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# Modeling Chemical Reactions (in Enzyme Active Sites)

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### Modeling Chemical Reactions (in Enzyme Active Sites)

1. 1. Modeling  Chemical    Reac0ons   (in  Enzyme  Ac0ve  Sites)   Jan  H.  Jensen   Department  of  Chemistry   University  of  Copenhagen   h4p://propka.ki.ku.dk/~jhjensen
2. 2. DOI:  10.1021/jo800706y
3. 3. We  measure  the  rate  (constant)  But  compute  the  ac0va0on  free  energy   d[4] d[4p] − = = k[4] dt dt 0.69 t1/2 = k The  connecGon  is  Transi0on  State  Theory   k≈ kBT − ΔG ≠ / RT h e ( 10 -1 −1 = 2.1 × 10 s K T ⋅ e − ΔG ≠ / RT ) ( k ≈ 10 s 10 13 -1 ) − ΔG ≠ /1.4 (room  T,  ΔG  in  kcal/mol)
4. 4. To  compute  the  rate  constant  we  need  to  ﬁnd     the  transi0on  state  Image:  h4p://en.wikipedia.org/wiki/TransiGon_state_theory
5. 5. Since  bonds  are  broken/formed  we  must  use     quantum  mechanics  to  ﬁnd  the  TS   (methods  like  B3LYP/6-­‐31G(d)  and  PM3)  Source:  Patrick  Rydberg   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?   h4p://en.wikipedia.org/wiki/Saddle_point
6. 6. The  free  energy  has  two  contribuGons:   PotenGal  (electronic)  energy  and  vibraGonal  free  energy   Approximate  TS  as  maximum  on  Minimum  (PotenGal)  Energy  Path  (MEP)   G X ≈ Eele + Gvib X XPoten0al  energy   E
7. 7. Approximate  TS  as  maximum  on  Reac0on  Coordinate  scan   the  Poten0al  Energy  Surface  (PES)     G X ≈ Eele + Gvib X XPoten0al  energy   E   O-­‐C  Distance   O-­‐C  distance  is  kept  ﬁxed  during  energy  minimizaGon
8. 8. Approximate  TS  can  then  serve  as  a  starGng  point  for  ﬁnding   the  real  transi0on  state   This  requires  an  (expensive)  frequency  calcula0on   G X ≈ Eele + Gvib X XPoten0al  energy   E
9. 9. 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   G X ≈ Eele + Gvib X X
10. 10. Building  a  TransiGon  State:  The  movie  h4p://molecularmodelingbasics.blogspot.com/2009/06/building-­‐transiGon-­‐state.html   h4p://molecularmodelingbasics.blogspot.com/search/label/transiGon%20state
11. 11. Modeling  Chemical  Reac0ons  in     Enzyme  Ac0ve  Sites   Enzymes  are  too  large  to  be  treated   quantum  mechanically  image:  10.1080/01442350903495417   Source:  Patrick   Rydberg   Image:  10.1021/jp805137x
12. 12. 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
13. 13. 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
14. 14. Ques0ons  Now?   Ques0ons  Later?   Leave  a  comment  on  h4p://proteinsandwavefuncGons.blogspot.com/2011/02/modeling-­‐chemical-­‐reacGons-­‐in-­‐enzyme.html