**1. Introduction**

Oxidoreductases catalyze redox reactions between two sets of redox substrate couples and are considered industrially useful catalysts due to their high activities and substrate specificities under mild conditions (room temperature, normal pressure, and neutral pH). However, most oxidoreductases, in addition to nicotinamide cofactor (NAD(P))-dependent enzymes, show low substrate specificities for one of the substrates. Such redox enzymes can accept or donate electrons from or to electrodes directly or via artificial redox mediators. The coupled reaction is called bioelectrocatalysis, and the catalytic function of the redox enzymes provides a variety of specific and strong catalytic activities to nonspecific electrode reactions. [1–5]. Bioelectrocatalysis provides a firm base for characterizing redox enzyme reactions and applying the concept and related technologies to useful bioelectrochemical devices such as biosensors [6–14], biofuel cells [11,15–21], biosupercapacitors [22], and other bioreactors [23].

Bioelectrocatalytic reactions are classified into two types according to the mode of the electron transfer described above: direct electron transfer (DET) and mediated electron transfer (MET), as shown in Figure 1. These reactions proceed in the following schemes in the simple case of the substrate's oxidation. On the other hand, we note here that some redox enzymes that have a catalytic site alone, without any other redox site(s), are also able to show DET-type bioelectrocatalysis, e.g., cytochrome *c* peroxidase [24], horseradish peroxidase (HRP) [25–27], ferredoxin-NADP <sup>+</sup> reductase [28], flavin adenine dinucleotide (FAD)-dependent glucose oxidase (FAD-GOD) [29,30], and FAD-dependent glucose dehydrogenase (FAD-GDH) [31].

**Figure 1.** Schematic of electron transfer processes in direct electron transfer (DET)- and mediated electron transfer (MET)-type bioelectrocatalysis for substrate oxidation. In this scheme, the enzyme is assumed to have both catalytic and electron-donating sites in the molecules.

The DET-type reaction is given by Equations (1) and (2):

$$\rm{^0S} + \frac{n\_{\rm{S}}}{n\_{\rm{E}}} \rm{E\_{O}} \xrightarrow{\rm Enzyme} \frac{n\_{\rm{S}}}{n\_{\rm{P}}} \rm{P} + \frac{n\_{\rm{S}}}{n\_{\rm{E}}} \rm{E\_{R'}} \tag{1}$$

and

$$\begin{array}{cccc} & \text{Electrode} & \\ \text{E}\_{\text{R}} & \rightleftharpoons & \text{E}\_{\text{O}} + \eta\_{\text{E}} \text{e}^{-} \\\end{array} \tag{2}$$

S Enzyme S S On the other hand, the MET-type reaction is given by Equations (3) and (4):

$$\text{S} + \frac{\eta\_{\text{S}}}{n\_{\text{M}}} \text{M}\_{\text{O}} \xrightarrow{\text{Enzyme}} \frac{\eta\_{\text{S}}}{n\_{\text{P}}} \text{P} + \frac{\eta\_{\text{S}}}{n\_{\text{M}}} \text{M}\_{\text{R}'} \tag{3}$$

and

$$\begin{array}{cccc} & \text{Electrode} & & \\ \mathbf{M}\_{\mathrm{R}} & \stackrel{\mathrm{\rightarrow}}{\rightleftharpoons} & \mathbf{M}\_{\mathrm{O}} + n\_{\mathrm{M}} \mathrm{e}^{-} \end{array} \tag{4}$$

– – – – where S, P, E, and M indicate a substrate, a product, an enzyme, and a mediator, respectively. *n*<sup>X</sup> is the number of electrons of the chemical species X. X<sup>O</sup> and X<sup>R</sup> are the oxidized and reduced forms of X, respectively. In DET-type bioelectrocatalysis, it is easy to construct relatively simple systems with minimum overpotentials in the electron transfer between the electrode-active redox center of an enzyme and an electrode from the thermodynamic perspectives. In this review, the electrode-active redox center means the site that can directly communicate with electrodes and is assigned to the catalytic active site (especially for redox enzymes that have the catalytic site alone) or an electron-donating/accepting site (other than the catalytic center) that constitutes the intramolecular electron transfer. However, the reported redox enzymes enable DET-type reactions are increasing but still limited in number because the electrochemical communication between an enzyme and an electrode occurs only when the electrode-active cofactor of the enzyme is close in distance to the electrode surface [32–35]. In MET-type bioelectrocatalysis, on the other hand, a variety of enzymes can be used in principle, and a suitable selection of mediators makes it possible to construct realistic systems. In addition, once both enzymes and mediators are stably immobilized on electrodes, the measurement systems work as pseudo-DET-type systems [10,11,36]. Particularly, redox polymers anchoring osmium complexes [3,37–45], ferricyanide [46,47], metallocenes [48–51], and viologen units [52–55] are constructed as polymeric mediators immobilized on electrodes. In summary, a DET-type system is often more ideal than a MET-type system, whereas it seems to be practical to utilize an MET-type system for several objectives.

Electrode

The overpotential in bioelectrocatalysis has two components: (1) thermodynamics; the difference in the formal potential between the substrate and the electron-donating site, and (2) kinetics; slow kinetics in the heterogeneous electron transfer (Figure 1). There is no way to avoid the problem concerning the first issue as long as one utilizes natural enzymes. Slow kinetics in heterogeneous electron transfer is compensated by the so-called overpotential of the electrode in the DET-type reaction and by the large driving force (that is, increased difference in the formal potential) between the enzyme and mediator. In this review, we will describe several techniques for improving the performance of enzymatic bioelectrocatalytic systems and summarize recent studies on their applications.
