DNA supercoiling plays an important role in a variety of cellular processes. The torsional stress related to supercoiling may also be involved in gene regulation through the local structure and dynamics of the double helix. To check this possibility, steady torsional stress was applied in the course of all-atom molecular dynamics simulations of two DNA fragments with different base pair sequences. For one fragment, the torsional stiffness significantly varied with small twisting. The effect is traced to sequence-specific asymmetry of local torsional fluctuations, and it should be small in long random DNA due to compensation. In contrast, the stiffness of special short sequences can change significantly, which gives a simple possibility of gene regulation via probabilities of strong fluctuations. These results have important implications for the role of DNA twisting in complexes with transcription factors.