modeling chemical reactions (in enzyme active sites)
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Modeling Chemical Reac0ons (in Enzyme Ac0ve Sites)
Jan H. Jensen
Department of Chemistry University of Copenhagen
h4p://propka.ki.ku.dk/~jhjensen
DOI: 10.1021/jo800706y
t1/2 =0.69k
−d[4]dt
=d[4p]dt
= k[4]
k ≈ kBTh
e−ΔG≠ /RT = 2.1×1010s-1K−1( )T ⋅ e−ΔG
≠ /RT
k ≈ 1013s-1( )10−ΔG≠ /1.4
We measure the rate (constant) But compute the ac0va0on free energy
The connecGon is Transi0on State Theory
(room T, ΔG in kcal/mol)
Image: h4p://en.wikipedia.org/wiki/TransiGon_state_theory
To compute the rate constant we need to find the transi0on state
Since bonds are broken/formed we must use quantum mechanics to find the TS
(methods like B3LYP/6-‐31G(d) and PM3)
Finding the TS is much trickier than finding the reactant and product (minima) structures
Finding minima: minimize E along all degrees of freedom Finding TS: maximize E along one* degree of freedom and minimize along rest
*but which one?
Source: Patrick Rydberg
h4p://en.wikipedia.org/wiki/Saddle_point
GX ≈ EeleX +Gvib
X
The free energy has two contribuGons: PotenGal (electronic) energy and vibraGonal free energy
Approximate TS as maximum on Minimum (PotenGal) Energy Path (MEP) Po
ten0
al ene
rgy
E
GX ≈ EeleX +Gvib
X
Approximate TS as maximum on Reac0on Coordinate scan the Poten0al Energy Surface (PES)
Poten0
al ene
rgy
E
O-‐C Distance
O-‐C distance is kept fixed during energy minimizaGon
GX ≈ EeleX +Gvib
X
Approximate TS can then serve as a starGng point for finding the real transi0on state
This requires an (expensive) frequency calcula0on Po
ten0
al ene
rgy
E
GX ≈ EeleX +Gvib
X
Once the real transiGon state is found the vibraGonal free energy can be calculated to yield the ac0va0on free energy
This requires another (expensive) frequency calculaGon
h4p://molecularmodelingbasics.blogspot.com/2009/06/building-‐transiGon-‐state.html h4p://molecularmodelingbasics.blogspot.com/search/label/transiGon%20state
Building a TransiGon State: The movie
Modeling Chemical Reac0ons in Enzyme Ac0ve Sites
Enzymes are too large to be treated quantum mechanically
Source: Patrick Rydberg
Image: 10.1021/jp805137x
image: 10.1080/01442350903495417
One opGon is to make a small (gas phase) model of the acGve site
Problems: Key interacGons missing System is too floppy
Can by fixed by going to larger models but expensive
Image: 10.1021/jp805137x
image: 10.1080/01442350903495417
Another opGon is QM/MM Red: QM region
Yellow & Green: MM
Problems: QM/MM Boundary Set-‐up is difficult
Schrodinger’s QM/MM: Qsite
Source: 10.1021/jp805137x
image: 10.1080/01442350903495417
Ques0ons Now?
Ques0ons Later?
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