  Inclusion of protein lysozyme molecules in lipidic monoolein cubic phase
induces a transition from a $\rm Pn\bar{3}m$ structure to $\rm Im\bar{3}m$ one.
Small-angle X-ray scattering (SAXS) method with high intensity synchrotron
radiation enabled us to follow closely the transition depending on the
conditions of lysozyme solutions. We showed that concentrated lysozyme
solutions induced the appearance of the $\rm Im\bar{3}m$ structure coexisting
with the $\rm Pn\bar{3}m$ structure. From the relation between the lattice
parameters of these two structures it was shown that they were related by the
Bonnet transformation of underlying triply periodic minimal surfaces. We found
that the transition also occurred at lower lysozyme concentration when NaCl
induced attraction between lysozyme molecules. The origin of the transition was
considered as a frustration in the cubic phase where lysozyme molecules were
highly confined. A simple estimation of the frustration was given, which took
into account of the translational entropy of lysozyme molecules. At the highest
concentration of lysozyme and NaCl the $\rm Im\bar{3}m$ structure was found to
disappear and left only the $\rm Pn\bar{3}m$ structure. This was probably
either due to the crystallization or phase separation of lysozyme solutions
ongoing microscopically, which absorbed lysozyme molecules from channels of the
cubic phase and thus removed the frustration.
