A kinematic representation of proteins.

<p><b>a)</b> A protein is represented by an acyclic graph <i>G</i> = (<i>V</i>, <i>E</i>) encoding a kinematic chain. A hydrogen bond <i>h</i>–<i>A</i> defines a distance constraint, which results in a closed loop. A perturbation to the position of <i>h</i> by DoFs along the subtree on the left side needs to be matched by a perturbation to <i>h</i> by DoFs on the right side. Similarly for the position of <i>A</i>.</p

Nullspace Sampling with Holonomic Constraints Reveals Molecular Mechanisms of Protein Gαs

<div><p>Proteins perform their function or interact with partners by exchanging between conformational substates on a wide range of spatiotemporal scales. Structurally characterizing these exchanges is challenging, both experimentally and computationally. Large, diffusional motions are often on timescales that are difficult to access with molecular dynamics simulations, especially for large proteins and their complexes. The low frequency modes of normal mode analysis (NMA) report on molecular fluctuations associated with biological activity. However, NMA is limited to a second order expansion about a minimum of the potential energy function, which limits opportunities to observe diffusional motions. By contrast, kino-geometric conformational sampling (KGS) permits large perturbations while maintaining the exact geometry of explicit conformational constraints, such as hydrogen bonds. Here, we extend KGS and show that a conformational ensemble of the α subunit Gαs of heterotrimeric stimulatory protein Gs exhibits structural features implicated in its activation pathway. Activation of protein Gs by G protein-coupled receptors (GPCRs) is associated with GDP release and large conformational changes of its α-helical domain. Our method reveals a coupled α-helical domain opening motion while, simultaneously, Gαs helix α₅ samples an activated conformation. These motions are moderated in the activated state. The motion centers on a dynamic hub near the nucleotide-binding site of Gαs, and radiates to helix α₄. We find that comparative NMA-based ensembles underestimate the amplitudes of the motion. Additionally, the ensembles fall short in predicting the accepted direction of the full activation pathway. Taken together, our findings suggest that nullspace sampling with explicit, holonomic constraints yields ensembles that illuminate molecular mechanisms involved in GDP release and protein Gs activation, and further establish conformational coupling between key structural elements of Gαs.</p></div

Direction of displacement of the AH-domain.

<p><b>a)</b> Relative frequency of the angles between KGS and iMC average displacements for each C_<i>α</i> of the AH-domain in the inactive (grey) and active states (orange/yellow). The average AH-domain displacement is shifted by 50 to 60 degrees for the states between the two methods. <b>b)</b> Differences in the directions of the mean displacement of the center of geometry of the G<i>α</i> AH-domain between the KGS (red) and iMC (blue) ensembles. <b>c)</b> Directionality of the CA displacements of the <i>α</i>₅-helix in the KGS (red) and iMC (blue) ensembles in the active state (top) and inactive state (bottom). The motion in the KGS ensemble is directed from the inactive conformation of <i>α</i>₅ to the active conformation. d) Superimposed Ras-domains from the KGS ensembles for the active state (yellow) and inactive (grey) states. The amplitude of the Ras-domain ensemble is limited, except for marked fluctuations of helices <i>α</i>₄ and <i>α</i>₅.</p

The normalized magnitude of the mean C_<i>α</i> displacement vectors of the KGS and iMC ensembles.

<p>The top panel shows the normalized displacements for the active state KGS and iMC ensembles. The bottom panel for the inactive state. The AH-domain is indicated by orange (active) or grey (inactive) shading. The <i>α</i>₅ helix is shaded in the same color on the far right. The location of the N-terminal part of <i>α</i>₄ helix in the Ras-domain is indicated by a pronounced “bump” in between residues 320 and 340 for the KGS ensemble (red).</p

Diffusion of the G<i>α</i>s AH-domain opening angle in the ensemble.

<p>The change in opening angle between the AH-domain and the Ras-domain is shown as sampling progresses for KGS, iMC (left panel), and CONCOORD (right panel). For KGS, the inactive AH-domain opens to nearly 30 degrees (dark-red), while the active AH-domain ranges from 84.8 to 96.5 degrees (red). The inactive opening angle of iMC reaches 9.9 degrees, and ranges from 79.6 to 103.7 degrees for the active AH-domain. The opening angle of activated G<i>α</i>s in the <i>β</i>₂AR:G<i>α</i>s crystal structure is indicated in the inset. The inactive opening angle of CONCOORD reaches around 18 degrees, and ranges from 74.6 to 111.4 degrees for the active AH-domain. For the active state, iMC and CONCOORD sample uniformly around the starting angle. The angle of the KGS samples slowly decreases towards the inactive state.</p

Heatmaps of conformational variability.

<p><b>a)</b> RMS fluctuations of DoFs for KGS (red) and iMC (blue) for 20,000 samples starting from the activated conformation (top two panels, orange) and the inactive conformation (bottom two panels, grey). The DoFs corresponding to the AH-domain and helix <i>α</i>₅ are colored in darker shades. Free DoFs are circles, cycle DoFs are squares. The horizontal lines correspond to the mean RMSF value of the DoFs plus 2<i>σ</i>. <b>b,c)</b> Heatmaps representing the contribution of DoFs to conformational variability for KGS (b) and iMC (c). Coupling in the GDP binding pocket (red circle, <i>α</i>₅, <i>α</i>₁, and the adjacent <i>β</i>₁–<i>α</i>₁ loop (P-loop)) extends to include helix <i>α</i>_<i>F</i> (bottom of the red circle), Linker II (SW I), and the N-terminus of <i>α</i>_<i>E</i> (right side of the blue oval).</p

Architecture of G<i>α</i>s.

<p><b>a)</b> The G<i>α</i>s subunit consists of a Ras-domain and an <i>α</i>-helical domain. Linker I and II are shown in yellow, and the binding site of the nucleotide in between the two domains is indicated by a blue circle. The location of donor and acceptor atoms of the hydrogen bonding network used for KGS are indicated with white (donors) and red (acceptor) spheres. <b>b)</b> The activated state of Gs (pale cyan) superimposed onto the inactive state. Upon activation, the <i>α</i>-helical domain undergoes a large rotational motion. Helix <i>α</i>₅ translates and rotates upward to interact with the cytoplasmic core of the receptor.</p

Sampling trajectories on the constraint manifold encode collective motions.

<p><b>a)</b> 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 <i>θ</i> (along the radius), and <i>ϕ</i> (along the circumference) of the center of mass of domain two with respect to domain one (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004361#sec002" target="_blank">Methods</a>). 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>b)</b> The KGS conformational distribution along the reaction coordinates <i>θ</i> 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 <i>θ</i> 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 [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004361#pcbi.1004361.ref029" target="_blank">29</a>]). Weak local maxima approximately corresponding to the ‘unlocked’ and ‘locked’ state can be observed in the distribution starting from the holo structure.</p

sars Mpro without mutation

sars Mpro without mutation</p

Sars Mpro mutation without ligand binding

Sars Mpro mutation without ligand binding</p