  The Born approximation to the quark-gluon-exchange mechanism for K$^+$N
scattering is used as a starting point to generate a potential for this system.
The valence quark wave function of the nucleon is generalized from a single
Gaussian to a sum of Gaussians in order to have a more flexible representation
than previous work. We obtain a potential derived from a valence density given
by lattice calculations. By comparing with a recent amplitude analysis it is
found that the strength of the quark-gluon based potential needs to be
increased by a factor of order 2-4 relative to the normalization given by more
traditional values of the governing parameters. The method is used to estimate
the change in effective K$^+$N amplitudes which would result from changes in
the valence quark distributions or strength of the interaction which might
arise from nuclear medium effects in K$^+$ scattering from nuclei.
