Dynamic energy landscape view of coupled binding and protein conformational change: induced-fit versus population-shift mechanisms

Abstract

Allostery, the coupling between ligand binding and protein conformational change, is the heart of biological network and it has often been explained by two representative models, the induced-fit and the population-shift models. Here, we clarified for what systems one model fits better than the other by performing molecular simulations of coupled binding and conformational change. Based on the dynamic energy landscape view, we developed an implicit ligand-binding model combined with the double-basin Hamiltonian that describes conformational change. From model simulations performed for a broad range of parameters, we uncovered that each of the two models has its own range of applicability, stronger and longer-ranged interaction between ligand and protein favors the induced-fit model, and weaker and shorter-ranged interaction leads to the population-shift model. We further postulate that the protein binding to small ligand tends to proceed via the population-shift model, whereas the protein docking to macromolecules such as DNA tends to fit the induced-fit model.

Fig. 1.

A schematic view of the dynamic energy landscape. Protein can reside on one of two energy landscapes, one landscape for ligand-unbound (U) and the other for bound (B) states. Each landscape has (at least) two minima, one for open (O) and the other for closed (C) conformations. Thus, there are four states, UO, UC, BO, and BC. Protein can jump between two landscapes by the ligand binding/unbinding.

Fig. 2.

A representative trajectory of the model protein. (A) The open and closed structures of glutamine-binding protein and its ligand, glutamine (blue). The ligand-binding residues are represented in red sticks. (B Upper) A representative time course of the conformational change coordinate χ. Its negative (positive) value corresponds to the open (closed) conformation. (B Lower) A time course of the ligand-binding energy, V_bind, for the same trajectory as Upper. (C) A small time window in the trajectory of B is magnified.

Fig. 3.

Two-dimensional free-energy surfaces as a function of protein conformational change (χ) and the ligand-binding energy (V_bind). (A) The case of the short-ranged interaction σ/r_0ij = 0.05. The black line is a representative trajectory. (B) The case of the long-ranged interaction σ/r_0ij = 0.15. The black and blue lines are two representative trajectories.

Fig. 4.

The first-passage analysis from UO to BC. Of 50 trajectories, the number of trajectories that went through BO (dashed line, denoted as induced-fit) and UC (solid line, denoted as population-shift) is plotted. (A) The ligand-binding strength (c_lig) is altered. (B) The interaction range σ is altered, whereas the strength of ligand interaction (c_lig) is tuned, in each point, so that the ligand is bound for half of the simulation time in equilibrium condition. In B, the ratio of the average ligand-binding energy in the BO state relative to that in the BC state, 〈V_bind〉_BO/〈V_bind〉_BC, is also plotted with the dotted line, for which the scale on the right applies.

Fig. 5.

The rate constants between the four states (in units of 10⁻⁵ per MD step). The binding rate constants here are apparent first-order rates at a given ligand concentration. (A) The case of the short-ranged ligand interaction (σ = 0.05r_ij). (B) The case of the long-ranged ligand interaction (σ = 0.3r_0ij). (C and D) The equilibrium titration curves of four states against the ligand concentration. c was derived from the equilibrium constants in a, and d was derived from the equilibrium constants in b.

Fig. 6.

Molecular examples that were suggested to show the population-shift (A) and the induced-fit (B) mechanisms. (A) An antibody, SPE7, and its ligand hapten DNP-ser. (Left) SPE7 dimer in cartoon with its binding sites in red sticks. Hapten DNP-Ser in blue stick. (Right) Hydrophobicity/hydrophilicity and the electrostatic potential of SPE7 are shown by color. The ligand-binding site is highly hydrophobic. (B) M.HhaI (DNA cytosine C⁵ methyltransferase) binding to DNA via the induced-fit mechanism. (Left) M.HhaI in cartoon with its binding sites in red-stick representation, and DNA is in blue. (Right) Hydrophobicity/hydrophilicity and the electrostatic potential of both molecules. The binding sites of M.HhaI (DNA) have high (low) electrostatic potential, indicating that their binding is via the electrostatic potentials. The electrostatic potentials were drawn by eF-site and PDBjViewer (38).