## 3 Results and Discussion
### Enhancement in Cellulolysis by Reversible Assembly of Catalytic Module and CBM  
As discussed above, a major effect of the assembly of multiple catalytic moieties of the cellulose-degrading enzymes is expected to be achieved by the cooperative binding of the domains to the crystalline substrate. Nevertheless, the assistance of the catalytic domain as a pseudo-CBM in the binding to the crystalline substrate should be less effective than that of CBM3a. Indeed, the activities of the bicatalytic complexes were lower than the highest activity observed when each of the components was assembled separately with P2-CBM3 (i.e., P1-Cel9**:P2-Cbh9A* vs. P1-Cbh9A*:P2-CBM3a; P1-Cel9*:P2-Cbh9A* vs. P1-Cel9*:P2-CBM3a). Given the weak assistance of the catalytic moieties in binding to the crystalline substrate compared to the CBM3, the contribution of the catalytic domain as pseudo-CBM should be masked by the strong substrate binding of CBM3a when the bicatalytic complexes are assembled with P3-CBM3a. Thus, the activities of the bicatalytic complexes with P3-CBM3a would be expected to be equal to the sum of the activities of the component enzymes when each is combined separately with P2-CBM3a, assuming that the two catalytic moieties do not cooperatively act on the crystalline cellulose substrate. However, these activities were higher than the sum of the activities of the components combined separately with P2-CBM3. We hypothesized that this over-enhancement is achieved by the unique characteristics of CBM3a. While the association of PCNA1 and PCNA2 is almost irreversible, the binding of PCNA3 to the PCNA1:PCNA2 heterodimer is reversible and the interaction is much weaker (\(K_{\rm d}\) of 2.0 \(\times\) 10\({}^{-7}\) M) than that between PCNA1 and PCNA2 (\(K_{\rm d}\) of 6.5 \(\times\) 10\({}^{-10}\) M) [31; 49]. Thus, a large excess of P3-CBM3a (2.5 \(\upmu\)M) was present in the reaction solution for the complete association of the bicatalytic complexes (0.1 \(\upmu\)M) with CBM3a. This excess presence of P3-CBM3a is a possible reason for the unexpected over-enhancement of the bicatalytic complexes by the association with CBM3a. To investigate the contribution of excess P3-CBM3a, the activities of the catalytic moieties fused to PCNA1 were evaluated in the presence of PCNA2 and P3-CBM3a (Figure 5). The hydrolysis by the complexes of the PCNA-fused catalytic moieties and PCNA2 (i.e., P1-Cel9*:P2, P1-Cel9**:P2, and P1-Cbh9A*:P2) was not significantly enhanced by the addition of equimolar amounts of P3-CBM3a (0.1 \(\upmu\)M). This is probably due to partial assembly of the catalytic moieties with CBM3a and the consequent binding of a small portion of them to the substrate. On the other hand, the hydrolysis by the catalytic moieties fused to PCNA1 was greatly enhanced by the addition of excess amounts of P3-CBM3a; the hydrolysis by Cel9* and Cbh9A* was enhanced by a factor of 3.4 and 2.4, respectively, in the excess presence of P3-CBM3a (25-fold of the PCNA1-fused modules). Interestingly, while the activity of P1-Cel9*:P2 in the excess presence of P3-CBM3a was similar to that of P1-Cel9*:P2-CBM3a, the activities of P1-Cel9**:P2 and P1-Cbh9A*:P2 in the excess presence of P3-CBM3a were significantly greater than those of P1-Cel9**:P2-CBM3a and P1-Cbb9A*:P2-CBM3a, respectively. Cel9* still has a CBM, unlike Cel9** and Cbb9A*, so the interaction between the PCNA1:PCNA2 dimer and PCNA3 in the P1-Cel9*:P2:P3-CBM3a complex would be enhanced by the coupled multivalent effect of Cel9* and CBM3a anchored to the crystalline substrate. Thus, P1-Cel9*:P2:P3-CBM3a is expected to function similarly to P1-Cel9*:P2-CBM3a. In contrast, the interaction between the PCNA1:PCNA2 dimer and PCNA3 in the P1-Cel9**:P2:P3-CBM3a and P1-Cbb9A*:P2:P3-CBM3a complexes is expected to still be reversible and weak, since Cel9** and Cbb9A*, both of which completely lack CBMs, could not enhance the interaction.