Magnetic field effect in natural cryptochrome explored with model compound

Many animals sense the Earth’s magnetic-field and use it for navigation. It is proposed that a light-dependent quantum effect in cryptochrome proteins, residing in the retina, allows for such an iron-free spin-chemical compass. The photochemical processes, spin-dynamics and its magnetic field dependence in natural cryptochrome are not fully understood by the in vivo and in vitro studies. For a deeper insight into these biophysical mechanisms in cryptochrome, we had introduced a flavin-tryptophan dyad (F10T). Here we present the magnetic field dependence of 1H photo-CIDNP NMR on F10T and a theoretical model for low-field photo-CIDNP of F10T. This model provides mixing mechanism of energy-levels and spin-dynamics at low magnetic fields. Photo-CIDNP has been observed even at Earth’s magnetic field (~0.05 mT). These experiments prove F10T to be an excellent model compound establishing the key mechanism of avian-magnetoreception and provide insight into the optimal behaviour of cryptochrome at Earth’s magnetic field.


Time-resolved solution-state photo-CIDNP 1 H NMR experimental setup.
Time-resolved solution-state photo-CIDNP 1 H NMR experiments were carried out in a Bruker (Avance III HD) 400 MHz NMR spectrometer using a probe modified to illuminate the sample from side ( Supplementary Fig. S1a). The pulse sequence for time-resolved photo-CIDNP experiments is shown in Supplementary Fig. S1b: bubbling with N2 ─ presaturation (Waltz16) 1,2 ─ laser pulse ─ evolution time ─ detection pulse ─ acquisition. The Boltzmann polarizations in the spectrum are suppressed by the presaturation pulses. Therefore, the signals of the polarized products formed due to laser irradiation appear only in the photo-CIDNP spectra. Supplementary Fig. S2. Experimental setup and pulse scheme to measure the magnetic field dependence of 1 H solution-state photo-CIDNP with field-cycling: (a) experimental setup and (b) The pulse-scheme of the light-induced CIDNP experiment with field cycling comprises of three consecutive steps: Step 1: the sample was kept at low fields (< 1 mT) for a time period of five times the T1-relaxation time to remove thermal polarization, then the sample was bubbled with nitrogen using the above-mentioned technique for 3 s followed by a delay time of 5 s; Step 2: the sample was irradiated with 20 laser pulses (~ 2 s) in the polarizing magnetic field Bp. Then the probe along with the sample was shuttled to the NMR detection field B0; Step 3: the application of an RF (π/2) pulse and acquisition at the detection field of B0. range from 0.1 mT to 7 T during a time period of less than 0.3 s; the time profile of field variation is precisely mapped. A Quantel Brilliant b Nd:YAG laser with a wavelength of 355 nm with a repetition rate of 10 Hz is used as light source.
A scheme presenting the field-cycling photo-CIDNP experiment, comprising of three consecutive steps, is shown in Supplementary Fig. S2b. In the first step, the sample was kept at low fields (< 1 mT) during five times the T1-relaxation time to remove thermal polarization. Then the sample was bubbled with nitrogen using the above-mentioned technique for 3 s followed by a delay time of 5 s. After that, the sample was irradiated with 20 laser pulses in the polarizing magnetic field Bp. Then the entire probe along with the sample was shuttled to the NMR detection field B0. The final step is the application of an RF (π/2) pulse and acquisition.

H photo-CIDNP depletion curves.
To prevent the photo-degradation of the flavin residue, 5 0.09 mM H2O2 was added to the solution of F10T and corresponding depletion curves for different protons of the flavin residue have been presented in Supplementary Fig. S3. Depletion curve is the variation of the intensity (polarization) with number of laser pulses. The depletion curves show that the addition of H2O2 (with given molar concentrations) has prevented the photo-bleaching of flavin residue in F10T.

Concentration dependence of 1 H photo-CIDNP.
Upon variation of the concentration of F10T in the solution, no changes have been observed in the photo-CIDNP 1 H NMR spectra ( Supplementary Fig. S5). In case of free FMN and Trp in solution, an increase in the intensity of CIDNP signal is expected with increasing the concentration. Hence the photo-CIDNP data demonstrate that the electron transfer in F10T occurs intra-molecularly and therefore, is independent of the concentration. The photochemistry and related reaction scheme for FMN and amino acids such as Trp, Tyr or His (histidine) added separately in solution have been studied widely in last few decades. The observed spin-dynamics is generally explained by the classical radical pair mechanism (RPM) 7,8 in which nuclear-spin interactions control the electron-spin dynamics and therefore the chemical fate of the product formation ( Supplementary Fig. S7). Upon illumination, FMN is excited to a molecular triplet state T FMN* and accepts an electron from the amino acid Trp to yield a geminate radical-pair T  The sign rule of photo-CIDNP. These observed sign of polarization at high magnetic field in liquid-state photo-CIDNP spectrum can be summarized using the multiplicative sign rule by Kaptein 9 in which the polarization of nucleus n is given by the product of four signs as equation (1) where is the sign of the hyperfine coupling constant of the i th nucleus, Δ is the sign of the -value difference − , where radical m carries nucleus i. μ is positive for triplet precursor and negative for singlet precursor, while ε is positive for recombination products and negative for escape products. The sign of Γ determines the sign of the polarization for nucleus i whether would be absorptive (positive) or emissive (negative).

Theory.
To fit the experimentally obtained magnetic field dependence curve for 1 H photo-CIDNP, we have used the theoretical model proposed by de Kanter 10 . In this theory, the spin dynamics of biradical has been described using the density matrix ( ), which evolves in time according to equation (2) where ( ) is a function of the spin state variables of the biradical and the reaction product and of the distance between the radical centres r. Liouville operator is related with the spin Hamiltonian (in angular frequency units) as Matrix is the Redfield relaxation matrix and describes the molecular motion. The chemical reactions are expressed in terms of . The biradical is formed at time = 0 in a certain spin state (S or T) and at a particular distance.
1 and 2 are the -factors of the two radical sites of the biradical. is the Bohr magneton and 0 is the magnetic field strength. is the hyperfine interaction with the nucleus at site 1. The exchange interaction ( ) is expressed as a decaying exponential function of the distance between two radical centers and with a adjustable parameter Using the direct product of the electron spin functions, S, T+, To and T-, and the nuclear spinfunctions α and β as basis, 0 is the diagonal and ′ is the off-diagonal part of . Off-diagonal matrix elements in L occur only within two 9  9 blocks corresponding to the basis functions , 0 , + and , 0 , ─ respectively.
For electron spin relaxation two relaxation mechanisms are considered: (1) Interactions which are uncorrelated at the two radical sites. These are represented by fluctuating local magnetic fields. They induce singlet-triplet transitions as well as transitions between the triplet levels.
(2) Correlated interactions which induce transitions between the triplet levels only. The most important contribution is given by fluctuations of the electronic dipole-dipole interaction.
The complex relaxation matrix can be written as Where is the relaxation contribution due to uncorrelated fluctuating local magnetic fields and is the dipole-dipole relaxation term.
For the dynamical behavior of the biradicals the restricted diffusion (RD) model has been taken into account. At first the equilibrium distribution C(r) of the end-to-end distance is calculated using a Monte Carlo simulation. The short-range interaction energy of the C and H atoms of CH2 groups separated by four or less bonds are described by the Buckingham potential. For the long-range interaction energy, which is described by a Lennard-Jones potential, the identities of the individual atoms in the CH2 groups are ignored.
The normalized distribution C(r) is divided into m segments with equal areas (equal probabilities): where ∫ denotes the integral over r between the minimum and the maximum values of r in the i th segment. The average distance in segment i is The motion is described by diffusional jumps between the different 's. Only transitions between neighboring segments are included. By the analogy with classical Brownian motion the transition rates of the jumps are taken as where D' can be considered as the effective diffusion coefficient for the restricted diffusion.
The chemical reactions of the biradical are represented by the term ( ) in equation (2) and can be written as Where describes the intramolecular coupling or disproportionation reaction and the scavenging reactions. The intramolecular reactions are only possible from the singlet state of the biradical provided it has the conformation with the smallest end-to-end distance (rd). The intramolecular reaction of the biradical is described by with kp the reaction rate constant and • the projection operator | , >< , | selecting singlet electronic states of the biradical for r = rd. Equation (12) is preferred to the alternative form proposed 11 for reasons of consistency 12 .
The scavenging reaction is independent of r and of the electronic state of the biradical. The decay of the biradical density matrix elements is given by where ks is the scavenging rate constant.
The nuclear spin polarization of the product is given by The solution of the equation of motion (eq. 1) is obtained via the Laplace transformation which yields where is obtained by the corresponding rewriting of . The other matrices remain the same. The starting conditions for 0 are determined by the spin state of the precursor and by the condition that the biradical is formed in the conformation or segment with the smallest value of . Assuming no initial electron spin polarization the non-zero elements are for a triplet precursor 0 = 1 = 2, 3, 5, 6, 7, 8 and for a singlet precursor The polarization of the product is now given by