Kinetic models of activity for β-galactosidases: influence of pH, ionic concentration and temperature
Introduction
The study of the stability of enzymes is an important aspect to consider in biotechnological processes, as this can provide information on the structure of the enzymes and facilitate an economical design of continuous processes in bioreactors. Deactivation mechanisms can be complex, since the enzymes have highly defined structures, and the slightest deviation in their native form can affect their specific activity. Better knowledge of enzyme stability under operating conditions could help optimize the economic profitability of enzymatic processes.
The activity and thermal stability of enzymes is influenced by diverse environmental factors (temperature, pH, reaction medium, shaking, shearing) which can strongly affect the specific tridimensional structure or spatial conformation of the protein [1], [2], [3], [4], [5]. The combination of different factors that can simultaneously deactivate the enzyme complicate the interpretation of the activity data. These effects will be more completely understood when the tridimensional structures of the enzymes, and how these are influenced by the environment, are known.
Therefore, knowledge of the effects that different environmental factors has on enzymatic activity and molecular structure would be highly useful to industrial applications. One of the most studied factors affecting the activity and stability of β-galactosidase is the influence of such ions as Ca2+, Mg2+, Na+, NH4+ and K+. Regardless of the origin of the enzyme, in all the works consulted, it is indicated that Ca2+ ions inhibit the functioning of the enzyme [6], while Mg2+ ions increase their activity. These latter ions are essential to avoid the deactivation in certain cases [6]. On the contrary, the effect that NH4+, K+ and Na+ ions have on the enzymatic activity and stability varies according to the author and species analysed [2], [7]. The effect caused by these ions appears to be related to the radii of the monovalent ions, so that the smallest ions, such as Na+ can enter the structure of the protein, inducing conformational changes in the enzyme structure which are able to deactivate the enzyme. Contrarily, the presence of NH4+ and K+, which have a similar ionic radius, boost the activity of the enzyme. Irrespective of the influence that these ions can have on enzymatic activity, they can also strengthen the resistance of the protein to thermal inactivation by reducing the flexibility of the polypeptide backbone.
Among the most widely used models to explain the thermal deactivation of β-galactosidases is the first-order deactivation model:where E is the concentration of native enzyme in the reaction medium, Ed the concentration of deactivated enzyme and kd the deactivation-kinetic constant. This model appears to reproduce mainly the experimental results for immobilised enzymes (Table 1). The form of first-order deactivation kinetics may be attributed primarily to the disruption of a single bond or sensitive structure, or the occurrence of a single lethal event or single hit [17].
To explain enzymatic deactivation of the enzymes, a deactivation series model has been proposed by [5]:This model considers two irreversible first-order steps and the presence of native enzyme (E) as well as modified enzymatic species (E1, E2), the latter two with a specific activity differing from that of the native enzyme. In the model, α1 and α2 are, respectively, the relative activities of E1 and E2 with respect to the specific activity of E. This model has been applied to experimental results involving β-galactosidases by [15], who determined k1, k2, α1 and α2 of immobilised lactases from Escherichia coli and Kluyveromyces lactis in different reaction mediums. The data are calculated for a single temperature, and therefore the fit of the kinetic constants to the Arrhenius equation cannot be verified.
In the previous model, if k2=0:This model was also used by [15] to explain the enzymatic deactivation of β-galactosidases.
Another model habitually accepted to explain the process of the denaturing of the proteins is the one proposed by [18] and applied by [1], [2], [3], [17], [19]. According to this model, protein can be transformed from an active native state (N) to a non-active state (D), this process being reversible. The enzyme D can also evolve to a non-active state (I), this being the irreversible step:
Nevertheless, most works analysed treat the stability of lactases under the experimental conditions used for lactose hydrolysis. Only a few authors include enzymatic deactivation within the kinetic model of lactose hydrolysis by β-galactosidases [9], [10], [13]. This may be because the enzyme is stabilised by the substrate (lactose) or the product (galactose), as is demonstrated by [19], [20], [21]. This implies that the enzymatic deactivation does not occur during the hydrolysis reaction.
Table 1 summarises the kinetic models proposed by different authors that have studied the thermal deactivation of β-galactosidases. The models proposed and activation energies calculated are shown.
In the present work, we analyse the activity of two β-galactosidase enzymes from different sources under contrasting experimental conditions. We study the influence of pH on the enzymatic activity and the thermal deactivation with different ionic concentrations proposing models that explain the results found. The good fit on applying the kinetic models proposed to the experimental data reported by other authors corroborates the assumptions considered.
Section snippets
Enzymes and enzymatic activity
The enzymes used were two commercial β-galactosidases:
- •
Lactozym 3000L HP-G (EC 3.2.1.23), derived from a selected strain of the yeast Kluyveromyces fragilis (supplied by Novo Nordisk), has a protein content of 35 g l−1, ρ=1.2 g ml−1 and a declared activity of 3000 LAU ml−1 (1 LAU: commercial enzyme which can produce 1 μmol of glucose per minute under standard conditions: 4.7% lactose concentration, pH=6.5, 30 °C, 30 min, standard milky buffer [22]).
- •
Maxilact-L/2000 (EC 3.2.1.23), derived from a selected
Influence of pH on enzymatic activity
The influence of pH on β-galactosidases activity is generally analysed only to determine the optimal pH range, without proposing kinetic models that might explain this dependence. The effect of pH on enzymatic activity is usually explained by a kinetic model in which the enzyme undergoes deprotonation, according to the model:
The equilibrium constants of the reactions, K1 and K2, were defined as:
Making an overall balance for the enzyme, and
Conclusions
The enzymatic activity of Lactozym and Maxilact present similar behaviour with different pH and temperature values and similar kinetic parameter values. This suggests that both enzymes are probably the same.
Kinetic models were proposed to predict the activity of β-galactosidase versus pH and temperature. The models proposed have been confirmed with the experimental results in the present work as well as of other researchers. The dependence of kinetic parameters versus pH and temperature was
References (27)
- et al.
Effect of monovalent cations on the stability and activity of Kluyveromyces lactis β-galactosidase
Lebensm.-Wiss.u-Technol.
(1996) - et al.
Studies on modelling and simulation of lactose hydrolysis by free and immobilized β-galactosidase from Aspergillus niger
Chem. Eng. J.
(1993) - et al.
A method for evaluating lactose hydrolysis in a fixed bed reactor with β-galactosidase immobilized on chitosan
Chem. Eng. J.
(1997) - et al.
Effects of temperature and pH on the catalytic activity of the immobilized β-galactosidase from Kluyveromyces lactis
Biochem. Eng. J.
(2001) - et al.
Kinetic modeling of lactose hydrolysis by a β-galactosidase from Kluyveromyces fragilis
Enzyme Microb. Technol.
(1998) - et al.
Packed-bed reactor performance with immobilized lactase under thermal inactivation
Enzyme Microb. Technol.
(1998) Hydrolysis of lactose in whey permeate by immobilized β-galactosidase from Kluyeromyces fragilis
J. Mol. Catal. B:Enzymatic.
(2000)- et al.
A new kinetic model proposed for enzymatic hydrolysis of lactose by a β-galactosidase from Kluyveromyces fragilis
Enzyme Microb. Technol.
(2002) - Volkin DB, Klibanov, AM. Minimizing protein inactivation. In: Creighton TE, editor. Protein function: a practical...
- et al.
On the role of reversible denaturation (unfolding) in the irreversible thermal inactivation of enzymes
Biotechnol. Bioeng.
(1983)
Effect of chemical modification on enzymatic activities and stabilities
Biotechnol. Bioeng.
A mathematical analysis of enzyme stabilization by a series-type mechanism: influence of chemical modifiers
Biotechnol. Bioeng.
Cited by (106)
Anchoring lactase in pectin-based hydrogels for lactose hydrolysis reactions
2022, Process Biochemistry