Restraining Interproton Angular and Distance Dynamics with KEnRef

Despite the increase in computational power, traditional NMR structure determination remains semiquantitative or even qualitative, especially because of the complicated mathematics involved in modeling the nuclear dipole-dipole interactions in nuclear Overhauser effect (NOE) spectra. Even advanced exact NOE (eNOE) and residual dipolar coupling (RDC) methods neglect the effects of interproton angular motion, limiting the physical realism of generated ensembles. We present KEnRef, an open-source C++ library implementing the Kinetic Ensemble approach to refine multistate protein structures using restraints that rigorously account for interproton distance and angular fluctuation. We introduce a loss function, using fractional exponents, that balances sensitivity across the target distance range. KEnRef interfaces with GROMACS to introduce forces calculated at each molecular dynamics time step. On synthetic ubiquitin data sets, single-structure simulations with a fractional exponent of 0.25 achieved an interproton RMSD of ∼0.2 Å and convergence time down to 2 ns. Two-structure ensembles showed 100-fold restraint energy decreases at high force constants and reproduced both rigid and dynamic behaviors with distance and angular fluctuation highly correlated to reference data (R > 0.85), validating KEnRef's capacity to capture localized motions. KEnRef enables integrated refinement of distance and angular fluctuations, yielding ensembles that faithfully model both structural and dynamic properties. Its performance on synthetic benchmark tests and modular design lay the foundation for ultraquantitative NMR-based ensemble refinement.