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ÁLVARO CORTÉS CABRERA Y CRISTINA RUEDA PÉREZ AN. R. ACAD. NAC. FARM.

2.4. Linear interaction energy

The LIE method is based on the assumption that ?G of the system
depends linearly on changes in the van der Waals and electrostatic
components. This is supported by observations that the free energy
of solvation on non-polar moieties often scale linearly with respect
to variables characterizing the size of the solute (12).

To perform the binding energy estimation for every complex, we
used this approach. LIE method evaluates separately the electrostatic
and van der Waals interaction energies of the ligand in bound and
free states. For this purpose, we carried out new molecular dynamics
simulations of all ligands in water to measure the coulombic and
van der Waals contributions of the free ligands with identical
protocol and considerations to the complex dynamics.

The approximated binding energy is obtained as it is shown:

?Gbind = a(<Evdw>complex – <Evdw>free) + ß(<Eqq>complex – <Eqq>free)

where <Evdw>complex and <Evdw>free denote the average van der Waals
interaction energies in the bound and free forms, and <Eqq>complex and
<Eqq>free denote the average electrostatic interaction energies in the
bound and free forms. The value of a, strongly depends on the
system, the force field and the computational methods applied. For
this reason, a proper value should be determined by comparing the
experimental and calculated binding energies. In addition, ß value
was originally fixed to 0.5, however the study of solvation energies
of various small substrates showed that ß decreases with the number
polar groups like hydroxyl so a consideration to this point have to
be done.

Training set to determine the values of a and ß, was composed
with dexamethasone, betamethasone and cortisol, all well known GR
ligands with Kd (constant of dissociation) experimentally measured
(Table 2). Exactly the same protocol for flavonoids was followed for
the three training compounds and 300 ps bound and free simulations
were carried out for each ligand.

To obtain binding energy values for the compounds in the
training set, we applied the equation:

?Gbind = -RT ln Kd

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