Evaluating the influence of initial magnetization conditions on extracted exchange parameters in NMR relaxation experiments: applications to CPMG and CEST.

Transient excursions of native protein states to functionally relevant higher energy conformations often occur on the μs-ms timescale. NMR spectroscopy has emerged as an important tool to probe such processes using techniques such as Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion and Chemical Exchange Saturation Transfer (CEST). The extraction of kinetic and structural parameters from these measurements is predicated upon mathematical modeling of the resulting relaxation profiles, which in turn relies on knowledge of the initial magnetization conditions at the start of the CPMG/CEST relaxation elements in these experiments. Most fitting programs simply assume initial magnetization conditions that are given by equilibrium populations, which may be incorrect in certain implementations of experiments. In this study we have quantified the systematic errors in extracted parameters that are generated from analyses of CPMG and CEST experiments using incorrect initial boundary conditions. We find that the errors in exchange rates (k ex ) and populations (p E ) are typically small (<10 %) and thus can be safely ignored in most cases. However, errors become larger and cannot be fully neglected (20-40 %) as k ex falls near the lower limit of each method or when short CPMG/CEST relaxation elements are used in these experiments. The source of the errors can be rationalized and their magnitude given by a simple functional form. Despite the fact that errors tend to be small, it is recommended that the correct boundary conditions be implemented in fitting programs so as to obtain as robust estimates of exchange parameters as possible.