Dynamic NMR Simulations: A Case Study of Solution-State CPMG-RD and CEST Experiments

Simulations are essential in NMR spectroscopy for understanding and quantitatively predicting the outcomes of experiments. Dynamic NMR experiments are influenced by relaxation and chemical exchange phenomena, which complicate their interpretation. The quantum mechanical theory behind NMR simulations is well established and enables simulations under various conditions or states of the system. In particular, the representation of the spin system in terms of the density matrix, energy and pulse operators, and relaxation and chemical exchange in Liouville space is straightforward and allows for the routine simulation of dynamic NMR experiments. In fact, several advanced open-source software packages are currently available-such as Spinach, GAMMA (pyGAMMA), Simpson, ChemEx, and NMR TITAN-which users can choose from based on their simulation needs. Many of these software packages are optimized for computational speed and make use of sophisticated bases, such as the irreducible spherical tensor basis. Here, we present simulations using the direct method (spin product basis), as implemented in GAMMA, which we believe will help users better understand the underlying theory and thereby explore the other available software resources more effectively. We chose two experiments-CPMG-RD and CEST-as a case study to understand the conformational changes in proteins or macromolecules occurring in the fast and slow exchange regimes, which are frequently investigated by structural biologists.