  Pion transition form factor for the process $\gamma*\gamma*\to \pi^0$ at
space-like values of photon momenta is calculated within the effective
quark-meson model with the interaction induced by instanton exchange. The
leading and next-to-leading order power asymptotics of the form factor and the
relation between the light-cone pion distribution amplitudes of twists 2 and 4
and the dynamically generated quark mass are found.
