Supplementary Information
moleculaRnetworks: an Integrated Graph Theoretic and Data Mining Tool to Explore
Solvent Organization in Molecular Simulation
Barbara Logan Mooney,* L. Rene Corrales, Aurora E. Clark*
Description of probabilistic algorithm for construction of the full-system graph and nearest
neighbor list
1.
Order waters along the x coordinate.
2.
Neighbor waters are nearby in order vector; choose the number of waters, W, on either
side in the order vector to test. This makes the algorithm probabilistic in that the
neighbor waters may not be the closest along one axis, and W should be sufficiently
large to rule out all cases besides the most pathological. Choosing W = N is the same as
calculating all water-water distances.
3.
Create a “sliding window”: a vector with each water padded with W waters on either
side in the order index.
4.
Account for periodic boundaries by allowing waters at the ends of the order vector to be
nearby waters at the other end.
5.
Convert the vector to a pairlist of each water and its possible neighbors.
6.
Eliminate duplicates in the pairlist.
7.
Repeat steps 1-6 along y and z.
8.
Concatenate the pairlists.
9.
Find and retain only the duplicate pairs in the concatenated pairlists (as these are close
enough to be neighbors in all three dimensions).
10.
Calculate vector distances for the retained pairs.
11.
Account for periodic boundary conditions by subtracting a boxside off values that are
too large.
12.
For H-bonding, use the pairlists to calculate all O-H distances and O-H-O angles.
13.
Remove pairs without a suitable O-H-O angle or too large an O-H distance from the list.
The remaining pairs are then used directly to create the H-bond network graph.
Figure S1. Page rank distribution of (A) bulk-like TIP3P water and (B) the waters within the
first solvation shell about Na+, within the simulation of Na+ in 216 TIP3P waters. A damping
factor of 0.85 was used.