Temperature Dependence of Charge and Spin Transfer in Azurin

The steady-state charge and spin transfer yields were measured for three different Ru-modified azurin derivatives in protein films on silver electrodes. While the charge-transfer yields exhibit weak temperature dependences, consistent with operation of a near activation-less mechanism, the spin selectivity of the electron transfer improves as temperature increases. This enhancement of spin selectivity with temperature is explained by a vibrationally induced spin exchange interaction between the Cu(II) and its chiral ligands. These results indicate that distinct mechanisms control charge and spin transfer within proteins. As with electron charge transfer, proteins deliver polarized electron spins with a yield that depends on the protein’s structure. This finding suggests a new role for protein structure in biochemical redox processes.


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The device surface was first cleaned by boiling in acetone and ethanol (10 min each), then cleaned by a 5 min ozone treatment (UVOCS), and was subsequently immersed in ethanol. After 30 min, the device was dried with N2 stream and azurin solution (1 mg/mL in buffer, pH=7) was immediately drop-cast on to the surface and stored in a sealed humidity box at room temperature for 4 hours. After incubation, the device was gently rinsed with DI water and dried with N2 stream.
After growing the monolayers of the azurin monolayer on the channel, the device chip was glued to a chip holder using double-sided tape. The pads of the electrodes were connected to a chip holder using wire binding. All the connections were passivated by using a high-quality RTV silicone glue to avoid charge leakage. To maintain the aqueous environment during the measurements, we prepared a polydimethylsiloxane (PDMS) cell with a 200 μL capacity that was glued on top of the device on the chip holder.
A glass coverslip coated with 100 nm gold was used as the gate electrode, and was placed on the top of PDMS cell that contained a 0.1 M HEPES buffer solution. A constant potential pulse of different magnitudes was applied to this coverslip, providing the electric field that polarized the monolayer. During the experiment, a constant current of 10 μA was maintained between the source (S) and drain (D) electrodes. The varying gate voltages and the constant S-D current were applied using a dual channel Keithley 2636A source measuring unit. The Hall voltage was recorded using a Keithley 2182A nanovoltmeter, and it was measured while constant current was maintained in both directions, i.e., from S to D and D to S, to correct for the error caused by the asymmetry of the Hall device. All measurements were performed in a dark Faraday cage.  . Time profiles of the voltage between silver and nickel layers for magnetic fields pointing towards or away from the organic layer (red arrows), as measured at 290 K for silver coated with a monolayer of 1,6-hexandithiol and wild type azurin illuminated by 532 nm. For establishing the spin dependent electron transport through the azurin under conditions that are as close as possible to the physiological one, we adsorbed the protein on the devices shown in Fig. S5A. These Hall devices are made of GaN/AlGaN structure with a two-dimensional electron gas (2DEG) interface layer. Notice that the device applied here is different from the common Hall device which is applied using an external magnetic field acting perpendicular to the surface of the device. As a result of the Lorentz force, electric potential can be measured perpendicular to the source-drain current and to the magnetic field. This potential is the "Hall potential". In the device used here, no external magnetic field is applied, but instead the protein is adsorbed on the surface of the device. In the experiment, the azurin is adsorbed on the device which is placed within the electrolytic solution using a PDMS cell. A top gold electrode is placed on the top of the solution facing S7 the device and it is used to apply the electric field. On the application of the electric field, the protein is charge polarized and if this charge polarization is accompanied by spin polarization, the spins that are injected from the protein into the device create a magnetic field which can be monitored by the Hall probes (Fig. S5B).

MD simulations.
The azurin coordinates were obtained from the PDB file with ID 1JZE. The MD simulations at the 290 K and 250 K temperatures were carried out using the NAMD 2.11 program. 1 Both the 290 K and 250 K systems were solvated with a water box extending 10 Å on each side of the protein. The resulting unit cell vectors were (in Å): (65.000, 61.000, 60.000).
H-O and H-H distances in the water molecules were constrained using the SHAKE algorithm. 2 We used the particle mesh Ewald summation method 3 (1Å grid spacing) to calculate the electrostatic potentials. Full electrostatic energy evaluations were performed every two time steps. The 1-4 electrostatic interactions used a scaling factor of 0.833333.
The cutoff distance for van der Waals interactions was 12 Å. Atomic pairs within 14 Å were considered for periodical interaction energy calculation.
Each system was minimized for 80000 steps. The energy minimization was followed by solvent equilibration (using Langevin dynamics with a damping coefficient of 1.0 ps -1 ) with fixed solute atoms at 293 K (original crystallization temperature of 1JZE 4 ) for 150 ps.
The positions of solute atoms were then released for the next 75 ps of equilibration. This equilibration was followed by further 50 ps of equilibration at 290 K for the first system.
The second system was equilibrated further 50 ps at each of the following temperatures in the order: 280 K, 270 K, 260 K, and 250 K. Next, 0.5 ns of NPT dynamics with Nosé-Hoover Langevin piston pressure control was carried out for each system (pressure = 1 atm, barostat oscillation period = 100 fs, damping time scale = 50 fs, damping coefficient = 2.0 ps -1 ).
The MD production run lasted 100 ns and 110 ns for the 290 K and 250 K systems, respectively, with a time step of 0.5 fs. The RMSDs of the 290 K and 250 K systems spanned ranges of about 1.27 Å and 0.65 Å, respectively ( Fig. S6 and S7). We extracted the MD snapshots every 0.1 ns from the time windows 20-100 ns at 290 K and 20-108 ns at 250 K.

Computational details about the ET pathway analysis.
The structure and electron transfer properties of the selected MD snapshots were analyzed using the Pathways 1.2 plugin 5 for VMD. 6 The 'strength' of the electron tunneling pathways is measured by the electronic coupling decay factor (or decay product) 7,8,9, Including the H atoms explicitly in the pathway analysis, we observed that the combination of a through-bond step (from the electron donor to the hydrogen atom) and a through-space step (from the hydrogen to the electron acceptor) corresponded to a smaller decay factor (and therefore a larger coupling factor) than the through-H bond step. Therefore, the pathway program described the H bonds as through-bond steps followed by through-space steps.

Structural parameters, coupling pathways, and charge transfer modeling.
We started our theoretical analysis with a geometry optimization of the Cu site, followed by a single-point electronic structure calculation. In the optimized geometry, Cu is out of plane on the side of the glycine axial ligand (Gly45) by 0.067 Å. The highest occupied molecular orbital (which is singly occupied) is mainly localized on the px and pz atomic orbitals of the methionine (Met121) ligand's sulfur atom, while the lowest unoccupied molecular orbital is distributed on the Cu and the py of the cysteine (Cys112) ligand's sulfur atom. Cys112 (which has been focus of mutation studies because its bonding interactions influence azurin spectroscopic properties 13 , 14 ) participates in the dominant Ru-to-Cu electron tunneling pathways (see Tables S1, S3).  Table S2.  15 The Cu-SD average distance obtained from the MD simulation at 290 K is a little larger than the crystallographic one. However, apart from the limits of comparing crystallographic and MD structures, this distance decreases with increasing temperature from 250 K to 290 K, and a possible further (nonlinear) decrease may occur near room temperature. The figure was generated using VMD. 6   Table S1. Frequency of occurrence of the strongest tunneling pathways between Ru III and Cu II (electron donor-to-acceptor transition) across the His83 protein dynamic evolution at the two indicated temperatures. The pathways involving the same amino acid residue sequence are marked with the same color. The listed tunneling pathways cover more than 90% of the system snapshots selected. One-letter codes are used for the amino acid residues.  Table S2. Average distances between the indicated atoms over the MD snapshots corresponding to the indicated dominant electron tunneling pathways (namely, all pathways, the 'tortuous' path 2, and the more direct pathways 3 and 4, as ordered for the H83 protein at 290 K). We obtain very similar values for the closest distance between C112 and N47 when we average this distance over the MD snapshots corresponding to tunneling pathway 2 or to pathways 3 and 4, and no significant difference is obtained at the two temperatures. Thus, we argue that the wide protein motion leading to the more frequent occurrence of pathways 3 and 4 (as well as a smaller Cu-Ru average distance) at 290 K than at 250 K does not affect appreciably the local relative arrangement of C112 and N47. The different pathway-related averages of the Cu site geometry at 290 K produce similar distances.

Reaction scheme
We make the reasonable assumption that 01 is much smaller than 10 . Moreover, considering the protein linkage to the electrode, and the proximity of the Ru center to the Ag electrode in particular, we assume that the downhill M → D process is much faster than the uphill A → D process. The converse is certainly ruled out by the experimental evidence. In fact, for > , the probability P in Equation S2, and hence the measured voltage, would depend on AD DA kk (where the D → A transition is activationless, while the activation of the D → A transition slows down with decreasing T) and would thus increase with decreasing temperature, against the experimental evidence. , and becomes proportional to such ratio if k10>>kDA. We make this further approximation to simplify the treatment. We also note that AM  may depend on T, but this dependence is not considered in this study. Since the proteins were linked to the silver film through the Cys3 and Cys26 residues, in order to obtain relative ()

AM
VT 2 values at 290 K and 250 K, we analyzed the electron tunneling pathways from copper to both residues, using the same MD snapshots employed for the D → A transition as a simplifying approximation. We found that, on average, the electron tunneling to Cys3 is more than one order of magnitude faster than the one to Cys 26, based on the mean square electronic couplings ( Table S5). The electron tunneling pathway analysis reported in Table S6 shows that the Met121 ligand to copper is mainly involved in the electron transfer. Furthermore, about 20% and 3% of the strongest electronic S16 tunneling pathways involve His46 at 290 K and 250 K, respectively. We also found that the coupling between Cu and Cys3 is much weaker than that between Cu and Ru (compare Tables S4 and S5). Table S5. Mean-square electronic coupling decay factor (decay product) <T 2 >, in (dimensionless) units of 10 -13 , for the electron tunneling from copper to the cysteine residues (C3 and C26) linked to the silver film (A → M transition), at the indicated temperatures. We also report the mean-square decay product for the tunneling pathways to Cys3 through the M121 and H46 ligands to the copper.

Model Calculations for Spin Dependent Transmission.
The model calculations, describing the temperature dependent spin polarization, are based on a description of two chiral molecules which are bridged by a single spin moment and mounted between two metallic leads, one which is ferromagnetic whereas the second is nonmagnetic. The chiral molecules are represented by discrete sets of equivalent sites carrying an electron level. Each site is coupled to its nearest neighbor sites via a simple spinconservative hopping and to its next nearest neighbor sites through a spin non-conservative hopping which ties together the spin-orbit interaction with the molecular chirality.
For the sake of proposing a model for charge transport through the complex of chiral molecules and a local spin moment, we begin by introducing the Hamiltonian: Here, the term ℋ = ∑ ∈ † , = , , defines the electronic properties of the left (L) and right (R) leads, where the spinor † ( ) creates (annihilates) an electron in the lead at the energy , whereas ℋ ML and ℋ MR comprise the electronic structures of the left and right molecules, respectively. Here, the left molecule is described by the Hamiltonian: 18 and analogously for the right molecule. The spinor † ( ) creates (annihilates) an electron at the site m with energy and Zeeman split ⋅ /2, where is the vector of Pauli matrices, generated by the external magnetic field . The second term describes hopping between nearest neighboring sites with rate while the last term accounts for the spin-orbit S18 interaction with strength and chirality ± in terms of hybridization between next-nearest neighbors. For more details, we refer to Ref 18. The local spin moment is mounted between the two chiral molecules and we model its presence by a tunneling between the sites and 1 in the left and right molecule, respectively, see fifth term in the expression for ℋ . The associated tunneling rate, , comprises spin-independent, 0 , and spin-dependent, 1 , contributions, such that =

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The currents are, in these expressions, given in terms of the lesser and greater Green functions < > Τ and < > Τ of the sites in the left molecule and 1 in the right, respectively.
Under the present construction, the chiral structures themselves do not generate spin selectivity. It is only through their interactions with the local spin moment such an effect takes place, if any. Hence, we can safely assume that the current 0 does not provide any contribution to the spin selectivity since the local spin moment is absent from this expression.
It should be noticed in this context that the Green functions for the left and right chiral structures are given in the atomic limit, that is, in absence of the local spin moments. This is justified since we are interested in whether a mechanism for spin selectivity can be achieved from the properties of the local moment and its coupling to the chiral environment.
Moreover, it is justified to neglect possible spin-selectivity mechanisms, e.g., electron correlations 18 or spin-dependent electron-phonon interactions, 20 in order to resolve the hypothesis that transport through the chiral molecules is the source of a local magnetic field which acts on the spin moment and, hence, generates spin-selectivity.
To the lowest order in the interaction with the spin moment, then, the current is provided by 1 . It can be seen that this current depends explicitly on the magnitude of the spin moment, hence, it may be finite only whenever the expectation value of the spin moment is. We refine the analysis of this current by introducing the approximation < > Τ ( ) = Furthermore, we are interested in the conditions that lead to a fixed local moment, wherefore, it is justified to assume that ⟨ ( )⟩ = ⟨ ⟩, such that the current can be written: Although we focus on the lowest order contribution to the current that depends on the local moment, we notice that also the current 2 depends on the local spin structure though the spin-spin correlation function ⟨ ( ) ( ′ )⟩ . However, this current adds an essentially negligible contribution to the spin-selectivity and is, therefore, omitted in the present discussion.

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Next, we consider the properties of the local spin moment, which interacts with the electronic current through the induced magnetic field , 21 and with the ionic structure through the electronically mediated exchange . 22 These two electronically mediated fields can be written as: where accounts for the spin-polarized current that passes through the system, and where e-ph is the parameter for the effective interaction between the electrons and the ionic motion. In terms of these fields, an effective mean-field model for the local spin moment can be written as where ⟨ ⟩ denotes the expectation value of the displacement operator. Hence, while the induced field depends only on the current flowing through the molecular complex, the induced field = ∑ ⟨ ⟩ depends on both this current as well as the ionic vibrations that couple to the spin. In this sense, the former field has no temperature dependence whereas that latter has, something which will become crucial in our subsequent discussion.
The ionic motion is subject to anharmonic forces, which, here, are modelled in terms of the cubic interaction term . In linear response theory, the expectation value of the displacement operator, can be expanded in terms of the pertinent interaction Hamiltonian In terms of these expression, the linear response quantum displacement becomes timeindependent and given by ⟨ ⟩ = − 2 ∑(1 + 2 ( )).
While the above calculation demonstrates that the ionic displacement may increase with temperature which, hence, leads to an increased vibrationally induced magnetic field acting on the local moment, it is not sufficient to generate a large difference in the induced field with the temperature increase. Therefore, we reconsider the phonon Green function in the anharmonic model, to lowest non-trivial order giving: (2) ( , ′ ) =

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Inserting the expansion of the phonon Green function, we obtain the displacement: