FK3 - 12 - Molekulska Mehanika in Molekulsko Modeliranje (12.01.10)
Transcript of FK3 - 12 - Molekulska Mehanika in Molekulsko Modeliranje (12.01.10)
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MOLEKULSKA MEHANIKA in MOLEKULSKO MODELIRANJE
MOLEKULSKAMOLEKULSKA MEHANIKA MEHANIKA inin MOLEKULSKOMOLEKULSKO MODELIRANJEMODELIRANJE
Š. L. 2009/2010ŠŠ. L. 2009/2010. L. 2009/2010
12. 1. 201012. 1. 201012. 1. 2010FK3FK3
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Prezentacija
molekul 1
Prostorski modeliCPK modeli
“Krogljice
in palčke”
Palčke
ASPIRIN
COOH
O
O
Površina molekuleaspirina dostopnavodi
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Prezentacija
molekul 2
CPK Elektrostatski
potencial
Molekulske orbitale
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Faze razvoja učinkovine
Spojina vodnica
Sinteza
Biološko
testiranje
Načrtovanje
vodnica
Optimizacija vodnice
Sinteza
Biološko
testiranje
Načrtovanje
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Temeljni principi molekulske mehanike •
Jedro in elektroni v atomu so toga struktura
•
Atomi so sferične strukture z efektivnim nabojem•
Interakcije popisujemo s prožnostjo in klasičnimi potenciali
•
Za izračune uporabljamo klasične fizikalne zakonitosti (Newtonova mehanika)
•
Želimo izračunati potencialno energijo molekule.
Povezava med makroskopskim in mikroskopskim svetom preko teorije statistične mehanike
Molekularno
modeliranje
je model realnega
sveta.Proučujemo in študiramo model
ne pa realnosti!
Model
velja,
če reproducira
realnost
sveta.
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Računske metode
MOLECULAR MECHANICSSEMI-EMPIRICAL QUANTUM MECHANICSab initio QUANTUM MECHANICSCORRELATED QUANTUM MECHANICSCORRELATED, RELATIVISTIC QUANTUM MECHANICS
1,000's atoms100's atomsup to 100 atomsup to 40 atomsup to 10 atoms
COMPUATIONAL METHOD MOLECULE SIZE
IncreasingAccuracy
DecreasingTime
Velikost molekuleRačunska metoda
Naraščajočanatančnost
Skrajševanjeračunanja
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Nekatere lastnosti molekule
Energije•
Prosta
energ.
(G)
•
Entalpija
(H)•
Entropija
(S)
•
Sterična
e. (G)
Molekularna
Spektroskopija•
NMR
•
IR •
UV
•
MW
Kinetika•
Mehanizmi
reakcij
•
Hitrostne
konstante
Elektronske
lastnosti•
Molekularne
orbitale
•
Distribucija
nabojev•
Dipolni
momenti
3D Struktura•
Razdalje
•
Koti•
Torzija
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Minimalni predpogoji za molekulsko modeliranje
Topološke
lastnosti:
Opis kovalentnih
povezav v molekuli: struktura
Strukturne
lastnosti:
Začetna
konformacija
molekule,
dobljena izkristalne strukture, NMR strukture ali
teoretičnega
modela.
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Molekulsko polje sil /Molecular
force
field/
Celotna energija molekule = Energije kovalentnih interakcij +Energije nekovalentnih
interakcij
E. kov. interakcij = ΣE(raztegovanje vezi) + ΣE(napenjanje kota)ΣE(torzije) + ΣE(nihanje izven ravnine)
E. nekov. interakcij = ΣE(VdW) + ΣE(ionske inter.) + ΣE(H-vezi)
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SploSploššnana
oblikaoblika
enaenaččbe polja silbe polja sil
pairs ,ticelectrosta
pairs , der Waalsvan
612Hbonds
1012
dihedralsangles
2
0bonds
2
0total cos1
ji ij
ji
ji ij
ij
ij
ij
ij
ij
ij
ij
b
rqq
rB
rA
rD
rC
nKKrrKV
Elektrostatska interakcija
H-vez Van der
Waals
Raztegovanje vezi
TorzijaDeformacija kota
r
O H
rr r
Časovno
najbolj
potraten del
Φθ
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nonbondedji ij
ji
nonbondedji ij
ij
ij
ijij
torsionsall
anglesall
bondsallb
rqq
rR
rR
nK
K
bbKU
, 0
,
612
20
20
4
2
cos1
21
21
Poenostavljena enačba polja sil
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Raztegovanje vezi 1
rEs
= 1/2 ks
(r-r0
)2
… + C3
(r-r0
)3 + C4
(r-r0
)4
r
E-
Realno stanje
.. model
(r-r0
)2
r0
A B
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Raztegovanje vezi
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Potencialna
energija
kot funkcija
dolžine kemijske vezi
Podobna odvisnost
velja za velenčne
kote:
Vbonds 12
Kbbonds b b0 2
Vangles 12
Kangles 0 2
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Raztegovanje kemijske vezi 2
C C
C
C
Tip
vezi r0
(Å) ks
(kcal/mol.A2)
C(sp3)-C(sp3) 1.53 700C(sp3)-C(sp2) 1.43 700C(sp2)-C(sp2) 1.33 1400C(sp3)-H 1.09 700
Es
= 1/2 ks
(r-r0
)2
kS
=700: E=3 kcal ~ r=0.09ÅE
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Deformacija valenčnega kota 1
Eb
= 1/2 kb
(θ-θ0
)2
θ
θ
E
θ0
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Deformacija valenčnega kota 2
C O
H
Tip
kota 0
(°) kb
(kcal/mol.rad2)
X--C(sp3)--X 109.471 100X--O(sp3)--X 104.510 100
E=3 kcal ~ =14°E
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Definicija torzijskega kota Φ
Φ
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V smeri urnegakazalca
V naspretnismeri urnegakazalca
Torzijski kot +60 Torzijski kot -60
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12
Ravnina: 1, 2, 3
Ravnina: 2, 3, 4
Torzijski kot
1
2 3
4
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Vdihedral Kdihedrals 1 cos n
Potencialna
energija in torzijski kot 1
0.0
0.5
1.0
1.5
2.0
2.5
0 30 60 90 120 150 180 210 240 270 300 330 360
MM2/MM3 torsional potential
V1V2V3
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Torzijski
kot
Etor
= V1
[1 -
cos
(-01
) ]V2
[1 -
cos
2(-02
)]V3
[1 -
cos
3(-03
)]
E
0 60 120 180
C C
V3
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Potencialna
energija
in torzijski kot
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Butan
0.0
4.0
8.0
12.0
16.0
20.0
Ene
rgy
0.0 90.0 180.0 270.0 360.0C-C-C-C HH
HH
CH3
CH3
antiC-C-C-C = 180
HH
CH3CH3
H
H
eclipsed 1C-C-C-C = 0
HH
CH3H
CH3
H
gauche+C-C-C-C = +60
eclipsed 2 C-C-C-C = +120
HH
CH3H
CH3
H
CH3
CH2 CH2
CH3
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Torzijski koti pri peptidih
Φ“fi”
Ψ“psi”
Ωomega
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-180 -135 -90 -45 0 45 90 135 18017.0
9452.0
18887.0
28322.0
Conformational Energy
C(4)-C(5)-O(7)-C(8)(degrees)
Ener
gy (k
cal/m
ol)
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-180 -135 -90 -45 0 45 90 135 180
-6.0-6.0
-5.0
-4.0
Conformational Energy
C(4)-C(5)-C(7)-C(8)(degrees)
Ener
gy (k
cal/m
ol)
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-180 -135 -90 -45 0 45 90 135 180
-4.0
-3.0
-2.0-2.0
Conformational Energy
C(4)-C(5)-C(7)-C(8)(degrees)
Ener
gy (k
cal/m
ol)
F
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N
N N
NH
-180 -135 -90 -45 0 45 90 135 180
11.0
15.0
20.0
25.0
Conformational Energy
C(4)-C(5)-C(7)-C(8)(degrees)
Ener
gy (k
cal/m
ol)
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-180 -135 -90 -45 0 45 90 135 18020.0
6066.0
12113.0
18160.0
Conformational Energy
O(11)-C(9)-C(10)-C(12)(degrees)
Ener
gy (k
cal/m
ol)
- 1 8 0 - 1 3 5 - 9 0 - 4 5 0 4 5 9 0 1 3 5 1 8 05 0 . 0
6 0 . 0
6 9 . 0
7 8 . 0
C o n f o r m a t i o n a l E n e r g y
C ( 9 ) - C ( 1 0 ) - C ( 1 2 ) - S ( 1 3 ) ( d e g r e e s )
Ener
gy (k
cal/m
ol)
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-180 -90 0 90 180-180
-90
0
90
1802213.75
25.70
kcal/mol
Conformational Energy
O(11)-C(9)-N(2)-C(1)(degrees)
O(1
1)-C
(9)-
C(1
0)-C
(12)
(deg
rees
)
dovoljeno
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alfa
beta
nedovoljeno dovoljeno Pogojno dovoljeno
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Polje sil CHARMM
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VdW
in ionske interakcije
Elektrostatska
interakcija
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Nevezne
interakcije: Van der
Waalsove
interakcije
E=D0 [(r0 /r)12-2(r0 /r)6](Lennard-Jones)
E=D0 exp[a(r0 /r)]-b(r0 /r)6(Buckingham; “exp-6”)
odboj: ~r-10
privlak: ~r-6
Rezultat
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Nevezne
elektrostatske
interakcij
--
atomski parcialni naboji:
Eij =(qi xqj )/(rij )
atomski/molekulski dipoli:
E=i xj /Dr3
+
++
+
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Potencialna energja
Šibek lokalniminimum
Lokalniminimumi
Globalniminimum
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MoleMolekkululskaska
didinaminamikaka• Algoritem
–
Za
atom i, veljajo
Newton-ove
enačbe gibanja
ri in mi sta pozicija
in masa
atom i in Fi (t) je
sila
na
atom i v času
t. Fi (t) lahko izrazimo kot gradient potencialne
energije
V je
potencialna
energija.
2
2
dd
ii i
tt m
t
rFi i iF m a
i iV F 2
2
dd
ii i
tV m
t
r
(1) (2)
(4)(3)