PMC

Structure of the open (blue)[] and closed (orange)[] forms of AKE, with the CORE domain spatially aligned (grey). ATP binds in the pocket formed by the LID and CORE domains. AMP binds in the pocket formed by the NMP and CORE domains. Figure prepared with VMD[].

Each point represents a contact between residue i and residue j that is unique to the closed form. The Y-axis is the distance between the C_α atoms of residues i and j in the open form and the X-axis is the distance in the closed form. The locations of the residue pairs are indicated by color. i.e., black circles indicate the contact is between a residue in the LID domain and a residue in the CORE domain. Contacts above the line of slope 1.5 (solid line) constitute the set Q_Ligand.

Free energy as a function of the distance between center of mass of the LID domain and CORE domain ( ) for ε₂ = 0.5 − 1.2 (incremented by 0.1, colored black to purple). ε₂ is the interaction strength of closed conformation contacts, which represent ligand binding. For ε₂ > 0.6 there are multiple minima indicating ε₂ can represent ligand binding accurately. For ε₂ < 0.7 there is only one minimum corresponding to the open form, indicating non-open interactions can exist without distorting the open form.

Free Energy surfaces for with four subsets of Q_Ligand and varied ligand binding parameter ε₂. (a) ε₂ = 0.0 represents the unligated AKE. (b) with ε₂ = 1.5 represents ATP binding. (b) with ε₂ = 1.9 represents AMP binding. (d) All Q_Ligand contacts, ε₂ = 1.3, represents Ap₅A binding, or simultaneous AMP and ATP binding. A predicted pathway generated via normal mode analysis[] (white line in (d)) shows excellent agreement with our results. 10 k_BT energy scale (dark blue to dark red).

(a) Free energy versus RMSD from the closed conformation for ε₂ = 1.2 (black) and ε₂ = 1.3 (red) shows the free energy barriers to close the LID domain (TSE I) and the NMP domain (TSE II). This result suggests NMP domain closure is rate limiting. Φ_Func-values mapped onto the closed structure for LID closure (b, rotated for clarity) and NMP closure (c). For residues with ΔΔG_{Y − X} < 0 (residues that resist closing), Φ_Func-values are colored white (= 0) to red (≥1). For ΔΔG_{Y − X} > 0 (residues that contribute to closing), Φ_Func-values are colored white (= 0) to blue (≥1). The dotted line represents the LID-NMP interface, which contributes strongly to NMP domain closure. Figures (b) and (c) prepared with VMD[].

Strain energy as a function of binding parameter, ε₂, and residue number (top left), colored blue (low strain) to red (high strain). Unfolding measure, <D_max>, by residue number (bottom left). Red and black lines correspond to <D_max> for LID and NMP transition. Average deviation from PDB dihedral values for dihedral angle 63 as a function of RMSD from closed form (inset). Strain energy for ε₂ = 1.7 mapped onto closed form of AKE. Red indicates high strain energy, blue indicates low strain energy and white indicated intermediate strain energy. The correlation between high strain energy and protein unfolding suggests unfolding is a mechanism by which strain energy is released during conformational changes. Analysis of individual domain motion (as seen in ) shows that each peak in strain energy and <D_max> is due to NMP or LID domain motion (not shown). Figure of structure prepared with VMD[].