (Copenhagen), a Fisherbrand FBC 620 cryostat, Fisher Scientific, an Electromagnetic Stirrer ES 21H (Piastów, Poland), an oxygen tank with reducing valve and a CO-501 Oxygen Meter, Elmetron (Zabrze, Poland) were also used. The following glass set was used to determine the imidazole released from the coordination sphere of the mixed complexes: suction flask, water suction pump, washer, Schott funnel POR 40 (see Additional file 4: Figure S4).
Measurement procedures
Oxygenation reaction of the Co(II)–l-α-amino acid–imidazole systems
The thermostated vessel was filled with a solution containing an exactly weighted sample of chosen amino acid, so as to obtain a predicted Co(II)–amac–Himid ratio when adding the [Co(imid)2]n polymer. Adjustment of the solution to constant ionic strength I = 0.5 M was achieved by means of potassium nitrate. The solution was topped up with water to 30 mL. A small glass vessel with 0.3 mmol of the [Co(imid)2]n polymer (hence the same 0.6 mmol of imid) was hung from a glass rod over the solution surface. After the entire vessel reached a temperature close to 0 °C [decrease of temperature inhibits the irreversible oxidation of Co(II)], the initial pH and the initial volume level in the gas burette was read and the main experiment started by inserting the polymer into the sample. The current values of pH and dioxygen volume were noted in definite time intervals up to saturation. A rise in pH was observed along with a change in color from entirely colorless to brown or even dark-brown. At the end of oxygenation, which occurred when reaching pH ≈9 to 10, the solution was acidified to the initial pH with a small aliquot of 4 M nitric acid solution. This caused a partial discoloration of the solution and evolution of dioxygen. The volume of dioxygen evolved against the total volume of dioxygen bound served as a measure of reversibility of oxygenation.
Determination of reaction stoichiometry of dioxygen uptake in the Co(II)–l-α-amino acid–imidazole systems by the molar ratio method
For each system under study, a dependence plot of the number of bound O2 (mmol) against the C
L/C
M ratio was prepared, where C
L—total amac concentration, C
M—total Co(II) concentration, which enabled the determination of stoichiometry of dioxygen uptake.
Confirmation of the coordination mode of the central ion by determination of the number of imidazole released from the coordination sphere of the Co(II)–l-α-amac–imidazole–O2 system
Exactly weighed samples of amino acid and the [Co(imid)2]n polymer were placed into a washer so as to attain a molar ratio of Co(II):l-α-amac: imidazole = 0.3: 0.9: 0.3 (mmol). The washer immersed in ice was filled with 2 mL of argonated water and then, during 15 min, the forming “active” complex was argonated continuously. After 10 min, argonation was changed to oxygenation. The final content of the washer, the freshly formed dioxygen complex, was quantitatively added to a Schott funnel previously filled with oxygenated acetone. The oxygen complex, insoluble in water, precipitated as a dark brown solid. At the moment a water suction pump was connected to the Schott funnel. Acetone was filtered off together with the water containing the imidazole released along with oxygen complex formation. The filtrate obtained was titrated potentiometrically with nitric acid. All the steps of experiment were carried out at temperature close to 0 °C.
Calculations of equilibrium concentrations of Co(II), amac and Himid as well as evaluation of the equilibrium \(K_{{{\text{O}}_{2} }}\) constants
The calculations were performed by means of a Mathcad 13 computer program [46]. The mass balance non–linear equation system was solved by the Levenberg–Marquardt method [47, 48], which enables a faster convergence of the solutions than the Gauss–Newton iteration. Such effect is due to the introduction of an additional λ parameter to the Gauss–Newton iteration formula, which corrects the appropriate direction of the procedure depending on whether the solutions go close to or far from the convergence series.
The procedure used the corresponding equilibrium concentrations [M], [L], [L′] (where: [M] = [Co(II)]), which were the searched unknown quantities x
1, x
2, x
3 of the following system:
$$\begin{aligned} f_{ 1} (x_{ 1} ,x_{ 2} ,x_{ 3} ) = \, 0 \hfill \\ f_{ 2} (x_{ 1} ,x_{ 2} ,x_{ 3} ) = \, 0 \hfill \\ f_{ 3} (x_{ 1} ,x_{ 2} ,x_{ 3} ) = \, 0 \hfill \\ \end{aligned}$$
(1)
The solution vector of the system:
$$X = \left[ {\begin{array}{*{20}c} {x_{1} } \\ {x_{2} } \\ {x_{3} } \\ \end{array} } \right]$$
(2)
follows Newton’s formula:
$$X_{{{\text{i}} + 1}} = X_{\text{i}} - \, \left( {F^{\prime} \, \left( {X_{\text{i}} } \right)^{ - 1} \cdot F\left( {X_{\text{i}} } \right)} \right)$$
(3)
after an appropriate initial estimation of the X
0 vector. The function vector is:
$$F (X) = \left[ {\begin{array}{*{20}c} {f_{1} (x_{1} ,x_{2} ,x_{3} )} \\ {f_{2} (x_{1} ,x_{2} ,x_{3} )} \\ {f_{3} (x_{1} ,x_{2} ,x_{3} )} \\ \end{array} } \right]$$
(4)
whereas the matrix of derivatives, i.e. Jacobi matrix, is:
$$F^{\prime}(X) = \left[ {\begin{array}{*{20}c} {\frac{{\partial f_{1} }}{{\partial x_{1} }}\quad \frac{{\partial f_{1} }}{{\partial x_{2} }}\quad \frac{{\partial f_{1} }}{{\partial x_{3} }}} \\ {\frac{{\partial f_{2} }}{{\partial x_{1} }}\quad \frac{{\partial f_{2} }}{{\partial x_{2} }}\quad \frac{{\partial f_{2} }}{{\partial x_{3} }}} \\ {\frac{{\partial f_{3} }}{{\partial x_{1} }}\quad \frac{{\partial f_{3} }}{{\partial x_{2} }}\quad \frac{{\partial f_{3} }}{{\partial x_{3} }}} \\ \end{array} } \right]$$
(5)
(F’(X))−1 in Eq. (3) denotes the inverted Jacobi matrix.
In the mass balance system all the ligand (both amac and Himid) protonation constants as well as the complex–formation constants with Co(II) were known from the previous reports [37, 45]. In cumulative form the formation constants may be written as:
$$\beta_{mll^\prime h} = {\raise0.7ex\hbox{${[{\text{M}}_{m} {\text{L}}_{l} L^\prime_{l\prime } H_{h} ]}$} \!\mathord{\left/ {\vphantom {{[{\text{M}}_{m} {\text{L}}_{l} L\prime_{l\prime } H_{h} ]} {[{\text{M}}]^{m} [{\text{L}}]^{l} [{\text{L}}^\prime ]^{l^\prime } [{\text{H}}]^{h} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${[{\text{M}}]^{m} [{\text{L}}]^{l} [{\text{L}}^\prime ]^{l^\prime } [{\text{H}}]^{h} }$}}$$
(6)
The functions used for the equation systems of l-α-alanine and l-α-asparagine were due to the fact that the mixed ML2L′ complex capable of dioxygen uptake (existing outside of the non-active mixed MLL′ complex) contains the sufficient three nitrogen donors in the coordination sphere, in accordance with Fallab’s “3 N” rule [49]:
$$f_{1} = C_{\text{M}} - Y[{\text{M]}} - \sum\limits_{l = 1}^{3} {\beta_{ml} [{\text{M]}}} \,[{\text{L}}]{\kern 1pt}^{l} - \sum\limits_{l' = 1}^{5} {\beta_{ml'} [{\text{M]}}} \,[{\text{L}}^{\prime}]{\kern 1pt}^{l'} - \sum\limits_{l = 1}^{2} {\beta_{mll'} [{\text{M]}}} \,[{\text{L}}]{\kern 1pt}^{l} [{\text{L}}^{\prime}] - 2C_{{{\text{O}}_{2} }}$$
(7)
$$f_{2} = C_{\text{L}} - Y_{1} [{\text{L]}} - l\sum\limits_{l = 1}^{3} {\beta_{ml} [{\text{M]}}} \,[{\text{L}}]{\kern 1pt}^{l} - l\sum\limits_{l = 1}^{2} {\beta_{mll'} [{\text{M]}}} \,[{\text{L]}}{\kern 1pt}^{l} [{\text{L}}^{\prime}] - 4C_{{{\text{O}}_{2} }}$$
(8)
$$f_{3} = C_{\text{L}^{\prime}} - Y_{2} [{\text{L}}^{\prime}] - l'\sum\limits_{l' = 1}^{5} {\beta_{ml'} [{\text{M]}}} \,[{\text{L}}^{\prime}]{\kern 1pt}^{l'} - \sum\limits_{l = 1}^{2} {\beta_{mll'} [{\text{M]}}} \,[{\text{L]}}{\kern 1pt}^{l} [{\text{L}}^{\prime}] - 2C_{{{\text{O}}_{2} }}$$
(9)
For l-α-histidine, the mixed not oxygen binding complex was a MLL′H species, in which the side group imidazole was protonated at the N3 nitrogen, thus the number of nitrogen atoms in the coordination sphere of the central ion was two, i.e. less than the minimum suggested by Fallab’s rule. However, as the number of nitrogen atoms was sufficient in the “active” complex ML2L′, capable of O2 was as follows:
$$f_{1} = C_{\text{M}} - Y[{\text{M]}} - \sum\limits_{l = 1}^{ 2} {\sum\limits_{h = 1}^{1} {\beta_{mlh} } } \,[{\text{M}}][{\text{L}}]{\kern 1pt}^{l} [{\text{H}}]{\kern 1pt}^{h} - \sum\limits_{l' = 1}^{5} {\beta_{ml'} [{\text{M]}}} \,[{\text{L}}^{\prime}]{\kern 1pt}^{l'} - \beta_{1210} [{\text{M}}][{\text{L}}]{\kern 1pt}^{2} [{\text{L}}^{\prime}] - \beta_{1111} [{\text{M}}][{\text{L}}]{\kern 1pt} [{\text{L}}^{\prime}][{\text{H}}]\, - 2C_{{{\text{O}}_{2} }}$$
(10)
$$f_{2} = C_{\text{L}} - Y_{1} [{\text{L]}} - l\sum\limits_{l = 1}^{ 2} {\sum\limits_{h = 0}^{1} {\beta_{mlh} } } \,[{\text{M}}][{\text{L}}]{\kern 1pt}^{l} [{\text{H}}]{\kern 1pt}^{h} - 2\beta_{1210} [{\text{M}}][{\text{L}}]{\kern 1pt}^{2} [{\text{L}}^{\prime}] - \beta_{1111} [{\text{M}}][{\text{L}}]{\kern 1pt} [{\text{L}}^{\prime}][{\text{H}}] - 4C_{{{\text{O}}_{2} }}$$
(11)
$$f_{3} = C_{\text{L}^{\prime}} - Y_{2} [{\text{L}^{\prime}]} - l'\sum\limits_{l' = 1}^{5} {\beta_{ml'} [{\text{M]}}} \,[{\text{L}^{\prime}]}{\kern 1pt}^{l'} - \beta_{1210} [{\text{M}}][{\text{L}}]{\kern 1pt}^{2} [{\text{L}^{\prime}]} - \beta_{1111} [{\text{M}}][{\text{L}}]{\kern 1pt} [{\text{L}^{\prime}][H]} - 2C_{{{\text{O}}_{2} }}$$
(12)
where: C
M—total concentration of the metal: Co(II), C
L—total concentration of the l-α-amino acid, \(C_{{L^{\prime}}}\)—total concentration of imidazole, \(C_{{{\text{O}}_{2} }}\)—concentration of the oxygen adduct, β
ml
—summary stability constants of the Co(II)–l-α-amino acid complexes, β
ml’
—summary stability constants of the Co(II)–imidazole complexes, β
mll’
—summary stability constants of the mixed Co(II)– l-α-alanine/asparagine–imidazole complexes, β
1210, β
1111—summary stability constants of the mixed Co(II)–l-α-histidine–imidazole complexes.
The hydrolyzed Co(II) aqua-ion and the protonated (not complexed) ligand forms were considered in expressions:
$$\begin{aligned} Y &= 1 + \left( {{\text{1}}/K_{{{\text{OH}}}} [{\text{H}}]} \right) \\Y_{1} &= 1 + \beta _{{{\text{LH}}}} [{\text{H}}] + \beta _{{{\text{LH2}}}} [{\text{H}}]^{{\text{2}}} \,&{\text{for}} \,{\textsc{{l}}}\text{-}\alpha{\text{-alanine and}}\,{\textsc{{l}}}\text{-}\alpha {\text{-asparagine}};\hfill \\ {\text{Y}}_{{\text{1}}}&= {\text{ 1 }} + \beta _{{{\text{LH}}}} [{\text{H}}] + \beta _{{{\text{LH2}}}} [{\text{H}}]^{{\text{2}}} + \beta _{{{\text{LH3}}}} [{\text{H}}]^{{\text{3}}}\;&{\text{for}}\, {\textsc{{l}}}\text{-}\alpha\text{-histidine} \hfill\\ Y_{2} &= 1 + \beta _{{{\text{L}}^{\prime } {\text{H}}}} \left[ {\text{H}} \right] \hfill\end{aligned}$$
where: K
OH—hydrolysis constant of tshe Co(II) aqua-ion = 10−9.8 [50], β
LH, β
LH2, β
LH3—summary (overall) protonation constants of the l-α-amino acid, β
L’H—protonation constant of imidazole.
It is noteworthy that solving the nonlinear equation system at very erroneous initial estimations may lead to quite different results or lack of convergence. However, in the case of the systems under study, the solutions [M], [L] and [L′] are not allowed to be negative numbers and they should be found within the limits of zero and the total concentrations C
M, C
L, C
L′. This makes it possible to reject the solutions without a chemical meaning.
The used summary protonation constants of l-α-amino acids and imidazole, the stability constants of the primary Co(II)–amac, Co(II)–Himid complexes, as well as the stability constants of the heteroligand Co(II)–l-α-amino acid–imidazole complexes have been determined previously in the same medium and the same ionic strength as in the present work (KNO3, I = 0.5) [37, 45]. The only different parameter was the temperature: 25.0 °C, instead of 0–1 °C. The lack of data due to the lower temperature is usually caused by lowered sensibility of the glass electrodes. Nevertheless, the systematic error of the stability constants recently used could be estimated on the basis of corresponding literature data as 0.1–0.2 in logarithm [51].
The obtained equilibrium concentrations [M], [L], [L′] were needed to calculate the \(K_{{{\text{O}}_{2} }}\) constant. In the present reaction scheme, the first step corresponded to formation of the “active” complexes:
$${\text{Co}}\left( {\text{imid}} \right)_{ 2} + {\text{ 2 Hamac }} + {\text{ H}}_{ 2} {\text{O}} \to {\text{Co}}\left( {\text{amac}} \right)_{ 2} \left( {\text{Himid}} \right)\left( {{\text{H}}_{ 2} {\text{O}}} \right) \, + {\text{ Himid}}$$
(13)
Consecutively the “active” complex takes up dioxygen by forming the dimeric oxygen adduct:
$$2 {\text{ Co}}\left( {\text{amac}} \right)_{ 2} \left( {\text{Himid}} \right)\left( {{\text{H}}_{ 2} {\text{O}}} \right) \, + {\text{ O}}_{ 2} \to \, \left[ {{\text{Co}}\left( {\text{amac}} \right)_{ 2} \left( {\text{Himid}} \right)} \right]_{ 2} {\text{O}}_{ 2}^{ 2- } + {\text{ 2 H}}_{ 2} {\text{O}}$$
(14)
By treating the O2 uptake as a reversible reaction:
the equilibrium constant may be calculated from the formula:
$$K_{{{\text{O}}_{2} }} = \frac{{[{\text{O}}_{2} \,{\text{adduct}}]}}{{[ \, {\text{"active"}}{\text{ complex}}]^{2} [{\text{O}}_{2} ]}}$$
(16)
where [O2 adduct]—equilibrium concentration of this part of the oxygen adduct, in which dioxygen was bound reversibly. The value was found by using the percentage of reversibility of O2 uptake, that is to say by rejecting the part of O2 adduct, in which the metal undergoes irreversible oxidation to Co(III) during the experiment. The equilibrium [O2] concentration was calculated on the basis of table data of dioxygen solubility in water [52].
According to Henry’s law, if the experiment proceeds at the same temperature but at decreased pressure, the volume of gas dissolved in water (or in a diluted solution) is proportionally lower. Under the experimental conditions we have:
$$V_{{{\text{O}}_{ 2} }} = V_{\text{g}} \cdot f = V_{\text{g}} \cdot p_{{{\text{O}}_{ 2} }} / 7 60$$
where: V
g = 0,04758 mL—table value of dioxygen solubility in 1 L of water, at temperature 1 °C under normal pressure 1013 × 105 Pa. \(p_{{{\text{O}}_{ 2} }}\)—partial pressure of dioxygen in the gas burette.
The \(V_{{{\text{O}}_{ 2} }}\) value gives the [O2] concentration after adjustment to the number of mmoles of O2 dissolved in 1 L of the solution.