Thermodynamic Equilibrium Constant Of Glutaraldehyde

then the thermodynamic parameters of the reaction (e.g., free energy, enthalpy and entropy changes) truly define the concept of stability. This definition is different from that used for kinetic experiments, where the biological activity is followed as a function of time in destabilizing conditions. In this case the reaction studied may be written as

where I is the irreversibly inactivated form of the protein or enzyme. The time dependence of the activity gives information on the overall N ^ I transition. These studies are missing a fundamental detail of the inactivation process (i.e., the unfolding reaction N U ), although they may be most interesting to the biotechnologists because of their practical consequences. Moreover, the N^ I transition often does not follow a simple single order kinetics, adding difficulties to the interpretation of the results. It can be argued that the unfolded state U may not be so well defined from the structural point of view as the N state. However, this is not a real problem insofar as the "unfolded state" (which can be only be a major "conformational change" of the molecule) is a well defined state from thermodynamic point of view. As a matter of fact, the reversible N U transition is well approximated by the two-states model (2).

Unfolding can be studied by differential scanning calorimetry (DSC). This technique gives directly the thermodynamic parameters of the unfolding transition, such as melting temperature, enthalpy, entropy and free energy change of the unfolding as well as the heat capacity changes. A comprehensive literature survey on protein thermodynamics, including the calorimetric results, has been collected by Pfeil (3).

How much is the biological activity affected by immobilization? Besides the catalytic activity of enzymes, biological reactions (such as ligand affinity or exchange, ion binding, and intermolecular interactions) can assess the integrity of the response of the biological macromolecule. In these cases, the most direct use of the calorimetric techniques is the determination of the heat change of the reaction (i.e., the reaction enthalpy change). This can be accomplished directly and precisely with a limited set of measurements, less than those currently required with other techniques (i.e., spectroscopic techniques) based on the study of the temperature dependence of the equilibrium constant of the reaction (van't Hoff methods). Isothermal batch calorimetry is the most suitable technique to determine enthalpy changes. Moreover, besides the enthalpy change, equilibrium data (i.e., the equilibrium constants) can be obtained without the use of other independent variables since the enthalpy change itself may be used as a variable reflecting the reaction progress. In these cases, titration calorimetry affords a full protein-ligand titration curve from a single experiment.

Fig. 1. Schematic representation of the protein macromolecule immobilized to the support by multipoint attachment (A), single-point attachment (B,C), and adsorption (D)

By comparison with the free enzyme in the same conditions, the direct assessment of the integrity of the protein-binding site can be obtained. Whatever the effects of the immobilization, support environment, or type of linking or entrapment on the active site, it will show up directly as a difference in the thermodynamic reaction coordinates. Thus equilibrium constants may be evaluated also in the presence of turbid, heterogeneous, multiphase, or multicomponent systems otherwise very difficult to study.

Protein immobilization can be accomplished mainly in three ways: covalent attachment to solid support, adsorption to surfaces, and entrapment in gels. The last will not be treated in this chapter. The first two methods are schematically shown in Fig. 1.

Enzymes can be covalently linked to a specifically functionalized surface by means of chemical bonds, whose number can vary from one (see Fig. 1B,C) through several (see Fig. 1A), or adsorbed on surfaces (see Fig. 1D). Single-point attachment may be obtained by carefully selecting the coupling conditions that depend on the reagents used.

In multipoint attachment (see Fig. 1A), the enzyme molecule is rigidly anchored to the support. The enhanced stability toward temperature increase and concentration of denaturants is often accompanied by a concurrent decrease of the catalytic or binding efficiency (4-6). This is a result of various factors such as an increased rigidity of the macromolecule, restricted accessibility of the binding or catalytic site, and uneven distribution of the attachment points.

Single-point attachment (see Fig. 1B) may give more "spatial freedom" to the anchored protein, without substantial limitations to the substrate accessibility with respect to the free molecule. However, this does not mean that interactions between macromolecule and the support surface (see Fig. 1C) do not occur. On the contrary, as we will see, this is by far the most common situation (7).

It is worth noting that interactions between protein and surface are unavoidable anyway, as clearly shown by visual inspection of Fig. 2. In this figure, the optimized simulated assembly of ribonuclease bound to CPC, controlled pore glass beads (glutaraldehyde C5 spacer arm) is shown. Atomic distances were refined by allowing the spacer arm to freely rotate. As can be seen, the molecule is quite close to the support surface, which implies that a great deal of the time during the macromolecule positional fluctuations is spent in the proximity of the surface. In the protein molecule, it is possible to recognize two structural lobes (domains)

Protein Molecule
Fig. 2. RNase A molecule linked to controlled pore carrier (CPC, aminopropyl derivative) glass surface. The linking reagent is glutaraldehyde (C5) coupled to the terminal lysine amino group. The assembly has been simulated with Insight II (Biosym, San Diego, CA).

divided by a deep cleft where the active site is located. As we will see, unlike in the native enzyme, these two domains will unfold as two independent units after immobilization.

A calorimetric approach to the study of immobilized proteins according to the different situations shown in Fig. 1 will be presented in detail in the following sections. A notable exception will be the multipoint attachment case, which has already been presented in the literature (4). For clarity sake, ribonuclease A will be selected as a protein reference case for all the techniques. However, detailed ther-modynamic and calorimetric analysis of the properties of several other unrelated immobilized proteins, such as papain (8), a-chymotrypsin (9), a-chymotrypsino-gen (10), and lipase (11) can be found in the literature.

1.1. Single-Point Attachment: Thermal Unfolding

1.1.1. DSC Results

Sepharose and other natural gels (e.g., cellulose, K-carrageenan, calcium alginate) are easily contaminated by bacterial growth during the manipulations. There-

Enzyme Immobilization

-a —__■___I_I___I___I__—I___i__<_I_I_■_t_p-I_I_

A Temperature fC) D Temperature fC)

Fig. 3. Temperature dependence on the excess specific heat capacity of RNase. Free enzyme in 50 mM acetate buffer, pH 5.0 (A); immobilized enzyme on CPC-silica through glutaraldehyde coupling, acetate 50 mM, pH 5.0 (B). Continuous curves are the experimental recordings. Dotted curves are the deconvolution best fit.

-a —__■___I_I___I___I__—I___i__<_I_I_■_t_p-I_I_

A Temperature fC) D Temperature fC)

Fig. 3. Temperature dependence on the excess specific heat capacity of RNase. Free enzyme in 50 mM acetate buffer, pH 5.0 (A); immobilized enzyme on CPC-silica through glutaraldehyde coupling, acetate 50 mM, pH 5.0 (B). Continuous curves are the experimental recordings. Dotted curves are the deconvolution best fit.

fore, other synthetic polymers or reactive glasses (silica) were preferred. Ribonu-clease A (RNase A) was immobilized on silica (glass) beads (CPC, controlled pore carrier, aminopropyl derivative) through glutaraldeyde-mediated chemical coupling. In Fig. 3 the thermal unfolding transitions of the free (see Fig. 3A) and immobilized (see Fig. 3B) enzyme studied by DSC are shown. The transition parameters (the unfolding middle point temperature, Tm, and the enthalpy change, AH) obtained from the deconvolution of the thermogram for the free and immobilized enzyme, respectively, are listed in Table 1.

The unfolding transition of the free enzyme (see Fig. 3A) can be well approximated by the two-states model. This is confirmed by a value of the co-operativity unit, Cu (i.e., the ratio of the van't Hoff to the calorimetric enthalpy changes), very close to 1 (Table 1) (2). This does not apply to the overall transition of the immobilized enzyme. In this case, two independent overlapping transitions (each with a Cu close to 1) (Table 1) are necessary to fit the experimental curve (12). This result implies that, as a consequence of the immobilization, the protein cannot be considered a single thermodynamic domain but the sum of two independent parts (domains) having different stabilities. Note that one domain of the protein has a Tm of about 70°C, higher than the Tm of the native enzyme (59°C). Stabilization of part of the macromolecule is therefore achieved by interdomain dissociation. However, the integrity of the macromolecule is somehow preserved because the overall AH is similar, or even slightly higher (Table 1), to that of the free enzyme. The presence of a different local environment near the domain chemically linked to the support (e.g., Fig. 1C), may modify interdomain free energy contributions causing domains to uncouple (13).

The binding of the inhibitor 3'-cytidine monophosphate (3'-CMP) slightly stabilized the protein as suggested by a small increase of both Tm and AH.

300 Battistel and Rialdi Table 1

Enthalpy of Unfolding

Tmi AHj Tm2 AH2 AHtot

RNase CPC 60.0 ± 0.5 232 ± 8 0.99 70.1 ± 0.5 195 ± 7 1.02 427

RNase CPC + 3'-CMP61.4 ± 0.4 261 ± 8 0.90 71.3 ± 0.5 200 ± 7 0.98 461

Note: AH, and middle-point transition temperature, Tm, of free and glutaraldehyde-immobi-lized RNase A at pH 5.0, acetate buffer 50 mM The subscripts 1 and 2 refer to domain 1 and 2 in the immobilized protein. 3'-cytidine monophosphate (3'-CMP) is an enzyme inhibitor. (From ref. 25. Copyright 2005, American Chemical Society.)

1.2. Single-Point Attachment: Binding Studies

1.2.1. Isothermal Titration Calorimetry

The support (CPC silica glass beads) containing RNase was loaded into the calorimetric cell and titrated with a solution of 3'-cytidine monophosphate (3'-CMP). 3'-CMP is a RNase inhibitor, able to bind tightly to the protein active site. The titrating solution was continuously added with an external peristaltic pump, whereas the heterogeneous phase within the calorimetric cell was slowly stirred. The experimental heat evolved (W, watts) of the binding of 3'CMP to immobilized RNase as a function of time is presented in Fig. 4, curve A. The calorimetric output has been corrected for the instrumental time response delay (Tian effect, Fig. 4, curve B) (18). The thermodynamic parameters obtained from this experiment (i.e., the apparent equilibrium constant, K, and the enthalpy change of the binding reaction, AH) are listed in Table 2.

The values of K and AH for the free enzyme listed in Table 2 were obtained either by batch calorimetry or flow isothermal titration calorimetry. The flow calorimeter is designed to measure the heat effects by mixing two liquids. Instead, batch calorimetry can easily monitor heat effects with heterogeneous samples conveniently titrated with an external liquid reactant solution. The heat of reaction is observed as long as reaction sites are present on the material inside the cell. As can be seen in Table 2, there is a good agreement between batch and flow techniques in the case of the binding reaction with the free enzyme. Moreover, immobilized RNase is still fully competent to bind the inhibitor, since the apparent equilibrium constant, K, and AH are quite close to those of the free enzyme.

Spectroscopic studies confirmed the results showed in Table 2 for five-carbon spacer arms,C5, or longer , up to C22 (13), whereas a dramatic decrease in binding affinity was instead observed for shorter-linking bridges (<C5) (13).

Table Equilibrium Constants

Fig. 4. Binding of 3'-CMP to immobilized RNase on CPC silica beads activated with glutaraldehyde. Acetate buffer 50 mM, pH 5.0. Immobilized RNase: 0.52 mg, 3'CMP titrating solution: 1.5 mM Flow rate: 1.2 |L/s. (A) power vs time experimental output. (B) Curve obtained after correction of the time response delay of the instrument. (From ref. 18. Copyright 2005, with permission from Elsevier.)

Table 2

Apparent Equilibrium Constant (K) and Enthalpy Change (AH) of the Binding of 3-CMP to RNaseA

Table 2

Apparent Equilibrium Constant (K) and Enthalpy Change (AH) of the Binding of 3-CMP to RNaseA


K (mol-1 x 10-4)

AH (kJ/mol)

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  • liisa
    How immobilization of enzyme affect the entropy change?
    8 years ago

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