Free energy perturbation (FEP) is a method based on
statistical mechanics that is used in
computational chemistry for computing
free energy differences from
molecular dynamics
Molecular dynamics (MD) is a computer simulation method for analyzing the physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a fixed period of time, giving a view of the dynamic "evolution" of th ...
or
Metropolis Monte Carlo simulations.
The FEP method was introduced by Robert W. Zwanzig in 1954. According to the free-energy perturbation method, the free energy difference for going from state A to state B is obtained from the following equation, known as the ''Zwanzig equation'':
:
where ''T'' is the
temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer.
Thermometers are calibrated in various temperature scales that historically have relied o ...
, ''k''
B is
Boltzmann's constant, and the angular brackets denote an average over a simulation run for state A. In practice, one
runs a normal simulation for state A, but each time a
new configuration is accepted, the energy for state B is also computed. The difference
between states A and B may be in the atom types involved, in which case the Δ''F''
obtained is for "mutating" one molecule onto another, or it may be a difference of
geometry, in which case one obtains a free energy map along one or more
reaction coordinates.
This free energy map is also known as a ''
potential of mean force'' or PMF.
Free energy perturbation calculations only converge properly when the difference
between the two states is small enough; therefore it is usually necessary to divide a
perturbation into a series of smaller "windows", which are computed independently.
Since there is no need for constant communication between the simulation for one
window and the next, the process can be trivially parallelized by running each window on
a different CPU, in what is known as an "
embarrassingly parallel
In parallel computing, an embarrassingly parallel workload or problem (also called embarrassingly parallelizable, perfectly parallel, delightfully parallel or pleasingly parallel) is one where little or no effort is needed to separate the problem ...
" setup.
Application
FEP calculations have been used for studying host–guest binding energetics,
pKa
PKA may refer to:
* Professionally known as:
** Pen name
** Stage persona
* p''K''a, the symbol for the acid dissociation constant at logarithmic scale
* Protein kinase A, a class of cAMP-dependent enzymes
* Pi Kappa Alpha, the North-American so ...
predictions,
solvent effects on reactions, and enzymatic reactions. Other applications are the
virtual screening of ligands in
drug discovery
In the fields of medicine, biotechnology and pharmacology, drug discovery is the process by which new candidate medications are discovered.
Historically, drugs were discovered by identifying the active ingredient from traditional remedies or b ...
, as well as for ''in silico''
mutagenesis studies. For the
study of reactions it is often necessary to involve a
quantum-mechanical
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qu ...
(QM) representation of
the reaction center because the
molecular mechanics (MM)
force fields used for FEP simulations can't handle
breaking bonds. A hybrid method that has the advantages of both QM and MM
calculations is called
QM/MM.
Umbrella sampling is another free-energy calculation technique that is typically used for calculating the free-energy change associated with a change in "position" coordinates as opposed to "chemical" coordinates, although Umbrella sampling can also be used for a chemical transformation when the "chemical" coordinate is treated as a dynamic variable (as in the case of the Lambda dynamics approach of Kong and Brooks).
An alternative to free energy perturbation for computing potentials of mean force in chemical space is
thermodynamic integration. Another alternative, which is probably more efficient, is the
Bennett acceptance ratio method. Adaptations to FEP exist which attempt to apportion free energy changes to subsections of the chemical structure.
Software
Several software packages have been developed to help perform FEP calculations. Below is a short list of some of the most common programs:
*FEP+
*
AMBER
Amber is fossilized tree resin that has been appreciated for its color and natural beauty since Neolithic times. Much valued from antiquity to the present as a gemstone, amber is made into a variety of decorative objects."Amber" (2004). In M ...
*
BOSS
Boss may refer to:
Occupations
* Supervisor, often referred to as boss
* Air boss, more formally, air officer, the person in charge of aircraft operations on an aircraft carrier
* Crime boss, the head of a criminal organization
* Fire boss, a ...
*
CHARMM
*
Desmond
*
GROMACS
*
MacroModel
MacroModel is a computer program for molecular modelling of organic compounds and biopolymers. It features various chemistry force fields, plus energy minimizing algorithms, to predict geometry and relative conformational energies of molecu ...
*
MOLARIS[{{Cite web , url=http://laetro.usc.edu/software.html , title=Archived copy , access-date=2015-01-18 , archive-date=2014-12-28 , archive-url=https://web.archive.org/web/20141228174404/http://laetro.usc.edu/software.html , url-status=dead ]
*
NAMD
*
Tinker
*
Q
See also
*
Thermodynamic integration
*
Umbrella sampling
References
Computational chemistry
Statistical mechanics