Modelling of the cathodic and anodic photocurrents from Rhodobacter sphaeroides reaction centres immobilized on titanium dioxide

As one of a number of new technologies for the harnessing of solar energy, there is interest in the development of photoelectrochemical cells based on reaction centres (RCs) from photosynthetic organisms such as the bacterium Rhodobacter (Rba.) sphaeroides. The cell architecture explored in this report is similar to that of a dye-sensitized solar cell but with delivery of electrons to a mesoporous layer of TiO2 by natural pigment-protein complexes rather than an artificial dye. Rba. sphaeroides RCs were bound to the deposited TiO2 via an engineered extramembrane peptide tag. Using TMPD (N,N,N′,N′-tetramethyl-p-phenylenediamine) as an electrolyte, these biohybrid photoactive electrodes produced an output that was the net product of cathodic and anodic photocurrents. To explain the observed photocurrents, a kinetic model is proposed that includes (1) an anodic current attributed to injection of electrons from the triplet state of the RC primary electron donor (PT) to the TiO2 conduction band, (2) a cathodic current attributed to reduction of the photooxidized RC primary electron donor (P+) by surface states of the TiO2 and (3) transient cathodic and anodic current spikes due to oxidation/reduction of TMPD/TMPD+ at the conductive glass (FTO) substrate. This model explains the origin of the photocurrent spikes that appear in this system after turning illumination on or off, the reason for the appearance of net positive or negative stable photocurrents depending on experimental conditions, and the overall efficiency of the constructed cell. The model may be a used as a guide for improvement of the photocurrent efficiency of the presented system as well as, after appropriate adjustments, other biohybrid photoelectrodes. Electronic supplementary material The online version of this article (10.1007/s11120-018-0550-8) contains supplementary material, which is available to authorized users.


SECTION 4 -ABSORBANCE PROPERTIES OF BOUND RCS
Binding of RCs to the surface of deposited TiO2 pastes caused some changes to the native absorbance spectrum of the bacteriochlorin cofactors ( Figure S4A). The band around 865 nm attributable to the primary donor BChls was missing, an often-observed effect that can be attributed to oxidation of P in the air-dried sample (Moss et al. 1991). In addition, the 800-nm band attributable to the two accessory BChls was reduced in intensity relative to the 760-nm band attributable to the two RC BPhes. There are two possible reasons for such a change. The first one is a damage to the RC protein such that a BChl is detached from its native binding pocket -such a change would be expected to cause a reduction in the absorbance bands at 865 and/or 800 nm and an increase in absorbance around 760 nm due to the appearance of "free" BChl. The second is pheophytinization of a proportion of the RC BChls such that their central Mg 2+ metal is replaced by two protons but they are retained in the protein scaffold in their binding pocket(s). To investigate this change, bacteriochlorin pigments were extracted using methanol from RCs in solution and immobilized on TiO2. For extraction of pigments with methanol (Avantor) a 2 µL aliquot of RC stock solution or a RC-coated TiO2 slide was immersed in 500 µL methanol and vigorously mixed for 1 min. The resulting solution was centrifuged at 12,100 g and the absorbance spectrum of the supernatant recorded using a Hitachi U-2800A spectrophotometer. The absorbance spectrum of pigments extracted from RCs immobilized on TiO2 showed a blue-shift of the longest-wavelength absorbance band relative to that of pigments extracted from RCs in solution ( Figure 2B). This spectral change is characteristic of a higher amount of BPhe relative to BChl, as the absorption maximum of BPhe in methanol is blue-shifted relative to that of BChl . This indicated that pheophytinization and not dissociation of BChl was responsible for the spectral changes shown in Figure 2A. In addition a band appeared at 680 nm in the spectrum of the TiO2 RC extract that was probably attributable to a small amount of BChl decomposition products other than BPhe, such as 3acetyl chlorophyll (Clayton 1966;Makhneva et al. 2016). With the assumption that a BPhe in a binding pocket normally occupied by a monomeric BChl has the same absorption spectrum as a BPhe in its native binding pocket, the spectrum of RCs deposited on TiO2 in Figure 2A was normalized to the same total number of four BPhe and monomeric BChl molecules as for native RCs in solution.

S7
This approach allowed estimation of a ratio of BPhe:monomeric-BChl of 2.8:1.2 in the TiO2-bound RCs, which means that an average of 0.8 monomeric BChls per RC had undergone pheophytinization (see next section for a full account of the derivation of these values and the normalization method).
Further evidence that the spectral change undergone by RCs on binding to the TiO2 electrode was due to in situ pheophytinization came from the similarity the ratio of amplitudes of the bands at 760 nm and 800 nm between the IPCE action spectrum for an I-50 electrode and the absorbance spectrum of the electrode. As free BChl pigments released from their binding pockets due to photodamage would not be expected to contribute to a cathodic photocurrent (Tsui et al. 2014), this matching supports the conclusion that RCs on the electrode surface had undergone some conversion of monomeric BChls to BPhe, producing the observed absorbance change. Furthermore, it suggested that the BChl being pheophytinized was BB (see inset in Figure 1), as it does not take part in the electron transfer process (Kamran et al. 2015). A pheophytinization of BA would be expected to suppress electron transfer in RC. The vulnerability of BB to pheophytinization could be related to the fact that it takes part in photoprotection against triplet states, so there is a bigger risk for it to be damaged (Frank et al. 1996). A final point to note is that the IPCE action spectrum had a band at 865 nm attributable to the P BChls, supporting the conclusion that this band is bleached due to P oxidation when RCs are adhered to the TiO2 electrode in air, but this bleaching is reversible after immersion in a solution of suitable redox potential.

SECTION 5 -ANALYSIS OF PHEOPHYTINIZATION
For normalization of absorption spectra of RCs bound to the surface of TiO2 the following assumptions were made: (1) absorbance at 800 nm comes only from the accessory BChls, while that at 760 nm comes only from BPhe; (2) the only change in spectrum comes from transformation of BChl into BPhe; (3) the extinction coefficient of BPhe is the same for both natural positions of BPhe in the RC (i.e. HA and HB) and for BPhe at a location normally occupied by a monomeric BChl (i.e. BPhe formed after pheophytinization of BA or BB). These assumptions lead to the following set of equations: Where: ( ) is the absorbance at xxx nm for RCs in solution, is the absorbance at xxx nm for RCs on TiO2 after normalization, is the absorbance at xxx nm for RCs on TiO2 directly from measurements, is a dimensionless quantity proportional to the extinction coefficient for species yyy, and is the experimental ratio of measured absorbances. Equations (S3) and (S4) take into account that there are normally two BPhes and two accessory BChls per RC molecule.
After solving equations S1 to S4, one obtains: The absorbance spectrum of RCs on TiO2 presented in Figure 2 was normalized to this value at the maximum around 760 nm. The normalized absorption spectrum was then used to calculate an average number (n) of BPhes and accessory BChls per RC molecule using the equations:

SECTION 6 -ELECTROCHEMICAL PROPERTIES OF THE ELECTROLYTE
The supporting electrolyte was 20 mM Tris-HCl (pH 8.0). TMPD, which has previously been used as a component of solar cells based on Rba. sphaeroides RCs (Tan et al. 2012;Ravi et al. 2017), has two steps of oxidation ( Figure S5). However only the first occurring at a formal potential of +260 mV vs SHE is of use because the doubly oxidized form, present at potentials over 700 mV vs SHE, undergoes decomposition with displacement of dimethylamine (Brownson and Banks 2014). The contribution of particular redox states to the electroactive species can be calculated by analysis of the values of stable currents in cyclic voltammetry (CV) scans on the right and left side of the formal redox potential ( Figure S5), as these currents depend on the bulk concentrations of either reduced or oxidized species (assuming similar diffusion coefficients for reduced and oxidized form) (Zoski 2007).
In the 1.2 mM solution the TMPD (neutral) and TMPD + (monocationic) forms dominated in a ~1:1 ratio (see lengths of A and B line segments in Figure S5 and next section for the derivation of the method; the diffusion coefficients of TMPD and TMPD + do not differ by more than 15 %) (Wang et al. 1997). The OCP of a freshly prepared solution of TMPD oscillated around +225 mV vs SHE, and so this potential was applied in all subsequent photocurrent measurements in order to minimize the dark current. It is also visible as the potential near which the CV curve in Figure S5 crosses zero current line.   Figure S5. Electrochemical properties of the electrolyte. Cyclic voltammogram of 1.2 mM TMPD in 20 mM Tris-HCl (pH 8.0) on a 25 µm platinum disc microelectrode at a scan rate of 100 mV s -1 . The structures of the three redox forms of TMPD (neutral, mono-and bicathionic) are presented. In this and similar solution used for photocurrent measurements the bulk concentrations of the neutral and monocationic forms are similar, as estimated from similar positive and negative currents at ~+480 mV (B) and ~+110 mV (A) potentials (vs SHE), respectively (see text for details). The two long vertical lines indicate the formal redox potentials of neutral/monocationic and monocationic/bicationic TMPD pairs at +260 mV and +700 mV, respectively. S10

SECTION 7 -DETERMINATION OF THE TMPD/TMPD + RATIO
The steady-state current in cyclic voltammetry measurements on a microelectrode is given by (Bard and Faulkner 2001): Where: is the number of electrons transferred within reaction, is Faraday's constant, is the diffusion coefficient of the reacting species (either the oxidized or reduced form), and * is the bulk concentration of the reacting species.
This equation is valid only for microelectrode, as it allows probing bulk concentration of species. It is because of the low current flow, which does not much affect the local concentration of species as well as diffusion around microelectrode is closer to the spherical one than that on the macroelectrode. Spherical diffusion ensures efficient mass transport of species to the surface of electrode from the bulk volume (Bard and Faulkner 2001).
Using values for the cathodic and anodic steady-state currents (lines A and B in Figure S5) one can determine the concentration ratio of the oxidized and reduced forms of the redox mediator from: * * = ℎ • (S9) S11

SECTION 8 -DESCRIPTION OF KINETIC MODEL
Physical details Figure S6 shows the processes and associated rate constants included in the model used to simulate experimental photocurrent data. For simplicity only the RC states involving the primary electron donor P and terminal quinone acceptor Q are considered due to the much shorter lifetimes of other RC states (Blankenship et al. 1995). It is assumed that only a fraction (1 − ) of RCs are fully functional meaning that they can efficiently conduct electron transfer between TiO2 and the mediator. The remaining fraction ( ) can absorb light but undergo wasteful charge recombination and dissipate energy without contribution to the photocurrent, and therefore represent parasitic absorption. The number of photons absorbed per second per area unit is counted from the absorbance of the whole system (see Equations S19 and S20). The triplet state P T can be formed only in RCs in a closed state (PQ -) as a result of P + HA -→P T HA charge recombination, with a quantum yield Ф that is used as a parameter.
Diffusion of TMPD is, for simplicity, simulated as the exchange of reduced and oxidized forms of the mediator near the working electrode (TMPD, TMPD + ) with the bulk volume (TMPDbulk, TMPD + bulk) and is characterized by rate constant . Thus, the flux of diffusion is proportional to the concentration difference between bulk and the region in immediate proximity of the working electrode (see Equation S17), which in general doesn't have to be strictly correct, especially while the concentrations of species are changing rapidly. It is a place for future possible improvements of the model. Figure S6. Schematic of the processes included in the kinetic model. The colors of arrows correspond to those indicating processes in Figure 5. Six RC states are considered: PQ, P + QA -, P + QA, PQA -, P T QA -, and P T QA. Four of these states may exchange electrons with TMPD/TMPD + : P + QA -, P + QA, PQA -, P T QA -. Two of the states may inject the electron to TiO2: P T QAand P T QA. Two of the states may accept an electron from TiO2: P + QAand P + QA. Two of the states may be excited by light: PQA and PQA -.

Mathematical model
The differential equations presented below (S10 -S20) are the mathematical expression of the model presented in Figure S6. Most of the symbols are self-explanatory or are presented in Figure S6 (those with "n" at the beginning depict RCs inactive in photocurrent generation). The others are: [ ] -concentration of state/species x, (S10) (S12)  [ The resulting current was calculated using Equation S30:

Model Parameters
Simulations of photocurrent transients for electrodes both treated with TiCl4 and not treated with TiCl4 were performed with the parameters presented in S31. The extinction coefficient is taken from literature . The thickness of the TiO2 layer is the value typical for DSSCs (Ito et al. 2007). Recombination rate constants are taken from literature (Blankenship et al. 1995;Frank et al. 1996). Values of − and − were taken from the literature for freely diffusing RCs with TMPD (Agalidis and Velthuys 1986). The concentration of RCs was calculated using the Beer-Lambert S14 law and the value of light absorption at the Qy maximum. The concentration of TMPD and the light intensity were as used in experiments. Two sets of values were used for the remaining parameters according to two models. The "inactive pool" (IP) model assumed that 90 % of RCs dissipate energy quickly and do not contribute to the photocurrent. The "RC-mediator interface limited" (RMIL) model assumed that 100 % of RCs undergo charge separation and do not dissipate energy, but the values of − and − are different from those available in the literature due to immobilization of RCs on the TiO2 surface which hinders access of the mediator to reduced and oxidized cofactors within protein. In the case of this second model the values of − and − were optimized to obtain the best fit to the photocurrent traces. The values for these parameters are shown in Table 1 in the main text.

Time-dependence of species concentrations
The time-dependence of the concentrations of all species are shown in Figures S9 and S10. Interpretation of these plots is presented in the main text.