Let $k\subseteq k'$ be a field extension. We give relations between the kernels of higher derivations on $k[X]$ and $k'[X]$, where $k[X]:=k[x_1,\dots ,x_n]$ denotes the polynomial ring in $n$ variables over the field $k$. More precisely, let $D=\{D_n\}_{n=0}^\infty $ a higher $k$-derivation on $k[X]$ and $D'=\{D_n'\}_{n=0}^\infty $ a higher $k'$-derivation on $k'[X]$ such that $D'_m(x_i)=D_m(x_i)$ for all $m\geq 0$ and $i=1,2,\dots ,n$. Then (1) $k[X]^D=k$ if and only if $k'[X]^{D'}=k'$; (2) $k[X]^D$ is a finitely generated $k$-algebra if and only if $k'[X]^{D'}$ is a finitely generated $k'$-algebra. Furthermore, we also show that the kernel $k[X]^D$ of a higher derivation $D$ of $k[X]$ can be generated by a set of closed polynomials.
The last step for biosynthesis of c type cytochromes, indispensable for photosynthesis in cyanobacteria and plants, involves heme transport across the membrane and its covalent attachment to the apoprotein. In cyanobacteria, heme attachment occurs in the thylakoid lumen and probably also in the periplasm and requires at least four proteins, believed to be organized in intrinsic membrane protein complex. To allow isolation and identification of such complex, CcsB protein was tagged with 6xHis tag on its N terminus and expressed under the strong psbAII promoter in the cyanobacterium Synechocystis sp. PCC 6803. Similarly, CcsA protein was tagged with FLAG tag under the control of the same promoter. Although expression of both proteins under strong cyanobacterial promoter did not increase steady state contents of the CcsB protein, the fusion tags did not influence properties of the CcsB and CcsA proteins and the resulting mutants had the same phenotype as the wild type. Protein fraction containing CcsBHis protein was partially isolated from the solubilised membranes under native conditions.