Abstract
Nuclear magnetic resonance spectroscopy is one of the few remaining areas of physical chemistry for which polynomially scaling quantum mechanical simulation methods have not so far been available. In this communication we adapt the restricted state space approximation to protein NMR spectroscopy and illustrate its performance by simulating common 2D and 3D liquid state NMR experiments (including accurate description of relaxation processes using Bloch–Redfield–Wangsness theory) on isotopically enriched human ubiquitin – a protein containing over a thousand nuclear spins forming an irregular polycyclic three-dimensional coupling lattice. The algorithm uses careful tailoring of the density operator space to only include nuclear spin states that are populated to a significant extent. The reduced state space is generated by analysing spin connectivity and decoherence properties: rapidly relaxing states as well as correlations between topologically remote spins are dropped from the basis set.
Highlights
The computing power required for nuclear magnetic resonance (NMR) simulations grows exponentially with the spin system size [1], and the current simulation capability is limited to about twenty spins [2]
After testing a variety of state space restriction methods [7,8,12,13,14,15], we propose the following procedure for generating the reduced basis set in liquid state NMR simulations: 1. Generate J-coupling graph (JCG) and dipolar coupling graph (DCG) from J-coupling data and Cartesian coordinates respectively
We found that missing J-couplings can be obtained with sufficient accuracy (±25% is required for 2D/3D NMR simulations reported) from atomic coordinates using semi-empirical estimates, and implemented a graph-theoretical estimator with the following stages: 1. The molecular bonding graph is partitioned into connected subgraphs of size two, and one-bond J-couplings are assigned from a complete database of atom pairs
Summary
The computing power required for nuclear magnetic resonance (NMR) simulations grows exponentially with the spin system size [1], and the current simulation capability is limited to about twenty spins [2]. Very promising recent algorithms, such as DMRG [5,6], are challenged by timedomain NMR simulations of proteins, which contain irregular three-dimensional polycyclic spin–spin coupling networks that are far from chain or tree topologies required by tensor network methods. In this communication we take advantage of the locality and rapid relaxation properties of protein spin systems and report a solution to the protein NMR simulation problem using restricted state spaces [7].
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