SAXS-guided Enhanced Unbiased Sampling for Structure Determination of Proteins and Complexes

Abstract

Molecular simulations can be utilized to predict protein structure ensembles and dynamics, though sufficient sampling of molecular ensembles and identification of key biologically relevant conformations remains challenging. Low-resolution experimental techniques provide valuable structural information on biomolecule at near-native conditions, which are often combined with molecular simulations to determine and refine protein structural ensembles. In this study, we demonstrate how small angle x-ray scattering (SAXS) information can be incorporated in Markov state model-based adaptive sampling strategy to enhance time efficiency of unbiased MD simulations and identify functionally relevant conformations of proteins and complexes. Our results show that using SAXS data combined with additional information, such as thermodynamics and distance restraints, we are able to distinguish otherwise degenerate structures due to the inherent ambiguity of SAXS pattern. We further demonstrate that adaptive sampling guided by SAXS and hybrid information can significantly reduce the computation time required to discover target structures. Overall, our findings demonstrate the potential of this hybrid approach in predicting near-native structures of proteins and complexes. Other low-resolution experimental information can be incorporated in a similar manner to collectively enhance unbiased sampling and improve the accuracy of structure prediction from simulation.

Figure 1

Predicting native folds of single domain proteins. The plots of individual MSM state free energy with respect to their average SAXS discrepancy values (χ²) for the (a) HP35, (b) protein G, and (c) α3D. Each dot represents a MSM state. The dot size and its color darkness are scaled by the equilibrium probability of that state estimated from the MSM. The errorbars for the SAXS discrepancy values of all states are shown in grey line. SAXS profiles of the target (red) and the predicted (blue) states, and overlays of the crystal structure (red) and the simulation predicted structure (blue) for (d) HP35, (e) protein G, and (f) α3D. The errorbars for the target SAXS profiles are also shown in the figure.

Figure 2

Enhanced efficiency in sampling the folding of HP35. Total simulation time required to reach the folded state from an arbitrary unfolded state for sets of samplings using (a) traditional long simulation, (b) random adaptive sampling, and (c) SAXS-guided adaptive sampling. Scaled trajectory length is the length of each individual trajectory in each specific sampling scheme by the lag time τ of the MSM. Number of trajectories is the total number of trajectories run for each sampling scheme, given by the product of the number of parallel trajectories and the number of sampling rounds. The average total required sampling times using the 3 different protocols over 1500 sets of samplings (excluding the sets of sampling that do not reach the target native state) are 235.03 μs, 27.61 μs, 9.76 μs.

Figure 3

Predicting the structure of MoaD-MoaE complex. (a) The plots of the average C_α distance of five evolutionarily coupled residue pairs of each MSM state with respect to their average SAXS discrepancy scores (χ²). Each dot represents an MSM state. The dot size is scaled by the equilibrium probability of that state estimated from the MSM. The 10 states with minimal average residue pair distances and the 10 states with minimal χ² are colored in green and cyan, respectively (with 3 overlapped states colored in green and the overlapped predicted state colored in blue). (b) SAXS profiles of the target (red) and the predicted (blue) states. The errorbars for the target SAXS profile are also shown in the figure. Overlay of the crystal structure (red) and the simulation predicted structure (blue) gives a C_α RMSD of 5.32 Å from the crystal structure.

Figure 4

Enhanced efficiency in sampling the association of MoaD-MoaE. Total simulation time required to reach the predicted dimeric state from an arbitrary unassociated state for sets of samplings using (a) traditional long simulation, (b) random adaptive sampling, (c) SAXS-guided adaptive sampling and (d) SAXS-EC-guided adaptive sampling. Scaled trajectory length is the length of each individual trajectory in each specific sampling scheme by the lag time τ of the MSM. Number of trajectories is the total number of trajectories run for each sampling scheme, given by the product of the number of parallel trajectories and the number of sampling rounds. The average total required sampling times using the 4 different protocols over 1500 sets of samplings (excluding the sets of samplings that do not reach the target state) are 113.28 μs, 61.16 μs, 41.57 μs, and 30.64 μs.

Figure 5

Predicting the PYR1 structure. (a) The plot of the average C_α distance of two residue pairs of individual state with respect to the SAXS discrepancy value χ². Each circle represents a single state from the clustering. The 10 states with the minimal average residue pair distances are colored in green, and the 10 states with the minimal χ² are colored in cyan, respectively. The blue star denotes the refined predicted PYR1 structure obtained after 20 ns MD simulation starting from the state with the minimal residue pair distance. (b) SAXS profiles of the target (red) and the predicted (blue) states are shown with the errorbars. Overlay of the crystal structure (red) and the best simulation predicted structure (blue) gives a C_α RMSD of 3.18 Å. The fitted SAXS experimental data are marked in grey circles.