Supplementary Information the Conversion of Monomers to Fibrils At

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Supplementary Information

0 rpm 50 rpm 100 rpm 200 rpm 300 rpm 400 rpm 500 rpm 1000 rpm

Supplementary Figure 1: Samples stirred at rates shown above at 70°C for 24 hours. Samples were

left for 24 hours before placing between cross polarisers. a, Insulin (pH2, 2mM) shows permanent

birefringence at stirring rates of 50 to 400 rpm, above this no permanent birefringence is observed.

b, HEWL (pH2, 2 mM) shows strong permanent birefringence from 50 rpm to 300 rpm, which

decreases at higher stir rates.

The conversion of monomers to fibrils at each stirring rate for the three proteins could not

be determined accurately due to the high random error associated with weighing the

unaggregated protein remaining after filtering and centrifuging all solutions with a 30 kDa

filter. From the technique above the measured conversion factor was between 50% to 80%

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in no particular order for samples and therefore the minimum conversion factor of 50%

(with error bars included to show the maximum possible volume fraction if the maximum

conversion factor was used i.e. 80%) was used for estimating the prediction of anisotropic

material using the Onsager theory.

Apect ratio of fibrils from TEM images were calculated by counting the maximum number

of pixels in fibril diameters and scaling by the pixel size (each pixel was approximately 5

nm, therefore only widths equal to multiple number of pixels can be given, i.e. 5, 10, 15

nm). Analysing the intensity profile perpendicular to the fibril axis would improve the

measurement accuracy. However, due to the unquantified systematic errors in the focus and

staining when using TEM, the pixel counting method is appropriate. Reducing the random

measurement error will not give any more information.

The entanglement of fibrils in all proteins at 200 rpm meant that measuring the full contour

length of individual fibrils was not possible. Therefore, at 200 rpm an estimate of the lower

limit contour length will be used to place a lower limit on the aspect ratio.

At 500 rpm, the contour lengths of 50 fibrils (taken as a crude measure of the persistence

length) were measured and averaged using the same method as before (counting and

scaling pixels). The standard error in the mean contour length at 500 rpm was used where

the number of fibrils, n =50. Due to upper diameter limits and lower contour length limits,

the minimum aspect ratio of fibrils for each protein at 200 or 500 rpm can be predicted.

This will lead to qualitative results which will allow trends to be analysed.

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The volume fraction of monomers were calculated as follows. Under acidic conditions and

elevated temperatures BLG fibrils have a line density of (i.e. monomers per unit length) 0.28nm-1

[1]. The volume of a monomer within a fibril is then:

π ⋅ 22 = 45nm3 (Equation 1) 0.28

where 2 nm is the radius of a fibril [2]. To calculate the volume fraction, the number density of

molecules in any BLG sample is:

2mM = 1.204×1021 molecules/L = 1.204×10−3 molecules/nm3

The volume fraction is then the volume of a monomer in a fibril, multiplied by the

molecular number density given above in a 2mM sample, which is

(1.204×10−3 )⋅ 45 ~ 0.05

(assuming 100% conversion). As mentioned previously, the minimum conversion factor of

monomer to fibrils is used, 50 %, giving a volume fraction of 0.025.

Using the aspect ratio calculated for BLG and the volume fraction calculated above, figure

2e indicates where samples stirred at 200 rpm (with liquid crystalliny) and 500 rpm (no liquid

crystallinity) lie on the Onsager phase diagram. Where the area between the lines given by:

Electronic Supplementary Material (ESI) for Soft Matter This journal is © The Royal Society of Chemistry 2013

d d v ' = 3.340 , v '' = 4.486 p l p l

is the biphasic region [3]. Anything that lies above vp” is anisotropic and anything below vp’ is

isotropic.

The line density for HEWL is 0.294 nm-1 [2]. As before, using equation 1, the volume of a

monomer in a fibril is 42.74 nm3, multiplying this by the molecular density will give a volume

fraction of 0.0257 at 50 % conversion of monomers to fibrils, which is very similar to the volume

fraction of BLG due to the similar size of monomers.

To calculate the volume fraction for insulin (line density of insulin is at present unknown),

the volume of a free monomer rather than the volume of a monomer within a fibril was calculated

and scaled using the difference in volume of a free monomer and a monomer in a fibril for BLG and

HEWL. For BLG, The estimated volume of a monomer, making the assumption of a spherical

shape, is:

4 π r 3 (Equation 2) 3

= 2.25×10−26 m3

= 22.5nm3

where r is monomer radius 1.75 nm [4]. The volume of a free monomer in BLG is therefore 2x

smaller than a monomer in a fibril which was using equation 1, 45 nm3.

The diameter of a HEWL monomer is 3.4 nm [5, 6], the volume of a free monomer using

equation 2 is 20.6 nm3, which is also approximately 2x smaller than a HEWL monomer in a fibril

which was calculated to be is 42.74 nm3. This may seem counter intuitive that a monomer in a fibril

is larger than a free monomer, however it agrees with the calculations of Aymard et al [1]. Possible

explanations for this phenomenon is that when forming the β-sheet backbone to form fibrils, the

native structure not involved is disrupted and cannot fold compactly. To calculate the volume

fraction, the order of magnitude of the volume of monomer is the most important aspect and hence a

factor of two between a free and fibril monomer will not affect the overall outcome.

For insulin, the volume of a free monomer using equation 2 is 4.2 nm3; scaling this up by a

factor of two which is the relationship between free monomers and monomers in a fibril for both

BLG and HEWL will give a volume of 8.4 nm3. Multiplying this by the molecular density will give

a volume fraction of 0.005 (50 % conversion). It should be noted that insulin is thought to have a

higher conversion rate than BLG when incubated at the same quiescent conditions [7]. However,

the conversion rate in this work varied considerably from 50 to 80 % with the minimum conversion

rate being applied to the Onsager prediction. It is likely in practice that the conversion rate for

insulin is significantly higher than 50 %.

The predicted phase for either HEWL or BLG will not be affected by an increase in aspect ratio

(decrease in diameter). HEWL samples at 200 and 500 rpm and BLG samples at 200 rpm will

still be predicted to be anisotropic with an increase in aspect ratio (decrease in diameter). As

discussed before, in order to affect the prediction of isotropic phase of BLG at 500 rpm i.e.

predict anisotropic phase, the diameter of the fibril would need to be less than 2 nm which was

deemed unlikely [8]. The average contour length of BLG at 500 rpm was calculated by

averaging 50 fibrils and therefore will not change the aspect ratio.

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