The Confine-and-Release Method: Obtaining Correct Binding Free Energies in the Presence of Protein Conformational Change - PubMed (original) (raw)

The Confine-and-Release Method: Obtaining Correct Binding Free Energies in the Presence of Protein Conformational Change

David L Mobley et al. J Chem Theory Comput. 2007.

Abstract

Free energy calculations are increasingly being used to estimate absolute and relative binding free energies of ligands to proteins. However, computed free energies often appear to depend on the initial protein conformation, indicating incomplete sampling. This is especially true when proteins can change conformation on ligand binding, as free energies associated with these conformational changes are either ignored or assumed to be included by virtue of the sampling performed in the calculation. Here, we show that, in a model protein system (a designed binding site in T4 Lysozyme), conformational changes can make a difference of several kcal/mol in computed binding free energies, and that they are neglected in computed binding free energies if the system remains kinetically trapped in a particular metastable state on simulation timescales. We introduce a general "confine-and-release" framework for free energy calculations that accounts for these free energies of conformational change. We illustrate its use in this model system by demonstrating that an umbrella sampling protocol can obtain converged binding free energies that are independent of the starting protein structure and include these conformational change free energies.

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Figures

Figure 1

Figure 1

Thermodynamic cycle for the confine-and-release framework. The quantity we want to calculate is ΔGbindo (top), the free energy difference for the process P + L_→_PL. Kinetic trapping (virtual confinement) or deliberate confinement can keep conformational changes from being sampled (shown graphically by a paperclip). When this happens, computed free energies are actually confined binding free energies, ΔGbind,Co (bottom arrow). To relate these to true binding free energies, it is necessary to compute the free energy of confining the protein in the absence of the ligand (left arrow), and releasing the protein in the presence of the ligand (right arrow).

Figure 2

Figure 2

Potential of mean force for rotating the valine 111 sidechain, with (b) and without (a) the ligand. Above each of the three regions is shown the free energy of confining Val111 to that metastable state. The apo metastable state corresponds to the first region on the left and the far right region (since the dihedral angle is periodic). Error bars represent statistical uncertainties corresponding to one standard deviation. Uncertainties for confinement to each well are given in the text.

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