I am a PhD student of neuroinformatics in UK and my background is computer science. I think I know a bit about the intersection of neuroscience and CS.
Theoretical/computational neuroscience is a growing field and as far as I am aware people with physics/CS background are very much needed. Experimentalists have a whole wealth of data but they usually don't have skills or time to analyse the data, create models, run simulations and obtain predictions.
You don't need publications to be accepted to a PhD programme. There are actually some PhD students who didn't publish a paper during their programme at all... Having good grades and recommendation letters helps but I would risk to say that primarily you need to show a genuine interest in the field, show that you want to find answers to certain questions etc. You already have an experience as a Research Assistant and definitely it is your strength. Focus on what skills you already have and not what you are lacking. If, for example, you are a brilliant programmer in a couple of languages and handle huge databases well, try to sell that. There must be some labs where your skills are on high demand.
Another thing is what university/lab you would like to aim at. If you want to work for top researchers in the field, it might get very competitive and not having good grades and publications works against you. But of course there is a number of less known labs that work on interesting projects and have various collaborators around the world.
Finally, as already mentioned in comments - get in touch with the professors, find out about their research, read their papers, raise some questions. And remember that some labs might be interested in working with you but cannot offer you any funding. In that case it still might work OK as there is various ways to obtain individual grants.