# AutoDock

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# Desolvation Free Energy Term in AutoDock 4

This page summarizes the AutoDock 4 desolvation free energy term, which is based on new atomic solvation parameters which depend on the absolute partial charge on the atom. This page also describes how the desolvation free energy grid map is calculated.

## Desolvation Free Energy Term in AutoDock 4

We begin with the simplest form of the equation for calculating the free energy change upon binding of a ligand to a receptor, ΔGdesolv:

## where:

```        i = index of atoms in the ligand
j = index of atoms in the receptor
Wdesolv = linear regression coefficient or weight for the desolvation free energy term
Si = solvation term for atom i
Vi = atomic fragmental volume of atom i
rij = distance between atom i and atom j (in Å)
σ = gaussian distance constant = 3.5 Å
```

The solvation term for atom i depends on the partial atomic charge of atom i, qi:

## where:

```        ai = atomic solvation parameter, ASP, for atom i, where:
Type    ASP             std. error
C       -0.001 43       0.000 19
A       -0.000 52       0.000 12
N       -0.001 62       0.001 82
O       -0.002 51       0.001 89
H        0.000 51       0.000 52
S       -0.002 14       0.001 18
k = charge-based atomic solvation parameter, QASP = 0.010 97  (std. error = 0.002 63)
qi = partial atomic charge on atom i
```

Substituting for Si in the equation for ΔGdesolv we obtain:

## Let us separate the terms that depend on the ligand atoms from the remaining terms, which can be precalculated and stored in grid maps:

This gives:

and:

## Now we can calculate a desolvation map, ΔGdesolv, ligmap, that will give the appropriate contribution for the desolvation free energy, ΔGdesolv, lig, when we know the partial atomic charge on the ligand atom, qi, at the docking stage:

## So, during the docking, when we finally know the partial charge on the ligand atoms, i, we can calculate the remaining part of the desolvation free energy of the ligand and receptor upon binding: 