  We investigate the properties of an antikaon in medium, regarding itas a MIT
bag. We first construct the MIT bag model for a kaon with$\sigma^*$ and $\phi$
in order to describe the interaction of$s$-quarks in hyperonic matter in the
framework of the modifiedquark-meson coupling model. The coupling constant
$g'^{B_K}_\sigma$in the density-dependent bag constant $B(\sigma)$ is treated
as afree parameter to reproduce the optical potential of a kaon in asymmetric
matter and all other couplings are determined by usingSU(6) symmetry and the
quark counting rule. With various values ofthe kaon potential, we calculate the
effective mass of a kaon inmedium to compare it with that of a point-like kaon.
We thencalculate the population of octet baryons, leptons and $K^-$ and
theequation of state for neutron star matter. The results show thatkaon
condensation in hyperonic matter is sensitive to the $s$-quarkinteraction and
also to the way of treating the kaon. The mass andthe radius of a neutron star
are obtained by solving theTolmann-Oppenheimer-Volkoff equation.
