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It has long been observed that trimethylamin N-oxide (TMAO) and ureademonstrate dramatically different properties in a protein folding process.Even with the enormous theoretical and experimental research work of the twoosmolytes, various aspects of their underlying mechanisms still remain largelyelusive. In this paper, we propose to use the weighted persistent homology tosystematically study the osmolytes molecular aggregation and theirhydrogen-bonding network from a local topological perspective. We consider twoweighted models, i.e., localized persistent homology (LPH) and interactivepersistent homology (IPH). From the localized persistent homology models, wehave found that TMAO and urea have very different local topology. TMAO showslocal network structures. With the concentration increase, the circle elementsin these networks show a clear increase in their total numbers and a decreasein their relative sizes. In contrast, urea shows two types of local topologicalpatterns, i.e., local clusters around 6 \AA~ and a few global circle elementsat around 12 \AA. From the interactive persistent homology models, it has beenfound that our persistent radial distribution function (PRDF) from theglobal-scale IPH has same physical properties as the traditional radialdistribution function (RDF). Moreover, PRDFs from the local-scale IPH can alsobe generated and used to characterize the local interaction information. Otherthan the clear difference of the first peak value of PRDFs at filtration size4\AA, TMAO and urea also shows very different behaviors at the second peakregion from filtration size 5\AA~ to 10 \AA.

Weighted persistent homology for osmolyte molecular aggregation and hydrogen-bonding network analysis