Protein Structural Change Upon Ligand Binding: Linear Response Theory

A simple formula based on linear response theory is proposed to explain and predict the structural change of proteins upon ligand binding. By regarding ligand binding as an external perturbation, the structural change as a response is described by atomic fluctuations in the ligand-free form and the protein-ligand interactions. The results for three protein systems of various sizes are consistent with the observations in the crystal structures, confirming the validity of the linear relationship between the equilibrium fluctuations and the structural change upon ligand binding.

Figure 1

Structural change of FBP upon binding of ${\mathrm{F}\mathrm{e}}^{3+}$. (a) Experimental (red) and predicted (green) structural changes of ${\mathrm{C}}_{\alpha }$ atoms, represented by arrows on the backbone trace of the average structure in the simulation (blue) (correlation coefficient, 0.95). The experimental displacement is the difference between the ligand-free form (PDB ID: 1D9V) and the bound form (1MRP). Upon binding of ${\mathrm{F}\mathrm{e}}^{3+}$ (gray sphere), the moving domain (residues 1-82, 88-101, 226-276, 308-309; left part) undergoes a closure motion against the fixed domain (residues 83-87, 102-225, 277-307; right part). The model force applied to $\mathrm{O}\epsilon 1$ of Glu58 (magenta, ball and stick) is depicted by a yellow arrow. (b) The magnitudes of the experimental (red) and predicted (green) displacements of ${\mathrm{C}}_{\alpha }$ atoms are in agreement (correlation coefficient, 0.98). The scale was adjusted so as to make the average the same as that of the observation. (c) The prediction is robust with respect to the direction and position of the applied force. Correlation coefficients of $>0.8$ are obtained for force vectors (yellow arrows) on $\mathrm{O}\epsilon 1$ of Glu58 and the attractive forces toward the ligand from the ${\mathrm{C}}_{\alpha }$ atoms (red).

Figure 2

Structural change of citrate synthase dimer. (a) Experimental (red) and predicted (green) structural changes, represented by arrows on the backbone trace of the average structure in the simulation (blue) (correlation coefficient, 0.78). The experimental displacement is the difference between the ligand-free form (PDB ID: 1CTS) and the bound form (2CTS). The moving domain (residues 1-4, 56-65, 273-379, 436-437) undergoes motion against the fixed domain (residues 5-55, 66-272, 380-435). Citrate and coenzyme A are represented by orange and gray spheres, respectively. The force applied to $\mathrm{N}\epsilon$ of His58 (magenta, ball and stick) is denoted by a yellow arrow. (b) The magnitudes of the experimental (red) and predicted (green) displacements of ${\mathrm{C}}_{\alpha }$ atoms are well correlated (correlation coefficient, 0.83).

Figure 3

Structural change of ${\mathrm{F}}_1$-ATPase. (a) Experimental (red) and predicted (green) structural changes, represented by arrows on the backbone trace of the free form (blue) (correlation coefficient of the two displacement vectors in ${\beta }_{\mathrm{E}}$, 0.84). The experimental displacement is the difference between the nucleotide-free form (PDB ID: 1BMF) and the bound form (1H8E). Superposition of the two structures is shown for all ${\mathrm{C}}_{\alpha }$ atoms. The nucleotide ligand is represented by the orange space-filling model. The force applied to ${\mathrm{C}}_{\alpha }$ of Gly161 is denoted by a yellow arrow. Close-up of $\gamma$ shows the direction of rotation. The experimental displacement is in the direction of ATP synthesis, while the predicted displacement is in the direction of ATP hydrolysis. (b) The magnitudes of the experimental (red) and predicted (green) displacements are well correlated (correlation coefficient, 0.85).