ONLINE SUPPLEMENTARY MATERIAL
Preferred area difference, a0
To see the equivalence between the area difference, A0, and the spontaneous curvature, C0, we need an
expression that relates the difference in area between the inner and outer bilayers, A, and the average
(over the surface whose area is A) of the mean curvature, H. The average of a quantity f(x,y) that varies
over a surface S = (x,y) is defined by
f 
1
1
f  dA 
f ( x, y )  dA( x, y )

A Surface
A ( x , y )S
It then follows that
A  2D H A
which can be easily verified in the case of a sphere. We can now rewrite Equation 1 (ignoring the EMS
term) as
b
2

(2 H  C0 ) 2 dA 
Surface

2 AD
2
 2 b H 2 A  2 b H C0 A 
 2 b H 2 A  2 b H C0 A 
 2 b H 2 A  2 H
2
 A  A0 

2 AD
2
 A
2
 4D

2
2
2
 2A  A0   constant
H
2

A2  4 D H A  A0  constant
2 AD
2 A  A0 D bC0 
A

 constant
D  A
 
where the constant depends on A0 and C0 (and other fixed parameters such as D and the stiffnesses, and
the surface area, A, which is always assumed to be constant), but does not depend on the shape of the
surface. The term in the square bracket is the normalized preferred area difference, a0, and includes
contributions from both the asymmetry of the leaflet areas (A0) and the geometry of the lipids
themselves (C0) [34].
S1Supplementary Figure
Supplementary Figure S1. Analysis of 3D RBC images.
A, L-curve for estimation of the RBC surface from one image stack. The functional G = 2+ Eb is
minimized for a series of regularization parameter values (. 2 is the sum of squares of the differences
between the trial RBC surface convolved with the point spread function of the microscope and the images
from the stacks. Eb is the membrane bending energy of the trial surface (Equation 1, left-hand term). The
parameter  smoothes the surface and prevents “overfitting”. The L-curve method provides an objective
value of  as the one corresponding to the highest curvature of the L-curve. This value, 0, corresponding
to the elbow in the curve, has both low 2 and low bending energy. The L-curve shown was calculated for
a discocyte that was imaged at [NaCl] = 154 mM with its long axis along the optical axis. Inset 1 shows
one frame at 0 (blue = raw data, red = fitted shape contour). Inset 2 shows the same frame after
minimizing G at 0. B, Shape coefficient amplitudes that correspond to an imaged discocyte (inset in
C) (errors are SD). C, A series of theoretical minimum energy shapes calculated under constraints of
fixed area and volume (from the smoothed surfaces) for a range of a0. The a0 value that corresponds to
the theoretical shape that matches the experimental data most closely (lowest mean-squared difference1
MSD 
1
4

L
  (C
L0 K  L
K
1,L
C2,K L )2 of shape coefficients of two shapes 1 and 2) is assigned to the cell.
Arrows point to the theoretically calculated shapes. D, Consistency check of the image analysis
procedure. We imaged the same RBC twice—before and after changing the morphology by changing the
salt concentration. For the top cell, the areas and volumes were (errors in SEM) 144.5  2.7 m2, 85.5 
1.6 m3 and 146.0  2. m2, 102.2  2.0 m3 in 250 mM NaCl (left) and 125 mM Na Cl (right)
respectively. For the bottom cell, the areas and volumes were 132.0  3.1 m2, 95.3  2.3 m3 and
132.2  3.5 m2, 111.5  1.9 m3 in 125 mM NaCl (left) and 55 mM NaCl (right) respectively. The
area—as expected—remained the same within error and values for V reflect the reaction to the osmolarity
change.
Supplementary Figure S2
Supplementary Figure S2. Assignment of a0 for an elliptocyte.
Same as Supplementary Figure 1C, except that here we use a model that does not take the MS into
account. Inset: two views of the elliptocyte for which the fitting is done. As in Figure 4C, the calculated
minimum energy shape had a0 = 0.21%.
Supplementary Figure S3
Supplementary Figure S3. The effect of urea when added before Triton X-100.
Left panel: an elliptocyte obtained after 2 hours of incubation at 1.25M urea concentration, 90 mM NaCl
at 37 °C. The cell was then incubated in physiological buffer for 2 hours 45 minutes at room temperature
before phase contrast imaging.
Middle panel: following treatment with Triton X-100, rhodamine-
phalloidin labeling of actin reveals that the MS is disrupted compared to a control cell not exposed to urea
(right panel).
Supplementary Figure S4
Supplementary Figure S4. Formation of elliptocytes by treating healthy discocytes with urea. (a)
Phase contrast image of freshly prepared discocytes in physiological buffer (154 mM NaCl), (b and c)
Phase contrast images after treatment with a solution of 1.1 M urea, 65.5 mM NaCl and 12.8 mM sucrose.
Bar: 10 m.
Reference
1. Gerig, G., M. Styner, D. Jones, D.R. Weinberger, J.A. Lieberman (2001) Shape analysis of brain
ventricles using SPHARM. in IEEE Workshop on Mathematical Methods in Biomedical Image Analysis.