  The paper is devoted to the construction of low-energy quark scattering
amplitudes. Bootstrap quark model allows to describe the light and heavy hadron
spectroscopy based on three principles: unitarity, analicity and crossing
symmetry. The resulting quark interaction appeared to be effectively
short-range. This interaction is determined mainly by the exchange in the gluon
channel: the constituent-gluon mass appeared to not be small. Our calculation
indicates an important role of an interaction which is induced by instantons.
Such an interaction is necessary for deriving both the pion mass and
$\eta$-$\eta'$ mass splitting. However, due to the rules of $1/N_c$-expansion
this interaction influences slightly the other channels while in the
$\eta$-$\eta'$ channel it provides the correct values of masses and gives the
angle of $\eta_1-\eta_8$ mixture close to that of the quark model. We discuss
the possibility of constructing the amplitudes which take into account the
quark confinement.
