You should be able to talk 100% fully about anything published or patented or publicly available about this project. You should also be able to talk freely about your own intellectual contributions to the work, but it would be better to let the PI know you intend to do this so that you are both comfortable knowing where to draw the line on what is OK to reveal or how to discuss particular things. Sharing confidential secrets from the lab that you are not part of is too much. As a mentor the PI should be OK with you discussing your own work with some detail (unless you signed a non-disclosure agreement in advance, which I doubt). Discuss with PI upfront to know how to phrase certain particulars (it's OK to avoid the sequence of the antigen or name of protein for instance while saying it is a novel protein in X disease related to ____) for instance.
You could even talk about your project in the context of a highly related comparable drug/antibody and sharing how that known one was developed while being relatively specific about how and what steps you contributed to, in the context of the known one (with the understanding you worked on a different target).
Also I would question how much you know about drug development if you call a monoclonal antibody a drug without qualifying that (drug is too non-specific to refer to most biologics.. most people think of chemical compounds as 'drugs'). So maybe clarify the right term for what you are working on. Just 2c.
