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).