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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