Speaker wires dont tend to interfere with each other.
But - AC power wires carry a signal that is audible and will interfear with speaker wires. (The fact that the AC power is a constant 60 hz adds to the problem.) Try to keep these apart or only cross them at 90 degrees.
The power wires generate a magnetic field around them. You want to keep speaker wires and interconnects away from this field. Image the field is 4-6 inches away (and it gets weaker farther away), but running the wires in parallel for many feet has the same effect as they would have bundled together tightly for 1 foot.
I was planning to run speaker cable under the floorboards, and to make it a little easier, I was going to use a cable tie to keep them together. Its the reason I asked. Would it be better to just leave them a little distance apart?