Derivation and numerical profile analysis of a hierarchically formulated microscopic model of hemoglobin oxygen binding

To address complex thermodynamic systems with multiple interacting events, we have developed the concept of hierarchical thermodynamic interactions. In this study, this concept is extended to protein-ligand systems with similar but not identical protein subunits, and applied to the analysis of previously published NMR and UV-vis monitored hemoglobin oxygen binding data. Non-linear regression provided estimated errors for statistically significant parameters, but not for null (zero) valued parameters. A numerical/graphical profiling approach was therefore used to assess confidence intervals and correlations for both the statistically significant and nulled valued parameters in this model. Individual parameters were set to fixed values around their best-fit value, and the subset of statistically significant parameters re-minimized against hemoglobin oxygen binding data. Plots provide a graphical representation of parameter confidence intervals and correlations, and demonstrate how the two different data types - UV-vis and NMR - constrain the range of values for each parameter. This analysis further illustrates the value of hierarchically formulated models for the analysis of complex state systems, and illuminates the complexity of parameter space around the derived minimum microscopic model of hemoglobin oxygen binding.