Radical rearrangement and transfer reactions in proteins

Radical rearrangement and transfer reactions play an important role in the chemical modifications of proteins in vivo and in vitro. These reactions depend on protein sequence, as well as structure and dynamics. Frequently, these reactions have well-defined precedents in the organic chemistry literature, but their occurrence in proteins provides a stage for a number of novel and, perhaps, unexpected reaction products. This essay will provide an overview over a few representative examples of radical rearrangement and transfer reactions.

Is the share of a central place in the population of the area, served by this central place, a constant for all levels of the Christaller’s hierarchy?

One of the conditions of the central place theory is the assumption of a constant k parameter – a share of a central place in the population of the area served by this central place – for all levels of the Christaller’s hierarchy. Nevertheless, we did not find a rigorous proof of this assertion (underlying the Beckmann-Parr equation) in the bibliography on the central place theory. If this condition is assumed true, it also remains unclear – whether for all or only for strictly defined k-values. We have established that if the chosen K-value of the Christaller’s hierarchy is constant at every lattice level, the Beckmann-Parr equation holds for all meaningful values of k. At the same time we found that the range of k-values for an ideal Christaller’s lattice is bounded above by not an asymptote at k = 1, but an exact almost twice smaller value equal to K-(K^2-K)^0.5. Since the latter changes very slightly during a radical rearrangement of the lattice from K = 3 to K = 7, we can state that we have discovered the new nonstrict invariant in the central place theory – the maximum value of k.

Radical rearrangement of N-sulfonyl-N-aryl propynamides: proceeding with homolytic N–SO2 bond cleavage and 6-endo-dig cyclization toward 3-sulfonyl-2(1H)-quinolinones

A di-tert-butyl peroxide-promoted radical rearrangement of N-sulfonyl-N-aryl propynamides has been developed, giving 2-sulfonyl-3-aryl-2(1H)-quinolinones in moderate to good yields.