binding free energy of one ligand (reference ligand) relative to another ligand
(target ligand) both binding to same receptor, by summing up the work carried to
convert one ligand to another in bound and free states in solution [226]. This
method can be significantly efficient when reference ligand is very similar to target
ligand, but if they are dissimilar then defining and sampling along the conversion
path may pose severe computational demand [226]. Since reference ligand to target
state conversion path is artificial, these methods are also called alchemical methods,
and excellent review on popular methods of this class already exists [227]. Absolute
binding free energy methods estimate standard binding free energy of interaction by
computing reversible work done in process of transferring it from binding site into
solution [226]. Absolute binding free energy methods have been reviewed by Shirts
et al. [228]. Practical aspects of free energy calculation have also been recently
reviewed [229, 230]. The accuracy of the binding free energy calculations is
influenced by adequacy of sampling (theoretically, accurate results require infinite
sampling), force field used for sampling, and correctness of the molecular model
used, e.g., usually simulation is performed using fixed protonation states of titratable residues, while protonation states might change in experimental conditions
[226].
6.1 Calculation of Enthalpy by MM-PBSA
The end-state free energy methods explained here are most common approaches to
calculate binding free energy. Linear response approximation (LRA), linear interaction energy (LIE), and molecular mechanics Poisson–Boltzmann surface area
(MM-PBSA), molecular mechanics generalized Born surface area (MM-GBSA)
[231] are such methods available in the literature. End-state free energy methods are
computationally less demanding, but the speed gain in CPU comes at cost of
compromised accuracy of the results [231]. These methods are required to be
plugged with estimation of configurational entropy which usually is obtained by
rigid-rotor approximation and normal mode analysis or quasi-harmonic analysis to
yield binding free energy [232]. However, these methods can be good for evaluating binding enthalpy for ligand–receptor interaction. In MM-PBSA/MM-GBSA
approaches (schematically shown in Fig. 11), the binding energy is calculated by
taking energy difference of free-form of protein (P), and ligand (L) from protein–
ligand complex form (PL) [232].
The free energy of each of the molecular species (say X) can be expressed as
sum of their molecular mechanics energy in gas phase E MM (X), solvation free
energy G solv (X), and entropic part—TS(X). The E MM (X) contribution can be
expressed as sum of bonded, electrostatics, and van der Waals energies, i.e.,
E MM (X) = E bond (X) + E elec (X) + E vdW (X) [231]. Similarly, G solv (X) can be
expressed as sum of polar and non-polar contributions G polar (X) and G non-polar (X),
where G polar (X) can be accounted using Poison–Boltzmann or its simplified version
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S. K. Panday and I. Ghosh
(target ligand) both binding to same receptor, by summing up the work carried to
convert one ligand to another in bound and free states in solution [226]. This
method can be significantly efficient when reference ligand is very similar to target
ligand, but if they are dissimilar then defining and sampling along the conversion
path may pose severe computational demand [226]. Since reference ligand to target
state conversion path is artificial, these methods are also called alchemical methods,
and excellent review on popular methods of this class already exists [227]. Absolute
binding free energy methods estimate standard binding free energy of interaction by
computing reversible work done in process of transferring it from binding site into
solution [226]. Absolute binding free energy methods have been reviewed by Shirts
et al. [228]. Practical aspects of free energy calculation have also been recently
reviewed [229, 230]. The accuracy of the binding free energy calculations is
influenced by adequacy of sampling (theoretically, accurate results require infinite
sampling), force field used for sampling, and correctness of the molecular model
used, e.g., usually simulation is performed using fixed protonation states of titratable residues, while protonation states might change in experimental conditions
[226].
6.1 Calculation of Enthalpy by MM-PBSA
The end-state free energy methods explained here are most common approaches to
calculate binding free energy. Linear response approximation (LRA), linear interaction energy (LIE), and molecular mechanics Poisson–Boltzmann surface area
(MM-PBSA), molecular mechanics generalized Born surface area (MM-GBSA)
[231] are such methods available in the literature. End-state free energy methods are
computationally less demanding, but the speed gain in CPU comes at cost of
compromised accuracy of the results [231]. These methods are required to be
plugged with estimation of configurational entropy which usually is obtained by
rigid-rotor approximation and normal mode analysis or quasi-harmonic analysis to
yield binding free energy [232]. However, these methods can be good for evaluating binding enthalpy for ligand–receptor interaction. In MM-PBSA/MM-GBSA
approaches (schematically shown in Fig. 11), the binding energy is calculated by
taking energy difference of free-form of protein (P), and ligand (L) from protein–
ligand complex form (PL) [232].
The free energy of each of the molecular species (say X) can be expressed as
sum of their molecular mechanics energy in gas phase E MM (X), solvation free
energy G solv (X), and entropic part—TS(X). The E MM (X) contribution can be
expressed as sum of bonded, electrostatics, and van der Waals energies, i.e.,
E MM (X) = E bond (X) + E elec (X) + E vdW (X) [231]. Similarly, G solv (X) can be
expressed as sum of polar and non-polar contributions G polar (X) and G non-polar (X),
where G polar (X) can be accounted using Poison–Boltzmann or its simplified version
152
S. K. Panday and I. Ghosh