Bridging the Micro-Macro Gap between Single-Molecular Behavior and Bulk Hydrolysis Properties of Cellulase

Takahiro Ezaki, Katsuhiro Nishinari, Masahiro Samejima, and Kiyohiko Igarashi

Phys. Rev. Lett. 122, 098102 – Published 7 March 2019

Abstract

The microscopic kinetics of enzymes at the single-molecule level often deviate considerably from those expected from bulk biochemical experiments. Here, we propose a coarse-grained-model approach to bridge this gap, focusing on the unexpectedly slow bulk hydrolysis of crystalline cellulose by cellulase, which constitutes a major obstacle to mass production of biofuels and biochemicals. Building on our previous success in tracking the movements of single molecules of cellulase on crystalline cellulose, we develop a mathematical description of the collective motion and function of enzyme molecules hydrolyzing the surface of cellulose. Model simulations robustly explained the experimental findings at both the microscopic and macroscopic levels and revealed a hitherto-unknown mechanism causing a considerable slowdown of the reaction, which we call the crowding-out effect. The size of the cellulase molecule impacted significantly on the collective dynamics, whereas the rate of molecular motion on the surface did not.

Received 5 October 2018
Revised 7 December 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.098102

Physics Subject Headings (PhySH)

Biochemistry Biomolecular processes Chemical kinetics, dynamics & catalysis Collective behavior

Physics of Living SystemsInterdisciplinary Physics

Authors & Affiliations

Takahiro Ezaki^1,2,*, Katsuhiro Nishinari¹, Masahiro Samejima³, and Kiyohiko Igarashi^3,4,†

¹Research Center for Advanced Science and Technology, The University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo 153-8904, Japan
²Precursory Research for Embryonic Science and Technology, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan
³Department of Biomaterial Sciences, Graduate School of Agricultural and Life Sciences, The University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-8657, Japan
⁴VTT Technical Research Centre of Finland, Tietotie 2, Espoo FI-02044, Finland

^*ezaki0705@gmail.com
^†aquarius@mail.ecc.u-tokyo.ac.jp

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 122, Iss. 9 — 8 March 2019

Reuse & Permissions

Access Options

Article Available via CHORUS

Download Accepted Manuscript

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Overview of the system. (a) Schematic illustration of cellulase molecules on crystalline cellulose. (b) Two types of binding: productive binding (left) and nonproductive binding (right). (c) Reaction mechanism of enzymatic hydrolysis of cellulose. (d)–(g) Definitions of the model. (d) A cellulase attaches to the bulk cellulose surface with a rate of $k_{on}$ in a nonproductive manner. A nonproductive cellulase leaves the surface with a rate of $k_{off}$ (detachment). (e) At the reducing end of each cellobiose chain (shown in yellow), complexation (decomplexation) occurs with a rate of $k_{c}$ ( $k_{d}$ ) if a nonproductive (productive) cellulase is present. (f) A productive cellulase moves forward by one cellobiose unit with a rate of $k_{pr}$ , decomposing the site where it was originally located. (g) Conformation of cellulose chains. The upper half of the structure is shown.
Reuse & Permissions
Figure 2
Comparisons between simulation and experimental results [5, 6]. (a) Sample time-space trajectories of cellulase molecules. We selected typical trajectories that occurred between $t = 0$ and $t = 10 000 s$ . (b) Time course of cellobiose production for $L = 500$ , 1000, and 2000. Shaded areas represent s.d. (c) Specific activity as a function of surface density at $t = 120 \min$ . (d) Relationship between the concentration of free cellulase (i.e., $k_{on}$ ) and total production at $t = 120$ and 240 min. (a,d) We set $k_{on} = 0.1 s^{- 1}$ . For more details of simulation conditions and experimental procedures, see the Supplemental Material [25].
Reuse & Permissions
Figure 3
Relationship between the layer number and degradation time. (a) Degradation time of each layer. The time at which each layer is completely decomposed is shown. (b) Intrinsic degradation time of each chain. (a),(b) We set $k_{on} = 0.1 s^{- 1}$ . (c),(d) Schematic representations of configurations of cellulase molecules for (c) layer 3 and (d) layer 15.
Reuse & Permissions
Figure 4
Impacts of cellulase properties on production rate at $t = 120 \min$ . The results for the original condition (gray circles) and two other conditions varying a single parameter (a) $R^{NP} = 2$ and 8 nm, (b) $R^{P} = 4$ and 16 nm, (c) $k_{pr} = 3.5$ and $14 s^{- 1}$ , (d) $k_{off} = 0.5$ and $2 s^{- 1}$ , (e) $k_{c} = 0.05$ and $0.2 s^{- 1}$ , and (f) $k_{d} = 0.05$ and $0.2 s^{- 1}$ are shown. The other parameters not explicitly shown in each panel were left unchanged. (g),(h) Number of productive cellulase molecules on the surface for different values of (g) $R^{NP}$ and (h) $R^{P}$ . For more details of simulation conditions, see Supplemental Material [25]. (i),(j) Schematic representations of the crowding-out effect. If $R^{NP}$ is smaller than $R^{P}$ (i), the productive cellulase is crowded out; otherwise (j), the effect is not observed. The colors of the areas and arrows, i.e., green and orange, represent productive and nonproductive bindings, respectively.
Reuse & Permissions

Physical Review Letters