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Perfectionnements et validation d’une approche de mecanique
moleculaire polarisable. Applications a des complexes d’inhibiteurs avec
des metalloproteines.
Atelier CF Bio, Evry, 14 Mai 2007
Nohad GreshLaboratoire de Pharmacochimie Moléculaire et Cellulaire
U648 INSERMUFR Biomédicale, Faculté de Médecine de Paris, France
Jean-Philip PiquemalLaboratoire de Chimie Théorique, Université Pierre-et-
Marie-Curie,
• Coauteurs:
Benoit de Courcy, Michel Vidal, Wanq-Qing Liu, Christiane Garbay*;IFR Biomédicale, Paris.
Claude Giessner-Prettre, Jacqueline Langlet, Hilaire Chevreau;Laboratoire de Chimie Théorique, Paris.
Emmanuel Bertounesque, Caroline Courme, Jean-Claude Florent*;Institut Curie, Paris.
Céline Roux, Johanna Foret, Laurent Salmon*, Clotilde Policar;ICMO, Orsay.
David Perahia;Laboratoire d’Ingéniérie des Protéines, Orsay.
Rob J. DeethUniversity of Warwick, Royaume-Uni.
Jens Antony;Freie Universitat Berlin.
Morris Krauss*, Hillary Gilson;CARB, Rockville, MD, USA.
G. Andrès Cisneros, Tom Darden*; NIEHS, Chapel Hill, NC, USA.
• Separability
• Anisotropy
• Nonadditivity
– Cooperativity in multiply hydrogen-bonded complexes and anticooperativity in polycoordinated complexes of divalent cations.
• Transferability
Requirements
Restricted Variational Space Analysis.Stevens, W. J., and Fink, W., Chem. Phys. Letts
1987, 139, 15
The SIBFA (Sum of Interactions BetweenFragments Ab initio computed) procedure
∆E is a sum of five separate contributions, each of which as a counterpart from ab initio quantum chemistry.
1. Electrostatic, EMTP, with distributed ab initio multipolesanisotropy
2. Short-range repulsion Erep, expressed as sums of bond-bond, bond-lone pair, and lone pair-lone pair interactions
anisotropy3. Polarization, Epol
non-additivity and anisotropy4. Charge-transfer, Ect
non-additivity and anisotropy5. Long-range dispersion, Edisp
Recent refinements.
-Inclusion of a penetration component Epen to the electrostaticmultipolar contribution EMTPPiquemal, Gresh, Giessner-PrettreJ. Phys. Chem. A., 2003, 107, 10353
-Inclusion of a Ligand Field contribution for open-shell transitionMetal cationsPiquemal, Williams-Hubbard, Fey, Deeth, Gresh, Giessner-PrettreJ. Comput. Chem., 2003, 24, 1963
Angular variations of Eexch(RVS) and Erep(SIBFA) in formate-water complex (Piquemal et al., JCTC 2007, 3, 824)
9
10
11
12
13
14
15
16
125 145 165 185 205 225
Rotation angle H-CO (degres)
Ener
gy (k
cal/m
ol)
Erep*
Eexc HF
classical Lennard-Jones
Stacked formamide dimer. Evolutions of first-order electrostatic and repulsion contributions upon rotation around the z axis (Piquemal et al.,
JCTC 2007, 3, 824).
Stacking formamide dimer z=3.3 A
-6
-4
-2
0
2
4
6
8
0 100 200 300 400
Rotation angle
Ele
ctro
stat
ic e
nerg
y (k
cal/m
ol)
Ec HF
EMTP*
classical EMTP
Stacked N-methylformamide dimer
Rotation angle(degrees)
0 50 100 150 200 250 300 350E
nerg
y (k
cal/m
ol)
0
2
4
6
8
10
Erep*Eéxc (RVS) Lennard Jones
Upon rotations around the z axis, the EMTP* curve is superimposed over the Ec(ab initio) curve. Erep* recovers the angular features of Eexch, while a 1/R12
formula has a flat behaviour
Representation of two water clusters with n=16 and n=20 molecules
water cluster (n=20)in a cubic ice structure;
water cluster (n=16) extracted from a Monte-Carlo
simulation
Interaction energies in water clusters (n=12-20) in energy-minimized cubic ice structures and (for n=16)
as extracted from a Monte-Carlo simulation
Number of water molecules 12 16 16(M-C) 20
RVS SIBFA* RVS SIBFA* RVS SIBFA RVS SIBFA
Ec/EMTP* -168.5 -167.6 -231.4 -230.9 -179.8 -179.5 -294.3 -293.2
Eexch/Erep 151.4 151.9 207.5 207.9 149.9 149.8 263.2 263.6
E1 -17.1 -15.8 -23.9 -23.1 -29.9 -29.7 -31.1 -30.6
EpolRVS/Epol* -34.7 -30.6 -47.8 -42.0 -35.5 -32.7 -53.1
EpolKM/Epol -44.7 -41.3 -61.7 -56.5 -45.1 -44.1 -78.6 -71.3
Ect -23.1 -22.1 -31.3 -30.2 -23.1 -22.6 -39.4 -37.3
∆E -80.1 -79.2 -110.4 -109.8 -94.8 -96.4 -139.1 -139.2
Interaction energies in water clusters (n=12-20) in energy-minimized cubic ice structures and (for n=16) as extracted from a Monte-Carlo simulation
Number of water molecules 12 16 16(M-C) 20
RVS SIBFA* RVS SIBFA* RVS SIBFA RVS SIBFA
Ec/EMTP* -168.5 -167.6 -231.4 -230.9 -179.8 -179.5 -294.3 -293.2
Eexch/Erep 151.4 151.9 207.5 207.9 149.9 149.8 263.2 263.6
E1 -17.1 -15.8 -23.9 -23.1 -29.9 -29.7 -31.1 -30.6
EpolRVS/Epol* -34.7 -30.6 -47.8 -42.0 -35.5 -32.7 -53.1
EpolKM/Epol -44.7 -41.3 -61.7 -56.5 -45.1 -44.1 -78.6 -71.3
Ect -23.1 -22.1 -31.3 -30.2 -23.1 -22.6 -39.4 -37.3
∆E -80.1 -79.2 -110.4 -109.8 -94.8 -96.4 -139.1 -139.2
Cu(II) polyligated complexes(Piquemal et al., JCC 2003, 24, 1963)
Energy-minimized square planar complex: ∆E(SIBFA =-328.9 kcal/mol
∆E(MP2) =-328.7 kcal/mol
Energy-minimized square planar complex: ∆E(SIBFA) =-334.7 kcal/mol∆E(MP2) =-339.6 kcal/mol
Spontaneous assembly of double-stranded helicates from oligobipyridine ligands and Cu(I) cations: Structure of an inorganic
double helix
Lehn, J.-M., Rigault, A., Siegel, J., Harrowfield, J., Chevrier, B., Moras, D.
Proc. Natl. Acad. Sci., 1987, 84, 2565
X-ray-derived binuclear binding site of β-lactamase with OH(-) and H2O ligands. The Zn-Zn distance is 3.5 A Gresh et al, JCC, 2005, 26, 1113
Alternative binuclear binding site of β-lactamase withOH(-) and H2O ligands. The Zn-Zn distance is 4.3 A
Values of the Q-C and SIBFA interaction energies in the Zn(II) binuclear binding site of β-lactamasea)-c) Standard complexes in the fragilis binding site; d) Complex derived from HF energy minimization.
a-c): Zn-Zn distances of 3.0, 3.5, and 3.8A, respectively. d): Zn-Zn distance of 4.8 A.
a) b) c) d) RVS SIBFA RVS SIBFA RVS SIBFA RVS SIBFA
Ec/EMTP -1351.8 -1373.4 -1346.3 -1367.1 -1330.7 -1364.7 -1321.0 -1345.4
Eexch/Erep 362.3 393.9 344.3 370.0 350.4 390.5 375.9 398.8
E1 -989.5 -979.5 -1002.0 -996.2 -980.4 -974.2 -945.1 -946.6
Epol(RVS)/Epol* -223.9 -221.2 -203.3 -198.9 -209.9 -211.2 -252.9 -246.9
Epol(HF)/Epol -184.9 -162.0 -173.6 -148.8 -185.6 -167.4 -216.9 -195.8
Ect -56.8 -43.4 -57.2 -45.9 -60.9 -45.1 -75.2 -51.7
Ect* -35.7 -36.5 -40.1 -56.3
∆E -1210.2 -1184.9 -1212.1 -1191.8 -1206.0 -1186.7 -1218.8 -1194.2
Values of the Q-C and SIBFA interaction energies in the Zn(II) binuclear binding site of β-lactamasea)-c) Standard complexes in the fragilis binding site; d) Complex derived from HF energy minimization.
a-c): Zn-Zn distances of 3.0, 3.5, and 3.8A, respectively. d): Zn-Zn distance of 4.8 A.
a) b) c) d) RVS SIBFA RVS SIBFA RVS SIBFA RVS SIBFA
Ec/EMTP -1351.8 -1373.4 -1346.3 -1367.1 -1330.7 -1364.7 -1321.0 -1345.4
Eexch/Erep 362.3 393.9 344.3 370.0 350.4 390.5 375.9 398.8
E1 -989.5 -979.5 -1002.0 -996.2 -980.4 -974.2 -945.1 -946.6
Epol(HF)/Epol -184.9 -165.7 -173.6 -152.4 -185.6 -172.9 -216.9 -199.2
Ect -56.8 -65.5 -57.2 -66.0 -60.9 -61.7 -75.2 -70.6
Ect* -35.7 -36.5 -40.1 -56.3
∆E -1210.2 -1207.0 -1212.1 -1211.9 -1206.0 -1203.4 -1218.8 -1213.0
Values of correlated (DFT and MP2) interaction energies and of ∆Etot(SIBFA) in the foβ-lactamase binding sites.
a
b c d
∆E(DFT)a
-1292.1 -1292.7 -1284.9 -1296.6
∆Etot(SIBFA)
-1324.0 -1323.5 -1311.2 -1325.1
∆E(MP2)b
-1327.6 -1324.3 -1313.5 -1325.7
a LACVP3** basis set; b CEP 4-31G(2d) basis set
D- and L- thiomandelate and D- and L- captopril
Monodentate complex d-II of captopril with β-lactamase active site(Antony et al, JCC, 2005, 26, 1131)
Monodentate complex d-III of captopril with β-lactamase
Bidentate complex d-IV of captopril with β-lactamase active site
Bidentate complex d-V of captopril with β-lactamase
Bidentate complex d-VI of captopril with β-lactamase
Monodentate complex l-I of L-captopril with β-lactamase
Bidentate complex l-V of L-captopril with β-lactamase
Bidentate complex l-VI of L-captopril with β-lactamase
Complex d-I of thiomandelate with β-lactamase binding site
Complex d-II of thiomandelate with β-lactamase
Complex d-III of thiomandelate with β-lactamase
Complex l-I of thiomandelate with β-lactamase
Complex l-III of thiomandelate with β-lactamase
Thiomandelate and captopril complexes to b-lactamase binding site : SIBFA vs. HF interaction energies
-1350
-1300
-1250
-1200
-1150
-1100d-I d-I
ad-Ib
d-II d-IIa
d-IIb
d-III l-I l-Ib l-II l-III d-I d-II d-III d-IV
d-V d-VI
l-I l-II l-III
Thiomandelate CaptoprilD
E in
ter (
kcal
/mol
)
SIBFA
HF (CEP 4-31G(2d))
HF (6-311G**)
Thiomandelate and captopril complexes with b-lactamase model binding site. Values of DE(SIBFA) with Edisp and correlaled
quantum-chemical interaction energies
-1550
-1500
-1450
-1400
-1350
-1300
-1250
-1200
-1150
-1100d-I d-I
ad-Ib
d-II d-IIa
d-IIb
d-III
l-I l-Ib l-II l-III d-I d-II d-III
d-IV
d-V
d-VI
l-I l-V l-VI
Thiomandelate Captopril
DE
inte
r(kc
al/m
ol)
SIBFA MP2(CEP 4-31G(2d)) DFT(CEP 4-31G(2d)) DFT(6-311G**)
Design of novel inhibitors of Zinc PhosphomannoseIsomerase.
Céline Roux, Johanna Foret, Laurent SalmonInstitut de Chimie Moléculaire et des Matériaux d’Orsay, Orsay, France
Jean-Philip Piquemal, Lalith E. PereraNIEHS, Research Triangle Park , North Carolina, USA
Benoit de Courcy, Nohad GreshIFR Biomédicale, Paris, France
Zn-dependent type I phosphomannoisomerase (PMI):
catalyzes the isomerization of D-fructose 6-phosphate to D-mannose 6-phosphate.
It is involved in:
-illness of immuno-suppressed individuals;
-opportunistic infections in patients with cystic fibrosis;
-leishmaniasis.
X-ray structure of Phosphomannoisomerase metalloenzyme
Interaction energies (kcal/mol) of the bifunctional inhibitors 5PAH and
5PAA in the model binding site (MBS) of PMI (Roux et al., JCC 2007, 28, 938)
-1299.9-1288.0-1295.4-1324.2-1300.9-1295.1-1349.8-1386.9-1358.5∆E(DFT)b
-618.8-1256.6-1242.4-1252.0-1278.7-1266.1-1264.9-1308.6-1344.9-1315.0∆Eb
-601.6-1233.7-1221.0-1227.5-1250.7-1240.4-1243.2-1278.2-1310.8-1283.6∆Ea
D'DC'CB'BA ''A'A
PMIePMI-5PAAc-dPMI-5PAHa-b
a: CEP 4-31G(2d) basis setb: 6-311G** basis set
Interaction energies (kcal/mol) of the bifunctional inhibitors 5PAH and
5PAA in the model binding site (MBS) of PMI.
-653.6-1308.0-1300.5-1302.4-1347.5-1301.1-1321.9-1370.8-1397.8-1374.0∆Εtot
-1299.9-1288.0-1295.4-1324.2-1300.9-1295.1-1349.8-1386.9-1358.5∆E(DFT)b
-618.8-1256.6-1242.4-1252.0-1278.7-1266.1-1264.9-1308.6-1344.9-1315.0∆Eb
-596.3-1231.4-1222.0-1224.0-1267.9-1224.6-1242.9-1285.4-1310.8-1287.9∆E
-601.6-1233.7-1221.0-1227.5-1250.7-1240.4-1243.2-1278.2-1310.8-1283.6∆Ea
D'DC'CB'BA ''A'A
PMIePMI-5PAAc-dPMI-5PAHa-b
a: CEP 4-31G(2d) basis setb: 6-311G** basis set
-1400
-1380
-1360
-1340
-1320
-1300
-1280
-1260
-1240
-1220
-1200A A' A'' B B' C C' D D'
DE
inte
r (kc
al/m
ol) DE(SIBFA)
HF CEP 4-31G(2d)
HF LACVP3**
DEtot(SIBFA)
DFT LACVP3**
Interaction energies (kcal/mol) of the bifunctional inhibitors 5PAH and
5PAA in the model binding site (MBS) of PMI.
Compared evolutions of ∆Gsolv(LC), Eel(LC), ∆Gsolv(PB) and Eel(PB) in complexes A-D’
The specificity of Acyl Transfer from 2-mercaptobenzamide thioester to the HIV-1 nucleocapsid
protein
Miller-Jenkins, L. et al., J. Am. Chem. Soc., submitted
M Q K * G N F R N Q R K T V K R A P R K * K G T E R Q A NC
F
N
CG
K E GH
IAK
N
C CW
K *C
GK * E G
HQ
MK *
D
C
Z n Z n
1 5 1 0
1 5
2 0
2 5
3 0 3 5
4 0 4 5
5 0 5 5
B
A
2 9 5 : R 1 = O C H 3
2 4 7 : R 1 = N H 2S
N H
R 1
O
O
O
C H 3
C y s C y s
H is
C O O H
L y s
C y s
Z nC
O
C H 3
R S
C y s C y s
H is
C O O H
L y s
C y s
Z nCO
C H 3
C y s C y s
H is
C O O H
N H L y s
C y sCO
C H 3
Z n
Energy-minimized complex of 2-mercaptobenzamide thioester(TC4) to C-terminal Zn-finger of HIV-1 nucleocapsid protein
Interaction energies (kcal/mol) of TC4 with the Arg32-Asn55 Zn-finger of HIV-1 NCp7
E1a 19.4
Epola -15.7
Ecta -9.8
Edispa -41.7
Etora 1.6
δEtota -46.2
δ∆Gsolv
a +27.0 δ∆Etot +δ∆Gsolv -19.2
a: After subtraction of the energies of the Zn-finger and of TC4 separately minimized.
Extensions
1) Additional open-shell metal cations.
2) Interface to a molecular dynamics engine and Particle Mesh Ewald techniques.
3) Interface to a Monte-Carlo engine.
4) Extraction of multipoles and polarizabilities derived from correlated density matrices.
5) QM/MM.
Gaussian Electrostatic Model (GEM)
JP Piquemal* and G. A. Cisneros*N. GreshT. Darden
• Towards a third-generationforce-field
• based on fitted densities (density fitting)
• follows the SIBFA energetic scheme up to CCSD
X-ray structure of isopentenyl diphosphate isomerase(Wouters et al., JBC 2003, 278, 11903
Acknowledgments
• Support by CNRS, la Ligue Nationale contre le Cancer, and generous access to the supercomputer Centers of CINES (Montpellier), IDRIS (Orsay) and CRIHAN (Rouen).
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