  We study BPS states in type IIA string compactification on a local Calabi-Yau
3-fold which are related to the BPS states of the E-string. Using
Picard-Lefshetz transformations of the 3-cycles on the mirror manifold we
determine automorphisms of the K-theory of the compact divisor of the
Calabi-Yau which maps certain D-brane configurations to a bound state of single
D4-brane with multiple D0-branes. This map allows us to write down the
generating functions for the multiplicity of these BPS states.
