Free Energy Diagram for the Heterogeneous Enzymatic Hydrolysis of Glycosidic Bonds in Cellulose

Abstract

Kinetic and thermodynamic data have been analyzed according to transition state theory and a simplified reaction scheme for the enzymatic hydrolysis of insoluble cellulose. For the cellobiohydrolase Cel7A from Hypocrea jecorina (Trichoderma reesei), we were able to measure or collect relevant values for all stable and activated complexes defined by the reaction scheme and hence propose a free energy diagram for the full heterogeneous process. For other Cel7A enzymes, including variants with and without carbohydrate binding module (CBM), we obtained activation parameters for the association and dissociation of the enzyme-substrate complex. The results showed that the kinetics of enzyme-substrate association (i.e. formation of the Michaelis complex) was almost entirely entropy-controlled and that the activation entropy corresponded approximately to the loss of translational and rotational degrees of freedom of the dissolved enzyme. This implied that the transition state occurred early in the path where the enzyme has lost these degrees of freedom but not yet established extensive contact interactions in the binding tunnel. For dissociation, a similar analysis suggested that the transition state was late in the path where most enzyme-substrate contacts were broken. Activation enthalpies revealed that the rate of dissociation was far more temperature-sensitive than the rates of both association and the inner catalytic cycle. Comparisons of one- and two-domain variants showed that the CBM had no influence on the transition state for association but increased the free energy barrier for dissociation. Hence, the CBM appeared to promote the stability of the complex by delaying dissociation rather than accelerating association.

Keywords: Hypocrea jecorina; Rasamsonia emersonii; carbohydrate-binding protein; cellulase; enzyme kinetics; enzyme mechanism; thermodynamics.

SCHEME 1.

Reaction path underlying the analysis. EC_m and EC_{m − 1} are interpreted as the Michaelis complexes of enzyme and a cellulose strand of either m or m − 1 cellobiose units. E and C represent free enzyme and cellobiose, respectively (see the companion article (71) for more details).

FIGURE 1.

Processivity estimated as the product ratio, n_p ∼ [cellobiose]/[cellotriose]. The concentrations were measured by ion chromatography after 1-h hydrolysis trials. Triangles identify enzymes with a CBM, and circles are for one-domain variants. Open and closed symbols signify enzymes from H. jecorina and R. emersonii, respectively.

FIGURE 2.

Temperature dependence of the rate constants _pk_on (left ordinate) and _pk_off (right ordinate) calculated from Equations 1 and 2 using data from the companion article (71). Triangles identify enzymes with a CBM, and circles are for one-domain variants.

FIGURE 3.

Transition state free energies determined from Equation 3 and plotted as a function of temperature for both one-domain (circles) and two-domain (triangles) variants of Cel7A from H. jecorina (open symbols) and R. emersonii (filled symbols).

FIGURE 4.

Eyring plots for association (calculated from _pk_on) and dissociation (calculated from _pk_off) for the four investigated enzymes. Triangles represent two-domain enzymes (i.e. with a CBM), and circles are for one-domain enzymes. The slope, α, specifies the activation enthalpy, α = −ΔH^≠/R.

FIGURE 5.

Examples of progress curves for Hj_CBM hydrolyzing Avicel at different temperatures. The points are raw data from biosensor measurements, and the lines are best fits of a kinetic model describing processive cellulases (see “Results” for details). The initial, sigmoidal part of the curves (e.g. the first ∼30 s at 25 °C) is the so-called burst phase, and the subsequent, near-linear course reflects quasi-steady state. The enzyme concentration was 150 nm, and the Avicel load was 3.0 g/liter at 5 °C and 5.0 g/liter at 25 and 50 °C.

FIGURE 6.

Energy diagram for Cel7A hydrolysis of a glycosidic bond in insoluble cellulose. The abscissa is the reaction path as discussed in the main text and illustrated by the schematics and equations below the figure. The ordinate shows changes in free energy (G; black curve), enthalpy (H; red curve), and entropy (−TS; green curve) along the reaction path. Note that the entropic contribution is given as its negative value, −TΔS. The diagram defines a total of five changes (three activated complexes and two equilibria), and the thermodynamic functions pertaining to each of these steps are specified by a set of super- and subscript. For the G function, these five steps are identified by the dashed lines in the figure, and the super- and subscripts are given in the associated symbols. The same set of super- and subscripts are used for the H and −TS functions in the text.