Uhm... sphere with tubes coming out of it... boolean them all together (2 at a time because else the boolean command goes bonkers) Smooth them up, bevel the edges.

Once you got the basic form of the phage (in spite of the edges looking rough) -- run the smooth command a couple of times. Then once you completely believe that you can possibly have no more polygons... displacement map using a noise shader and convert to polygons.

There you go, exactly like the neuron cell picture.

... you're on your own for the procedural shader used to material it though.

Note: You'll end up with a **lot of polygons**.