Chemistry Reference
In-Depth Information
FREE ENERGY SIMULATIONS
The thermodynamic quantity, free energy, defines binding affinity. The binding pose is the orientation of a ligand in
a protein binding pocket whereas the enthalpy is the energy of interaction for a singly such pose. Entropy represents
the sum over all possible poses since not only the optimum poses, but also multiple poses are possible. The entropy
will be high when multiple low enthalpy poses are possible and low if a single pose is favored. It is a very
demanding problem to determine entropy by summing over the enthalpies of multiple poses [27-76].
At constant pressure and temperature a system will spontaneously evolve in the direction of decreasing Gibbs free
energy until equilibrium is reached (∆G=0; ∆G=∆H - T∆S). ∆S and ∆G are changes in entropy and enthalpy
respectively. This equation reflects the tendency for the thermal motion to disrupt association and bond formation
and the natural preference for lower potential energies, i.e the enthalpy-entropy compensation phenomenon whereas
various combinations of unfavorable/favorable entropy/enthalpy components can lead to protein-ligand binding (∆H
reduces to the change in internal energy).
The equilibrium between a ligand A and its receptor B can be witten as a dissociation/association phenomenon,
whereas at temperature T=298 K and P = 1 atm with reactants and products at a concentration of 1 M, ∆G` (free
energy change in a hypothetical standard reference state) can be written as a function of the concentrations of the
species using the law of mass action, leading to ∆G`= RTln([A]
eq
[B]
eq
/(AB]
eq
) = RT ln
K
. The exponential
relationship between the free energy and equilibrium constant (
K
d
) indicates that even small changes in free energy
have considerable effects on the equilibrium constant.
The calculated values of ∆G needs to be accurate to be helpful. The quality of the potential used to represent
molecular energies as well as conformational sampling is important. At least the most populated states needs to be
probed for free energy calculations and it is necessary to sample the various configurations as extensively as
possible. Since at physiological temperatures proteins populate many conformational states, the notion of molecular
simulations to obtain thermodynamic ensembles of conformations is intricately associated with that of free energy
calculations.
In order to calculate affinity differences, initial efforts focused on approaches whereas one ligand is transformed
incrementally into another via a series of
in-silico
non-physical states. Any path between the two states is legitimate
(state function). Physical-chemistry determines the transformation. Firmly rooted in statistical mechanics, these
protocols are Thermodynamics Integration (TI) and free energy perturbation (FEP). Each state along the
transformation has to be coupled to the chemical topologies of both end points. The methods can be computationally
expensive.
The increase in reference experimental results has been very important for improvement of theoretical predictions of
affinities, receptor-ligand structures and empirical scoring functions. Although effects such as hydrogen bonding and
apolar contacts may not be accurately incorporated, the chemically intuitive nature of the empirical scoring
functions is important for computing and ranking quickly, large libraries of diverse compound docked to a target`s
active site.
Fundamental to understanding the thermodynamic properties of many biologically important systems and
phenomena, are the free energy simulation methods which are used to estimate protein stability, protein-ligand
binding affinities as well as hydration free energies. From the difference in the free energies associated with the
chemical transformation of one ligand into the other, in the solvent and bound environments, it is possible to
determine the binding affinities of ligands. Effectively, the free energy of binding is the force behind ligand binding
with target-protein in biomolecular systems.
The subtle balance between entropic and energetic effects yields the free energy originating from loss of
conformations, translational, orientational degrees of freedom, direct ligand-protein interactions as well as (de)
solvation effects of both ligand and host. Different specificities arise mainly from differing entropies and enthalpies.
There is thus a need for methods that focus on entropy and binding energy accurately in order to reliably predict and
reproduce novel drug activities. Consequently, computational techniques that estimate binding free energies play a
