In this note we investigate the diffusive behaviour and the boundary conditions of DNA nanodevices using the toe hold mediated strand displacement method. The goal is to extract the basic principles governing the difference observed in diluted solution and in confined environment where the devices are tethered on a DNA Origami. We note that the excluded volume interaction between the two strands running in opposite direction must give a sub diffusive behaviour that can lead to very long waiting times between jumps. When the Boundary Conditions generate a strong asymmetry in the device, the probability to perform the logical operation, thus to remove the output strand, is one. However, we envision unexpected marked differences between diluted solutions and confined environment both for controlling the boundary condition and the sub diffusive behaviour. These differences rise new questions on the interest to use the toe hold mediated strand displacement method on DNA Origamis.