Download Quantum mechanical model assembly calculations of energetics of

Biochemical SocietyTransactions ( 1 996) 24
Quantum mechanical model assembly calculations
energetics of binding of ligands to protein receptors
of
-18
143s
4
MMAEL PERAKYLA* and TAPANI A. PAKKANEN
Department of Chemistry, University of Joensuu, P.O. Box. 1 1 I ,
80 10I , Joensuu, Finland
Computational approaches that can predict and explain the
origin of the relative binding affinities of ligand to protein
receptors face a challenge in the size and complexity of these
systems Molecular dynamics with free energy perturbation
methods has provided a usefd tool for this purpose [ l ] The
electronic structures of the ligands and bioreceptors and accurate
energies of interaction between the ligands and the active sites are
prerequisite for properly understanding the interactions To this
end, a method based on the calculation of direct receptor-Egand
interaction energies using ab rnrtro model assemblies of the active
sites was employed to estimate the relative energies of binding of
ligands to protein receptors [2,3] The ligand-binding energies (A
EBlnd) were calculated from ( I ) by using the approximations
shown in the thermodynamic cycle of Scheme 1
dEB;,,d is calculated with the equation
dEBind=
- AGSop ’ddEES
(1)
AEl,,, is the interaction energy between the ligand (L) and the
protein (P) in gas phase calculated from the energy of the isolated
ligand, the energy of the model assembly without a ligand, and the
energy of the model assembly with a ligand molecule. These
energies were calculated with ab initio quantum mechanics. The
model assemblies consist of the ligand and the essential ligandbinding amino acid residues, which are replaced by the
corresponding carehlly selected model compounds [4-61.
ACsok is the solvation energy for the ligand, calculated with
AMI-SM2 solvation model [7].
M E E is~ the relative electrostatic interaction energy between
the static charge distributions of the ligand and the protein matrix.
The distance dependent dielectric constant was used and the
charge distributions were described with a point charge
approximation.
It has been assumed here that the solvation energies of the
ligand-free protein (AGsoP) and the protein-ligand complex
(AGGFP) do not affect the relative binding energies. It must be
noted that due to the approximations employed only relative
ligand-binding energies can be reproduced.
Scheme 1. Thermodynamic cycle showing approximations used in
the evaluation of the binding energies(AEB,,d)
,
-180
-160
-140
-120
-100
AEBlnd(kJ moll)
Fig. 1. Correlation between the calculated A E B , ~and
~
experimental A G B , (kJ
~ ~ mol”) for binding of various substituted
p-hydroxybenzoates to p-hydroxybenzoate hydroxylase [31
Table 1. Calculated &<I,,[, dG‘so/-,d d E ~ sand dEBlnd and the
experimental AC,;,,d values (kl mol-I) [8] for binding of ligands to
L-arabinose binding protein
Ligand
&In1
“Sok
MEES
&Bind
AGBind
-380.8
-55.6
0.0
-325.2
-40.0
L-arabinose
D-fucose
-372.9
-57.4
4.5
-311.0
-30.9
D-galactose
-417.7
-70.0
-5.7
-353.4
-37 9
The method for the calculation of binding energies was applied
to calculate the energies for binding of ligands to p hydroxybenzoate hydroxylase [2] (Fig. 1) and L-arabinose-binding
protein (Table 1) [3].
In spite of the success of the applications presented it is clear
that structural coupling between the model assembly and the
protein matrix and solvent and a better description of the
electrostatic interactions in the bioreceptor-ligand complexes need
to be incorporated into the models in order to get more reliable
results and to widen the applicability of the approach.
Simultaneous geometric optimisations of the quantum mechanical
active site and the protein matrix and solvent could be carried out
by using the hybrid quantum mechanicaVmolecular mechanical
(dynamical) methods [9. lo]. More accurate estimates of the longrange electrostatic interactions might be obtained by incorporating
polarization of the protein atoms or by using continuum solvation
models [11,12].
1. Kollman, P. (1993) Chem. Rev. 93,2395-2417
2. Perakyla, M. & Pakkanen, T.A. (1995) Proteins 21, 22-29.
3. Perakyla, M. & Pakkanen, T.A. (1994) Proteins 20, 367-372.
4. Lindroos, J. Perakyla, M. Bjorkroth, J.-P. & Pakkanen, T.A.
(1992) J. Chem. SOC.Perkin Trans 2 2271-2277.
5. Perakyla, M. & Pakkanen, T.A. (1993) J. Chem. Res. (S) 296297, J. Chem. Res. (M) 1845-1872.
6. Perakyla, M. & Pakkanen, T.A. (1 993) J. Am. Chem. SOC.115,
10958-10963.
7. Cramer, C.J. & Truhlar, D.G. (1992) Science256, 213-219.
8. Miller, D.M. 111, Olson, J.S. Pflugrath, J.W. & Quiocho, F.A.
(1983) J. Biol. Chem. 258, 13665-13672.
9. Singh, U.C. & Kollman, P.A. (1986) J. Comput. Chem. 7, 718730.
10. Field, M.J. Bash, P.A. & Karplus, M. (1990) J. Comput.
Chem. 11, 700-733
11. Shen, J. Quiocho, F.A. (1995) J. Comput. Chem. 16,445-448.
12. Mackerell, A.P. Jr. Sommer, M.S. & Karplus, M. (1995) 247,
774-807.