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relaxation of the system temperature, as opposed to the second-order
(oscillatory) relaxation of the NH thermostat. Although the Berendsen
thermostat was never formally shown to reproduce any known thermo-
dynamical ensemble, 21 it is still widely used in MD applications because
of its fast convergence and the absence of spurious oscillations.
Often in laboratory experiments, the volume of the experimental sys-
tem is not fixed, but the external pressure P is. This situation corresponds
to the isobaric-isothermic or NPT ensemble. The corresponding distri-
bution function is
-
b
((,)
Hrp pV
+
)
r
NPT (, )
rp
ยต
e
.
The NPT ensemble can be generated for explicit solvent simulations, in
which the volume of the periodic box containing the system is allowed
to fluctuate. The size of the system becomes a dynamical variable con-
trolled by a feedback mechanism adjusting the instantaneous pressure to
the reference pressure P , in a fashion similar to the NH temperature
control.
4. Free Energy Calculations
Free energy represents the most important quantity to describe the
behavior of a molecular system. The probabilities of the different states
of a system are, indeed, directly related to the value of their free energy.
In the case of proteins, for example, the conformational change
between two states, the folding process, the association between two
monomers, or the affinity of a small molecule for its receptor are all
described by the free energy. For this reason, much effort has been
devoted to the development of computational methods that allow reli-
able estimates of this quantity for a given molecular system and a given
process under investigation.
The theoretical foundations of free energy simulations can, to a large
extent, be attributed to John Kirkwood for his pioneering developments
in the 1930s on the computation of free energy differences using ther-
modynamic integration (TI), 22 and to Robert Zwanzig for the free energy
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