Thermodynamics and kinetics of thermal deactivation of catalase Aspergillus niger

Abstract The thermal stability of enzyme-based biosensors is crucial in economic feasibility. In this study, thermal deactivation profiles of catalase Aspergillus niger were obtained at different temperatures in the range of 35°C to 70°C. It has been shown that the thermal deactivation of catalase Aspergillus niger follows the first-order model. The half-life time t1/2 of catalase Aspergillus niger at pH 7.0 and the temperature of 35°C and 70°C were 197 h and 1.3 h respectively. Additionally, t1/2 of catalase Aspergillus niger at the temperature of 5°C was calculated 58 months. Thermodynamic parameters the change in enthalpy ΔH*, the change in entropy ΔS* and the change Gibbs free energy ΔG* for the deactivation of catalase at different temperatures in the range of 35°C to 70°C were estimated. Catalase Aspergillus niger is predisposed to be used in biosensors by thermodynamics parameters obtained.


INTRODUCTION
Temperature is one of the causes of enzyme inactivation in addition to pH, heavy metals, salts, solvents, detergents and mechanical agitation pressure 1, 2 . The thermostability of an enzyme is one of the most important parameters in determining its industrial applications in the long term processes carried out in biosensors. This stability of enzyme-based biosensors may change over the lifetime; particularly if storage conditions such as temperature are not controlled. The residual activity, deactivation rate constants and half-life time are the basic parameters to be known before designing the process.
Catalase is one of the fi rst enzymes to be purifi ed and has been the subject of intense study. Catalase catalyzes the breakdown of H 2 O 2 into water and oxygen. The catalase in different industrial applications such as the food industry 3 , the textile industry 4 and immobilized catalase 2-6 is used. Moreover, catalase is used to decompose the hydrogen peroxide, which being formed in the reaction with the use of oxidases 7 . Several various methods of measuring the activity of catalase, such as spectrophotometry 3-9 , oxygen electrode method 1, 10, 11 and, electrochemistry 12, 13 are used. Most of the presented other's authors studies were prepared with the use catalase bovine liver 5 .
One of them was known and was used with catalase Aspergillus niger 13 . Microbial catalase from fungus Aspergillus niger is used for commercial purposes due to the higher stability in conditions of extreme pH and temperature values as well as H 2 O 2 content 3, 8, 9 .
Cantemir et al. 14 determined the thermal deactivation of kinetics parameters for catalase bovine liver. The kinetic parameters of thermal deactivation for Terminox Ultra were analyzed in the previous work 10 . This is the fi rst report providing information on the thermal deactivation kinetics and the thermodynamic parameters of catalase Aspergillus niger. The studies and the obtained results can be used for modelling the process with use catalase Aspergillus niger.

Thermal deactivation
The thermal deactivation of catalase Aspergillus niger was determined at temperatures The solution of catalase Aspergillus niger, adjusted to pH 7.0 with phosphate buffer (2 · 10 -2 μl enzyme/ml buffer), was used in all experiments. The enzyme solution was divided into 5 ml samples and these were immersed in a water bath at a temperature of 35 o C. After a specifi ed storage time of the catalase at a special temperature, one sample of the enzyme was taken away and the activity of the catalase was investigated. The data were collected within 150 sec. The activity of the catalase was examined using the oxygen electrode method 1, 10, 11 .

Method of measuring the activity of catalase
The catalase activity was determined by measuring the quantity oxygen production. In fl ask fi tted with a dissolved oxygen sensor for the quantifi cation of dissolved oxygen the 100 ml 0.01 M hydrogen peroxide solutions in 0.02 M phosphate buffer (pH 7) was inserted. Measurements were carried out at 20 o C, in a jacketed vessel. The hydrogen peroxide was degassed with N 2 . Measurements of catalase activity were initiated by injecting the 0.1 ml catalase solution into the reaction vessel and the data were collected. On the basis of the results of the measurements at specifi c temperatures, a quantity of oxygen was calculated in relation to the initial quantity of oxygen at time t = 0. The activity of catalase was defi ned as a quantity of O 2 in percent's, in relation to the keeping time at a specifi c temperature. The catalase activity was normalized in relation to the initial activity. The thermal deactivation was studied by taking the measurements over 150 s. The catalase activity was assayed in a temperature range of 35 o C to 70 o C after an incubation time between 0 and 30 h. Temperatures and value pH has been standardized by used the certifi cated thermometer and pH-meter was calibrated by standard's buffers.

Kinetic model
The thermal deactivation of catalase was described by the following the fi rst-order model 10, 11, 14, 15 . The thermal deactivation of the catalase was assumed to follow fi rstorder kinetics E→D, which can be represented as follows (1) where E is a concentration of the active enzyme, and k D is a deactivation rate constant (h −1 ).
Solution of Eq. (1) with an initial condition E(t = 0) = E 0 (E 0 is initial enzyme concentration), yields (2) Usually, a dimensionless enzyme activity, a, is expressed by the following equation a = E/E 0 . Substituting into Eq. (2) gives (3) that expresses the change in the activity of the enzyme as a function of the time.
A dependence between a deactivation constant k D and a temperature T is also given by the Arrhenius equation (4) where k D0 is a pre-exponential factor and E D is activation energy for the enzyme deactivation.
One of the important practical problems is to determine the occurring constants in Eq. (4).
Usually from the plot of ln (a) versus t by Eq. (3) slope gives the value of the deactivation rate constant k D
Other scientists used the reference temperature T ref

10, 17, 18
to decrease the correlation among the parameters in Eq. (4), then the equation takes the following form (5) Taking into account Eq. (5), the change of the enzyme activity can be described with the following expression (6) where: i -number of measurements (0,1,2...n), T j -temperature at which the measurement was executed Based on Eq. (6) the values of k D,Tref and E D were found using nonlinear regression of the Levenberg-Marquardt procedure 8-10, 19 .
A standard technique used to solve a nonlinear equation by least squares method of fi nding the minimum of the function is a sum of squares estimate of errors SSE (7) where: -experimentally determined enzyme activity, -enzyme activity calculated based on Eq. (6) in which, the time t i , the temperature T j and the reference temperature T ref are known. Equation (7) allows fi nding the solution of the objective function with a given set of parameters. The global minimum of the objective function was determined by many local minima in the parameter estimation process.
The enthalpy ΔH* and entropy of activation ΔS* and the Gibbs free energy ΔG* values can provide some clues about enzymes and thermostability 20 . Low enthalpy values ΔH* indicate the effectiveness of the transition state. The changes in entropy ΔS* indicate the stability of the transition state and the affi nity of the substrate for the enzyme. The entropy ΔS* for the enzymatic reaction decreases with increasing enzyme stability. The change in the ΔG* is the energy barrier for the catalase deactivation. This parameter is a measure of the spontaneity of the deactivation process and can refl ect the effect of temperature on enzyme activity. The higher ΔG* is, the more stable is the enzyme.
The thermodynamic parameters such as energy, entropy and enthalpy of the catalase deactivation can be estimated by making use of absolute reaction rates. The thermodynamic parameters were calculated by the rearranged equation in which the temperature dependence on the deactivation rate constant can be expressed as 16, 20 (8) where k D is the deactivation rate constant (h −1 ), T is the absolute temperature (K), k is the Boltzmann constant (1.3806 · 10 −23 J K −1 ), h is the Planck's constant (2.3854 · 10 −30 J h), R is the gas constant (8.314 · 10 −3 kJ mole −1 K −1 ), ΔS* is the change in entropy (kJ mole −1 K −1 ) and ΔH* is the change in enthalpy (kJ mole −1 ).
The values of ΔH* and ΔS* can be calculated from the slope and intercept of the plot of ln(k D /T) versus (1/T) respectively. The change Gibbs free energy ΔG* of the catalase can be found by the following formula ΔG* = ΔH* − TΔS* (9) The half-life is defi ned as the time required for the enzyme to lose half of its initial activity, expressed in hours and is given by

Statistical analysis
Statistical analysis is a very useful technique to analyze, interpret, and summarize the experimental data. All the experiments were carried out in triplicate. Results were expressed as average values with error bars indicating the standard deviations. Deactivation rate constant k D values were determined by fi tting the data points to fi rst--order kinetics according to Eq. (6) by performing linear regression. The trials with R 2 ≥ 0.994 were selected for plotting the graphs. The data is reported as mean ± SD. p values less than 0.05 are considered to be signifi cant. Data obtained from the results were analyzed using nonlinear regression with the help of SigmaPlot 12.3.

Thermal deactivation studies and estimation of thermal deactivation constants
The obtained values of the parameters in Eq. (6) are calculated using nonlinear regression with SigmaPlot 12.3 and represented in Table 1. The Pearson correlation coeffi cient R for the obtained parameters was 0.9970 and the determination coeffi cient (correlation coeffi cient squared) R 2 was 0.9940, however, the standard error of the estimate was equal to 0.0693, with the statistical probability of parameters P <0.0001. the same buffers. The retained activities were 98%, 70% and 25% respectively. The presented in Fig. 1 results of the thermal stability of catalase Aspergillus niger activity are higher than those presented earlier.
The activity of catalase Aspergillus niger at specifi c times and temperatures was calculated using Eq. (6) with the estimated parameters from Table 1. The residual analysis of catalase activity results for temperatures in the range of 35°C to 70°C was shown in Fig. 2.  The energy of thermal deactivation E D catalase Aspergillus niger indicated good stability of the enzyme at higher temperatures, and requirement of comparatively high energy to thermally deactivate the catalase Aspergillus niger.
Having at our disposal the constants of the thermal deactivation of the catalase k D,Tref and E D at the reference temperature calculated with the transformed Arrhenius equation it is possible to calculate the value of the pre-exponential thermal deactivation rate constant k D0 for catalase, which equals 1.18 · 10 19 (h −1 ). Calculated by Eq. (4) the thermal deactivation constants k D were presented in Table 2.  Table 1.
The fi rst-order model can be adequately fi tted at all the temperatures by results analysis. At a temperature of 70°C, the catalase Aspergillus niger is rapidly deactivated to less than 20% of the initial activity after the incubation time of 4 h. While almost 90% of the initial catalase activity remains when it was kept at 30 h at 35°C. Akertek and Tarhan 3 presented thermal stabilities of catalase Aspergillus niger after incubation for 15 h in the temperatures of 32°C, 40°C and 50°C only; and in The regular distribution of residuals without patterns is observed, indicating the adequacy of the estimated parameters. The residual analysis of results presented in Fig. 2 was in the range ± 0.06 but the value of average absolute residuals was equal to 3.05 · 10 −3 . The accomplished statistical analyses at s pecifi c temperatures in the range of 35 o C to 70 o C for catalase Aspergillus niger confi rm that the assumption of fi rst-order kinetics is well-founded.

Half-life time of the catalase Aspergillus niger
The effect of temperatures on the half-life times t 1/2 and Gibbs free energies ΔG* of the catalase Aspergillus niger was calculated from Eq. (10) and Eq. (9), respectively and were presented in Table 2.  Table 3 presents calculated values of ΔH*, ΔS*, ΔG* for catalase Aspergillus niger. They have been compared with thermodynamic parameters of catalase of various origins.
The values of the activation energy for the thermal deactivation reaction for catalase Aspergillus niger presented in Table 3 are over 1.48 times higher than the values of the activation energy for the thermal deactivation reaction determined for bovine catalase 11 . The positive values of ΔH* indicate that the thermal deactivation of catalase Aspergillus niger is an endothermic reaction. Positive values of ΔH* have also been reported for catalase Aspergillus niger 24 and catalase bovine liver 25 . The value thermodynamic parameters catalase A. niger 24 was calculated by measurements at only two different temperatures 27 o C and 37 o C. The ΔG* values were calculated at different temperatures according to the Eq. (9) and included in Table 2. Since the Gibbs free values energy ΔG* catalase Aspergillus niger decreases with increasing temperature whereas ΔH* and ΔS* are constants values, one could point out that entropy changes ΔG* are the result of the thermal deactivation of proteins in catalase 26 . The Gibbs free values energy ΔG* catalase bovine liver was also decreasing; in the range of 6 kJ/mol to − 9 kJ/mol for temperatures in the range of 55 o C to 75 o C. Catalase bovine liver is less stable than catalase Aspergillus niger. There is not much information available about the energy of the thermal deactivation of E D of catalase. It has been reported that the energy of the thermal deactivation E D of catalase should be between 86.00 kJ/mol and 116.00 kJ/mol during the deactivation (Table 3). Therefore, the obtained value of E D of catalase Aspergillus niger was  As can be seen in Fig. 3, the values of the half-life time of the decrease in activity, calculated for catalase Aspergillus niger, are situated in the range of values for t 1/2 determined by other researchers. The results are different when the enzymes of various origins are used. Although catalases, which are produced by most aerobic microorganisms, are very well studied enzymes, there are only a few reports on the half-life time t 1/2 thermostable catalase 22, 23 . Fig. 3 also shows the half-life time t 1/2 for catalases from thermostable bacterium: Bacillus sp. 22 and Proteus mirabilis 23 . At pH 7.0 and temperatures of 37 o C, 50 o C, 60 o C and 70 o C, the half-life time t 1/2 for catalase from Aspergillus niger was approximately fi ve to ten times longer than the half-life time t 1/2 for catalase Proteus mirabilis 23 . The reported value of the half-life time t 1/2 at a temperature of 55 o C for catalase from Aspergillus niger 2 was equal to about 3.2 h, which was three times smaller than the value in Table 2. Hooda 21 reported that values t 1/2 at a temperature of 75 o C for catalase from Aspergillus niger, were similar to those presented and were equal to about 0.55 h.
Jürgen-Lohmanna and Legge 11 presented that the constant thermal deactivation rates for catalase from the bovine liver can be established at temperatures in the range of 40 o C to 65 o C. However, the calculated values of the half-life time t 1/2 for catalase from Aspergillus niger at temperatures of 40 o C and 60 o C were, respectively, 150 and 80 times the longer than the values of the half-life time for bovine catalase.

Thermodynamic parameters
The change in enthalpy ΔH* and the entropy ΔS* during the thermal deactivation of catalase Aspergillus niger were calculated within the temperature range between equal to 126.94 ± 1.65 kJ mol −1 and was the highest value among the designated ones.
The knowledge of the thermal deactivation constants allows for the design, modelling and optimization of work of sensors within a short period. The long-term stability of catalase in biosensors when it comes to the low and medium temperature range will take months or years. Based on the parameters presented in Table 1 it is possible to calculate, from Eq. (6), the thermal stability of the catalase activity for the temperature in the range of 5 o C to 30 o C as presented in Fig. 5. the temperature on biosensors and optimization of the batch bioreactors 30 .

CONCLUSIONS
The presented work includes determination of thermodynamic parameters for catalase Aspergillus niger, based on tests in the range of from 35 o C to70 o C. The kinetic parameters of thermal deactivation were determined on the basis of Eq. (6), taking into account the results of measurements of catalases activity over time, taking into account changes in the catalases activity under the effect of the temperature.
It was found that the thermal deactivation of catalase proceeded according to fi rst-order kinetics. This consideration is validated by the accordance between the measured and the calculated values. Thermal deactivation rate constants varied depending on the temperature, following the Arrhenius equation. The activation energy for the thermal deactivation process for catalase Aspergillus niger was 116.00 ± 0.63 kJ mol −1 .
Change in entropy ΔS* and change in enthalpy ΔH* of the thermal deactivation of catalase Aspergillus niger were 0.2045 ± 0.1061 kJ mol −1 K −1 and 132.56 ± 7.21 kJ mol −1 , respectively. The change in Gibbs free energies ΔG* were from 69.57 kJ mol −1 to 62.42 kJ mol −1 with increasing temperature. The stability of catalase Aspergillus niger and the half-life time in low temperatures were also calculated.
The presented methodology of measurement can be used to determine the half-life time of commonly used catalases, which are less stable than catalase Aspergillus niger.

ACKNOWLEDGEMENTS
The author would like to thank prof. Marek Wójcik for his constant help and support. -pre-exponential thermal deactivation rate constant, M -1 h -1 P -the statistical probability, -  ig. 5 clearly shows a signifi cant advantage of the presented method. The stability of the bovine catalase biosensor 13 was 91.3% of its initial activity after storing it for two months at 4°C. The thermal stability catalase A. niger presented in Fig. 5 was 97.5% of its initial activity after storing it for two months at 5°C.

NOTATION
The half-time for catalases at the temperature in the range of 5 o C to 30 o C was calculated and presented in Table 4. Literatures information about the half-time for catalases of various origins in low temperatures was presented in the same Table. The half-life of catalase Aspergillus niger at 30 o C is about 19 days. It would take about 58 months to determine the half-life times for catalase Aspergillus niger in the temperature of 5 o C using common isothermal techniques. The thermal stability of catalase Aspergillus niger at 5 o C is considerably higher than catalase from Aspergillus terreus 29 . The obtained results confi rm the universally acceptable opinion, that the catalase of microbiological origins is more stable than bovine catalase.
Catalase Aspergillus niger is a suitable enzyme for its use in biosensors (Fig. 4, Table 4). The value of the halflife time at room temperature equals about 3.5 months. The obtained parameters for this enzyme can be used in mathematical models for predicting the infl uence of R -the gas constant, 8.314 · 10 −3 J mol -1 K -1 T -temperature, K T j -temperature at which the measurement was executed, K T ref -the reference temperature, K t -time, h t 1/2 -the time of half-life activity of enzyme, h SSE -the sum of squares estimate of errors, -ΔS* -the change in entropy, kJ mol −1 K −1 ΔH* -the change in enthalpy, kJ mol −1 ΔG* -the change Gibbs free energy, kJ mol −1