Circular Dichroism as a Measure of Superhelix Density: A Theoretical Study

In chromatin, the DNA helix is itself helically coiled to form a superhelix, the tightness of which affects the transcription accessibility. Elucidation of the possible role of supercoiling in the control of gene expression requires an accurate and non-destructive method to measure superhelix density, and in this paper we show how the sensitivity of circular dichroism (c.d.) to supercoiling can be exploited. The chromatin c.d. at 270 nm shows a reduction to 45-70% of that of straight, non-supercoiled B-DNA. This has been attributed variously to secondary structural changes or tertiary interactions between adjacent superhelical turns. We investigate this effect by calculating the ratio of the c.d. of supercoiled and of straight DNA as a function of superhelix density with the use of the Tinoco model, but introducing a novel metric technique to relate c.d. to curvature. Tertiary interactions are shown to cancel one another, leaving the c.d. of chromatin unchanged, so the observed depression must arise from secondary structural effects. We investigate c.d. as a function of secondary structure, and find that base-twisting affects the c.d. much more than base-tilting, and can produce a strong depression. We therefore introduce a model of supercoiled DNA with base-twisting in proportion to the local Riemann curvature of the bent helix, and this reduces the chromatin c.d. to 70% of that of non-supercoiled DNA. Further reduction to 45% is achieved if chromatin forms a left-hand supersuperhelix. These results suggest that c.d. has considerable potential as a quantitative measure of supercoiling.