Spectral Graph Analyses of Water Hydrogen-Bonding Network and Osmolyte Aggregate Structures in Osmolyte-Water Solutions.

Recently, it was shown that the spectral graph theory is exceptionally useful for understanding not only morphological structural differences in ion aggregates but also similarities between an ion network and a water H-bonding network in highly concentrated salt solutions. Here, we present spectral graph analysis results on osmolyte aggregates and water H-bonding network structures in aqueous renal osmolyte solutions. The quantitative analyses of the adjacency matrices that are graph-theoretical representations of aggregates of osmolyte molecules and water H-bond structures provide the ensemble average eigenvalue spectra and degree distribution. We show that urea molecules form quite different morphological structures compared to other protecting renal osmolyte molecules in water, particularly sorbitol and trimethylglycine, which are well-known protecting osmolytes, and at high concentrations exhibit a strong propensity to form morphological structures that are graph-theoretically similar to that of the water H-bond network. Conversely, urea molecules, even at similarly high concentrations, form separated clusters instead of extended osmolyte-osmolyte networks. This difference in morphological structure of osmolyte-osmolyte aggregates between protecting and destabilizing osmolytes is considered to be an important observation that led us to propose a hypothesis on the osmolyte aggregate growth mechanism via either osmolyte network formation or segregated osmolyte cluster formation. We anticipate that the present spectral graph analyses of osmolyte aggregate structures and their interplay with the water H-bond network structure in highly concentrated renal osmolyte solutions could provide important information on the osmolyte effects of not only water structures but also protein stability in biologically relevant osmolyte solutions.