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We isolated and characterized four new PKCd isoforms, PKCdIV, dV, dVI, and dVII, specifically expressed in the mouse testis. These isoforms possess neither V1 nor C2-like domains. Moreover, PKCdVI and dVII have a different last exon as their V5 domain. The transcription of PKCdIV, dV, dVI, and dVII is initiated from the same site in the upstream region of exon4 of the PKCd gene. They are expressed exclusively in the testis in an age-dependent manner. PKCdIV and dV are expressed in spermatids with sperm maturation stage-specific manner, and that PKCdVI and dVII are expressed in spermatogonia and spermatocytes.

The formulation for zero mode of a Bose-Einstein condensate beyond the Bogoliubov approximation at zero temperature [Y.Nakamura et al., Phys. Rev. A 89 (2014) 013613] is extended to finite temperature. Both thermal and quantum fluctuations are considered in a manner consistent with a concept of spontaneous symmetry breakdown for a finite-size system. Therefore, we need a proper treatment of the zero mode operators, which invoke non-trivial enhancements in depletion condensate and thermodynamical quantities such as the specific heat. The enhancements are visible in the weak interaction case. Our approach reproduces the results of a homogeneous system in the Bogoliubov approximation in a large particle number limit.