What you are describing seems to be a very interesting effect, which I'm sure ATK can be helpful in explaining. It might not be a trivial task, and will probably involve a lot of thinking and clever application of your general knowledge of chemistry.
The approach I described, sweeping the voltage from 0 V to, say, -2 V, is not the same thing as what happens in the experiment, however. In ATK, each bias is a static calculation, the only thing related to the "sweep" is that we use the already converged state of a lower (absolute) bias to provide a good starting guess at a higher bias.
Most likely the effects you are seeing in the experiment have something to do with conformational changes in the molecule, driven by the changing bias. What ATK could help you verify, is if you have an understanding of the different geometries that might be involved (and for that you have to use your chemistry knowledge, or some direct or indirect measurements), you can compute the current and see if they are very different. That could then be used to corroborate your assumption about the conformational changes.
Of course, I'm just providing ideas here; without detailed knowledge of your system, that's all we can do.