Exploiting the Propagation of Constrained Variables for Enhanced HDX-MS Data Optimization

Nonlinear programming has found useful applications in protein biophysics to help understand the microscopic exchange kinetics of data obtained using hydrogen-deuterium exchange mass spectrometry (HDX-MS). Finding a microscopic kinetic solution for HDX-MS data provides a window into local protein stability and energetics allowing them to be quantified and understood. Optimization of HDX-MS data is a significant challenge, however, due to the requirement to solve a large number of variables simultaneously with exceptionally large variable bounds. Modeled rates are frequently uncertain with an explicate dependency on the initial guess values. In order to enhance the search for a minimum solution in HDX-MS optimization, the ability of selected constrained variables to propagate throughout the data is considered. We reveal that locally bound constrained optimization induces a global effect on all variables. The global response to local constraints is large and surprisingly long-range, but the outcome is unpredictable, unexpectedly decreasing the overall accuracy of certain data sets depending on the stringency of the constraints. Utilizing previously described in-house validation criteria based on covariance matrices, a method is described that is able to accurately determine whether constraints benefit or impair the optimization of HDX-MS data. From this, we establish a new two-stage method for our online optimizer HDXmodeller that can effectively leverage locally bound variables to enhance HDX-MS data modeling.