ELECTRONIC SUPPLEMENTARY MATERIAL
Effect of residual stresses on the determination of ZP mechanical properties
The ZP membrane surrounding the oocyte is similar to a spherical shell and hence possesses an
intrinsic curvature. For this reason, when the ZP membrane is spread out onto a rigid substrate (i.e.
the glass slide) to carry out AFM nanoindentation experiments as it was done in this study,
differential residual stress may be generated within the membrane. The residual stress field could
lead to incorrect estimations of ZP mechanical properties. In order to check if the material
identification procedure described in this paper is sensitive to the presence of residual stress,
another finite element model was developed.
Figure ESM-1 shows a schematic of the whole oocyte with the ZP membrane surrounding the
cell. Let us assume that the oocyte is a sphere of mean radius R while the ZP is a thin spherical shell
of thickness t. A diametrical section of the cell is represented in Figure ESM-1a. If a portion of ZP
membrane of length L (evaluated in correspondence of the mean radius R) is extracted from the
oocyte, the corresponding angle  can be determined as =L/R. The lengths of the inner and outer
layers of the extracted ZP portion hence are LIN =∙(R t/2) and LOUT =∙(R+t/2), respectively. The
difference in length (LOUT –LIN) between the inner and outer layers of the ZP segment hence is ∙t,
that is L∙t/R.
If the ZP segment is made to be planar, as it occurs in AFM experiments, the outer layers tend
to stretch the inner layers. Therefore, the outer layers are subject to compressive stresses while the
inner layers undergo tensile stresses. Figure ESM-1b shows a schematic of the ZP slab model. The
length difference L between outer and inner layers is (LOUT –LIN)/2, that is L∙t/2R. Since the length L
of the ZP slab is 60 m, the ZP thickness t is 10 m and the oocyte radius R measured for the
specimens analysed in this study is 75 m, it follows L=4 m.
LOUT
L
AFM tip
ZP membrane
LIN

t
RIN
ROUT
LIN /2
R
L/2
LOUT /2
(a)
(b)
Figure ESM-1. (a) Schematic of the oocyte with a portion of ZP, defined by the angle , extracted
from the cell; (b) Schematic of the axial-symmetric model of the ZP slab spread out on the rigid
substrate for indentation and bi-triangular displacement field imposed to FE model.
A two-step finite element analysis was performed. In the first step, a bi-triangular displacement
field changing linearly from  m (i.e. L/2, to simulate the compression of the outer layer) to 2
m (i.e. L/2, to simulate the tension of the inner layer) was imposed on the right edge of FE
model. Such pre-deformation (displacement vectors are highlighted in red in Figure ESM-1b)
causes the length of all layers of ZP membrane to become constant through ZP thickness and equal
to the length L in correspondence of the mean radius R. The displacement field obviously produces
compressive stresses in the upper part of the slab and tensile stresses in the bottom part of the slab.
Whilst the pre-deformation given in the case of mature ZP and for the outer layer of fertilized
ZP is the same as that indicated in Figure ESM-1b, the bi-triangular displacement field imposed to
the FE model must be reversed in the case of the inner layer of fertilized ZP as this region,
according to Figure ESM-1a, experiences tensile residual stress.
Once differences in length between ZP layers were recovered, the indentation process was
simulated in the second step of FE analysis. The same mechanical properties of the ZP optimized by
ABAQUS in the case of the Arruda-Boyce hyperelastic constitutive model were given in input to
the FE model. For the 200 nm indentation depth, the resulting force-indentation curve was obtained
and compared with that computed by the FE analysis performed without including residual stresses.
Figure ESM-2. Comparison between force-indentation curves obtained in the absence or in the
presence of residual stresses.
Figure ESM-2 presents the results obtained for the mature and fertilized oocyte’s ZP
membranes. It can be seen that residual stresses did not affect significantly the process of
determination of the elastic properties of ZP membrane. This was somehow expected because the
rectified length L=60 m of the ZP slabs analyzed in the experiments is about 1/8 of the 2R length
of the oocyte midline (see Figure ESM-1a). Remarkably, the largest difference between indentation
forces computed by FE models including or neglecting residual stresses never exceeded 1%.
Tensile residual stresses developed in the inner layers of ZP lead to indentation forces slightly
smaller than those registered without residual stress (Figure ESM-2). The contrary occurs in the
case of outer layers (Figure ESM-2). In summary, the proposed procedure for nanomechanical
characterization appears to be insensitive to the sign of residual stress developed in the region (i.e.
inner or outer) that comes in contact with the AFM tip.