Ambient isotopic equivalence from knot theory is emerging as an effective mathematical model for dynamic visualizations of molecular simulations run on supercomputers. During a related talk on April 11, 2011, illustrative images and preliminary mathematical results were presented.

This talk extends to more mature mathematics for ambient isotopic approximations of splines. Recent applications to examples from the protein data base will be shown, accompanied by demonstrations of supportive visualization software that is being developed in an ongoing collaboration with IBM Research.