How can I calculate the binding energy of a ligand to a protein? How is it different from the free energy of the ligand.
To give a general answer for a complex comprising a receptor and a ligand, you calculate the energy difference of the system in its bound state vs its unbound state:
E_binding = E(complex) - [ E(receptor) + E(ligand)]
Now, you have to decide, which energy function you choose to describe your system. There are many programs and functions around, most of them work with empirical parameters. You may, however, also use quantum chemistry methods to obtain the energies. Depending on the choice of your energy function you will obtain different energy values for the complex, receptor, and ligand, and also for the derived binding energy.
To account for thermal motion and allow some flexibility in the receptor and ligand, you may analyse not only a single complex structure, but a set of several structures. These may be generated e.g. from molecular dynamics simulations.
To obtain the Free Energy of binding, Delta_G(binding), you have to recall basic thermodynamics:
Delta_G = Delta_H - T * Delta_S
Thus, you not only need the interaction energy, which approximates the enthalpy H, but you also have to account for the entropy S, which makes things slightly more complicated.
There are (automated) methods within molecular dynamics packages (e.g. MM/GBSA in Amber) that try to address this issue in a very elegant way.
However, the Free Energy of the ligand, G_ligand, would be a property rather difficult to compute, because it's an absolute value. Normally, people ask for relative values, like the Binding Free Energy.
I recommend further reading e.g. in the AmberTools manual (ambermd.org), where a complete section deals with the MM/GBSA or MM/PBSA method and gives some theoretical background as well.
Hope this helps,
Anselm
To give a general answer for a complex comprising a receptor and a ligand, you calculate the energy difference of the system in its bound state vs its unbound state:
E_binding = E(complex) - [ E(receptor) + E(ligand)]
Now, you have to decide, which energy function you choose to describe your system. There are many programs and functions around, most of them work with empirical parameters. You may, however, also use quantum chemistry methods to obtain the energies. Depending on the choice of your energy function you will obtain different energy values for the complex, receptor, and ligand, and also for the derived binding energy.
To account for thermal motion and allow some flexibility in the receptor and ligand, you may analyse not only a single complex structure, but a set of several structures. These may be generated e.g. from molecular dynamics simulations.
To obtain the Free Energy of binding, Delta_G(binding), you have to recall basic thermodynamics:
Delta_G = Delta_H - T * Delta_S
Thus, you not only need the interaction energy, which approximates the enthalpy H, but you also have to account for the entropy S, which makes things slightly more complicated.
There are (automated) methods within molecular dynamics packages (e.g. MM/GBSA in Amber) that try to address this issue in a very elegant way.
However, the Free Energy of the ligand, G_ligand, would be a property rather difficult to compute, because it's an absolute value. Normally, people ask for relative values, like the Binding Free Energy.
I recommend further reading e.g. in the AmberTools manual (ambermd.org), where a complete section deals with the MM/GBSA or MM/PBSA method and gives some theoretical background as well.
Hope this helps,
Anselm
thank you for you valuable answers. Will be back in case of any trouble.
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