  We study a version of the James model for the loop space of a suspension in
unstable ${\mathbb A}^1$-homotopy theory. We use this model to establish an
analog of G.W. Whitehead's classical refinement of the Freudenthal suspension
theorem in ${\mathbb A}^1$-homotopy theory: our result refines F. Morel's
${\mathbb A}^1$-simplicial suspension theorem. We then describe some
$E_1$-differentials in the EHP sequence in ${\mathbb A}^1$-homotopy theory.
These results are analogous to classical results of G.W. Whitehead's. Using
these tools, we deduce some new results about unstable ${\mathbb A}^1$-homotopy
sheaves of motivic spheres, including the counterpart of a classical rational
non-vanishing result.
