The spontaneous breaking of chiral symmetry implies the presence of a short-distance scale in the QCD vacuum, which phenomenologically may be associated with the size of the constituent quark, 0:3 fm. We discuss the role of this scale in the matrix elements of the twist-4 and 3 quark-gluon operators determining the leading power (1=Q 2 )-corrections to the moments of the nucleon spin structure functions. We argue that the flavor-nonsinglet twist-4 matrix element, f uÿd 2 , has a sizable negative value of the order ÿ2 , due to the presence of sea quarks with virtualities ÿ2 in the proton wave function. The twist-3 matrix element, d 2 , is not related to the scale ÿ2 . Our arguments support the results of previous calculations of the matrix elements in the instanton vacuum model. We show that this qualitative picture is in agreement with the phenomenological higher-twist correction extracted from an NLO QCD fit to the world data on g p 1 and g n 1 , which include recent data from the Jefferson Lab Hall A and COMPASS experiments. We comment on the implications of the short-distance scale for quark-hadron duality and the x-dependence of higher-twist contributions.