At first, my idea was to create numerous cell objects and use Python or C++ code to scale each shape (i.e. cell growth). I was hoping that Maya's physics engine would take care of the collisions. However, collision during scaling seems to work differently from collision during translation events.
Now, I am trying a different idea using the nParticles feature in Maya. In the screenshot about the "instancer replacement" option is used to replace the instance of each particle with the shape of a cell (roughly). The particle self-collision is turned on. Next step is to see whether I can control the movement and behavior of each particles. More importantly, the particles need to replicate. I am hypothesizing that perhaps I can make each particle into a particle emitter. The emitters would have to be slow, otherwise they will clog the screen and CPU.