On the Dispersion of DNP in Radical Enzymes

1. Introduction

‘Highlighting radical sites through polarized neutron scattering from AFP-modulated polarized protons’ [1] opens new perspectives for the investigation of very dilute paramagnetic substances. The catalase molecule with one of its amino acids, here a tyrosine, converted into a radical turned out to offer ideal conditions for the observation of the interplay of dynamic nuclear polarisation (DNP) [2,3,4] and the reversal of the proton polarisation by the method of adiabatic fast passage (AFP) [5,6].

The structure of bovine liver catalase (BLC) being known to atomic resolution from single crystal X-ray crystallography [7] offers a solid platform for tracing the proton polarisation in space and time by polarised neutron scattering. Tyrosyl doped catalase is in solution. Polarised neutron small-angle scattering will provide information about the proton polarisation at nanometric resolution.

Each living system has it: the redox enzyme catalase which converts hydrogen peroxide into the molecular oxygen and water. The neutralization of hydrogen peroxide occurs at a very fast rate. There is a way to block he catalase molecule, simply by replacing one of the hydrogens of the peroxide by acetyl. The catalase accepts the derivative of hydrogen peroxide but the reaction takes another way which finishes with the conversion of one of its tyrosine amino-acids into a tyrosyl radical [8,9].

More precisely, one out of the four tyrosine amino acids per catalase molecule will find itself converted into a radical. Thus, a catalase molecule susceptible to radical formation may contain up to 4 tyrosyls, one per subunit. In that case, the occupancy would be 1.

It is the influence of the occupancy on the efficiency of DNP which is the subject of his paper. The results of our earlier studies using a sample with 0.58 tyrosyls per subunit shown in Figure 1 will be compared with that of a sample much richer in tyrosyl. Some properties of these samples called A and B are shown in Table 1.

2. Results

The variation of the efficiency of DNP in a radical enzyme rich in radicalized amino acids is shown in Figure 2. The occupancy of tyrosyl with respect to the heme in each of the four equal subunits of the catalase molecule is 0.78 (Table 1).

Each contains one iron bound to a protoheme IX group. Solvent 1:1 glycerol-d_n: D₂O

The dispersion of DNP appears to follow an EPR line which is slightly different from that shown in Figure 1. In fact, the original EPR obtained by [9] has been shifted to lower microwave frequencies and the width of the spectrum has been slightly enlarged to make the red squares follow the blue dots in Figure 2.

The red squares in Figure 2 like those in Figure 1 have been obtained from time-resolved polarised neutron scattering. They denote the efficiency of DNP at varies microwave frequencies in terms of the polarisation of the protons very close to the radical site.

2.1. Time-Resolved Polarised Neutron Scattering

Time-resolved neutron scattering from AFP modulated polarised protons of catalase B rich in tyrosyl (occupancy 0.78) is shown in Figure 3 and Figure 4. The intensity of polarisation dependent neutron scattering is around one per thousand of the total intensity of small-angle scattering of BLC. The latter from sample B is lower by factor 1.3 compared to the corresponding intensity from sample A [1].

Having said this, the statistical accuracy of the polarisation dependent intensity turns out to be a severe problem. In a first step, these residual intensities were drastically smoothed by averaging. The same procedure has been applied to the polarisation dependant intensities derived from the model in section 2.2. The error of the reduced data in the polarisation dependent intensities reaches about 0.10 at low moduli of momentum transfer Q.

Let us select the neutron scattering intensities at the frequency of 97.2 GHz and 97.25 GHz. The evolution of the neutron scattering intensity is dictated by a sequence of events dictated by the following time-table.

T=0s: Reverse the proton polarisation by AFP, Start neutron scattering. Proton polarisation will relax, approaching that at thermal equilibrium.

T=46s: invert the proton polarisation by AFP, and restart neutron scattering with microwaves ON, i.e., with DNP, until T= 86s.

T=92s: end of the cycle. Go back to T=0s.

Most remarkable is the change of the sign of the polarised neutron scattering intensity by the application of AFP at the end of each of the half-cycles (Figure 3 and Figure 4). We quantify it by the efficiency

$$\epsilon =-{\displaystyle \frac{polarisationbeforeAFP}{polarisationafterAFP}}$$

The efficiency ε is close to 0.8, both in Figure 3 and Figure 4. Complete reversal of the polarisation is characterized by ε= 1.

As for the sign of the polarisation dependent intensity keep in mind that catalase is dissolved in a deuterated solvent. Its ‘native’ contrast at P=0 is negative. Hence, an increase of the proton polarisation will lower the contrast and the intensity which goes with it. During the half-cycle of DNP, the intensity of the intensity of neutron scattering is decreasing pointing out a positive direction of DNP.

At a microwave frequency of 97.25 GHz, NMR data indicate a negative proton polarisation for the sample B in contrast to sample A with DNP in positive direction. This is not visible in Figure 4. It needs to be verified by a model-based analysis in section 2.2. Moreover, the change of polarised neutron scattering intensity in unusually low. This may be due to two counteracting forces: 1) negative DNP driving the intensity to higher values and 2) a drift of the polarisation towards more positive polarisation at thermal equilibrium at Pe = +0.35% (see 3).

The evolution of polarised neutron scattering from sample B at E = 97.20 GHz shown in Figure 3 differs considerably from that of catalase sample A with low tyrosyl occupancy [1]. At the onset of DNP, the intensity of polarised neutron scattering from sample A starts from a value close to zero. We have an exact repetition of the full cycle. This is not the case in Figure 4 where the polarised neutron scattering intensity (or a part of it) has been piled up in the course of 70 repetitions od the cycle.

2.2. The Model

A detailed description of the model is presented in [1]. We will bring to your attention its essential features needed in this context.

The repartition of the catalase molecule into various regions has been guided by a microscopic picture of the creation of proton polarisation by DNP and of its diffusion into the bulk. At the onset of DNP a few polarized protons close to the radical will find themselves in an ocean of unpolarised protons. We call this island of 1 nm diameter R1. It contains around 25 protons. Each of the four subunits of the catalase molecule has its R1 and a heme. The initially localized proton polarization will spread out crossing various nuclear spin diffusion barriers [10,11,12]. We find up to a hundred close protons of R1 in front of about 12000 protons of the catalase molecule. NMR studies aiming for the direct observation of a magnetic nuclear spin diffusion barrier suggest the creation of a larger space R2 for not so close protons in a hollow sphere of 2 nm diameter [13] surrounding R1 [11,12]. The enlarged minority of close and not so close protons in R1 and R2 respectively, now counts around 600 protons among around 12000 residual protons of the catalase molecule.

As already mentioned in Table 1, each of the four subunits of catalase contains one heme group. As it presents a kind of magnetic inhomogeneity it might influence the migration of the proton polarisation towards the molecular surface. The four iron atoms of the heme group are roughly on a surface of a sphere of 6 nm diameter centred at the midpoint of the catalase molecule. The protons, around 5000 inside this sphere except those of R1 and R2, belong to R3.

The regions R1, R2, R3, R4 and R5 are coupled in series forming an onion like structure. The driving force of DNP is the electron spin reservoir R0 with P₀ close to 1 which creates a proton polarisation far from equilibrium, primarily in R1 and R2 which then diffuses into the reservoir of higher order. Five rate equations govern the flow of proton polarisation between the six reservoirs R0 to R5 coupled in series.

$${\displaystyle \frac{d{P}_n}{dt}}={\displaystyle \frac{W_{n-1,n}}{N_n}}\left(P_{n-1}-P_n\right)+{\displaystyle \frac{W_{n,n+1}}{N_n}}\left(P_{n+1}-P_n\right)+{\displaystyle \frac{t_1}{N_n}}\left(P_n-P_e\right)n=1,2,3,4,5$$

(1)

The rate constants $W_{i,j}$ regulate the flow of proton polarization $P_n$ between the reservoirs Rn. It is this picture which helps to simulate a global polarization which might have been obtained from NMR. In practice, the individual proton polarization $P_n$ are the heart of time-resolved polarized neutron scattering.

Following the notation in [3] Eq. 7.52 ibid, the only term of nuclear spin contrast variation depending on the neutron polarization, p, is a mixed term

$$I_{0,P}\left(Q,t\right)=pRe\left(B^{\left(0\right)}\left(Q\right){\sum }_{j=1}^{j=5}{P}_j\left(t\right)B^{*\left(j\right)}\left(Q\right)\right)$$

(2)

It contains both the amplitude of the unpolarized sample, $B^{\left(0\right)}\left(Q\right)$, and that of the proton polarisation dependent amplitude, $P_j\left(t\right)B^{*\left(j\right)}\left(Q\right)$, the latter being time-dependent. The amplitudes $B^{\left(0\right)}$ and $B^{*\left(j\right)}$ are developed as a series of spherical harmonics. The calculation of the intensity of small-angle scattering is described in [1,11,12]

The root mean-square deviation between experimental data and those derived from the model is minimized. Important players in this procedure are the transition probabilities $W_{i,j}$ in Equation (1), the efficiency of AFP, and the drift towards P_e = +0.35%.

Figure 5. A map of the catalase structure [7]. It defines the repartition of the 80 tyrosine amino acids (light green) among the five reservoirs of the catalase molecule. Four of them (marked in dark blue) are potential radical sites. They are assigned to tyr-369 [1,11,12]. A high proton polarisation is concentrated in R1. It decreases rapidly in R2 and it is almost inexistent in the reservoirs of higher order.

Figure 5. A map of the catalase structure [7]. It defines the repartition of the 80 tyrosine amino acids (light green) among the five reservoirs of the catalase molecule. Four of them (marked in dark blue) are potential radical sites. They are assigned to tyr-369 [1,11,12]. A high proton polarisation is concentrated in R1. It decreases rapidly in R2 and it is almost inexistent in the reservoirs of higher order.

2.3. The Evolution of Proton Polarisation in Space

The evolution of proton polarisation obeys a sequence consisting of 46 seconds of relaxation followed by 40 seconds of DNP separated by the application of AFP (Adiabatic Fast Passage) each 46 seconds.

Polarised neutron scattering from polarised protons as described by equ.2 is the starting point for the evaluation of the experimental data. In a first step, each tyrosine is supposed to be converted into a radical state. The best fit of the calculated I(Q,t) with the experimental I(Q,t) is obtained with tyr-369 in agreement with earlier studies [1,8,9,11,12].

Moreover, the four heme appear to form a witch circle impeding the free diffusion of the polarisation. This property well-known from our studies on sample A, which justifies the existence of R3, appears to exist for sample B as well though in a less pronounced way.

We selected in Figure 2 two neighbouring microwave frequencies at 97.20 GHz and 97.25 GHz, respectively, giving rise to opposite direction of DNP. There is positive DNP at 97.20 for both samples A and B. At 97.25 GHz the direction of polarisation is negative for the sample B rich in tyrosyl (Figure 7). Note that at the same frequency the direction of DNP is positive for the sample A with lower tyrosyl content (Figure 1).

Figure 6. Evolution of the proton polarisation of sample B at E= 97.20 GHz. (red spheres) R1, (green spheres) R2, (sky blue spheres) R3, (orange spheres) R4, (blue spheres) R5, (red circles) R1 from the method using alternating direction of DNP [12]. The method of AFP is applied at 46s and 92 s. The proton polarisation reaches a value of 0.1 in R1. The proton polarisation in the neighbouring R2 drops to 0.006. The magnetic nuclear spin diffusion barrier at the surface of R1 turns out to very efficient. The polarisation in R3, R4 and R5 is a small fraction of one per cent.

Figure 6. Evolution of the proton polarisation of sample B at E= 97.20 GHz. (red spheres) R1, (green spheres) R2, (sky blue spheres) R3, (orange spheres) R4, (blue spheres) R5, (red circles) R1 from the method using alternating direction of DNP [12]. The method of AFP is applied at 46s and 92 s. The proton polarisation reaches a value of 0.1 in R1. The proton polarisation in the neighbouring R2 drops to 0.006. The magnetic nuclear spin diffusion barrier at the surface of R1 turns out to very efficient. The polarisation in R3, R4 and R5 is a small fraction of one per cent.

Figure 7. Evolution of the proton polarisation of sample B at E= 97.25 GHz. Symbols as in Figure 6. The method of AFP is applied at 46s and 92 s. The proton polarisation reaches a negative value of -0.09 in R1. The proton polarisation in the neighbouring R2 inverts its sign and becomes positive. The magnetic nuclear spin diffusion barrier at the surface of R1 turns out to very efficient. The polarisation in R3, R4 and R5 are a small fraction of one per cent. Except P₁, the proton polarisation in R2 to R5 shows a significant drift to thermal equilibrium polarisation at Pe= +0.0035.

Figure 7. Evolution of the proton polarisation of sample B at E= 97.25 GHz. Symbols as in Figure 6. The method of AFP is applied at 46s and 92 s. The proton polarisation reaches a negative value of -0.09 in R1. The proton polarisation in the neighbouring R2 inverts its sign and becomes positive. The magnetic nuclear spin diffusion barrier at the surface of R1 turns out to very efficient. The polarisation in R3, R4 and R5 are a small fraction of one per cent. Except P₁, the proton polarisation in R2 to R5 shows a significant drift to thermal equilibrium polarisation at Pe= +0.0035.

The evolution of the proton polarisation in sample A less rich in tyrosyl shown in Figure 8 differs considerably from those of sample B with 0.78 tyrosyl per heme shown in Figure 6 and Figure 7. The change of polarisation between the reservoirs of A is less abrupt. Thus, P₂ in R2 is about half the polarisation in R1. Similarly, the polarisation in R3 is about one third of that in R2.

We summarize the evolution the evolution of the proton polarisation in samples B rich in tyrosyl. The polarisation of the protons close to a tyrosyl radical is large. It rises very quickly at the onset of microwave irradiation and remains nearly constant during the second half-cycle. The nuclear spin polarisation barrier protecting the polarisation of the protons in R1 is quite efficient leaving a very low polarisation in R2 surrounding R1. The inflow of polarised protons from R2 to the subsequent R3 to R5 is almost negligible. The changes of the polarisation in these regions are largely due to the application of AFP and the drift of proton polarisation towards that at thermal equilibrium.

The high polarisation of the close protons in R1 is intriguing. Certainly, an increase of the occupancy by tyrosyl radicals in the core of the catalase molecule may be for something. A more convincing argument comes from Table 2. On passing from the sample A to the sample B the repartition of the tyrosyl radicals undergoes major changes. We note an important increase of the presence of 4 tyrosyls per catalase molecule. The probability to find 4 tyrosyl per catalase B molecule is 0.352, more than three times known from sample A. This is one of the secrets of the high polarisation of the protons in R1 of sample B.

But there may be another one due to the geometry of the tyrosyl arrangement shown in Figure 5. The x,y coordinates presentation of the catalase molecule shows the four (filled) radical sites. The distances along the edges of the nearly quadratic structure are close to 2 nm. A diagonal connection would amount to about 3 nm. The z values of the radicals are close to zero.

This result merits to be seen in context with the very active search of molecules which support DNP. Certainly, the aim to reach a high dynamic polarisation throughout the sample is rather different from ours. It concerns almost exclusively NMR spectroscopy [15,16,17]. But, the inter-radical distances in their preferred biradical structures are quite similar to those we reported on a radical enzyme in this paper.

3. Materials and Methods

3.1. The Sample

The preparation of the radicalized catalase molecule has been described in our earlier papers on time-resolved polarised neutron scattering [1,11,12]. We mention some points that are important in this context. As a rule, efficient DNP of solution requires a homogeneous dispersion of the solute in the solvent. Proteins for instance are best dissolved in mixture of equal volumes of glycerol and water. Peroxyacetic acid, a false substrate, is added to the solution of catalase at a temperature close to 0° C. Once the peroxyacetic acid gets fixed to the catalase molecule it initiates the formation of a porphyrin-π-cation followed by the slow development of a deep red colour due to the tyrosyl radical. From the EPR measurements the concentration of radicals per heme is obtained.

3.2. The Environment of the Sample

The experiments of time-resolved neutron scattering from AFP modulated polarised protons have been done at the Institut Laue-Langevin (ILL) at Grenoble. We used the small-angle scattering instrument D22 in the neutron guide hall of the ILL.

The set up for the dynamic nuclear polarisation of the PSI, Villigen, Switzerland, had temporarily been installed at D22. Small the heart of the set up (Figure 9) appears to be, its operation requires a lot of ancillary equipment ranging from the microwave source, the magnetic resonance circuit, to the powerful pumps ensuring the low temperature of 1K inside the cryostat. The sample was kept in a magnetic field of 3.5 T. [18,19].

The samples under investigation were shock frozen in a copper mould kept at liquid nitrogen temperature. The NMR coil was detached to allow a safe insertion of the fragile platelet. Then the coil was soldered to the end of the microwave guide. This delicate operation was done in an atmosphere of very cold nitrogen gas.

Microwaves for DNP at frequencies close to 97 GHz for DNP were obtained from an IMPATT diode. Continuous Wave NMR monitored the polarisation of the sample [20]. The direction of polarisation depends on the choice of the microwave frequency as has been outlined in detail above.

Let us conclude with the method of Adiabatic Fast Passage (AFP). It uses the same coil as for Continuous Wave NMR described above. A higher RF field amplitude and a slower speed of 0.3s are required to achieve the conditions of adiabaticity resulting in an efficient reversal of the proton spin polarisation [5,6,21].

4. Conclusions

The dispersion of DNP is strongly influenced by the occupancy of tyrosyls in the core of the catalase molecule. At higher radical occupancy a major part of the potential radical sites is filled. The gain in local polarisation with respect to samples with lower occupancy of tyrosyl radicals is impressive. It may amount to one order in magnitude, particularly at microwave frequencies giving rise to DNP in the negative direction.