Many nitrosomonas are motile and free swimming - most hang out on the rocks.... Nitrobacter are non-motile. I do know know about some of the 'newer' candidates for nitrogen cycling (archaea etc). In any case - I have not understood for 10 years the idea that you need to spend weeks with an empty tank testing minute by minute for ammonia, nitrite and nitrate - when its quite simply happening either on its own - or with bacteria added - with a fish (according to instructions) - not the old fish- cycling method. I mean no disrespect to those that do it 'the long way' - but it seems to me that most of that thinking is that 'nothing good happens quickly in this hobby' - which 'sounds good' - but for an experienced person - (as compared to a beginner) - that knows what to put in the tank 'when' - there is no reason to go through a (I mean I have seen up to 6 months) long cycle.