For n≥3, the natural map Out(Fn)→Aut(Kn) from the outer automorphism group of the free group of rank n to the group of simplicial automorphisms of the spine of outer space is an isomorphism.
Martin R. Bridson. Karen Vogtmann. "The symmetries of outer space." Duke Math. J. 106 (2) 391 - 409, 1 February 2001. https://doi.org/10.1215/S0012-7094-01-10625-X