Orientations and water dynamics of photoinduced secondary charge-separated states for magnetoreception by cryptochrome

In the biological magnetic compass, blue-light photoreceptor protein of cryptochrome is thought to conduct the sensing of the Earth’s magnetic field by photoinduced sequential long-range charge-separation (CS) through a cascade of tryptophan residues, WA(H), WB(H) and WC(H). Mechanism of generating the weak-field sensitive radical pair (RP) is poorly understood because geometries, electronic couplings and their modulations by molecular motion have not been investigated in the secondary CS states generated prior to the terminal RP states. In this study, water dynamics control of the electronic coupling is revealed to be a key concept for sensing the direction of weak magnetic field. Geometry and exchange coupling (singlet–triplet energy gap: 2J) of photoinduced secondary CS states composed of flavin adenine dinucleotide radical anion (FAD−•) and radical cation WB(H)+• in the cryptochrome DASH from Xenopus laevis were clarified by time-resolved electron paramagnetic resonance. We found a time-dependent energetic disorder in 2J and was interpreted by a trap CS state capturing one reorientated water molecule at 120 K. Enhanced electron-tunneling by water-libration was revealed for the terminal charge-separation event at elevated temperature. This highlights importance of optimizing the electronic coupling for regulation of the anisotropic RP yield on the possible magnetic compass senses.

mT is due to the spin-lattice relaxations with T1 = 1.4 µs and T23 = 1.8 µs in Supplementary Table 5. S6 conformation in Fig. 3a, indicating that the WB(H) is oxidized by the charge-separation at 120 K. When assuming D = -1.5 mT from the separation distance of 1.2 nm between FAD and WB(H) in Fig. 1, the experimental results again deviate from the calculations at any position of the oxidized tryptophan (g, h, i). We also computed the EPR spectra with D = - parameter together with its distribution determined by T2J*, we examined the susceptibility by the parameters of J and T2J*. Because of these strong sensitivities to J and T2J*, we are confident about the determinations of the several parameters on the molecular geometries and the isotropic exchange couplings from a series of the simulations. For the later delay times at 0.45 µs and 0.6 µs, the similar small but existing differences between the blue and red spectra caused by the laser polarization in Fig. 3 strongly denotes the geometries of the secondary CS states are unchanged by the delay time, while the J and T2J* are time-dependent, as shown in Fig. 4. The error in J is evaluated to be ±0.1 mT. Figure 6. Dependence of T23 value on the TREPR spectrum, showing strong susceptibility of this relaxation parameter. The inner A/E polarization becomes stronger than the outer A/E component when T23 is small. This effect can be used to characterize the fast solvation response in the W324F from XlCry-DASH at 120 K (Supplementary Figure 7). Notably, the calculated spectra obtained by T23 = 0.2 and 0.5 µs are evidently distinguished from the computed results in Supplementary Figures 4-5 using the other parameters. This denotes that the several input parameters of T23, D, q, f, J, and T2J* can be separately determined from the present simulation of the magnetophotoselection effects for the different delay times. Figure 7. a-c) td-dependent TREPR spectra obtained by the depolarized 450 nm laser irradiation of W324F from XlCry-DASH at 120 K, showing E/A/E/A patterns. The red lines were obtained with (J, T2J*) = (2.35 mT, 4 ns), (0.59 mT, 5 ns) and (0.19 mT, 20 ns) at td = 0.1, 0.3 and 0.6 µs, respectively. While the E/A/E/A spin polarization pattern of the mutant is very similar to that of the WT (see Fig. 2), the width of the spectrum becomes quickly narrows within 0.3 µs. This is interpreted by an immediate decrease in J from 2.35 to 0.29 mT. From our SCRP model calculations (Supplementary Table 4), T23 ≈ 0.1 µs and T1 ≈ 0.2 µs were required and explain both the drop in J and the narrowing of the TREPR spectrum, thus denoting that the solvation time is 0.16 µs. c) Accelerated solvation model by lack of the steric hinderance in the water molecule to account for the quick Xp response of dotted line in Fig. 5a for W324F. The shaded residue represents the WC(H) conformation of the wild type obtained from the x-ray structure. This was plotted as a function of the magnetic field (B0) from EPR resonance center field with setting J = 1.45 mT determined at 0.2 µs (Fig. 3d). The red line was obtained with T2J* = 3 ns, while T2J* = 30 ns was used for the blue line. The peak-to-peak splitting (PPS) is unchanged by the variation in T2J*, while the spectrum linebroadening is simply determined by 1/(2pT2J*). This denotes that the red curve for B0 > 0 is approximated to represent the inhomogeneous distribution function (i.e. the energetic disorder) in the J-coupling determined by the variation of 1/(2pT2J*) = 1.9 mT for the secondary CS state. From this, the function FF(B0) were plotted against B0 in Fig.  4a for B0 > 0, as the distribution functions of the singlet-triplet gap i.e. PPS in Supplementary Figure 9, as follows:

Supplementary
Relating to Supplementary Equation 2, from our previous report, 4 the microwave transition of rS+ affected by the exchange coupling was expressed by the stochastic-Liouville equation, as follows: where rS0 denotes the S-T0 coherence developed by frequency of the energy difference between the |2> and |3> levels. Q+ and Q-are determined by the sum and difference in the Larmor frequencies of the two radicals in the SCRP, respectively. When the Q-term is ignored as 2|J| >> Q-, the S-T+ transition spectrum is described by the imaginary part  Figure 11. The Sumi-Marcus electron-transfer model representing the fast nuclear response via vibration motions (vertical axis) and the slow response by the water reorientation (horizontal axis which is X in Fig. 4b) as the connection between the ET mechanism and the solvation dynamics in the present study to interpret the inhomogeneous distribution determined by T2J*. The sub-microsecond response in Fig.  5a is regarded as the secondary relaxation in the product state by the slow reorientation at 120 K. In the ET reaction, several nuclear coordinates are participating including the energy relaxation process. The response time may vary with nature of the coordinate. In the present case, the secondary CS state, i.e. FAD −• WB(H) +• could be generated at picoseconds regime via the vibrationally hot exciton in the primary CS state of FAD −• WA(H) +• . In this regard, the very quick nuclear and/or solvent motions may be involved forming the secondary CS immediately as reported previously. 6 Thus, the slow water dynamics in Fig. 4 is regarded as the secondary relaxation. In the present model of Fig.   4b, however, the reorganization energy was assumed to be determined by the single l value (0.41 eV) for the simplicity of the treatment to predict the heterogeneous distribution of the exchange coupling (Fig. 4c).
Moreover, we approximated the distribution by the Gaussian functions (Fig. 4b) to simply evaluate the inhomogeneous J-distributions, although the non-relaxed states were treated. This is because a previous study apparently exhibited the Gaussian S15 distribution shapes to explain the solvation dynamics. 7 The present simplified assumption by the equilibrium Gaussian distribution is probably the reason for the slight differences between the distributions around the low-J regions in Fig. 4a and 4c because the distribution width is anticipated to be larger than the standard deviation of the equilibrium Gaussian distributions. Although more rigorous treatments invoking the Langevin equation should be forthcoming, which is out of scope in the present interpretations, there is no doubt about the present main conclusion on the involvements of the slow water reorientation causing the J-distribution.
Supplementary Figure 12. Time profiles of the transverse magnetization of WT XlCry-DASH at 120 K with two different microwave powers (1 mW and 3 mW for the red loglived and blue short-lived profiles, respectively at B0 = 340 mT). Rabi oscillation frequency is 1.7 time higher in the blue profile than that in the red profiles and thus is caused by the transient nutation, demonstrating that the T1 and T2 relaxations (not the relaxation parameter determined by T2J*) are larger than 1 microsecond. This wavy profile thus excludes the dynamic transverse relaxation with the nanosecond time regime and is consistent with a larger longitudinal spin relaxation times in Supplementary Table 1, denoting that the line shapes are determined by the inhomogeneous distribution of the exchange coupling. S16 Supplementary Figure 13. Crystal structure of Columba livia CRY4 of pigeon from the PDB code: 6PU0. GOL represents glycerol and is not located between W372 and W318. The distance between GOL and Flavin is 0.93 nm, denoting that the solvation energy is negligibly small by GOL in the secondary RP state compared to the energy by the water solvation. S17 Supplementary Figure 14. Crystal structure of Chlamydomonas reinhardtii (PDB code:5ZM0). GOL represents glycerol and is not located between W376 and W322. Both distances between GOL molecules and flavin and between GOL and W376 are too long, denoting that the solvation energy contributions are negligible by GOL. The primary CS character can be participating in the secondary CS state as the wavefunction admixture via the electronic coupling. From the perturbation theory, this coefficient of the wavefunction participating to the secondary CS is readily evaluated to be VHHAB/ l ≈ (140 cm -1 / 3200 cm -1 ) = 0.04 from Supplementary Figure 15 that explains the time-dependence of the S-T gaps with their distributions (Fig. 4a). This denotes only 0.2 % of the primary CS character via the superexchange model around X = 1 in Fig. 4b, meaning that the primary CS character is much smaller than 1 % even at 0.2 microsecond because the solvation relaxation already proceeded with Xp = 0.4 in Fig. 4b. This well coincides with the magnetophotoselection results that showed the time-independent d-direction of (q, f) = (58°, -65°) with d = 65° in Fig. 3a, as the dominant CS state. Chromophore-bound protein with ferricyanide treatment (blue broken line), chromophore-removed protein without (black solid line) and with (red solid line) ferricyanide treatment proteins. Molar extension coefficient of chromophore-removed CRY-DASH was estimated by protein concentration by Bradfrod method, the molecular mass of the calculated His6-tagged protein, and the absorption spectrum. The absorption spectrum of chromophore-bound protein was superimposed with FAD cofactor's extinction coefficient as 1.0×10 4 M -1 cm -1 at 450 nm.
Oxindole absorption peak is reported to appear around 340 nm with an extinction coefficient of 1×10 4 M -1 cm -1 . 9 Oxidized tyrosine species from DOPA exhibits similar absorption bands around 300 nm and 470 nm. 10 Estimated from the enlarged absorbances around 330 nm (Inset), oxidized forms of tryptophan or tyrosine are thus 0.3 residues/molecule. A small absorption around 470 nm suggests existence of oxidized tyrosine of dopachrome with the extinction coefficient of 3.7×10 3 M -1 cm -1 at 475 nm, 11,12 indicating that 0.1 residues/molecule are oxidized in tyrosine. Possible candidates for oxidized tryptophan and tyrosine residues were shown in Supplementary  Figure 18, where 8 tryptophan and 12 tyrosine residues were exposed to the surface of the protein including W324 corresponding to WC(H). (See below.) It is thus concluded that the oxidation of WC(H) occurs less than 0.02 residues per molecule from a very small amount of free iron impurity. This minor (< 2 %) possibility of pre-oxidation in WC(H) is very consistent to the observation of the terminal CS state assigned to DASH.

Supplementary Tables
Supplementary Table 1. EPR parameters for the simulations of the td-dependent EPR data (Fig. 3d) of the photoinduced CS states at 120 K. reported for a complex of water and tryptophan cation radical. 14 b) Estimated from the reported coupling constants of the neutral radical and the computed spin densities (rN1 = 0.16, rC2 = 0.13, rC5 = 0.26, and rC7 = 0.17) at the aromatic ring for the complex of water and tryptophan cation radical. 14 Because of rN1 ≈ rC7, the principal values in H1 proton were assume to be the same as the values for H7. An example of the X and Y principal axes, these axes directions are represented in H7. The Z axes are perpendicular to the aromatic plane for all of the anisotropic couplings.  MHz because these four isotropic coupling constants from these protons are similar. 2 We expect that the -CH3 group freely rotate at 120 K. Thus, only the isotropic couplings were considered at 120 K and at 240 K.  It is reported that a perturbation from the excited state may allow the spin-orbit coupling (SOC) to participate in the exchange coupling, resulting in the anisotropy in the exchange parameter, as the origin of the g-factor is in organic radical species in frozen systems. (Bencini and Gatteschi, "EPR of Exchange Coupled Spins" (2012) Dover Publication Inc. pp. 27.) 15 Based upon their formalism, this anisotropic exchange interaction is negligibly minor in the present CS state because 1) third order perturbation treatment of the SOC via the excited state is required and 2) the excited state energy in FAD − •* possessing the n-orbital character must be very high, which is relevant to very small g-anisotropy in Supplementary Figure 2. Furthermore, from our present analyses of the electron spin polarization, it was demonstrated that the time-dependent J is caused by isotropic transfer integrals of V between the separated FAD − • and WB(H) + • radicals with Equation 1. As described in the manuscript, the transfer integrals are simply determined by the orbital overlap of VHH between FAD and WA(H) and by VHHAB between WB(H) and WA(H) via the bridgemediated tunneling interactions. These orbital overlaps are all isotropic interactions with |VHHAB| = 140 cm -1 (Supplementary Figure 15). Because this coupling term accounts for the electron transfer rate of 6.4×10 10 s -1 at the contact edge-to-edge separation (0.39 nm) between WA(H) and WB(H) (Supplementary Figure 15), it is concluded that the S-T gaps in Fig. 4 are all isotropic in the present system. This means that the J-coupling in the present distant radical pair is not anisotropic and is dominated by the isotropic transfer integrals as the configuration interaction. This is self-consistent with the longrange electronic coupling causing the distant exchange interaction isotopically at 1.4 nm for the secondary CS state. Overall, the anisotropic exchange coupling is concluded to be negligible in the present study.  Table 1. This is highly deviated from the experimental result of 0.08. Furthermore, three of the crystal structures of the PDB codes 6X24, 5ZM0 (Supplementary Figure 14) and 6PU0 (Columba livia CRY4 of pigeon: Supplementary  Figure 13) are reported on cryptochromes to which the glycerol molecules are bound. Like Fig. 1, the CRY4 was also found to possess the relevant water binding site between WB(H) and WA(H). However, glycerol molecules are not bound to these positions but the different sites for three of the cryptochromes as shown in Supplementary Figure 14.

Supplemental
Because it is widely accepted that glycerol molecules play a role to surround the protein surface area to protect the native protein structure, as reported by Vagenende et al., 16 we exclude the possibility of the glycerol binding to impact the solvation dynamics in Fig.  4.