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Supporting Information

High Intrinsic Mechanical Flexibility of Mouse Prion Nanofibrils
Revealed by Measurements of Axial and Radial Young’s Moduli
Guillaume Lamour, Calvin K. Yip, Hongbin Li and Jörg Gsponer

Contents:

Supplementary Methods
Protein expression and purification
Fourier transform infrared spectroscopy
Statistical analysis of fibril shape fluctuations
AM-FM AFM
Tables S1–S4
Figures S1–S10
Notes S1–S5
Supplementary References

S1

Lamour et al.

Supporting Information

Supplementary Methods

Protein expression and purification
The gene for MoPrP23-231 was purchased from DNA2.0. All reagents were purchased from Sigma and
Fisher except for the nickel-NTA resin, which was purchased from Qiagen. Mutagenesis was performed
using standard protocols from the QuikChange Site-Directed Mutagenesis Kit (Stratagene). All genes
(MoPrP23-231, MoPrP(23-231)-P102L, MoPrP(23-231)-S170N-N174T and MoPrP(23-231)-L108FT189V) were inserted into a pET15b(+) vector between XhoI and EcoRI restriction sites. Expression
constructs were verified by DNA sequencing. Recombinant proteins were expressed in Eschericia coli
BL21(DE3) host cells in LB medium supplemented with 100 μg/ml ampicillin. The cultures were grown
at 37oC until an OD600 = 0.8 was reached and then induced with 1.0 mM IPTG for 18 hrs at 37 oC. After
post-induction incubation, the cells were harvested by centrifugation for 20 min at 9060 × g (4oC). All
prion proteins were isolated from the inclusion bodies and purified via refolding on the Ni-NTA column.
The cell pellets from 1 L of the LB medium were re-suspended in 25 mL of the lysis buffer (50 mM Tris,
100 mM NaCl, 5 mM EDTA, 0.1% NaN3, pH 8.0) and lysed by sonication (using Fisher Scientific
Ultrasonic Dismembrator Model 500 with microtip probe for 6 × 15 sec pulses at 40% power) on ice with
addition of PMSF and Triton X-100 to final concentrations of 0.1 mM and 0.5% respectively. The
mixture was incubated on ice for 15 min followed by centrifugation at 17400 × g for 20 min (4 oC). The
supernatant was removed and inclusion bodies were cleaned by two washing steps with lysis buffer
containing 0.5% Triton X-100. Triton X-100 was removed by washing the pellet twice with lysis buffer
only. Inclusion bodies were centrifuged at 17400 × g for 20 min (4 oC) after every wash and supernatant
was removed. Clean protein pellets were resuspended in 30 mL of the solubilisation buffer (10 mM Tris,
100 mM sodium phosphate, 10 mM reduced glutathione, 8 M Urea, pH 8.0) and left for overnight
incubation at room temperature followed by centrifugation at 48400 × g for 1 hr at 25oC. The Ni-NTA
resin (40 mL bed volume) was pre-equilibrated with solubilisation buffer and mixed with clarified
supernatant. The mixture was incubated (with slow rotation) at room temperature for 10 min and packed
into the column. Unbound proteins were removed by column wash with 5 bed volumes of the
solubilisation buffer. Prion protein was refolded on a column by decreasing Urea concentration from 8 M
to 0 M. Linear gradient of solubilisation buffer and refolding buffer (10 mM Tris, 100 mM sodium
phosphate, pH 8.0) was applied to the column. Non-specifically bound proteins were washed out of the
column with 5 bed volumes of the washing buffer (10 mM Tris, 100 mM sodium phosphate, 50 mM
Imidazole, pH 8.0). Prion protein was eluted from the column with elution buffer (10 mM Tris, 100 mM
sodium phosphate, 500 mM Imidazole, pH 5.8). Fractions containing protein were identified by SDSPAGE gel and mixed. His-tag was not removed from the prion protein. Protein solutions were then
dialyzed to bring imidazole concentration down to 1 μM (at least 5 buffer changes were performed, each
dialysing step lasted at least 4 hrs). The protein concentration was determined using an extinction
coefficient at 280 nm (MoPrP23-231 extinction coefficient is 56650 M-1cm-1). The protein solution was
then lyophilized and protein powder kept at -20˚C until further use.

S2

Lamour et al.

Supporting Information

Fourier transform infrared spectroscopy
Fourier transform infrared spectroscopy (FTIR) spectra of several samples (see Figure S1) were measured
using a Perkin-Elmer Frontier spectrometer. FTIR spectra were background corrected by subtraction of a
spectrum of the blank buffer, and recorded by integrating 400 scans with a resolution of 2 cm -1. The
deconvolution of the amide I’ band between 1600 and 1700 cm-1 was performed by applying a smoothing
filter on the raw data and by calculating the second derivative of the spectra in PeakFit 4.11 software
(Systat Software Inc). Gaussian peaks were added at local minima of the second derivative spectra.
Secondary structure assignments relatively to peak wavenumbers 1,2 are indicated in Table S2.

Statistical analysis of fibril shape fluctuations
AFM heightmaps were first imported into Matlab (Mathworks). We then used custom-designed
Matlab scripts to fit the contour of fibril traces to a parametric spline. 3,4 For each fibril, the least-square
fit was adjusted so that the interval between two spline knots corresponded to approximately 30 ± 10 nm
(see Table S4); this value is slightly higher than the lateral resolution of AFM images. Then, we
calculated the deviations  from the fibril to the midpoint of a secant of length L joining two knots of the
spline for each combination of knots over the fibril contour length. For quite rigid fibrils where the
analyzable length is lower than the persistence length of the fibril, the following equation (derived from
the worm-like chain model5 for a polymer chain that is free to move in 2 dimensions) was used to derive
the persistence length PL:
 δ2 2D 

L3
.
48PL

(Eq. S1)

In Figure S6b and in Figure S7c: middle graph, L is assimilated to the distance along the fibril contour,
since for
< PL the difference between secant length L and contour length
is negligible. For more
flexible polymers (PL< 500 nm), we monitored the decay of tangent-tangent correlations6:

 cosθ 2D  e



2PL

,

(Eq. S2)

where θ is the angle between the tangent vectors to the chain at two points separated by a distance
along the fibril contour. In addition, this expression can be reformulated6 to express the mean square of
the end-to-end distance R as a function of PL and :
 2P 

 R 2 2D  4PL 1  L 1  e 2PL






 .



(Eq. S3)

It has to be stressed that this latter measure provided better fits to the experimental data and could be
applied for longer
values than both models described by Equations 1 and 2. In practice, we used
Equations 2 and 3 for fibrils with PL < 0.5 µm, Equations 1 and 3 for fibrils with P L > 0.5 µm. Under
these conditions, different measures usually returned similar values of the persistence length. In the rare
occurrences they did not (which is most probably related to heterogeneities of P L in fibril population), we
S3

Lamour et al.

Supporting Information

systematically chose the measure that returned the higher value of P L, provided data fit looked sound
(coefficient of determination Cd > 0.9; the Cd value is a mean of the ten Cd generated in each resampling
procedure, see next paragraph). Matlab scripts using Equations 1-3 to derive the persistence length of
the fibrils were tested on in silico polymers with known persistence length that were generated by MonteCarlo simulations.6 We found very good correlation between predicted and measured persistence lengths
over wide ranges of measurements (0.05 ≤ PL ≤ 5200 μm).
Uncertainties in the derived persistence lengths were determined via random resampling: for each set of
fibrils belonging to a particular sample, half the total number of fibrils was randomly selected.  δ2  ,
 cosθ  , or  R 2  values were binned at regular length intervals, as in Figures S6 and S7. Data were
then fitted according to the models described previously. The whole operation is repeated 10 times, and
the mean of the 10 values of the persistence length returned at each operation is the persistence length of
the fibril sample. The standard deviation on the 10 values of P L returned is the uncertainty on the value of
PL (related to vertical error bars in Figure 2).
As already noted by Knowles et al.,3 it is interesting that, due to the equipartition theorem, corresponding
equations for fibrils equilibrating in 3 dimensions would result in a fit returning a persistence length value
that is exactly two times of what it is in 2D. In our study, we clearly could not take the risk of
underestimating the persistence length, since it would shift axial moduli to lower values. In addition, we
clearly observed that fibrils adsorbed on mica did not fully equilibrate (contrary to fibrils adsorbed on
glass, see Figures S6 and S7). Therefore, although we used the 2D model for fitting the data of all our
samples, in the case of fibrils adsorbed on mica we applied a correction factor of 1.5 to the calculated
persistence length, which corresponds to calculating the midpoint fluctuations between 2D and 3D, as in
Smith et al.4 The fractional dimension is then considered to be 2.5 ± 0.5, and this experimental
uncertainty is propagated to the final error estimate. This method is found to be well accurate when
comparing P L calculated on glass and the corrected P L on mica (Figure S6). For W3A, W3B and FV2A
samples, we used the uncorrected 2D model since we had measurements available on glass. The
uncorrected 2D model was also used for FV1A sample, though adsorbed on mica, because its PL and
contour length are very close to that of FV2A, and at such low range of both contour length and P L values
(see Tables S2 and S3 and Figure S6) the fibrils seem to undergo full equilibration in 2D.

Calculations of second moment of area and of the elastic modulus E
Fibril heights (h) and widths (w) were used to calculate the second moment of area. Fibril heights were
measured in cross-section analyzes by semi-automated scripts written under IgorPro. Each fibril section
was fitted to a Gaussian, allowing baseline points corresponding to background heights to be fitted
correctly. Fibril widths were estimated by manual measurements performed with the ImageJ software
(Wayne Rasband, NIH). The second moment area (I) was calculated using three distinct models of fibril
structure, corresponding to distinct geometries of the cross-sectional area (in parentheses): “Helical”
(circular; IC), ellipsoidal (ellipsoidal; IE), and tape/ribbon-like (rectangular; IR), respectively. The
following expressions were used to calculate I as well as I– and I+ for each of the three models:

S4

Lamour et al.

Supporting Information

IC 

π.h 4
π.( h  h)4
π.( h  h) 4
; IC  
; IC+ 
64
64.ζ
64

(Eq. S4)

IE 

π.w.h 3
π.( w  w).( h  h)3
π.( w  w).( h  h)3
; IE  
; IE+ 
64
64.ζ
64

(Eq. S5)

IR 

w.h 3
( w  w).( h  h)3
( w  w).( h  h)3
; IR  
; IR + 
12
12.ζ
12

(Eq. S6)

In these equations, ζ is a parameter calculated from the parallel axis theorem and which is related to the
effect (on I) of offset 1  rn from the center of the filaments, where rn is the radius of one of the n tightly
packed protofilaments inside a unit circle (equivalent to fibril cross-sectional perimeter). ζ was taken
equal to 2.66, as in Knowles et al.,3 who determined that this number could be applied to the
experimentally known range of 6 protofilaments (at maximum) in the mature fibril, which also
corresponds to what we observed (Figures S2 and S3).
Once the persistence length PL and the second moment of area I are known, the elastic modulus E that
reflects the strength of intermolecular forces along the fibril axis (i.e. the packing of β-strands) can be
easily obtained using E = PL .k B .T/I , where T is the room temperature (taken equal to 298.15 K) and kB
the Boltzmann constant.

AM-FM AFM
Samples with known elastic moduli were used to calibrate the frequency shifts of the second resonance.
The main test sample combines polystyrene and scattered islands of low-density polyethylene (PS-LDPE,
Bruker) with respective elastic moduli of ~2.2 and 0.2 GPa. We also used a PS film (Bruker) with
nominal modulus of E = 2.7 GPa, as well as Ultra-High Molecular Weight PolyEthylene (UHMWPE, E =
1.15 GPa; test specimen provided as a courtesy by ASTM International Committee E37 on Thermal
Measurements, West Conshohocken, PA.) to further test the calibration.
In one experiment, we estimated the spring constants of the cantilevers. We used hard surface such as
clean glass and recorded one single force peak with trigger point set at 1 nN. The slope of the forcedistance curve in the vicinity of the surface (related to its modulus) was used to determine the optical
lever sensitivity. After capturing thermal data, the software (IgorPro, WaveMetrics, with macros)
returned the value of k1 = 28.83 N/m for AC160TS and k1 = 1.76 N/m for AC240TS. Using k2 =
k1.(f2/f1)2, we calculated a value of k2 = 911 N/m for AC160TS, and of k2 = 483 N/m for AC240TS.

S5

Lamour et al.

Supporting Information

Table S1. Summary of fibril samples.

Prion
construct

§

Buffer
used

Monomer
concentration

Rotation
speed (rpm)

Fibrillation
time

Seeds used

Abbreviated
sample name

W

#1

1 mg/mL

150

62h

No

W1A

W

#1

1 mg/mL

225

24h

No

W1B

W

#1

1 mg/mL

225

24h

Yes

W1C

W

#3

1 mg/mL

140

120h

No

W3A

W

#3

0.5 mg/mL

140

120h

No

W3B

W

#3

1 mg/mL

225

24h

Yes

W3C

L

#1

1 mg/mL

150

62h

No

L1A

L

#1

0.25 mg/mL

125

24h

Yes

L1B

NT

#1

1 mg/mL

150

62h

No

NT1A

NT

#1

1 mg/mL

225

48h

No

NT1B

NT

#3

1 mg/mL

150

62h

No

NT3A

NT

#3

0.25 mg/mL

125

48h

Yes

NT3B

FV

#1

1 mg/mL

125

40h

No

FV1A

FV

#2

1 mg/mL

125

67h

No

FV2A

FV

#3

1 mg/mL

125

40h

No

FV3A

FV

#3

1 mg/mL

225

24h

No

FV3B

*



All constructs (including wild-types and mutants) are based on the mouse prion (MoPrP) 23-231
sequence (so-called “full-length”, as opposed to the “truncated” MoPrP 89-231).
The “W” letter refers to the wild-type construct. Abbreviated letters “L”, “NT”, and “FV” refer to the mutant
constructs. P102L (L) is located in the intrinsically unfolded region of MoPrP 23-231, whereas the
mutations S170N and N174T (NT) are located in its folded region. The L108F-T189V construct (FV)
contains a mutation in both the folded and intrinsically unfolded regions of MoPrP.
*

§

7

Buffer preparations are as follows: #1 is GdnHCl 1M, Urea 4M, NaCl 0.4M, NaOAc 50mM pH 5.0, #2 is
8
GdnHCl 2M, Urea 3M, NaCl 0.4M, NaOAc 50mM pH 5.0, and #3 is GdnHCl 2M, MES 50mM pH 6.0.


The letters and numbers refer to a type of sample described by a specific set of experimental conditions
used to make the fibrils (e.g. “W1B” for “Wild-type – Buffer #1 – B type”).

S6

Lamour et al.

Supporting Information

Table S2. Peak attribution and distribution of secondary structure content determined from fitting
and deconvoluting the FTIR amide I’ band.

Secondary structure (%)
Insulin

W1A

W1C

L1A

L1B

NT1A

NT1B

FV1A

β-sheet 1

25

15

20

14

21

17

16

β-sheet 2

30

18

19

20

21

19

18

β-sheet total

55

33

39

34

42

38

34

26

Random coil

11

19

19

19

14

19

21

26

α-helix

11

21

21

19

32

17

19

25

Turns

23

27

20

27

13

23

26

23

*

26

Wavenumbers (cm-1)
β-sheet 1

β -sheet 2

Random coil

α -helix

Turn 1

Turn 2

Insulin

1620

1634

1644

1652

1661

1671

W1A

1622

1634

1645

1656

1668

1680

W1C

1626

1637

1648

1660

1669

1678

L1A

1621

1633

1644

1654

1665

1676

L1B

1622

1636

1646

1658

1670

1677

NT1A

1618

1632

1644

1655

1665

1678

NT1B

1623

1634

1645

1656

1666

1678

1645

1657

1671

1680

FV1A

*

1628

*

The FTIR spectra of FV1A sample shows only one clear peak at around 1628 cm -1, instead of 2 peaks at
-1
around 1622 and 1634 cm as in every other sample (see Figure S1).

S7

Lamour et al.

Supporting Information

Table S3. Morphological and mechanical parameters used in the determination of the axial elastic
modulus for each sample.

*

Sample

Persistence
Length (µm)

*

Height, nm

Width, nm

§

With “hair” (N)

Without “hair”

With “hair” ( N/Nfib)

Without “hair”

W1A

1.3 ± 1.2

5.2 ± 1.3 (212)

4.4 ± 1.3

19.1 ± 4.8 (225/14)

18.3 ± 4.8

W1B

1.6 ± 0.7

4.4 ± 1.4 (415)

3.6 ± 1.4

20.4 ± 4.0 (151/17)

19.6 ± 4.0

W3A

0.6 ± 0.2

3.5 ± 0.5 (295)

2.7 ± 0.5 (¶)

19.5 ± 2.3 (138/30)

18.7 ± 2.3

W3B

1.1 ± 0.3

5.0 ± 0.7 (217)

4.2 ± 0.7

14.2 ± 2.6 (219/38)

13.4 ± 2.6

W3C

5.2 ± 2.4

4.6 ± 0.4 (512)

3.8 ± 0.4

23.4 ± 4.8 (199/14)

22.6 ± 4.8

L1A

3.7 ± 2.2

4.6 ± 0.6 (140)

3.6 ± 0.9 (¶)

12.3 ± 3.1 (268/15)

11.5 ± 3.1

L1B

2.9 ± 2.3

4.7 ± 1.1 (196)

3.9 ± 1.1

18.2 ± 3.6 (199/3)

17.4 ± 3.6

NT1A

10.6 ± 5.3

4.2 ± 1.4 (92)

3.4 ± 1.4

17.2 ± 6.4 (267/27)

16.4 ± 6.4

NT1B

11.4 ± 8.6

5.4 ± 0.7 (214)

4.6 ± 0.7

10.9 ± 2.2 (243/21)

10.1 ± 2.2

NT3A

1.1 ± 0.6

4.4 ± 0.8 (128)

3.6 ± 0.8

20.4 ± 4.6 (197/33)

19.6 ± 4.6

NT3B

0.8 ± 0.4

3.1 ± 0.3 (324)

2.3 ± 0.3

20.4 ± 5.7 (176/14)

19.6 ± 5.7

FV1A

0.07 ± 0.02

2.5 ± 0.6 (87)

1.6 ± 0.3 (¶)

7.1 ± 1.5 (174/9)

6.4 ± 1.5

FV2A

0.07 ± 0.01

2.6 ± 0.4 (178)

1.9 ± 0.4

6.2 ± 1.0 (192/53)

5.5 ± 1.0

FV3A

0.6 ± 0.2

3.6 ± 0.5 (243)

1.7 ± 0.3 (¶)

19.0 ± 1.8 (353/37)

17.9 ± 1.8

FV3B

0.11 ± 0.05

3.1 ± 0.4 (210)

2.4 ± 0.4

6.0 ± 1.0 (145/16)

5.3 ± 1.0

*

In cases where heights or widths distributions gave rise to multiple peaks: all bins were nevertheless
fitted to one single Gaussian whenever it was possible, or only the most probable distribution per sample
is displayed here and taken into account in the calculations of the second moments of area and of elastic
moduli.
§

N/Nfib indicates the total number of measurements made on the total number of fibrils.



Samples for which we have direct measurements of heights after treatment by proteinase K. For all
other samples we subtracted 0.7 nm from non-treated single filaments heights and widths (FV), and 0.8
nm from non-treated mature fibrils heights and widths (W, NT, and L).

S8

Lamour et al.

Supporting Information

Table S4. Details of the thermal fluctuations analysis.

*

*

Sample

Substrate

Medium

N fibrils
(∑contour, μm)

Measured fibril length,
μm (Max. value, μm)

§

W1A

mica

air

45 (42.0)

0.9 ± 0.5 (1.9)

29 ± 5

30,981

W1B

mica

air

253 (241.7)

1.0 ± 0.5 (2.8)

26 ± 5

254,341

W3A

mica

air

91 (212.7)

2.3 ± 1.9 (8.7)

27 ± 7

656,641

W3A

glass

air

83 (221.4)

2.7 ± 2.1 (9.0)

29 ± 5

593,813

W3A

mica

liquid

55 (185.2)

3.4 ± 2.2 (10.0)

35 ± 6

351,308

W3A

glass

liquid

66 (181.9)

2.8 ± 1.7 (9.6)

42 ± 12

198,983

W3B

mica

air

160 (100.9)

0.4 ± 0.3 (2.2)

30 ± 5

49,884

W3B

glass

air

136 (121.9)

0.5 ± 0.4 (5.2)

25 ± 4

134,957

W3C

mica

air

231 (166.8)

0.7 ± 0.4 (2.4)

41 ± 17

63,917

L1A

mica

air

157 (92.7)

0.6 ± 0.3 (1.7)

36 ± 8

27,968

L1B

mica

air

71 (50.7)

0.7 ± 0.5 (2.9)

26 ± 5

38,411

NT1A

mica

air

44 (43.0)

1.0 ± 0.7 (3.4)

26 ± 9

49,835

NT1B

mica

air

132 (41.1)

0.2 ± 0.1 (0.9)

35 ± 8

6,902

NT3A

mica

air

92 (74.3)

0.8 ± 0.5 (3.1)

35 ± 6

34,439

NT3B

mica

air

83 (99.5)

1.0 ± 0.5 (3.6)

26 ± 5

139,866

FV1A

mica

air

98 (17.3)

0.2 ± 0.1 (0.3)

20 ± 6

4,802

FV2A

mica

air

115 (34.6)

0.3 ± 0.1 (1.1)

26 ± 8

9,407

FV2A

glass

air

125 (31.6)

0.2 ± 0.1 (0.7)

24 ± 7

9,470

FV3A

mica

air

43 (148.2)

3.4 ± 2.6 (13.1)

27 ± 10

564,409

FV3B

mica

air

198 (31.4)

0.1 ± 0.1 (0.4)

15 ± 4

13,222

Knots
intervals, nm



Data
points

“∑contour” means the sum of the contour length of all of the N fibrils analysed per sample.

§

The average distance between spline knots is designated by “Knots interval”.



“Data points” corresponds to the total number of points available for statistical analysis, i.e. those that
were binned and fitted according to the equations of the worm-like chain model for semi-flexible polymers
undergoing thermally-driven fluctuations in shape (Equations S1–S3).

S9


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