8.4 Heterologous Expression & Peroxisomal Targeting of Proteins
9.1.1 Optimal X-ray Powder Diffraction From Yeast In Vivo
For powder diffraction experiments in tramsmission geometry, it is easy to calculate the optimum sample thickness. The attenuation of X-rays follows
a simpleLambert-Beer law and is therefore exponentially increasing. On the other hand a linear dependency exists between Thomsonscattering and sample thickness (equiv. crystal content). Thus the maximum of scattered signal relative to beam attentuation is obtained at a sample thickness of 1/µ, withµ being the attenuation coefficient of the investigated material. By using the Cromer-Liberman algorithm [23], integrated in an available Python script [171], it has been possible to estimate the attenuation coefficient of yeast powder in a capillary.
Table 9.1: Anomalous scattering coefficients & absorption of the atomic composition CH1.8O0.5N0.2 at a density of 1.09 g/cm3 for an X-ray beam at 12.8 keV
Element ∅ Comp. f’ f” µ [barn]
C 1.0 0.007 0.003 17.64
H 1.8 0.000 0.000 0.00
O 0.5 0.021 0.012 32.57
N 0.2 0.013 0.007 7.15
The calculation considered a yeast-specific average atomic composition of CH1.8O0.5N0.2 [67] and average mass density of about 1.09g/cm3 [8]. If a high energy beam at 12.8 keV (0.97 Å) is assumed, an approximate attenuation coefficient of 1.53 cm−1 is obtained. Assuming the usage of largeMiTeGen MicroRTT M tubes with 2 mm diameter, a beam transmission of 73.67% is re-trieved. For the considered elements different anomalous scattering coefficients were calculated, which are listed in table 9.1. The variation ofµwith the beam energy is shown in an additional plot in figure A.2.
Obviously the attenuation length 1/µ approximates to 6.5 mm to reach a trans-mission of1/e(≈37%). Thus for the investigated in vivo sample, an increased sample thickness could still be beneficial for the detection ofDebye-Scherrer rings. On the contrary samples will tend to reabsorb X-rays at low 2Θ angles and effectively reduce the visibility of Debye-Scherrer diffraction. Capillar-ies with increased diameter were not conveniently available for measurements and hence the 2 mm diameter can be considered as the best achievable pa-rameter for these studies. Fig. 9.1-A shows an exemplary powder diffraction pattern recorded from a cell pellet composed of wildtype yeast cells 24 hrs after
WT - 24 hrs
2500 2400 2300 2200 2100 2000 1900 1800
1800 2000 2200 2400
Px 0
500 1000 1500 2000 WT - 24 hrs
2500 2400 2300 2200 2100 2000 1900 1800
1800 2000 2200 2400
Px 0
500 1000 1500 2000
0 500 1000 1500 2000
Int. PD Pattern In Cellulo AOX - WT 24 hrs
Intensity [a.u.]
−50 0 50 100 150 200 250 300
2-theta [°]
0,4 0,6 0,8 1 1,2 1,4
2
A B
1 2
3 4
5
6 7
Figure 9.1: (A)2D powder diffraction pattern and the(B)corresponding post-processed 1D pattern from wildtype H. polymorpha yeast cells with inducded AOX crystal formation after 24hrs of growth; Data was obtained according to sec. 4.1 with setup parameters listed in table 9.2, exposure time: 1 s
IV
PAOX induction (P14, DESY). A detailed description of sample production is given in section 6.2. Setup-specific parameters for data collection are listed in table 9.2. Fig. 9.1-B shows an azimuthal sum of the data. The data has been additionally processed in terms of a rolling ball baseline subtraction (see sec.
4.1).
Table 9.2: Setup Parameters for Powder Diffraction Experiments at beamline P14
Parameter Value
Photon Energy 12.8 keV (0.97Å)
Total Beam Flux 1.2·1012ph·s−1
Detector Distance 2000 mm
Beamstop Distance 30 mm
Oscillation Range 90°
Slit Size 150µm
Capillary Diam. 2 mm
It is an apparent feature of methanol-induced wildtype yeast cells that smooth Debye-Scherrer rings appear at low resolution of about 160-50 Å, corre-sponding to 2Θ angles of 0.3°to 1.2°. These rings appear due to the presence of nano-sized alcohol oxidase (AOX) crystals that are enclosed in peroxisomes (see sec. 2.2). Their appearance is related to the extremely increased intensity contribution of the Lorentz factor at low diffraction angles, that follows the relation1/(sin(2Θ)sin(Θ)[19, 26]. The smoothness of the rings indicate a perfectly random orientation of specimen, as it can be expected forin cellulo crystals.
Since the diffracted signal on the detector obeys Poisson statistics and the re-lated SNR increases only withN/√N(N=photon count), an increase of intensity (or likewise a longer exposure time) will not be sufficient to visualize atomic res-olution diffraction in this setup. Still, since only extremely low resres-olution rings are visible, the repetition of a powder experiment with an increased exposure time might still be realistic to visualize Debye-Scherrer rings at slightly higher resolution. A prerequisite is of course, that the increased exposure time does not exhaust the dynamic range of the detector. Radiation damage will most likely not be a cause of signal deterioration at higher exposure times since only extremely low 2Θ angles are being investigated. AOX crystal-containing wildtype cells were subjected to a second powder diffraction experiment at an increased exposure time of 15 s. All other measurement-related parameters were kept fixed. Instead, 10 consecutive measurements were conducted on
First Derivative of 1D Pattern (0.3°-1.2°)
Intensity [a.u.]
−6×105
−4×105
−2×105 0 2×105 4×105 6×105
2-theta [°]
0,4 0,6 0,8 1 1,2
MEAN STDEV
Debye-Scherrer Rings 1-7
A B
Mean of Data StDev of Data
First Derivative of 1D Pattern (1.2°-2,5°)
Intensity [a.u.]
−6×103
−4×103
−2×103 0 2×103 4×103 6×103
2-theta [°]
1,5 2 2,5
Debye-Scherrer Rings 8-23
Figure 9.2: First derivative of a 1D powder diffraction pattern for2Θangles between(A) 0.3°to 1.2°and(B)1.2°to 2.5°; Setup parameters are listed in table 9.2, exposure time: 15 s
different areas of the cell pellet. Data was processed in terms of azimuthal inte-gration and background subtraction. Afterwards 2Θ-dependent first derivative mean and standard deviation were calculated to simplify the search for high resolution peaks.
Fig. 9.2-A/B show the results of a manual analysis of 2Θ ranges from 0.3°to 1.2°, showing the already known diffraction peaks, and from 1.2°to 2.5°, re-vealing additional 17Debye-Scherrer peak positions (blue dashed lines). A peak position is identified by a downward-going zero crossing. The red curve represents the corresponding standard deviation and can be used to estimate false zero-crossing positions. In an automated search a simple threshold would be used.
It is obvious from a comparison with control data (H.p.-12DAC4 cells, fig.
A.3), that the newly identified peak positions do not arise from artifacts during processing and indeed must be related to crystal diffraction. The peak positions are listed in table 9.3. Peak intensities have been determined from gaussian fits of the corresponding peak areas. The extraction of peak intensities was increasingly problematic for higher 2Θ angles. Thus data has been processed three times with the first 7, 12, and 23 peaks by using theMonte Carloindexing softwareMcMaille[98]. Results were only obtained for calculations considering 7 and 12 peaks, respectively. For both calculations a body(I)-centered cubic lattice with equilateral unit cell dimensions of ∼228 Å is given as the most plausible solution. However a consideration of more than 12 peaks did not yield any solution. hkl indices are assigned according to the systematic absence of odd h+k+l reflections in the presumed Bravais lattice. Intriguingly some even reflections like (2 1 1), (2 2 0), (2 2 2), (3 3 2) and (4 4 0) are missing as well.
Their absence could be indicative for anisotropic disorder in the crystals (cp.
fig. A.4). A further increase of the exposure time beyond 15 s did not reveal any new features of the diffraction pattern (data not shown). Furthermore it has been tried to increase the detectable diffraction signal by different growth conditions, to expedite crystal growth. Unfortunately these efforts did not yield any better results.
Therefore it seems plausible to suspect, that AOX crystals in yeast cells are imperfect crystals and show only very weak high resolution diffraction, as it
Table 9.3: 2Θangles, d-spacing and millerian indices for AOX in cellulo crystal reflections in a 1D powder patter from H. polymorpha wildtype cells, indexed as a body(I)-centered cubic lattice
Nb. 2Θ [°] d-Spacing [Å] hkl Refl.
1 0.35 163 (1 1 0)
2 0.49 115 (2 0 0)
3 0.77 73 (3 1 0)
4 0.91 61 (3 2 1)
5 0.97 57 (4 0 0)
6 1.03 54 (3 3 0) / (4 1 1)
7 1.09 51 (4 2 0)
8 1.19 47 (4 2 2)
9 1.24 45 (4 3 1) / (5 1 0)
10 1.33 42 (5 2 1)
11 1.42 40 (4 3 3) / (5 3 0)
12 1.46 38 (4 4 2) / (6 0 0)
has already been shown by Van der Kleiet al.[33] forin vitro crystals of AOX.
This hypothesis is in fact in agreement with the biological functioning of the AOX crystal, as being a solid-state catalyst crystal. Consequently diffraction experiments under optimized conditions at a free-electron laser X-ray source might provide a solution to obtain higher resolution data (see ch. 10).
9.1.2 Estimation of the Minimal Detectable Volume Fraction