**1. Introduction**

Bioelectrocatalysis, which couples an enzymatic catalysis with an electrode reaction and thereby transforms the chemical energy of the reactant into electrical energy (or vice versa), plays an important role in various applications, including biological fuel cells [1], biosensors [2], and bio-electrosynthesis [3]. Redox enzymes in solutions usually show significantly high catalytic efficiency toward their natural substrates. However, enzymes immobilized on the surface of a solid electrode usually do not enable sufficient electron transfer kinetics between the redox-active sites and the support owing to electrical insulation of the redox-active site by the surrounding polypeptides.

In general, mechanisms of electron transfer between enzymes and electrodes are classified into mediated electron transfer (MET) and direct electron transfer (DET) [4] (Figure 1). In an MET-type system, an extrinsic redox-active species, referred to as a mediator, is utilized to shuttle electrons between the enzyme redox site and an electrode [5]. In this case, the redox enzyme catalyzes the oxidation or reduction of the mediator as a co-substrate. The reverse transformation (regeneration) of the mediator occurs reversibly or quasi-reversibly on the electrode surface. The use of small, low-molecular-weight electron mediators that require low overpotentials can be beneficial because they can enable rapid electron transfer between an enzyme and an electrode with low power loss. However, the cost, stability, selectivity, and ability to exchange electrons in the immobilized state of such mediators must also be considered. In contrast, in a DET-type system, fast electron transfer to or from a solid electrode occurs through the intrinsic electron relay system in the protein [6] (such as

a series of ion-sulfur clusters [7], hemes [8], copper atoms [9], or some amino acid residues [10,11]). Accordingly, the electrode surface acts as a co-substrate of the redox enzyme, and the enzymatic and electrode reactions proceed simultaneously. From this viewpoint, a DET-type bioelectrocatalysis constructed with only an enzyme and an electrode is mostly an ideal system that provides high selectivity for electrochemical biosensors and a high cell voltage for enzymatic biofuel cells without a proton exchange membrane.

**Figure 1.** Schematic of electron transfer routes of (**left**) MET-type and (**right**) DET-type bioelectrocatalysis.

Over the past few decades, significant efforts have been devoted to improving the performance of DET-type bioelectrocatalysis, including protein engineering, electrode materials, and bio-interfacial engineering [12,13]. The interfacial electron transfer rate constant (*k*), according to Macrus's theory [14,15], is governed by the potential difference, re-organization energy, and most importantly, the distance between the active center of the enzymes and the electrode surface. The electron transfer rate constant between the redox site and the electrode decreases exponentially with increasing distance. Because redox enzymes are sizable proteins with anisotropic properties and their active sites are not always located in the central region, the distance between the active site and the electrodes should be varied according to the orientation of the enzymes when immobilizing at the electrode surfaces. Therefore, controlling the orientation of the enzyme on the electrode surface is a key factor in realizing a fast interfacial electron transfer [16,17].

π π Carbon nanomaterials, such as carbon nanotubes (CNTs), graphene, carbon nanoparticles, and their combinations thereof, have been widely utilized in DET-type bioelectrocatalysis owing to their high conductivity, chemical stability, and low cost. CNTs are nanowires constituted from one or more layers of seamlessly rolled graphene (single-walled and multi-walled CNTs, respectively) with large specific surface areas (in a precise sense, with large values for surface-to-weight ratio) and behave electrically as metals or as semiconductors [18]. Moreover, purified CNTs are usually electrochemically inert and do not exhibit voltametric response in the potential window commonly used [19]. In contrary to CNTs, graphene is a two-dimensional sheet of sp<sup>2</sup> bonded carbon atoms possess unique properties, like ballistic conductivity, high specific surface area, and rapid heterogeneous electron transfer [20]. For example, it has been reported that the specific surface area of graphene sheets is frequently larger than that of single-walled CNTs. Unlike structurally more defined CNTs and graphene, structurally less-defined carbon nanoparticles are considered more economical than other carbon nanomaterials because they are produced commercially in bulk quantities and also often formed as waste byproducts during the formation of other nanomaterials, such as CNTs [21]. In addition to these intrinsic properties mentioned above, carbon nanomaterials can be easily modified for different purposes through various approaches, including diazonium grafting, amine electrochemical oxidation, and π-π interactions. An increasing number of redox enzymes, including glucose dehydrogenase [22], fructose dehydrogenase (FDH) [23], cellobiose dehydrogenase [24], formate dehydrogenase (FoDH) [25], hydrogenase (H2ase), bilirubin

oxidase (BOD), laccase (Lac) [26], cooper efflux oxidase (CueO) [27], and peroxidase [28], have been reported to be capable of DET at a suitable carbon nanomaterial-based electrode. Notably, although many researchers in the previous decades have claimed that glucose oxidase, a well-known enzyme utilized in glucose biosensors and biofuel cells, achieves a DET capability in carbon nanomaterials, recent studies have concluded that no evidence supports the idea that native glucose oxidase undergoes DET in carbon nanotubes or graphene [29–31]. Understanding the mechanisms and roles of carbon nanomaterials in direct biolectrocatalysis is essential to identifying whether a DET reaction occurs and for preparing a suitable platform for DET-type bioelectrocatalysis with a high performance.

In this mini review, we start with the significance of carbon nanomaterials in promoting direct bioelectrocatalysis of redox enzymes. The effects of the pore distribution and surface chemical properties of carbon nanomaterials on DET-type bioelectrocatalysis are emphasized. Following a summarization of the surface modification of carbon nanomaterials, the oriented immobilization of redox enzymes in rationally functionalized carbon nanomaterials via different strategies is reviewed. Techniques to probe the redox enzymes on the carbon nanomaterial surfaces are also described.
