Osmotic pressure arising from a higher total chemical concentration inside proto-cells is thought to have played a role in the emergence and selection of self-replicating proto-cells. We present two chemical schemes through which different equilibrium compositions can coexist on each side of a semi-permeable membrane. The first scheme relies upon the concept of moieties and associated number of degrees of freedom. The second scheme relies upon the concept of siphons and of pass reaction capable of transferring matter from outside a siphon into it. Using simple example reaction networks, we show that both schemes are compatible with stationary proto-cell growth with up-concentration, but suffer from shortcomings. To alleviate these we propose a third scheme derived from the second one by having the pass reaction catalyzed by the membrane surface instead of occurring in bulk solution. This may have proven an intermediate step before having the pass reaction occurring only when the nutrient crosses the membrane. This suggests an evolutionary path for the emergence of active transport.