pdepe with cauchy boundary conditions?

I want to solve a 1D heat transfer equation in the following form ∂u/∂t = a ∂²u/∂x² by "pdepe" where both of the boundary conditions are defined in the right hand side; (1) u(x=1) = u1(t) (2) ∂u/∂x(x=1) = 0 What I should do with pl, ql, pr and qr?

I can not use the optimization by guessing the left boundary condition, because it is also time varying due to the physics of the system.