  We show the existence of a duality between the c-map space describing the
universal hypermultiplet at tree level and the matrix model description of
two-dimensional string theory compactified at a self-dual radius and perturbed
by a sine-Liouville potential. It appears as a particular case of a general
relation between the twistor description of four-dimensional quaternionic
geometries and the Lax formalism for Toda hierarchy. Furthermore, we give an
evidence that the instanton corrections to the c-map metric coming from
NS5-branes can be encoded into the Baker-Akhiezer function of the integrable
hierarchy.
