  We examine the plausibility of crossing the cosmological constant ($\L$)
barrier in a two-field quintessence model of dark energy, involving a kinetic
interaction between the individual fields. Such a kinetic interaction may have
its origin in the four dimensional effective two-field version of the
Dirac-Born-Infeld action, that describes the motion of a D3-brane in a higher
dimensional space-time. We show that this interaction term could indeed enable
the dark energy equation of state parameter $\wx$ to cross the $\L$-barrier
(i.e., $\wx = -1$), keeping the Hamiltonian well behaved (bounded from below),
as well as satisfying the condition of stability of cosmological density
perturbations, i.e., the positivity of the squares of the sound speeds
corresponding to the adiabatic and entropy modes. The model is found to fit
well with the latest Supernova Union data and the WMAP results. The best fit
curve for $\wx$ crosses -1 at red-shift $z$ in the range $\sim 0.215 - 0.245$,
whereas the transition from deceleration to acceleration takes place in the
range of $z \sim 0.56 - 0.6$. The scalar potential reconstructed using the best
fit model parameters is found to vary smoothly with time, while the dark energy
density nearly follows the matter density at early epochs, becomes dominant in
recent past, and slowly increases thereafter without giving rise to
singularities in finite future.
