Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs
Fig 3
Sampling trajectories on the constraint manifold encode collective motions.
a) KGS conformational distributions starting from three ligand-free holo crystal structures (leub, algi, osmo) are biased toward the apo structures. The polar plots show the distribution of the angles θ (along the radius), and ϕ (along the circumference) of the center of mass of domain two with respect to domain one (see Methods). The domains open, reorient, and deform upon adopting the apo conformation (red circle), affecting the relative position of the centers of mass of the domains. The orientation of domain two starts out at the origin. The colors of samples are red-shifted toward higher sampling number. The conformations diffuse toward the apo state as sampling progresses. b) The KGS conformational distribution along the reaction coordinates θ and RMSD (in Å) to the holo crystal structure of apo and holo human lysozyme. The holo distribution samples more broadly, and more towards smaller θ angles than the apo distribution, in agreement with the free-energy landscape observed from RDC restrained simulations (left panel). The middle and right panel show the sampling distribution for apo and holo in more detail. (Inset: free-energy landscapes from RDC restrained MD simulations. Images adapted from [29]). Weak local maxima approximately corresponding to the ‘unlocked’ and ‘locked’ state can be observed in the distribution starting from the holo structure.