The Porphyrin Ring Rather Than the Metal Ion Dictates Long-Range Electron Transport Across Proteins Suggesting Coherence-Assisted Mechanism

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The porphyrin ring rather than the metal ion dictates long-range electron transport across proteins suggesting coherence-assisted mechanism

Yuval Agama, Ramesh Nandia, Alexander Kaushanskya, Uri Peskina, and Nadav Amdurskya,1

aSchulich Faculty of Chemistry, Technion–Israel Institute of Technology, 3200003 Haifa, Israel

Edited by Harry B. Gray, California Institute of Technology, Pasadena, CA, and approved November 2, 2020 (received for review May 4, 2020) The fundamental biological process of electron transfer (ET) takes distances, has also been observed across the multicellular body of place across proteins with common ET pathways of several nano- cablebacteria(19–21). The only common feature of long-range meters. Recent discoveries push this limit and show long-range extracellular ET is the presence of large multiheme cytochromes. extracellular ET over several micrometers. Here, we aim in deci- The mechanism of this extraordinary ET as well as the nature of phering how protein-bound intramolecular cofactors can facilitate the bacterial nanowire is a source of great scientific debate. The such long-range ET. In contrast to natural systems, our protein- two most frequently discussed ET mechanisms are: 1) incoherent, based platform enables us to modulate important factors associ- nonadiabatic electron hopping across the Fe ions within the heme ated with ET in a facile manner, such as the type of the cofactor (8, 22, 23); and 2) metallic-like or coherent ET across the bacterial and its quantity within the protein. We choose here the biologi- nanowire, perhaps involving an aromatic sidechain of the protein cally relevant protoporphyrin molecule as the electron mediator. (13, 14, 24). Recent electron-beam (e-beam) diffraction studies Unlike natural systems having only Fe-containing protoporphyrins, have revealed the presence of a rather amazing type of protein i.e., heme, as electron mediators, we use here porphyrins with nanowire of the G. sulfurreducens, composed solely of the hexa- different metal centers, or lacking a metal center. We show that heme cytochrome OmcS (25, 26). The existence of this unique the metal redox center has no role in ET and that ET is mediated one-dimensional (1D) wire assembly of heme molecules strongly solely by the conjugated backbone of the molecule. We further suggests that they mediate ET, regardless of the ET mechanism. discuss several ET mechanisms, accounting to our observations CHEMISTRY with possible contribution of coherent processes. Our findings While bacterial mutants may be created in order to study the role contribute to our understanding of the participation of heme mol- of the different proteins participating in the ET pathway, it is nearly ecules in long-range biological ET. impossible to specifically investigate the role of the heme molecules in ET, due to the ubiquity of the iron-containing heme molecule. In G. sulfurreducens electron transfer | conductive polymers | heme | porphyrin | biopolymers thecaseofthe nanowires of the OmcS protein, the coordination with the Fe ion iswhatdrivestheself-assembly process, and, therefore, the iron cannot be removed. ron-containing protoporphyrin, also known as heme, is one of Here, we introduce a completely different approach to the the most important molecules in nature, participating in nu- BIOPHYSICS AND COMPUTATIONAL BIOLOGY I study of very-long-range ET across proteins. We achieve this by merous biological processes, including the binding of gas mole- creating an artificial protein-based fibrillar platform, in which we cules (as O ) to its iron ion. The proper activity of heme 2 can control the number of ET-mediating cofactors inside the pro- molecules is dependent on the ability of specific proteins, which tein, as well as their chemical nature. Inspired by the extraordinary are referred to as hemeproteins, to bind them. The natural activity of heme is owed to its exceptional heme-iron coordination with gas molecules or specific amino acids. In fact, an iron-free Significance porphyrin or a degraded product of heme, bilirubin, can result in certain diseases, such as porphyria or jaundice, respectively. Other Electron transfer (ET) across proteins is fundamental in many metal-containing protoporphyrins are far from being as ubiquitous biological processes, such as photosynthesis and aerobic res- as the iron-containing one. Although there are many kinds of piration. Recent discoveries from the bacterial world have hemeproteins with different functionalities, such as hemoglobins, shown that proteins can support long-range ET pathways on myoglobins, cytochromes, and peroxidases, we will focus here on the order of micrometers. Here, we introduce a protein plat- their ability to mediate electrons (1). Hemeproteins participate in form that allows us to explore how proteins can support long- all major electron transfer (ET) chain reactions in nature, the range ET, and what are the important molecular features and most noteworthy being the aerobic respiration system in our mi- ET mechanisms that enable it. We focus on the role of the metal ion within heme molecules in long-range ET and find tochondria and the photosynthetic system in chloroplasts. In ET that the molecular ring surrounding the metal ion is the ET reactions, electrons are shuttled by the redox of the Fe ion within mediator, and not the metal ion. We suggest a coherence- the heme (Fe2+ ⇌ Fe3+), whose redox potential is highly de- assisted ET mechanism as a possible explanation for our high pendent on the heme-binding site within the protein (2, 3). measured ET efficiency. Until recently, all of the natural ET pathways studied were on

the nanometer scale (usually below 10 nm), and the heme was Author contributions: N.A. designed research; Y.A. and R.N. performed research; A.K. and located at the correct place along the electrochemical gradient, U.P. contributed new theoretical/analytic tools; Y.A., R.N., A.K., U.P., and N.A. analyzed with other cofactors (such as quinones or FeS clusters) that data; and Y.A., U.P., and N.A. wrote the paper. participate in the ET chain reaction as well. Recent examples The authors declare no competing interest. from the bacteria world have shown, however, that specific bacteria This article is a PNAS Direct Submission. (namely, Geobacter sulfurreducens and Shewanella oneidensis MR- Published under the PNAS license. 1) can mediate ET with very high efficiency over very long distances 1To whom correspondence may be addressed. Email: [email protected]. in the order of micrometers, and even up to millimeters, from This article contains supporting information online at https://www.pnas.org/lookup/suppl/ the bacteria’s body to nearby metal-oxide rocks across a bacte- doi:10.1073/pnas.2008741117/-/DCSupplemental. rial nanowire (4–18). Extremely long ET, over centimeter-scale

www.pnas.org/cgi/doi/10.1073/pnas.2008741117 PNAS Latest Articles | 1of7 Downloaded by guest on September 27, 2021 extracellular ET observed with OmcS nanowire, we chose here only S3). This result clearly implies that the observed long-range ET protoporphyrin as the electron-mediating cofactors across our across our protein platform is not mediated by the metal ion protein-based platform, although other macromolecules are known within the PPIX and that charge-carrier mobility is enhanced by to participate in various biological pathways. Using our platform, the conjugated π-system of the porphyrin rings themselves. To we can now change the metal ion inside the porphyrin, remove the establish this assumption, we also examined bilirubin as a dop- metal ion altogether, or even use bilirubin (the open form of the ring) ant, since its molecular structure has the same conjugated tet- as ET mediators. We used electrochemical impedance measure- rapyrrole motif as PPIX, albeit linear rather than cyclic. We ments, as well as three-terminal transistor measurements, to explore found that bilirubin indeed exhibited similar improvements in the role of the porphyrin variant in mediating ET. Our results allow conductivity, as was observed for the other porphyrin dopants us to discuss possible mechanisms of ET across our protein platform, (Fig. 2A). To further explore the ET mechanism across the dif- involving either incoherent or coherence-assisted ET. ferent mats, we measured the temperature dependence of the EIS response, displayed in the form of a Nyquist plot (the im- Results pedance imaginary part as a function of the impedance real part) The protein-based macroscopic platform that we use here is (SI Appendix, Fig. S4). The plot shows a semicircle in the high- based on electrospun bovine serum albumin (BSA) mats, which frequency area, corresponding to bulk conductivity, and a curved were shown to be able to bind heme molecules, resulting in long- tail in the low-frequency area, attributed to double-layer capac- range ET across this artificial platform (27). As stated, here, we itance at the electrolyte and blocking-electrode interface, inter- aim to understand how protoporphyrins mediate ET. Accord- rupted by the ionic diffusion process. In these temperature- ingly, we molecularly doped the BSA mats with different vari- dependence studies, we found that all of the doped mats had a ants: metal-free protoporphyrin IX (PPIX), the common Fe- similar activation energy in the order of 0.2 ± 0.03 eV (SI Ap- containing PPIX (heme), PPIX with three other transition pendix, Table S1). The similar activation energy values imply that metals (Co, Cu, and Zn), and bilirubin. The successful doping of all of the mats we used, some of which contained a metal ion the BSA mat is easily observed by a distinct color change of the within the PPIX and some of which did not, share a similar ET mat in accordance with the porphyrin color (Fig. 1). Moreover, mechanism (as discussed below). the doping level, i.e., the number of dopants per volume within After establishing that the conductivity of the doped mats is the mat, can be easily modulated by the duration of the doping determined only by the amount of porphyrin bound to the BSA process and can be verified by using ultraviolet-visible (UV-Vis) mat, regardless of the metallic element (in analogy to semicon- “ ” spectroscopy. ductors, we refer to this property as doping density ), we then determined how doping density influences conductivity. In this Impedance Measurements. Following the successful doping of the context, we need to consider that each of the different molecular mat, which we refer to as full doping (vide infra), we turned into dopants in this study has a different affinity to the BSA scaffold. electrical characterization. It is important to mention that even This property determines the number of molecules that the mat though all of our electrical measurements were performed in the will absorb in any time range and with any initial parameters. solid-state (i.e., not in solution), the used protein mats retained a Hence, any comparison between doped mats must consider their substantial amount of water, consisting of ∼150 wt% of the mat; doping density. Since absorbed molecule quantity is dependent hence, the environmental conditions were more a like biological on factors such as doping time and concentration of porphyrins ET. At first, we used alternating current (AC) electrochemical in the doping solution, it is essential to determine these relation- impedance spectroscopy (EIS) over a wide frequency range (10 ships for each specific sample. Accordingly, we prepared numerous to 107 Hz) to investigate the macroscopic electrical properties different samples with different doping densities, which were de- (across 2.5 mm) of the various doped mats. Our results are termined by measuring the amount of porphyrin dopant that was SI Appendix displayed in the form of a Bode plot, showing the absolute value absorbed into the mat from the dopant solution ( ,Table B of impedance as a function of frequency (Fig. 2A). We extracted S2 and discussion within). As can be seen in Fig. 2 , which plots the the bulk conductivity of the doped mat using an equivalent cir- change in extracted bulk resistivity (as determined by EIS mea- cuit fitting (SI Appendix, Fig. S2). Before doping, the mat had a surements at 25 °C) as a function of doping density, the resistivity of − relatively low conductivity of 0.1 mS·cm 1 due to proton con- each of the mats clearly depends on the porphyrin molecule density, ductance (28). To our surprise, following full doping with the irrespective of the particular porphyrin dopant. Even metal-free various metal porphyrins and with metal-free PPIX, all of the PPIX and bilirubin exhibited the same correlation. These findings mats exhibited a similar (∼30-fold) increase in conductivity (to a support our claim that transport efficiency is not related to the − π value of ∼3 ± 0.4 mS·cm 1), which we attributed to ET, and not metal redox potential, but solely to the similar conjugated -system to a change in the ionic conductivity across the mat or any that is common to the different molecular dopants. structural change due to the dopant solution (SI Appendix, Fig. Transistor Measurements. Next, we used field-effect transistor (FET) measurements (29–31), in which our doped mats acted as the active layer, to determine the charge-carrier type (electrons vs. holes), their mobility, and the number of charges that contribute to the measured conductivity (charge-carrier density). FETs are three-terminal devices, consisting of a gold contact, which serves as the transistor’s source and drain, on a SiO2/Si substrate with a bottom Si gate, in which the doped mat is placed on the gold contacts (Fig. 3A). Fig. 3B and SI Appendix, Fig. S5 show that the source-drain current (IDS), as a function of the source-drain voltage (VDS), decreased when the gate voltage (VGS) was changed from negative bias to positive bias. This behavior is indicative of a p-type carrier behavior, as negative gate Fig. 1. Molecular doping of BSA mats. Photo and scanning electron mi- bias gives rise to an accumulation of positive charges in the FET croscopy image (see also SI Appendix, Fig. S1) of the BSA mat (Left) and channel, thus increasing the source-drain current. Accordingly, photos of mats after doping with different PPIX-based molecular dopants we can conclude that the porphyrin molecules in the doped mats (Right) are shown. facilitate hole transport (rather than electron transport), as reported

2of7 | www.pnas.org/cgi/doi/10.1073/pnas.2008741117 Agam et al. Downloaded by guest on September 27, 2021 Fig. 2. Impedance measurements. (A) Bode plots of impedance response across the fully doped mats at 25 °C with interelectrode distance of 2.5 mm. (B)EIS bulk resistivity at 25 °C of different samples as a function of doping density.

for most porphyrin-based materials (32–35),aswellasforS. onei- charge-density values of the mats are indeed related to the cal- densis nanowires (17). We further extracted the hole mobility using culated doping density. However, only a fraction (∼3%) of the a modified equation for gate voltage-dependent mobility (31): porphyrin dopants contribute to the observed hole-transport process. From a physical point of view, it is clear that not all of the ∂IDS L porphyrin molecules within the mat can contribute to the charge μ =± · , [1] ∂VGS WCGSVDS density. The low calculated fraction of charge density, compared with the doping density, further supports our suggestion that ∂IDS IDS VGS VDS CGS electron conduction probably occurs via distinct pathways along where ∂VGS is the gradient of vs. with a constant ; is the gate dielectric capacitance per unit area; and L and W are the protein fibrils comprising the sample. the transistor’s length and width, respectively. We found that all

of our doped mats exhibited similar mobility values in the range Discussion CHEMISTRY − − of0.008to0.01cm2·V 1·s 1 (SI Appendix,TableS3), further sup- In Results, we showed that the tetrapyrrole conjugated π-system porting our notion that the transport is due solely to the conju- of the porphyrin backbone is the electron mediator of long-range gated porphyrin ring. Moreover, and very importantly, mobility ET across proteins, regardless of the nature of the bound metal values were found to be similar for different doping densities. If ion or even its presence. This conclusion supports several theo- the molecular dopant had been spread randomly within the pro- retical works that suggested electron delocalization across the tein matrix, we would have expected much higher measured mo- conjugated macrocycle, from the early works of Hopfield to bilities for larger dopant densities. Since this was not seen, and more recent works (36–40). The immediate question we would mobility values for different doping densities were similar, this like to discuss in this section is: What ET mechanism appears to BIOPHYSICS AND COMPUTATIONAL BIOLOGY suggests that there is a strong preference in the location of the be the most plausible in our system? molecular dopants in specific locations inside the protein. Doping While referring to solid-state measurements, the lack of the density, therefore, mainly influences the charge-carrier density, metal-center involvement within the porphyrin in mediating which was calculated by using the common conductivity relation: electrons has been observed in a molecular-junction configuration, meaning that an electron transport (ETp) process was σ = μne, [2] followed (distinguishing itself from the common ET notion) for distances of ∼3 nm (41, 42). Recently, Blumberger and co- where σ is the mat conductivity, n is the charge density, and e is workers (43) explored the ETp mechanism across a multiheme the elementary charge. As can be seen in Fig. 3B, the extracted containing protein in a molecular-junction configuration using

Fig. 3. FET measurements. (A) Typical FET measurement of ISD as a function of VSD for different Vg, across a doped BSA mat sample (FePPIX in this case; the others are presented in SI Appendix, Fig. S5). A, Inset shows a schematic view of our bottom-contact FET device. (B) Calculated charge-carrier density as a function of doping density for the various FET devices with different molecularly doped BSA mats.

Agam et al. PNAS Latest Articles | 3of7 Downloaded by guest on September 27, 2021 density functional theory (DFT + Σ) calculations and found that delocalized orbitals over several heme molecules dominate the transport in the off-resonant tunneling regime. However, the short distance of molecular junctions permits specific ETp mechanisms, such as cotunneling between the leads, which may not apply directly for long-range ET across numerous porphyrin molecules as discussed here (only one to four porphyrin units are present between the electrodes in the reported molecular junction experiments). Nevertheless, the irrelevance of the metal to the conductivity in our results implies that, regardless of the ET mechanism (discussed below), the electrons will not be trans- ported via molecular orbitals involving the metal center within the molecular dopant, but, rather, across the molecular orbitals Fig. 4. ET mechanisms. Different ET mechanisms: hopping (A) vs. mixed associated with the conjugated porphyrin backbone. While this is coherent-hopping (B) mechanism. also confirmed by naïve DFT calculations of porphyrins in the gas phase (SI Appendix, Computational Details), which show that the frontier molecular orbitals (FMOs) do not reside on the from our measured activation energy (0.2 eV), resulting in λ = metal center of the porphyrin, we cannot rely on these calcula- 0.8 eV. tions in our study, as the use of the BSA mat does not permit us Using our calculated charge-mobility values, we can calculate to know the exact protein structure, the exact binding configu- the electron-diffusion coefficient using the mobility definition: ration of the porphyrins to the BSA, and, accordingly, the for- mation of any axial ligands to the metal center. The latter axial μk T D = B [4] ligands, such as to histidine residues or water molecules, are e , crucial for the location of the molecular orbitals (39, 44). In- stead, the mentioned DFT calculations of Blumberger and co- reaching a diffusion coefficient value in the order of 2.3 (±0.3) × − − workers (43), based on a known crystal structure of the protein, 10 4 cm2·s 1 for all different molecularly doped mats. Since our do show a molecular-orbitals delocalization of the valence band system comprises a uniform chain of molecular dopants, the dif- across several heme molecules and argue that this valence-band fusion coefficient can be expressed as: delocalization is responsible to efficient ETp involving a coherent transport mechanism. Moreover, and what seems to be most 2 relevant to our study, they show that, while molecular orbitals D = kET d , [5] involving the metal center can be located within the conduction band, such orbitals do not contribute significantly to the ETp where d is the distance between adjacent molecular dopants. mechanism, and replacing the metal center did not result in a One of the main experimental difficulties in our system is our change in the calculated ETp efficiency across the junction. inability to resolve the exact structure of the protein matrix and, Upon switching from molecular junctions to natural biological thus, also the exact location (i.e., binding sites) of the different systems, meaning in ambient (and usually surrounded by water) porphyrins used here. We can, therefore, only estimate the dis- conditions, ET takes place usually for distances of <10 nm, and tance between the porphyrins, d. The doping density cannot be d the most common ET mechanism used to describe such ET used to calculate , since the electrospun mat is porous, and only pathways involves a change in the redox state of the cofactor. the protein fraction can bind the dopant. Indeed, the highest This is a nonadiabatic ET mechanism, whose multiple steps are measured doping density (fully doped samples), which is around × 19 −3 d referred to as sequential hopping. However, unlike most bio- 3 10 cm , corresponds to a value of 3.2 nm. This value is logical short-range ET pathways that usually comprise different not realistic, as it is too large to support any ET across the film. electron mediators, each of which has a different redox potential, A close inspection of several scanning electron microscopy im- SI Appendix in our system, the chemical identities of all of the mediators in a ages of the mat (such as the one in , Fig. S1) suggests given sample are identical. This is in line with the probable long- that around 20 to 25% of the mat volume is composed of fibrils; range ET across the OmcS-based G. sulfurreducens bacterial hence, this latter value should be factorized. We can calculate wire, which is self-assembled from hexaheme OmcS cytochromes the average numbers of porphyrins per BSA molecule in the mat, (25, 26). given the number of porphyrin molecules inside the mat (doping The identical chemical identity of the electron mediators in density) and the number of proteins in the mat, obtained by our system can support several possible ET mechanisms (Fig. 4). weighing the nondoped mat. The latter calculation results in We will start with the mentioned common incoherent nonadia- an average of 10 porphyrin molecules per BSA molecule in the batic hopping mechanism, which is also the immediate suspect mat. Our upper estimation for the distance between porphyrins for our system as well (Fig. 4A). The electron (hole) hopping rate is, therefore, based on their alignment along the very long axis of is commonly described by the Marcus–Hush formula: the BSA protein, which is around 8 nm, resulting in an average distance of 0.8 nm between porphyrins, which is a realistic value. √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ π (λ + ΔG0)2 Moreover, in line with our claim that the FMO of the porphyrin 2 kET = |H| exp[ − ] [3] is the ET mediator, the real distance should be the edge-to-edge 2 λk T Z λkBT 4 B , distance between the porphyrin rings; hence, the latter value is probably an overestimation. Using this value and the calculated where H is the electronic coupling energy between electron do- diffusion coefficient, we can calculate kET (Eq. 5) to be in the − nor and acceptor, i.e., the two porphyrin moieties in our case; λ is order of 3.6 × 1010 s 1. Using Eq. 3, we can now estimate the the reorganization energy; kB is the Boltzmann constant; T is the average electronic coupling (H) between the porphyrins to be in 0 absolute temperature; and ΔG is the driving force, i.e., the en- the order of 65 meV. Since our distance (d) is most probably an ergy difference between electron donor and acceptor. Since the overestimation, our estimated kET and H are probably under- ET in our case is between two identical molecules (porphyrins), estimated values. Notice that our estimated H values already 0 we assume that ΔG is close to zero. Under the latter assump- seem too high to be realistic (4, 5). Indeed, these values are tion, the rate-limiting reorganization energy can be calculated unrealistically high for two porphyrins that are 0.8 nm apart, or

4of7 | www.pnas.org/cgi/doi/10.1073/pnas.2008741117 Agam et al. Downloaded by guest on September 27, 2021 even for much closer porphyrin rings (39). An important ratio- facilitated by protein vibrations (thermal fluctuations), via an nale for large electronic-coupling matrix elements can be attrib- incoherent (Marcus-like) hopping step. Considering two neigh- uted to an increase in the packing density (ρ) of protein atoms in boring blocks (Fig. 4B), Eq. 3 is replaced by a set of hopping the volume between donor and acceptor centers. This empirical rates from the mth superposition state on the nth block, into the approach was first introduced by Dutton and coworkers (45) to (m′)th state of the (n′)th block: provide a rationale for the ET within proteins for distances up to ’ 2 1.4 nm between redox centers. However, using the empirical (n) (n ) ⃒ ⃒ ((«m −« )−λ ’ ) √̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅ m’ n,n formula for averaged packing density (as described in ref. 45), ’ 2 ⃒ (n, n )⃒ π λ k T 4 n n’ B the packing density needed to explain that our estimated elec- k ’ ’ = ⃒H ’ ⃒ e , [6] n,m→n ,m m,m 2 . Z λ ’ k T tronic coupling, ρ = 1.75, is unrealistically high, as all discussed n,n B proteins showed 0.5 < ρ < 1. It should be noted that since the ’ «(n) − «(n ) λ detailed spatial arrangement of the porphyrins in the system Here, m m’ and n,n′ are, respectively, the corresponding cannot be revealed, we cannot exclude the possibility that, for driving force and reorganization’ energy. The electronic tunnel- H(n, n ) specific intramolecular orientations, the overlap between nearby ing matrix element, m,m’ , depends on the proximity and relative rings might increase the electronic coupling to such unusually orientation of the terminal porphyrin units from the two differ- high values. ent blocks, as well as on the projections of the coherent super- Another possibility is that the seemingly too large coupling positions within each block, on the terminal units. In most cases values are obtained within the assumption of a sequential hop- (46), the mixed coherent-hopping mechanism promotes long- ping mechanism (Eq. 3), whereas a different transport mecha- range ET, where the larger the block size, the smaller the inter- nism may be consistent with smaller, more realistic, values. porphyrin electronic coupling needed to obtain the same diffu- SI Appendix Indeed, it was recently suggested that an ET along a bacterial sion coefficient. In , we demonstrate this effect for wire of G. sulfurreducens, which is self-assembled from the PilA the relevant parameters associated with the present system, as- SI Appendix protein, can involve a combination of coherent and incoherent suming a quasi-1D local diffusion pathway ( , Fig. S6). transport across a chain of aromatic amino acids (Phe and Tyr) The latter calculations show that our extrapolated diffusion co- (24). We also recently suggested a mixed coherent-hopping efficient is resulting in electronic coupling values of below 20 mechanism for ET through the multiheme OmcS-based bacte- meV for block chains of above 15 porphyrin molecules. This rial nanowire (46). The chemical identity of the mediators in the electronic coupling value is much more reasonable compared present system may also permit unique charge-transfer mecha- to the one obtained by using the hopping model. While these nisms that involve some coherent ET, or, rather, a combination numbers for the interporphyrin couplings seem to be in accor- CHEMISTRY of coherent and incoherent transport, which most probably dance with the data, the conclusion that the transport is facili- cannot take place in common short-range protein-based ET. The tated by delocalization over 15 porphyrin molecules appears to set of densely packed porphyrins with similar local molecular stretch the currently believed delocalization limit, associated with environments can be associated with a uniform energy land- a small number of molecules, and, thus, to be in conflict with the scape. This formally implies that differences between the vertical common view of suppressed delocalization in the presence of ther- ionization energies of the different porphyrins can be smaller mal fluctuations. Indeed, the proposed model assumes that an ex- 0 than the interporphyrin electronic couplings, namely, ΔG < H ceptionally rigid molecular environment within the fibrillar protein

(Eq. 3). In this case, delocalized charging states can be formed amounts to exceptionally low local-reorganization energies. Con- BIOPHYSICS AND COMPUTATIONAL BIOLOGY that extend over several neighboring porphyrins (46). Such sequently, thermal fluctuations within such islands are suppressed, delocalized charging states can promote charge transport over which facilitates persistent electronic delocalization over several long distances only if the rate of dephasing between the different porphyrins on the time scale of ET between islands. porphyrins is slow on the charge-transfer time scale (1/kET). For Concluding Remarks this to hold, the electronic coupling to the molecular and solvent vibrations must be sufficiently weak. This implies a relatively In conclusion, we have shown here that long-range (2.5 mm) ET rigid molecular environment, which seems plausible for the fi- across a protein-based matrix containing various protoporphyrin brillar protein backbone in the present case. It is important to cofactors is mediated by the conjugated macrocycle ring and is note in this stage that the described conditions for this mecha- not related to the metal center. Hole-mobility values of ∼0.01 2 −1 −1 nism to hold are untraditional, while taking into consideration cm ·V ·s were obtained, corresponding to a charge-diffusion −4 2 −1 the floppy nature of biological molecules in natural conditions. coefficient of ∼2 × 10 cm· s . We discussed the possibility of Nevertheless, the recent accumulation of evidence for the role of several ET mechanisms from purely incoherent processes delocalized electronic states in coherent ET through multiheme (electron hopping) to coherence-assisted mechanisms. Using our proteins (43), as well as the unique features of our synthetic experimental values for molecular doping density, charge mo- protein system, encourage us to discuss the relevance of this bility, and activation energy, we showed that if the common se- rather unconventional mechanism in some detail below. quential hopping mechanisms between metal redox centers were Following the latter evidence for a charge delocalization over responsible for the observed ET, it would have required an several porphyrin molecules, we turn now to a mixed coherent- unrealistically high electron-coupling element (∼65 meV) be- hopping transport model for explaining the long-range nature of tween localized redox centers. We proposed that, due to the charge transport through the multiporphyrin protein scaffold. involvement of identical molecular dopants in each experiment Nevertheless, detailed structural information is still needed in and the suggested rigidity of our system, the charging states of a order to confirm the possibility for any charge delocalization group of dopants can be delocalized over a larger area and form over several porphyrin molecules in our system; hence, our a local band-like structure, which merits a mixed coherent- mixed coherent-hopping transport model is of a speculative na- hopping transport model. ture, though, as will be discussed below, it gives the best fit to our In this study, we explored the role of protoporphyrin in results in terms of realistic energetic landscape. The emerging ET. Although many macrocyclic nonprotoporphyrins containing physical picture (SI Appendix, Mixed Coherent ET Model) is that different metal centers, such as Mg-containing chlorophylls or the ET mechanism involves porphyrin blocks, which are pro- bacteriochlorophylls, Co-containing cobalamines (vitamin B12), tected from coupling to molecular vibrations, and where each and Ni-containing coenzyme F430, as well as metal-free pheo- such block supports coherent superpositions of several locally phytins, have been shown to be involved in several ET pathways charged porphyrins (Fig. 4B). Diffusion between these blocks is in nature, the only macrocyclic compound shown, to date, to

Agam et al. PNAS Latest Articles | 5of7 Downloaded by guest on September 27, 2021 participate in the very-long-range bacterial extracellular ET is quartz cuvette with a 1-cm path length. Doping-density evaluations were the Fe-containing heme. It is interesting to hypothesize why carried out by using the same spectrometer, by measuring the absorption nature exclusively chose heme for this purpose. Our first spec- spectra before and after placing the mats in the dopant solutions. ulation concerns the availability of the heme molecules. Due to the ubiquity of heme in nature, the enzymatic machinery re- Metal-Finger Electrode and Three-Terminal Device Fabrication. Heavily quired in order to produce it is well established in various bio- p-doped silicon wafers with SiO2 dielectric layer (110 nm) and glass micro- logical systems; hence, it is easier to use heme than any other scope slides were used as substrates for the devices used in the transistor and metal-containing porphyrin, even though we showed here that impedance measurements, respectively. The substrate was sonicated for the metal center is not actually important for ET. Our second 5 min in the following series of solvents: acetone followed by methanol, isopropanol, and, finally, ethanol. After the last sonication, silicon substrates speculation relates to the use of the Fe ion for structural reasons were washed with distilled water and dried on a glass Petri dish heated to rather than an ET mediator. As shown in the recently published 120 °C. Glass substrates were washed with distilled water and dried using − structure of the pili of hexaheme cytochrome OmcS (25, 26), the hot air. Using an e-beam evaporator at a deposition rate of 2 Å·s 1 under 5 × − protein subunits self-assemble by coordination to the Fe ion, 10 7 Torr at room temperature, 100 nm of Au on 10 nm of Cr was evapo- i.e., two His residues from two different proteins are coordinated rated through shadow masks. Both finger electrodes and the transistor’s to one heme molecule. source-drain electrodes were deposited simultaneously on the glass and silicon substrates, respectively. Mats were placed on finger electrodes or Methods three-terminal devices and gently dried with filter paper to remove excess Electrospinning of BSA Mats. Electrospinning solution was prepared by dis- water. The water weight percentage within the BSA mat in all electrical solving BSA (MP Biomedicals) in 90% 2,2,2-trifluoroethanol (Apollo Scientific) experiment was around 150 wt%. for a final BSA concentration of 14% (weight [wt]/volume [vol]). After 12 h, Impedance measurements. Impedance measurements were performed by using β 5% (vol/vol) -mercaptoethanol (Alfa Aesar) was added. Electrospinning was an MTZ-35 impedance/gain-phase analyzer (Bio-Logic). Mats on finger performed in a custom-built system with grounded collector. A 15-kV bias electrodes with interelectrode distance of 2.5 mm were contacted by using a was applied on a 24-gauge blunt needle with injection rate of 1.5 mL/h. The probe station micromanipulator. A 50-mV AC bias was applied during the needle was fixed 12 cm above the collector. Final mat thickness was 60 μm. measurements without direct-current bias. A frequency range of 10 MHz to 10 Hz was used. Temperature dependence was studied by using a Peltier- Synthesis of Metal Protoporphyrins. Metal protoporphyrins were synthesized containing probe station (INSTEC) in the range of 5 °C to 25 °C. following a procedure described in the literature (47, 48) with modification. FET measurements. FET measurements were carried out by using two source- Two milligrams of PPIX (STREM Chemicals) was dissolved with the respective measurement units (B2901A, Keysight) connected together via GPIB cables. metal salt (zinc chloride, copper chloride, and cobalt acetate) at a molar μ ratio of 1:10 in 1 mL of dimethyl sulfoxide (DMSO; Carlo-Erba). The solutions Mats were placed on a bottom-contact, three-terminal device with 100- m were then heated to 60 °C for 12 h and, after cooling, were centrifuged for interelectrode distance and 1.35 or 2.7 cm width. Source-drain and gate 30 min. DMSO was used as a solvent due to the high solubility of PPIX electrodes were contacted by using a probe-station micromanipulator. in DMSO. Source and drain currents were measured in the range of 0 to 1.5 V, while an Doping process. Stock solutions were prepared by dissolving hemin (Sigma- alternating gate voltage was applied between −8 and 8 V. Aldrich), PPIX (STREM Chemicals), and bilirubin (AK Scientific) in 1 mL of DMSO (Carlo-Erba) for a final concentration of 3.2 mM. These stock solutions, Data Availability. All relevant data, materials, protocols, computational de- as well as synthesized Co–,Zn–,Cu–PPIX stock solutions, were then diluted tails, and theoretical analysis are included in the manuscript and SI Appendix. with 1 mL of DMSO and 5 mL of phosphate-buffered saline buffer to yield doping solutions of the desired concentration. The mats were then placed ACKNOWLEDGMENTS. N.A. was supported by Ministry of Science and Tech- in the doping solutions on a stirring plate without light exposure for at nology (MOST) Grant 3-16243 in nanoelectronics; N.A. and U.P. were supported least 24 h. by MOST Grant 3-16312 in quantum biology; and U.P. was supported by Israel UV/Vis absorption. UV/Vis absorption of synthesized metal-protoporphyrins in Science Foundation Grant 1243/18. We thank Y. Eshel with assisting with the ET DMSO was measured with an Agilent Cary 60 spectrophotometer using a mechanism simulation; and J. Blumberger for a discussion of our results.

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