More Google water

Some time ago, I highlighted how Aurora Clark and her colleagues were using a modified version of the Google PageRank algorithm to analyse networks of water molecules. You can read more details in My monthly column on ChemistryViews. I retweeted the headline for that item earlier today and a correspondent going by the name of Curmudgeonly Chymist point out the similarities with this new approach and one developed in the 1960s, the so-called Morgan Algorithm. Intrigued, I turned to Clark to find out more and to learn whether or not she had factored in this algo when working on the Google PR for H2O. This is what she had to say:

Glad to hear that this is still garnering attention. It appears that there are some similarities and important differences in how the Morgan algorithm and the PageRank work. Both are based on graph theory, which takes a chemical system and makes atoms into vertices that are linked together by edges. Both assign unique numbers to atoms that have specific connectivity patterns.

The mathematical basis for the algorithms look quite different, and as such the implications and applications I think vary significantly. The Morgan method is an iterative process to achieve a unique number for an atom based on connectivity, in contrast the PageRank expression written in a matrix form is mathematically unique which means that there is only one value for a specific degree sequence/connectivity pattern. This means that if we analyze the same set of molecules, the PR software would do a single calculation, whereas the Morgan method would do lots of calculations to find this unique number. This would make the Morgan method probably not practical for analyzing millions of structures in a single shot.

Further, in the moleculaRnetworks software program we can impart chemical restraints to the PageRank expression that lets us distinguish not just between connectivity differences but between different 3D geometries of that connectivity (for example, we can use PR to map the inversion vibration of ammonia, starting at trigonal prismatic, then trigonal planar, then trigonal prismatic again)ŠI do not think that the Morgan method can do this based on the blog you sent. The moleculaRnetworks software is intended to analyze data taken over the course of time (from statistical mechanical simulations) and so we can use the PR to see how geometries and interactions evolve in time.

Finally, we can change our definitions of a “connection” or “link” between atoms such that we can look at different types of interactions (not just covalent bonds indicated in Morgans method). So, we can look at the H-bonding network in water and we can do that for a simulation box that contains thousands or millions of water molecules; so our moleculaRnetworks code has the ability to zoom in on the local geometry of specific atoms (as is the goal of the Morgan algorithm) AND it can zoom out and look at the connectivity at a more global scale.

She adds that at the local scale the Morgan algorithm and the PageRank algorithm could give very similar results. “I will have to code it up and check,” she told me.